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  1. MatterBeam

    Cold, Laser-Coupled Particle Beams

    To produce a very high Isp engine, you can use simple particle beams and adjust the beam velocity to match your Isp and thrust requirements. There is no need to keep the beam focused after it exits your spaceship, so a Laser-Coupled Particle Beam is of no use here.
  2. MatterBeam

    Cold, Laser-Coupled Particle Beams

    I point you to the previous ToughSF post: It covers many of the points you just mentioned.
  3. Hi all! This is from: This is a follow-up to the Particle Beams in Space post. This time, we look at two concepts that can massively increase the effective range of particle beam: one is being applied every day in modern accelerators, and the other is an outgrowth of a tool used in biophysics. Everything here is based on science that has been worked upon by physicists and engineers, and will be referenced when possible. Performance limits The key characteristics of a particle beam are its divergence, particle energy and average power. Improving these characteristics leads to increases in overall performance. However, we know that there are limits to the performance that is possible. One limit is the ion source. The emittance of current ion sources are where they are at today due to the need to vaporize the ions into a gas (which imposes a minimum temperature) and the interactions between ions and energetic electrons or strong magnetic fields (which disturbs the ions). Expanding the beam to convert emittance into low divergence introduces its own errors and disturbances. Another limit is the neutralization step. Even when an ion beam and an electron beam are exactly matched in velocity and direction, their recombination into an atom releases energy that kicks particles in random directions. The magnitude of the kick cannot be reduced by any means, so there is a minimum divergence in neutral beams. Optimizing the beam composition to reduce emittance introduces other problems. The elements that vaporize at a low temperature and have a low ionization energy for their weight (like Cesium) are always heavy. For the same energy added to them, they end up travelling much slower than light elements. For example, 250 MeV added to Cesium only pushes it to travel at 0.063 C while hydrogen atoms of the same energy zip past at 0.613 C. This increases the travel time necessary to reach a target, leading to greater beam spread and a lower hit chance. Finally, there are the accelerator limitations. For a specific emittance, you can reduce divergence linearly by expanding the beam or speeding it up. Beam expansion becomes more and more difficult in terms of magnetic lens field strength requirements as the beam energy and current increases. Speeding up the beam requires quadratic length increases for each small gain in velocity. Attaining the desired level of performance might lead to gargantuan accelerators. Beating the laser The limitations of particle beams are particularly relevant when comparing them to lasers. Both are directed energy technologies that try to cross great distances while maintaining a small beam diameter. A fair comparison between the two would use emittance and divergence. The neutral particle beams that we can produce today are equivalent in emittance to laser beams with wavelengths of about 100 to 200 nanometers. Lasers struggle to produce these wavelengths efficiently and so particle beams should have the upper hand. However, lasers can work around their emittance by using large mirrors. Just like a particle beam expander, laser optics allow for very low divergence even when using longer wavelengths, such as 700 to 800 nanometers. Cooled diode lasers are achieving efficiencies of over 80% when producing those wavelengths, eliminating that advantage from a particle beam. In essence, lasers can trade the complex and heavy equipment needed to beat particle beams on an emittance basis, for the simple and lightweight solution that is large mirrors. Even better, mirrors can relay the beam over great distances with minimal losses, resulting in a Laser Weapon Web. The cutting edge of existing technology, paired with beam expanding optics and the use of heavy ions, could produce neutral particle beams with a divergence of 1 to 10 nanoradians. Equivalent laser beams of 1 to 10 nanometers can only be produced by an X-ray Free Electron Laser (XFEL). Comparing between advanced particle beams and XFELs is more nuanced. XFELs use the same accelerator technology to create a high energy stream of electrons. The electrons can be recycled many times and their energy recovered, leading to efficiencies perhaps greater than particle beam accelerators. At the ranges where an advanced particle beam and an XFEL are effective, light lag is significant. Lasers win out here again as they are many times faster than heavy neutral beams. However, XFELs have their own unique challenges. They need an undulator to convert the energy of their electrons into photons. It can only extract 0.1% of the electron energy with each pass. Recently, we have devised solutions, such as tapered undulators, that extract up to 10% of the electron energy. This is far below the 100% utilization of a particle beam, so while they may have a 10 to 20% advantage in efficiency, they could end up with a 10 to 100 fold penalty to power density. In other words, for the same mass budget, a spaceship is likely to output much less beam power when using an XFEL than when compared to using a particle beam. X-rays are very hard to manipulate. There exists no mirror that can reflect them and no lens which can focus them. An XFEL would have to rely on grazing-incidence optics to aim and focus its beam. Grazing-incidence optics are nestled cones of a dense metal like gold angled at 1 degree or less. Such an optic would need many, many such cones even at small sizes. As the focal distance increases, the angle of the cones must decrease. A 1 meter diameter optic focused at a spot 10,000km away requires cones of an angle 2.86 *10^-6 degrees. This leads to optics composed of no less than millions of cones, which is incredibly impractical and necessarily heavy. It should also be noted that grazing incidence optics cannot adjust their focal point. The alternative is a Fresnel Zone plate. It is not as delicate or as intricate as a grazing incidence optic, can adjust its focus and can be a rather lightweight device even when several meters wide. The ‘catch’ is that it absorbs between 50 and 75% of the laser beam. The plate also needs to be actively cooled and reduces the efficiency of an XFEL far below that of a particle beam accelerator. Does this mean particle beams are safe? Not yet! XFELs might regain the upper hand by using new methods of focusing X-rays. Bent diffraction crystals can reach high diffraction efficiency, which would make them very good at focusing X-rays. There could be further development of highly efficient Kinoform lenses. Alternatively, XFELs enjoying improvements in accelerator technology and undulator field strength can produce extremely short wavelengths, lower than 0.0001 nanometers, without requiring structures of several hundreds of meters in length. No focusing optics are needed in this case! Even a millimeter wide opening from an undulator is enough to produce beams of 0.3 nanoradian divergence. This performance is no more than 10x what is achievable today. We could therefore expect XFELs to end up creating 60 cm spot sizes at million kilometre distances. Their only limitation would be light lag. Can particle beams be competitive with such lasers? Cold Ions The most effective way to reduce the divergence of a particle beam down to its neutralization-imposed minimum is to reduce the emittance of the ion source. The ions released from an ion source usually have a ‘temperature’ of about 1 eV. We have assumed so far that the particle accelerator uses the ions at this temperature and does not significantly increase or decrease it. This does not have to be the case. Ions can be cooled after exiting their source and before they are accelerated to higher energies. Beam cooling techniques that can be used here include stochastic, radiative and electron cooling. Stochastic cooling inside a low-energy ring uses electromagnets to try to correct the path of a beam so that all the particles have a very similar temperature instead of a range of temperatures. Radiative cooling only works practically with electron beams. It forces the electrons to wiggle to maximize their energy loss through Bremsstrahlung radiation. Energy is then added back to the electrons only in the longitudinal direction, leading to a gradual reduction in transverse temperature. Electron cooling involves mixing hot ions with cold electrons (themselves cooled radiatively) to reduce the ion temperature. After mixing, the beam is bent by electromagnets so that the ions and electrons separate into different paths. All these techniques require multiple passes to be truly effective and therefore work best in a ring-shaped accelerator. Low energy ions produced by an ion source are easily bent into a circle by lightweight magnets. Over the course of several seconds or even minutes, ions are run around and around the the ring and passed multiple times through a cooling section. Eventually, the ion temperature approaches that of the electrons. Regular electrons will have the temperature of their emitter, 2000 to 3000 K, which corresponds to 0.17 to 0.26 eV. A photocathode emitter, where laser light is used to expel electrons from a surface, can produce electrons as cool as 1.5 meV or 17.4 K. They will be further cooled down to the tens of kelvins. If such low electron temperatures are accessible, and a ring accelerator can be used to bring ions down to similar temperatures, then there is the possibility of of creating cryogenic ion beams. They would have a near-zero emittance if it were not for electrostatic repulsion and internal collisions between the charged particles. Cryogenic particle beams are the solution to obtaining divergence no greater than the minimum imposed by neutralization disturbance, and this does not involve any expanding or focusing optics. There is a secondary advantage to cryogenic particle beams that can allow them to reach divergence even lower than the neutralization minimum. A bunch of neutral atoms travelling through space in a dense stream is not really different than a quick-moving gas. Cold gases condense. Cold hydrogen atoms condense into H2 droplets. Nitrogen condenses into N2. Cesium atoms condense into solid metal balls. The higher the vaporization temperature (hydrogen boils at 10 K in vacuum, but nitrogen only needs to be cooler than 63 K), the more likely that the particle beam condenses into a stream of higher molar mass entities. When two atoms join into a molecule, they average their transverse velocities. This effectively reduces the divergence of a particle beam by 42%. The square root of the mass ratio between the final condensed product and the individual atoms gives the reduction in divergence. This phenomenon was critical to Geoffrey A. Landis’s ‘Interstellar Flight by Particle Beam’ paper, where he suggested that mercury atoms would condense into million-particle droplets. With ion cooling and condensation, we can obtain the sub-nanoradian particle beams necessary to compete with future XFEL performance. Going further, we could expect beams of multiple species. Carbon and hydrogen beam are especially interesting. Carbon atoms at 1000 MeV could be released in parallel with hydrogen atoms at 80.3 MeV. Some of the hydrogen condenses into H2 and eventually diverges away, but they only carry a fraction of the energy. Carbon and hydrogen could instead condense into methane. The divergence of the carbon beam would be reduced by a 13.4%, and that of the hydrogen beam by 50%. When the methane molecules strike a target surface, they separate back into carbon and hydrogen. The carbon would stop very quickly and deposit all of its energy near the surface. The hydrogen is much more penetrating and would continue deeper into the material. A methane beam would deliver both thermal and radiation damage and help defeat protection optimized for one or the other, all while maintaining a divergence much smaller than a pure radiation beam. Even better, the carbon would help ‘carry’ penetrating hydrogen particles through magnetic fields that would otherwise deflect lightweight hydrogen on its own. Methane is after all just 8% easier to ionize than hydrogen but 16 times harder to deflect. Laser Coupled Particle Beams There is another method of reducing emittance which is radically different from those mentioned so far. It is based on optical tweezers that are known for trapping and manipulating tiny particles using laser beams. The same method can be used to control the motion of particles in a particle beam. It is studied as part of NASA’s Innovative Advanced Concepts, promising diffractionless beams across interstellar distances. We will call them ‘Laser-Couple Particle Beams’ or LCPBs. Can be applied in the context of distances on the order of 1,000 to 1,000,000 kilometers? A laser beam can be used to create a column of light pointed at a target. The intensity of the laser varies from the edge to the center of the column in a gaussian profile. To simplify, we can say that the laser at the center of the column is twice as intense as the average intensity. When a particle beam is inserted into the column and travels parallel to it, it experiences a force pushing its particles towards the center of the column. That is the gradient force. We are solely interested in particles sitting at the edge of the column, as they determine the divergence. They experience the full pull of the gradient force. As best that can be determined, the maximal acceleration towards the center of the laser column that a particle experiences is as follows: Average Particle Acceleration = (0.5 * AP * IG * DRF)/PM Average Particle Acceleration is the acceleration of a single atom in m/s^2. AP is the atomic polarizability. IG is the intensity gradient of the laser, in W/m^2/m AAG is the average acceleration factor, drawn from the table below. PM is the particle mass in kg. The AAG is the result of the particles experiencing less and less gradient force drawing them towards the center of the laser column as they come closer. It is the result of the intensity gradient falling as they do so. The greater the reduction in divergence we want, the lower the average acceleration the particles experience. From the table, we can read that if we want to reduce the divergence by a factor 8, the average acceleration the particles experience is 34% of the initial acceleration. AP values can be found here ( in multiples of the radius cubed. Hydrogen, with a radius of 5.29 * 10^-11 m, would have a polarizability of 0.667 * (2.5 * 10^-11)^3: 1.04*10^-32. Potassium, with a radius of 2.2*10^-10 m, would have a polarizability of 43 * (2.2*10^-10)^3: 4.58*10^-28. IG for a gaussian beam is roughly twice the average laser intensity (W/m^2) divided by the laser beam’s radius. Using three worked examples, we can clearly see that LCPBs can have massively extended ranges when compared to either lasers or particle beams alone. We assume that they have received the beam cooling treatment and that their initial divergence is roughly equal to the minimum imposed by neutralization. In the first example, we will calculate the laser parameters needed to reduce the divergence of a 1 meter wide, 100 MeV hydrogen beam from 54 nanoradians to 5.4 nanoradians within a distance of 1,000 km. Hydrogen at 100 MeV is travelling at 0.428 C or 128,360 km/s, so it crosses a distance of 1,000 km in about 7.79 milliseconds. An initial divergence of 54 nanoradians implies that it spreads at a rate of 6.93 m/s. We therefore need to reduce the transverse velocity from 6.93 m/s to 0.69 m/s within 7.79 milliseconds. That is an acceleration of 801 m/s^2. We’re trying to reduce the divergence by a factor 10, so the average acceleration is 29.3% of the initial acceleration. Conversely, the initial acceleration will have to be 3.41 times greater to achieve the desired average acceleration, about 2732 m/s^2. We input PA = 2732 m/s^2, AP = 1.04*10^-32 and PM = 1.67*10^-27 kg. From that, we determine that IG = 8.8*10^8 W/m^2/m Since the beam is 1 meter in diameter, it has a radius of 0.5 meters, so average laser intensity will be 219.4 MW/m^2. This is not unreasonable. The total laser power required is 172.3 MW. It is quite a big penalty to the power requirements of the particle beam. In the second example, we will calculate the laser parameters needed to reduce the divergence of a 1 meter wide, 300 MeV Xenon beam from 2.5 nanoradians to 0.25 nanoradians within a distance of 1,000 km. Xenon at 300 MeV is travelling at 0.0697 C or 20,890 km/s, so it crosses a distance of 1,000 km in about 47.87 milliseconds. An initial divergence of 2.5 nanoradians implies that it spreads at a rate of 0.05 m/s. We therefore need to reduce the transverse velocity from 0.05 m/s to 0.005 m/s within 47.87 milliseconds. That is an acceleration of 0.982 m/s^2. The divergence reduction factor is 10, so the average acceleration is 29.3% of the initial acceleration. We therefore need an initial acceleration of 3.34 m/s^2. We input PA = 3.34 m/s^2, AP = 5.04*10^-30 and PM = 2.18*10^-25 kg. From that, we determine that IG = 2.89*10^5 W/m^2/m The average laser intensity will be 72.4 kW/m^2 and total laser power is just 56.7 kW! This is a very minor penalty to a particle beam accelerator with a several megawatt output. In the final example, let’s try for a very narrow beam, using condensation to produce a molecule with very low initial divergence and high polarizability. Lets’ also be generous with the particle energy. Starting with 1000 MeV Cesium (min divergence 0.43 nrad) and 955 MeV Iodine (min divergence 1 nrad), we expect to end up with Cesium Iodide with a polarizability of 1.94*10^-28, based on an average of the two element’s Van der Wall’s radii figures fromhere. The divergence of the molecule is 0.7 nrad and it will be travelling at 0.126 C or 37,800 km/s. What laser is needed to reduce the divergence of a 1 millimeter wide, Cesium-Iodine beam from 0.7 nanoradians to 0.035 nanoradians within a distance of 1,000 km? The 0.126 C beam crosses a distance of 1,000 km in about 26.45 milliseconds. An initial divergence of 0.7 nanoradians implies that it spreads at a rate of 0.021 m/s. We therefore need to reduce the transverse velocity from 0.021 m/s to 0.00108 m/s within 26.45 milliseconds. That is an acceleration of 0.776 m/s^2. The divergence reduction factor is 20, so the average acceleration is 18% of the initial acceleration. We therefore need an initial acceleration of 4.3 m/s^2. We input PA = 4.3 m/s^2, AP = 1.94*10^-28 and PM = 4.32*10^-25 kg. From that, we determine that IG = 1.92*10^4 W/m^2/m The average laser intensity will be 4.78 W/m^2 so total laser power is a rather incredible 0.37 … milliWatts. Summary of results: Example 1 Particle: 100 MeV Hydrogen Initial divergence: 54 nrad Final divergence: 5.4 nrad Power required: 172.3 MW Example 2 Particle: 300 MeV Xenon Initial divergence: 2.5 nrad Final divergence: 0.25 nrad Power required: 56.7 kW Example 3 Particle: 1000 MeV Cesium and 955 MeV Iodine Initial divergence: 0.7 nrad Final divergence: 0.035 nrad Power required: 0.37 mW These are the theoretical minimum values, assuming maximal optical tweezer gradient force and that 100% of the laser energy goes towards pushing particles together. However, if even a fraction of this performance is attainable (you can always compensate with stronger lasers, rising from milliwatts to watts), then particle beams with a tenth of a nanoradian in divergence are attainable. In the final example, we find that LCPBs are able to act like ‘pencil beams’ that barely spread from the moment they exit their millimeter-sized ports to when they produce spot sizes on the order of 3.5 cm at 1 million km. Fighting with LCPBs It should be evident by now that if we start off with a beam of low divergence and narrow diameter, we can use very moderate laser power to significantly reduce divergence. LCPB ‘pencil beams’ would be able to produce small spot sizes at extreme distances. They would dominate the field of directed energy weapons and would be the ideal power transmission tool for interplanetary or interstellar propulsion. A 0.1 nanoradian divergence beam would concentrate its energy within a 0.03 m^2 spot at a million kilometers, or catch a 100 meter wide receiver from a distance of 500 million km. The latter is 33% more than the distance from the Earth to Mars… if they were on opposite sides of the Sun! LCPBs will dominate only within distances that they can reliably hit a target though. Their main limitation would be their velocity. The beam velocity does not matter when aiming at something that does not move appreciably in the time it takes the beam to reach it, or has a well defined trajectory, like an asteroid or a space station. LCPBs suffer instead when aiming at randomly maneuvering targets. The same random ‘jinking’ used to avoid lasers at distances where light lag is significant can be used at shorter ranges against the slower particle beams. Let’s take an enemy warship with a hull 10 meters wide. It can accelerate sideways at 1m/s^2. If the beam travels at 0.07 C, like in the second example, then it will only hit that warship with 100% certainty out to a distance of 66,000 km. Accepting a hit rate of 50% only increases the distance to 77,000 km. It is a great distance, but only a tiny fraction of what the LCPB is capable of. The enemy warship can reduce these ranges by accelerating harder. At 10m/s^2, the 100% hit distance is ‘just’ 21,000km. Of course, this consumes ten times more propellant. A dumb but surefire way to defeat this enemy warship is to keep firing the LCPB until the jinking has consumed of its deltaV and renders it a non-maneuvering target. This might take minutes to days depending on the capabilities of the propulsion technology, and can be greatly extended by moving further away and reducing the acceleration. During this period, the enemy is firing back, a unenviable situation. Smarter heads would choose to fire along a pattern that touches upon all potential positions the enemy warship can take. This way, a low hit chance can be converted into a low hit rate. For example, a 0.07 C beam targeting a 10m wide target with 1 m/s^2 of acceleration would only have a hit chance of 1/82 at a distance of 200,000 km. Instead of shooting spots at a random within the area of probable positions the target can take, the area is divided into sections, with each section given a fraction of the beam’s output. This way, instead of doing full damage with a 1.22% chance, we deal 1.22% damage all the time. A 1000 MW LCPB with a 0.1 nanoradian divergence would have a spot size of 4 cm at 200,000 km. It should be able to burn through 24.6 m/s of graphite or 9.72 m/s of steel against an immobile target. Even after being divided and spread into 82 section to ensure a 100% hit chance, this is enough to maintain an average penetration rate of 30 cm/s against graphite and 11.8 cm/s against steel. Closing the distance greatly improves these numbers, as the beam becomes more intense and the target can take up less positions, so the beam power doesn’t have to be divided as much. Performance table for a 1000 MW 0.1 nanoradian beam vs 10m target: Base penetration rates Target Material/Distance: Penetration rate Graphite / 500,000 km: 0.843 m/s Graphite / 250,000 km: 3.36 m/s Graphite / 100,000 km: 20.8 m/s Steel / 500,000 km: 1.76 m/s Steel / 250,000 km: 6.46 m/s Steel / 100,000 km: 32.9 m/s Beam velocity: 0.01 C Target acceleration/Distance/Sections: Average penetration rate vs graphite 1m/s^2 / 500,000km / 7,716,050: 0.11 micrometers/s 1m/s^2 / 250,000km / 482,250: 7 micrometers/s 1m/s^2 / 100,000km / 12,345: 1.7 millimeters/s 10m/s^2 / 250,000km / 48,225,300: 0.07 micrometers/s 10m/s^2 / 100,000km / 1,234,570: 16.8 micrometers/s Beam velocity: 0.1 C Target acceleration/Distance/Sections: Average penetration rate vs graphite 1m/s^2 / 500,000km / 771: 1.1 mm/s 1m/s^2 / 250,000km / 48: 70 mm/s 1m/s^2 / 100,000km / 1: 20.8 m/s 10m/s^2 / 250,000km / 4,822: 0.7 mm/s 10m/s^2 / 100,000km / 123: 169 mm/s Beam velocity: 0.5 C Target acceleration/Distance/Sections: Average penetration rate vs graphite 1m/s^2 / 500,000km / 1: 0.843 m/s 1m/s^2 / 250,000km / 1: 3.36 m/s 1m/s^2 / 100,000km / 1: 20.8 m/s 10m/s^2 / 250,000km / 8: 0.42 m/s 10m/s^2 / 100,000km / 1: 20.8 m/s Based on these findings, LCPBs for combat would best be designed around produce a beam balanced between having enough speed to catch maneuvering targets and enough weight (molar mass) to maintain a low divergence. Against large, relatively immobile targets like a space station or an asteroid fort, it is very easy to create very slow and very heavy beams that maintain an extremely low divergence across interplanetary distances. Space Station. Such ‘anti-fort’ beams would have penetration rates that could poke holes through hundreds of meters of rock and steel. The huge mass that serves as a great heatsink and helps ward off smaller warships using weapons of greater power and thus range in a laser vs laser scenario becomes a hindrance in an LCPB vs LCPB scenario. The asteroid forts could try to retaliate with their own beams, but they will not be able to hurt maneuvering targets (look at how much average penetration drops as the number of sections increases) using LCPBs nor match their range using lasers. Therefore, we can safely say that any large, mostly immobile structure can be defeated by a maneuvering LCPB-equipped spaceship. The situation is more nuanced when it is a maneuvering spaceship against a Laser Weapon Web. LCPBs will lose if the LWW is able to bring their ‘terminal mirrors’ close to the LCPB to match its range faster than the LCPB or a radiation weapon can destroy them. This assumes the battles does not start with the LCPB-equipped spaceship already in range of a Laser Weapon Web, and if the power source of the LWW isn’t a planet protected by a thick atmosphere that particle beams cannot get through… For SF authors and game designers, LCPBs have interesting tactical consequences. The name of the game is balance. The low-risk strategy in a one vs one situation is to spread the beam’s output and wait for the armor to be whittled away. A high-risk alternative is to drag the beam at random around the target and hope that when the beam does connect, it’s full-power penetration rate is enough to cut through the armor layer and get at the vital internal components. With computers and predictive software, a middle ground is likely to be sought instead: the target’s motions are predicted to lie along a certain path, and it is better to try to focus on getting a few good hits that get through the armor to start reducing the target’s ability to maneuver or fire back. Minimize cross-section. Because of these tactics, it is suicidal to have no armor but also pointless to have too much armor. An unarmored craft can be destroyed by a sweep of a low powered beam while even a hundred meter boulder of graphite can be cut through end to end by a good hit from a LCPB. A balanced strategy with an optimum level of armor would deal damage the quickest and avoid harm the longest. Having massively more powerful beams, thicker armor or faster acceleration will not gain any decisive victory. That is only passive armor though. We must include the threat from radiation beams and the option of active defenses. Radiation beams would easily pass through the ‘optimal armor’ from an LCPB-balanced design. They require powerful magnetic fields to deflect instead. However, the power requirements and weight of equipment to surround a spaceship with a magnetic field sufficient to deflect the beam from an accelerator a fraction of the size and weight quickly becomes untenable. Instead of increasing the field strength to match the bending radius of more and more energetic particles, it is possible instead of physically move a smaller field outwards and into the beam path. Smaller magnetic field generators can be fitted on drones and placed a kilometer or so away from the main spaceship. The ‘mag-shield’ drones only need to be strong enough to cause the incoming radiation to bend by an angle sufficient to miss the main spaceship. For example, protecting a 10 meter wide spaceship using a mag-shield drone 1000 meters in front of it only requires that incoming beams be deflected by 0.29 degrees! This naturally allows for very small and weak fields to be used. The downside to mag-shield drones is that they only work against beams coming from a small number of directions. An unexpected attack would be devastating. It wouldn’t have to be very powerful or intense to severely harm a living crew or sensitive electrons, as was demonstrated in the previous Particle Beam post. In fact, it could be the ideal weapon for deployment by cryogenic stealth craft, as they are the ones which could sneak into flanking attack vector and the low power requirements of a radiation weapon allows its waste heat to be entirely absorbed by the on-board cryogenic heatsink for minutes or even hours at a time. A second line of defense in the form of quick response mag-shield drones, that shoot out into the direction of an unexpected radiation beam, could be the difference between 0.1 seconds of sickening radiation and death. What is the relationship between mag-shield drones and LCPBs? The same concept can be used at even greater distances. The magnetic field will not be powerful enough to promptly ionize heavy particle beams approaching far below the speed of light, but it can work use its field to hold in a bubble of plasma. LCPB particles traversing a plasma can be quickly ionized, allowing them to be affected in turn by the magnetic field. The further away the mag-shield drones are from the main ship, the weaker and lighter they can be, but also protect it from fewer directions. Counter-beaming is another option. A LCPB’s arrival will be announced by a guide laser to give several seconds of warning at longer ranges. The targeted ship could aim down the beam path with its own laser. This ‘counter-LCPB’ beam would have an intensity profile opposite to that of a gaussian beam: weak in the center and intense at the edges. It would use the same Laser Coupling technique to push particles out of the center of the beam and therefore increase divergence. C-LCPBs will have a tough time as they have a narrow window of opportunity to get themselves aligned as well as possible with the incoming LCPB. They can never be perfectly parallel with the incoming beam, so they are less efficient. Worse, their need for large lenses makes them hard to protect when they become targets themselves. From a visual perspective, battles involving LCPBs are more interesting than laser-dominated combat. The neutralization step emits a small bit of light at the beginning of the particle beam's journey. Its guide laser will leave a dim trail of scattered photons from where it interacts with the particle beam. A brighter flash will occur where an ionizing laser meets an incoming LCPB, with the most spectacular sight being the interaction with a plasma bubble. C-LPBs have to make up for their reduced efficiency by using more power. This power ends up scattered as photons anyone can see. This was prepared with the gracious help of GerritB, Kerr and Imallett.
  4. MatterBeam

    THE BARTDON PAPERS - "Cancel all previous directives."

    Thanks for taking the time to show those... mistakes! Turbo-electric turboprops is an interesting choice. I would think that if fuel is the limiting factor, then fuel-electric-motor-prop is a less efficient use of it than simply fuel-motor-prop.
  5. MatterBeam

    THE BARTDON PAPERS - "Cancel all previous directives."

    I love all these VTOL plane designs and the use of turboprops instead of whiny jets.
  6. This is quite awesome. Would love to see more.
  7. MatterBeam

    Particle Beams in Space!

    You're thinking of an induction accelerator, which does not use RF fields like a conventional particle accelerator.
  8. MatterBeam

    Particle Beams in Space!

    It all came to this. Ion thrusters produce 'beams' of a few keV of energy. The accelerators discussed in the blog posts are in the hundreds of MeV to several GeV. Not really. The gas particles aren't travelling in the same direction. Coilguns have a massively higher time to target and don't have the massive effectiveness of radiation beams in certain situations. Also, particle beams here spread to many dozens of cm in diameter after travelling thousands of kilometers, so what you see on that man is unlikely to be relevant.
  9. MatterBeam

    Particle Beams in Space!

    Hi all! I am sure you will find this interesting: Particle Beams in Space Science fiction is missing a realistic and grounded look at particle beams. We plan to do just that now. After reading this, you might decide to give particle beams their rightful place alongside lasers as a means of transmitting power, propelling spacecraft or dealing damage at long distances. This post focuses on particle beams deployed and used in space. All claims and calculations here are based on paper and studies referenced through links throughout. The first sections focus on the hard science behind particle beams and the performance achieved by existing accelerators. We then move on plausibly extrapolated performance and then to informed speculation on how they can be designed and used before ending on topics most relevant to sci-fi authors and worldbuilders. Particle Beams A particle beam is a stream of electrons, ions or neutral atoms that have been accelerated to a high velocity by an accelerator from a particle source. Particle beams are used in a huge variety of ways. Everything from electron microscopes to cancer treatment involves a particle beam. A common example of a particle accelerator is a medical X-ray. It produces a beam of electrons that emit X-ray light when they hit a metal target. They are used in research extensively. Some of the most expensive research projects ever are centred around particle accelerators, such as the Large Hadron Collider or the Stanford Large Accelerator Center. The beams produced there are usually composed of electrons or protons, but also heavy ions such as lead and uranium. In fact, any charged particle can be accelerated in a particle accelerator. This technology was also a focus of the Strategic Defense Initiative back in the 1980s, which culminated in an accelerator-equipped satellite being launched into space to test the performance of particle beams at different altitudes. To describe the characteristics of particle beams, we could use standard units such as velocity in meters per second or particle energy in joules. However, the typical beam is highly relativistic (90%+ the speed of light or 0.9 C) and each particle has a very small amount of energy (a hundredth billionth of a joule or less). A specialized set of units is used instead and a relativistic energy calculator is the best tool to handle them. We use the Beta factor B, with values between 0 and 1, to describe the ratio of particle velocity to the speed of light. B = 0.875 means that the beam is travelling at 0.875 C. The Lorentz or Gamma factor describes the intensity of the relativistic effects. A 0.875 C, a particle has a gamma factor of 2.065, meaning that it experiences time 2.065 times slower than anyone else around. The relativistic energy calculator provides these values. If we input an ion mass (carbon has 12 g/mol molar mass so put ‘12’ in the mp box) and an ion energy (3.2 * 10^-8 joules, equivalent to about 2 * 10^9 electronvolts or 2 GeV), we obtain a Beta of 0.528 and a Gamma of 1.177. If we have a current of these carbon ions travelling in a beam (for example, 0.00001 Amps or 10 uA), we can multiply it by the particle energy in eV to work out the total beam power in watts (2 GeV * 10 uA : 20,000 watts or 20 kW). These figures will be critical to understanding the performance and requirements of a particle accelerator. The accelerator The characteristics of a particle accelerator are resumed in their efficiency (%), acceleration gradient (volts per meter or V/m) and mass per meter length (kg/m). Launching and building equipment in space is inherently expensive. Moving it around is even more so. The expense is proportional to the equipment mass, so the best accelerator is therefore the one which has the highest performance per kg. High efficiency is good, because it means less mass dedicated to cooling systems. A high acceleration gradient is desirable for shorter and lighter accelerator. A low mass per meter is also needed. It is with these characteristics that we evaluate the major types of particle accelerator. The first and oldest type is the electrostatic accelerator. It works by applying a strong voltage difference between an anode and a cathode, separated by a gap. The maximum voltage possible is limited by electrostatic breakdown, which is when electrons jump across the gap on their own. Van de Graff accelerators are the primary example of this design. Currently, the maximum voltage is roughly 25 million volts (MV), with the acceleration gradient averaging 0.5 MV/m. Tandem electrostatic generators have achieved 40 MV in total. To achieve higher energies and better acceleration gradients, induction accelerators are used. Betatrons are an example of this design, and they are a type of cyclotron. The acceleration gradient is about 1MV/m, but it quickly falls when the particles start reaching relativistic velocities. Radio-frequency accelerators are the dominant type of high-energy accelerator in use today. They use radiofrequency (RF) cavities to produce a voltage difference that particles are accelerated over. The cavities are simply 'mirror boxes' for radio waves. They bounce up and down at a very specific rate within the boxes. When a particle beam enters one end of the cavity, it encounters the radio wave. The wave has an electric field that pulls the beam along, which corresponds to a voltage. Once the particle beam exits the cavity, it enters a drift tube that shields it from the radio wave's pull in the opposite direction. A series of cavities continuously accelerates the beam in this way. Dividing the voltage difference between the ends of the cavities by the distance the beam crosses gives us an acceleration gradient. Typical particle accelerators have an acceleration gradient of 20 MV/m. They are limited by RF waves being absorbed in the walls as heat. The alternative is to use superconducting RF accelerators. Cryogenically cooled cavities made of niobium metal have no electric resistance and do not absorb the RF waves. This means that very high acceleration gradients are possible without worrying about heating problems. Superconducting RF (SRF) accelerators regularly reach 25 to 40 MV/m. Certain configurations, such as travelling wave accelerators, are needed for highly relativistic electrons, but it is not the case for much more massive ions. This allows very short accelerators reach very high energies. SRF accelerators can be circular or linear. Circular accelerators allow a short acceleration length to be used again and again. However, it needs powerful and therefore heavy magnets to keep bending a beam into a circle as the particle energies increase. Furthermore, bending a beam releases synchrotron radiation that drains particle energy. A small circular accelerator that can fit inside a spaceship would be limited in the particle energies it can achieve and would have multiple sources of inefficiency. Linear accelerators or ‘linacs’ do not bend the beam. All energy expended goes towards accelerating the beam. Only a single pass is possible however, so strong acceleration gradients are needed. You don’t have to choose strictly one or the other. A circular accelerator can be used to bring particles up to speed and then pass them onto a linac for the final boost. A recirculating linac could be selected as a sort of hybrid: after passing through the accelerating section, the beam is turned 180 degrees for a second pass. Whatever the choice of the exact configuration, the SRF accelerator on a spaceship will have a length and therefore mass proportional to the particle energy we want to achieve. If we want particles with an energy of 100 MeV, we divide the energy by the number of charges and the acceleration gradient to find the accelerator’s length. For example, Oxygen 2+ ions and a 25 MV/m gradient would reach 100 MeV in just 2 meters while Lithium 1+ ions and a 10 MV/m gradient would need 10 meters. A new accelerator technology has emerged in recent years: plasma wakefield accelerators. They use an intense laser pulse to create a tube of plasma emptied of electrons. The electrons rush back in as a wave. Multiple pulses create a series of waves travelling at relativistic velocity. They can pull along particles in their ‘wake’, allowing for extreme acceleration gradients on the order of 10 GV/m. However, their efficiency is abysmal (~0.1%) and their acceleration lengths are in the centimetres, making them unsuited for anything but researchers. Even more recent developments could remedy their faults. For the rest of this post, we will assume that SRF linacs are being used. Particle beam divergence In space, distances are huge. Particle beams would have to traverse thousands of kilometres to be useful. Divergence is very important in space because of these distances. Divergence is the ratio of lateral spread to forward motion, noted in radians. For most cases described here, we will use milliradians ‘mrad’ or microradians ‘urad’. To correct for relativistic factors, it must be further divided by the gamma factor ‘y’. A high divergence means that the beam spreads its energy over a large area within a short distance, making it hard to use for purposes such as power transmission or propulsion. A low divergence allows it to be focused onto a spot small enough to become a damaging weapon. The lower the divergence, the greater the range at which a beam remains useful. Particle beams are said to spread too quickly to be used over long distances. This is true… for charged particle beams. All accelerators produce charged particle beams. The self-repulsion between ions of similar charge causes electrostatic bloom. This is a very rapid widening of the beam that de-focuses it and spreads its energy rapidly. Even worse, if a beam were near a planet’s magnetic field, its trajectory would be bent off-course. Shooting charged particle beams also confers a strong electrostatic charge to the firing platform, which could lead to dangerous sparks and arcs. The radius doubling distance for a charged particle beam is: RDD = 5586 * BR * B^1.5 * y^1.5 * (M / (Z * IB))^0.5 RDD is the radius doubling distance in meters. BR is the initial beam radius in meters. B is the Beta factor. y is the Gamma factor. M is the ion mass in g/mol. IB is the beam current in Amps. Z is the particle charge. We can work out that a 0.1 mA beam of 200 MeV carbon ions with a charge of 3+ (B: 0.186, y: 1.02, IM: 12 and Z: 3) and an initial radius of 0.1 m would have a radius doubling distance of 9,232 meters. It crosses this distance in 165 microseconds. Because the radius increase causes the doubling distance to also increase, it would take 330 microseconds for the radius to double from 0.2 to 0.4 m, and 660 microseconds to increase from 0.4 to 0.8 meters and so on. The exponential nature of the radius doubling distance means that to find out the distance at which a beam expands by a ratio Charged particle beams cannot cross the thousands to tens of thousands of kilometers that separate objects and ships in space without expanding to huge sizes. It doesn’t have to be this way though. Electrostatic bloom can be prevented by taking an extra step after a charged particle beam passes through an accelerator: neutralization. This converts charged particles into neutral atoms, either by adding or subtracting electrons. Neutral beams do not suffer from electrostatic bloom but are still affected by thermal expansion. Thermal expansion is due to the random motion of particles within the beam. This motion is the same as that of molecules within a gas and is proportional to the temperature and molar mass of the particles. Perfect gas laws allow us to work out the velocity of the particles that results in thermal expansion. The velocity of particles in a gas depends on their temperature and molar mass. Specifically, the velocity in meters per second is equal to 17009.6 * (Temperature/Molar mass)^0.5, if we use electronvolts for temperature and g/mol for molar mass. Lithium particles with a temperature of 1 eV and a molar mass of 7g/mol would expand by 6.43 km/s in all directions. This is negligible velocity in the longitudinal direction (the lithium particles would be accelerated to several thousands of km/s by the accelerator) but is critical in the transverse directions. Divergence is the simple ratio between the beam’s rate of expansion and rate of travel. If we divide the transverse velocity by the beam velocity, we get a divergence in radians. Multiplying that divergence by the distance the beam must travel gives the beam radius at the distance. It is also called the spot radius, analogous to the size of a spotlight’s spot on the ground. If a lithium beam were accelerated to a velocity of 72,330 km/s (a beam energy of 200 MeV), and it had a temperature of 1 eV, we can work out a divergence of 0.0000889 radians, or 88.9 microradians. If the beam must travel 1,000 km, it would have a beam radius of 88.9 meters (and a beam diameter of 177.8 meters). Its energy would be spread over the surface area of that spot. By reducing the temperature or increasing the particle mass, we could expect a lower divergence. If we used ions with a temperature of 0.1 eV instead of 1 eV, we would expect a 3.16 times lower divergence. If we switched out the lithium ions (7 g/mol) for Cesium ions (133 g/mol), we would expect a 4.36 times lower divergence. A lower divergence allows for a smaller spot size at all distances and a better focusing of the beam’s energy. This is where most writing on particle beams ends. Further research has shown that particle beam divergence is not so simple. A heavier particle, for example, would also be travelling proportionally slower. Divergence is a ratio, and if both the transverse and longitudinal velocity are reduced by the same amount, the ratio is maintained. Beam temperature is a complex topic. Superconducting accelerators with good control over the beam should cause next to no heating of the particles. What determines the temperature in the first place then? What of all the other factors that go into determining the rate of beam spread? Why does ‘divergence’ not give many search results online? This is because actual particle physicists use a different measure for the performance of accelerators: emittance. Let’s try to explain what it is and use it to answer our questions. Emittance, emittance growth and ion sources In scientific literature, the divergence of a particle beam is rarely given or used. ‘Emittance’ is used in its place. It is the result of multiplying the divergence of a beam by its radius to produce a measure in ‘meters-radians’. Because of the low values in most accelerators, ‘millimeters-milliradians’ or mm-mrad is preferred. One m-rad is a million mm-mrad. Emittance describes the average spread of particles, like divergence does, but it also helps factors in the width of the beam, any perturbations or errors, any imperfections in the accelerator and other factors. A ‘normalized’ emittance divides the measured emittance by the gamma factor to account for any relativistic effects. Emittance is more useful that simple divergence because it is flexible and can be applies to different accelerators that can be scaled, stretched or used in different ways… so long as the parameters determining the emittance are similar. To get divergence back from emittance, use this: Divergence: Emittance / (Beam radius * 10^6) Divergence will be in radians. Emittance is in mm-mrad. Beam radius is in meters. Emittance is a very useful measure for predicting the performance of future accelerators. If we took the results of a small laboratory accelerator with a 1 mm wide beam, we can work out the divergence of a beam from a scaled-up version with a 10 cm wide beam. Sadly, emittance is reported very inconsistently. One emittance reading in one paper will mean something different from another reading in another publication. The way emittance is reported has changed over time too. Early studies could give a figure in ‘mm-mrad’ that did not take into account relativistic effects. More recent paper would give ‘normalized’ emittance in ‘π mm-mrad’. To convert from one to another, you’d have to divide by π and calculate the gamma factor… despite both being called ‘emittance’. Also pay attention to whether the value is reported at the entrance, midway or at the exit of the accelerator. To muddle things further, emittance can count the beam radius as starting from different distances from the beam centre, creating hugely varied readings for the same beam. With all these caveats in mind, we can start to take a quick look at the emittance of past and present accelerators. -0.43 mm-mrad for the Indian Spallation Neutron Source, -0.2 mm-mrad for TRASCO 100 MeV proton design. -0.2 mm-mrad for the Independent Superconducting Cavity Linac, -0.25 mm-mrad for the variety of heavy ions from the ATLAS accelerator, -0.16 mm-mrad from the hydrogen ion accelerator specifically designed to lower divergence in the BEAR experiment, -0.06 mm-mrad for the FRANZ proton linac, As we can see, there is potential to improve. If you look into the documents linked above, you will see multiple emittances reported, at the exit of injectors or at the entrance of accelerators and so on. As the beam travels through the accelerator, it is disturbed a small amount by magnetic fields and heated up slightly by inter-particle collisions. This leads to a gradual increase in emittance from entry to exit. We call this ‘emittance growth’. Much effort has been put into reducing emittance growth. As we can see from these studies, emittance growth in modern accelerators can be as low as 5% or as high as 90%. The valuable truth is stated in the introduction of this paper: emittance is due mainly to the ion source. Ion sources are therefore the primary determinants of an accelerator’s emittance. We can see in the BEAR experiment that the emittance at the exit of the ion injector is the same as that at the exit of the entire accelerator. An ion source, as the name states, is the device that feeds an accelerator with ions. There are a large number of options with different currents (charged particles per second released), current densities (current per area), efficiencies, voltages and other parameters. We won’t detail the entire list. In general, ion sources are a small fraction of the power consumption, weight and size of a particle accelerator. However, the properties of the beam produced by an ion source determine the overall performance. It makes sense that we would select ion sources that produce high quality beams even if we must sacrifice efficiency or equipment mass to produce them. As we will prove again later, having an ion source with a low emittance is crucial to a low final divergence of the particle beam. Searching through published performance of ion sources finds emittances as low as 0.004 (hydrogen) to 0.0075 (argon) mm-mrad. It is consistent with an ion temperature of about 0.1 eV and an aperture of 3 mm when using this equation from a study on heavy ion beams accelerated by the MBE-4 linacs: Ion Source Emittance = 65 * Aperture Radius * (T/M)^0.5 Emittance will be in mm-mrad. Aperture radius must be in meters. T is in eV. M is molar mass in g/mol. Inputting the figures from the study (0.1 eV Argon 1+ beam of 18 g/mol, leaving through a 1.5 mm radius aperture) we find a very similar emittance of 0.0073 mm-mrad. To bring this back to divergence for a moment, we can work out that the MBE-4 linacs have a divergence of 4.8 microradians. The equation also suggests that the smaller the aperture of the ion source, the smaller the emittance. However, the ion current is proportional to the surface area of the aperture, so this might limit how much current is available… unless multiple small radius ion sources are combined into one beam to have the best of both worlds: lowest emittance and high current. Another way around a low current is to use a pulsed mode of operation. A small, lightweight low-energy storage ring can accumulate the output of an ion source working continuously and release it periodically in a high current burst. The low emittance from an ion source like the one used in the MBE-4 linac is only possible because it produces ions with single charges. They require the least heating and the least intense magnetic fields to handle. In many cases, an ion with multiple charges is desirable. An ion with more charges gains energy proportionally faster than an ion with less charges. An Uranium 12+ ion, for example, would gain 120 MeV of energy after passing through a 10 MV accelerating gradient. An Uranium 35+ ion would gain 350 MeV instead. The potential reduction in the accelerator length required to reach a certain energy level is very interesting as it would lead to great reductions in accelerator mass. The best source for highly charged ions is the Electron Cyclotron Resonance ion source. It is capable of handling all elements and achieving very high charge states by bombarding ions with an energetic electron beam again and again. The collisions deliver the required ionization energy to the ions, which can reach several keV. The ions are forced to orbit within a small circle by magnetic fields so that they can be contained. However, the rotation within the magnetic fields adds a radial velocity to the ions. The result is an emittance dominated by the strength of the magnetic fields and the charge to mass ratio of the ions. The equation for the emittance of an ideal ECR ion source is: ECRIS emittance: 0.032 * Aperture Radius^2 * B / MCR Emittance is in mm-mrad. Aperture Radius is in millimeters. B is the magnetic field strength in Tesla. MCR is the mass to charge ratio. For heavy ions, B is about 0.5 to 2 Tesla and the MCR for something like Oxygen 2+ is 16 over 2 (which is 8). We find emittances as low as 0.03 to 0.05 mm-mrad using heavier elements Bismuth and Krypton. With an ECRIS, we want the heaviest ions and the smallest apertures to minimize emittance. ECRs can become rather heavy. They need large magnets and consequent cooling systems. For cases where achieving the lowest possible emittance is not a priority but producing highly charged ions is, there exists an alternative: foil or gas strippers. It involves two steps. First, an ion is given a small charge and accelerated to moderately high energies by a separate accelerator. The ion then impacts the stripper, which is a certain length of gas (light ions) or a certain thickness of metal (heavy ions). The impact releases enough energy to strip off a large portion of the electrons around the ion. Extreme charge states are possible, such as Pb 82+, if the particles were given sufficient energy to start with. The stripping process leaves most of the beam’s energy preserved, but emittance suffers. Modern ion strippers achieve emittances on the order of 0.1 mm-mrad. Emittance alone is not enough to make a particle beam useful. A very low emittance in a beam released through a very small opening still makes for a high divergence beam. In ion sources, trying to achieve a lower emittance also involves making their aperture even smaller, which does not lead to improvements in divergence. If particle beams cannot achieve low enough divergence, then lasers will remain as the better option... Beam optics The beam radius can be increased through the use of beam optics. Increasing the radius of a beam with low emittance will lead to a very low divergence. Just like beams of light that can be bent, focused or defocused by lenses, particle beams can be manipulated using electrostatic or magnetic lenses. Electrostatic lenses work by introducing a voltage gradient from a particle beam’s centre to its edge. A charged particle travelling near the centre is unaffected. A particle travelling nearer the edges is either pushed inwards (focusing) or pulled outwards (expanding) by the voltage gradient. Electrostatic lenses become less effective as the beam velocity increases. This means that they work fine for non-relativistic beams but the voltage gradients needed to act on high energy beams quickly become impractical (electrostatic lenses are limited by the same 10MV/m as electrostatic accelerators). Electromagnetic lenses use magnetic fields to deflect ions. They become more effective as the beam velocity increases, allowing them to handle relativistic beams much more easily. They are larger and heavier than electrostatic lenses for the same focusing ability due to the need for strong magnets however. Two lenses working together can decrease divergence. The beam would first be expanded from its narrow diameter to a larger diameter. Then its expansion would be corrected and it would be focused on a far-away spot. Emittance does not change during this process. A 1 mm radius beam with 0.1 mm-mrad emittance would have a divergence of 0.1 mrad without beam optics. If it is expanded to 20cm, it would have a new divergence of 0.0005 mrad. Beam expansion to reduce divergence can be found most prominently in the neutral particle beam space experiment ‘BEAR’ from the Los Alamos National Laboratory. It was and still is the only high powered particle beam flown into space. The accelerator produced a negatively charged hydrogen beam with a beam radius of 2mm, which was then expanded to 11mm by electrostatic optics. This would theoretically allow the divergence to fall by a factor 5.5 before neutralization. The effect of magnetic lens radius on the size of beam spot at a certain distance is determined by: Spot radius = Emittance * Distance * 10^-6 / Lens Radius Spot radius will be calculated in meters. Emittance is in mm-mrad. Distance must be given in meters. Lens radius is also in meters. You might notice that this is the equation used by lasers to determine spot size, if the wavelength of the photons were replaced by the emittance of the particles. In other words, a particle beam of emittance 0.1 mm-mrad has the same performance, given any distance and lens radius, as a laser of wavelength 100 nanometers (soft X-rays). The implication is that particle accelerators can produce and handle beams with performance equal to lasers with extremely short wavelengths. Neutralization This is the step that allows a tightly focused particle beam to reach its destination without spreading into uselessness. Necessarily, it is the last step in a particle’s journey from ion source to space. After an ion becomes a neutral particle, it can no longer interact with magnetic fields and so cannot be further cooled, accelerated, focused or aimed. Neutralization disturbs the particles in a beam. It imposes a minimum divergence that depends on the charge state of the ion, its energy and mass, and most importantly on the neutralization method being used. All neutralization requires an input of energy to strip an electron off a neutral ion, or releases energy when adding electrons to a positive ion. This energy is equal to the ionization energy. Three main neutralization methods exist: using charge exchange, using electron beams or using lasers. Charge exchange neutralization requires that an ion from a particle beam travel through a gas, plasma or foil. When the ion strikes a component of that gas, plasma or foil, it gains or loses electrons and becomes a neutral atom. The advantage is that this method requires no power input (the neutralization energy comes from the beam itself) and can be a very lightweight solution. The major downside is that impacts between an ion and a neutralizing particle tends to scatter the beam significantly. Gas or plasma neutralizers have the extra disadvantage of requiring heavy flow through a pressurized chamber, which is directly contrary to the requirement for keeping the accelerator tube in a perfect vacuum. Design documents on the DEMO neutral beam injectors state that plasma neutralization becomes exceedingly inefficiency as particle energy increases above the 100s of keV. Gas neutralization fails above 1 keV. This is not a good solution for high energy particle beams. Electron beam neutralization combines the ion beam with an electron beam of the same velocity. The two beams merge into a plasma with an overall neutral charge. Within microseconds, the ions pull on the electrons to become neutral atoms. This is known as ‘recombination’. Recombination energy is equal to ionization energy. As the electrons are travelling at the same speed as the ions, there are no impacts that scatter the beam. The massive mass difference between an electron and an ion means that the electrons retain almost all the energy being released by recombination. The electrons emit that energy as photons of specific wavelengths. The downside to this method is that you need an additional accelerator for the electrons and can only neutralize positive ions, but it is a small price to pay for the low divergence beams that are produced. The latest option being developed is neutralization by lasers, also called photo-neutralization. High energy photons from a short wavelength laser are sent to interact with an ion. The photons are absorbed by the outermost electrons of the ion. If enough energy is delivered to an electron, it jumps out of position. Photo-neutralization can turn negative ions into neutral atoms by removing electrons in this manner. The advantage is that photons are the most delicate neutralization tool and disturb the beam’s ions the least. However, it only works on negative ions and the laser power needed to strip high velocity beams after they have been expanded by beam optics is incredibly high. Photo-neutralization power = 8.853 * 10^-5 * BV * BR / Laser wavelength Photo-neutralization power will be in watts. BV is the beam velocity in m/s. BR is the beam radius in meters. Laser wavelength is also in meters. That equation applies only to negative H ions. We work out that at 1 GeV energy (262,000 km/s) and in a beam 1 m wide (BR 0.5), we would need a laser power of over 11.6 GW when using the longest practical wavelength of 1 micrometer. This is to neutralize just 63% of the beam. Neutralizing a full 98% of the beam requires 46.4 GW. This paper describes the development of an optical cavity that can bounce the laser up to 10,000 times through the particle beam to reduce the power required down by a factor 10,000. In our case, it is a reduction down to 4.64 MW. In non-laboratory conditions, that cavity might not have the same performance, but the real problem is that your multi-megawatt particle accelerator also needs a multi-megawatt laser to neutralize it. Considering the characteristics of all these methods, we will focus on electron beam neutralization. There will be designs for which the other methods make sense, such as a single-use close range particle beam using a foil stripper or an interplanetary ultra-low-divergence power transmission beam using a photo-neutralizer, but we won’t focus on those here. Let's continue to look at electron beam neutralization. When adding or removing charges from an ion, they get a ‘momentum kick’ that can be seen as the difference in beam velocity before and after neutralization. The minimum divergence imposed by neutralization is: Neutralization divergence = (0.56 * IE/M) / (B * C * y) Neutralization divergence is given in radians. IE is Ionization energy in eV. M is Molar mass is in g/mol. B is the particle beta. C is the speed of light, about 3 * 10^8 m/s. y is the Lorentz Factor. For a hydrogen ion, ionization energy is 13.6 eV. At 100 MeV, beta is 0.428 and y is 1.1065. We can work out that the minimum divergence of such a beam is 53.6 nanoradians. If it is accelerated to 1 GeV energy, beta becomes 0.875, y is 2.065 and the minimum divergence becomes 14 nanoradians. This divergence is to be added to that of the beam before neutralization. In the real world, the neutralization disturbance will be greater than the theoretical minimum. You will notice that the ions with the lowest ionization energy per mass, accelerated to the highest energies, will have the lowest minimum divergence. Cesium, for example, is particularly good. It has an ionization energy of just 3.89 eV while having a mass of 133 g/mol. At 250 MeV of energy, Cesium would have a minimum divergence of 0.86 nanoradians. Francium is even better but it is rare and very radioactive. Bright beams? The neutralization step releases the excess energy from recombination in the form of photons. Recombination usually involves the release of a photons with a total energy equal to the ionization energy. The SDI proposal for neutral particle beams used gas strippers for hydrogen atoms. It was expected for about 7% of the atoms to exit the stripper in a metastable excited state. Shining a laser on those metastable atoms would have caused them to quickly release their energy as 656 nm wavelength photons, which is a bright cherry red. Without the laser, it would take about 125 milliseconds for the photons to be released. Different ions emit different photon wavelengths as a ‘Radiative Recombination Continuum’. Going straight from the excited state (the electron has just arrived) to the ground state (all excess energy has been released) is rare, with a graduated release much more likely. For example, a lithium atom would release a photon with an energy of 5.39 eV and a Cesium atom would release photons with an energy of 3.89 eV. Any division of these energies would correspond to visible wavelengths. Multiplying the ionization energy (1 eV = 1.6 * 10^-19 Joules) by the current (1 A = 6.242 * 10^18 atoms per second) gives the total watts of visible light being emitted. For 1 Amp of Cesium atoms, this is 3.89 Watts. For a 250 MeV beam, this means that 1.6 millionth of a percent of the beam energy becomes visible light. This ratio only gets worse for beams with higher particle energies. These watts are spread over the distance the beam travels during its recombination time. In other words, particle beams could be visible, and will certainly be detected by sensors across even large distances, but they are mostly invisible to the naked eye. As the beam traverses interplanetary space, it encounters about five million protons per cubic meter near Earth, falling to 300,000 per m^3 at Saturn’s orbit. A 10 nanoradian divergence beam would traverse a volume of about 0.015 m^3 over a distance of 10,000 km. It encounters 78.5 thousand particles at most. Even if even proton is is struck, and all of the collision energy between the protons and beam particles were absorbed, and all of that energy was to be re-radiated as visible wavelength photons, then this would only amount to 2.34 femtowatts per meter for 0.063 C particle, or 0.45 nanowatts per meter for 1 GeV particles. Neither makes for visible beam. The situation changes near a planet. The particle density above an atmosphere is much higher than in the interplanetary medium, even when hundreds of kilometers over the surface. At 1000 km altitude above Earth, there are enough particles to create a mass density of 5.85 * 10^-15 kg/m^3. This would release 0.8 W/m from a 1 m diameter 0.063 C beam and 201 W/m from a 0.875 C beam. Relativistic beams are likely to be visible to the naked eye when fired over an atmosphere. Near the top of Earth's atmosphere, at 200 km altitude, we would expect very bright beams of 55.9 kW/m (0.063 C) or 10.78 MW/m (0.875 C). The huge energy losses experienced by fast beams make them impossible to use in such conditions unless they are very, very small (mm wide beams). All in all, the particle beams are likely to be detected by sensors but unlikely to be visible to bystanders. Final divergence We now have all the elements in place to work out the divergence of a very good particle accelerator. Final divergence= ((SE/LR * EG * 10^-6 + 0.56 * IE/(M * BV))/y SE is source emittance in mm-mrad (refer to the ion source equations). LR is the lens radius in meters. EG is the emittance growth throughout the accelerator, dimensionless. IE is the ionization energy in eV. M is the molar mass in g/mol. BV is the beam velocity in m/s. y is the gamma factor. We can work out that a 10 meter long accelerator built using modern technology, using a Microwave Ion Source to produce extract single-charge Cesium ions with 0.0018 mm-mrad emittance, expanding the beam from 1 mm radius to 0.05 meter radius (LR = 0.05), causing 10% emittance growth (EG = 1.1) and using electron beam neutralization (IE 3.89, M 133, BV 18,900,000), could be expected to produce 250 MeV particles with a divergence of just 40.5 nanoradians. This beam would cross a distance of 1,000 km in about fifty milliseconds and would remain focused within a spot just 8.1 cm wide. Even better focused beams could be produced if negatively charged ions are accelerated. The ionization energy for a negative ion can be very low, such as 0.47 eV for Cesium instead of 3.89 eV. Bigger accelerators can use larger optics and achieve higher particle energies, making particle beam performance scale up favourably. Equipment design The mass of a particle accelerator system seems to be dominated by the RF power generators and the cooling system, at least according to a footnote on the SDI report on the feasibility of Neutral Particle Beam weapons for ballistic missile defence. RF power, specifically in the frequencies that heavy ion SRF accelerators use, can be generated by solid-state devices. The best example of commercially available performance is from the Nautel generators produced specifically for the VASIMR rocket. They operate at over 98% efficiency and have a power density of 2 kW/kg. However, they lose efficiency as the RF frequency asked of them increases. For the dozens of MHz minimum that accelerators need, they are closer to 65% output efficiency. Inductive Output tubes are another option. This design by Relltubes produces an impressive 16 kW/kg at 73% output efficiency. The low frequencies achieved by solid state devices or Inductive Output tubes limit them to accelerating the heaviest ions to rather low velocities. Higher frequencies are needed for light ions or to achieve relativistic velocities. For higher RF frequencies required to push light particles to relativistic velocities, a magnetron is the best option. The most modern designs boast 14.7 kW/kg at 88% output efficiency. Solid state amplifiers, inductive output tubes or magnetrons can all expect to operate at rather warm temperatures. The amplifiers obtain good efficiency at room temperature (298 K) but can sacrifice efficiency down to operate at up to 473 K. The same goes for inductive output tubes, while magnetron performance seem to be unaffected by temperature even when operating at 423 K. The Klystons needed for the highest frequencies struggle to surpass 1 kW/kg. However, NASA designs for klystrons to be used in the SPS program were to achieve 1.96 kW/kg before cooling equipment was included. These temperatures are critical for telling us whether the waste heat from the RF source can be radiated directly or requires heat pumps to increase the radiating temperature (at the cost of more electricity and equipment mass). Lighter radiators can accommodate lower temperature waste heat. Better heat pumps significantly reduces radiator mass. For example a 1 MW magnetron would mass 68 kg and would need 95 kg of 1 mm thick graphite radiators radiating at 400 K to get rid of 120 kW of waste heat. The RF power reflected in an accelerator’s cavities is not absorbed. Over 100 MW of RF power per meter length of accelerator is possible. However, the superconducting walls are subjected to eddy currents from the megavolt electric field gradients running through them. These currents encounter a very small resistance, on the order of nanoOhms. Even cooling below 2 Kelvin temperatures cannot eliminate this ‘residual’ resistance. Typical SRF efficiency is therefore about 99.9%. Residual resistance causes about 0.1% of the power that an accelerator handles to become heat in the cavity walls. A 1 MW accelerator, for example, would cause 1 kW of heating. Most superconducting accelerators operate at 4.5 Kelvin temperatures to handle this heating. The empty spaces around a cavity’s walls are actually filled with helium. Helium boils at 4.2 Kelvin in standard atmospheric pressure. Having the cavity walls sit at a temperature just above the boiling point of helium allows any heating to be carried away by helium’s phase transition from liquid to gas state. The transition absorbs 20 kJ of heat per kg of helium. Accelerators that operate in the 4 to 5 Kelvin temperature range are made possible today through the use of niobium-tin alloys. A 1 MW accelerator should be prepared to lose 50 grams of helium per second. For a spaceship that only intends to use the accelerator in short bursts, releasing the helium vapours into space is acceptable. If the usage period extends to many hours, it is advisable to use a cryogenic heat pump to compress the vapours and increase their temperature from 4.2 K to 13.8 K. The latter temperature is where liquid hydrogen boils in near vacuum. Using hydrogen as an expendable coolant instead of helium is much more interesting, as it can absorb 455 kJ/kg. Even with the increased heat load of the pumps, the coolant expenditure is reduced by a factor 10 with liquid hydrogen. A closed loop alternative to expending helium or hydrogen is to install many more heat pumps to raise temperatures to the point where the heat can be effectively emitted from a radiator’s surface. A 300 Kelvin radiator emits 459.3 W/m^2 of exposed area. Pumping heat from 4.2 K to 300 K adds an additional 7042% to the heat load. If we want to get rid of 1 kW of heat, 7043 kW need to be emitted from 7667 m^2 of double-sided radiators. The question is whether the mass dedicated to the heat pumps (14 tons at 500 W/kg as deduced from Lockheed’s aerospace cryocooler) and the radiators (17.6 tons for 1mm thick graphite fins) is advantageous compared to few grams per second of liquid hydrogen expenditure using the previous solution. Only serious improvements to heat pump technology can reduce the mass of equipment needed to carry heat across large temperature differences and make closed loop cooling a better alternative. After the RF power source and the cooling equipment comes the mass of the accelerator cavities themselves. We can work this out. A half-wavelength cavity made for particles of moderate relativistic velocity (0.6 to 0.9 C) has 59 kg of niobium per meter length according to this design. With its titanium structure, it comes out to 130 kg/m. Other figures that we can use are those of the non-superconducting BEAR accelerator at 53.7 kg/m, the Indian IUAC at 316 kg/m or the much more modern cavities of the superconducting LHC at 125 kg/m. The main reason behind the mass per meter difference between the superconducting and non-superconducting cavities is the addition of a pressurized helium tank. We can settle on 130 kg/m as being a reasonable estimate. A 40 m long accelerator is expected to add 5.2 tons to equipment mass. This is expected to fall as technology progresses. The beam must pass through an electromagnetic lens and a neutralizing step. The High Energy Beam Transport section of the BEAR accelerator is an example of an electromagnetic lens. This is another example. All figures available online for magnetic lenses assume energetic beams being focused to a spot just a few centimeters to meters away from the lens. Deflecting the beam over such a short distance requires strong magnets, hence the improve magnet masses you can find. A particle accelerator in space will want to focus its beam over thousands to hundreds of thousands of meters. This greatly reduces the magnet strengths needed. For example, a typical magnetic lens with an aperture of 10 millimeters will focus a beam over a distance of 1 meter. Our lens would have an aperture of 1 meter and focus a beam over a distance of 100,000 meters at a minimum. The magnetic field requirements for our lens would be about a thousand times lower than a typical magnetic lens. For example, a 0.5m wide magnetic lens trying to focus 250 MeV heavy Cesium ions a spot 100 km away needs a magnetic field strength of just 0.000188 Tesla. In other words, the mass of magnetic optics for long range particle beams is negligible. The neutralizing step requires an electron accelerator. Electrons of the same velocity as a heavy ion are very low energy particles. Producing and accelerating them therefore requires very little mass dedicated to electron accelerators, on the order of kilograms. For a 10 MW beam of 250 MeV particles, a Cesium current of 40 milliAmps is required. 40 milliAmps of electrons would be needed to neutralize the ions. The Cesium ions are travelling at 18,947 km/s so the electrons would need an energy of just 1 keV to reach the same velocity. A 40 mA, 1 keV beam of electrons can be created by a <1 kg device. Other equipment such as an ion source are a small contribution to overall mass. A permanent magnet ECR called LAPECR1 managed 2.5 mA using just 25 kg of equipment. An even better example is the Dresden ECRIS-2.45M ion source for low charge ions, where 10 mA can be produced by a device of just 35 kg. 40 mA of Cesium might need less than 0.14 tons. Using the figures for modern accelerators, we can expect a 10 MW 250 MeV beam to require 0.14 tons for the ion source, 1.3 tons for the cavities, 0.68 tons for the RF power source, and 0.64 tons for 400 K radiators. We add a 25% ‘other equipment’ margin to bring the total mass to 3.45 tons. About 50.2 grams of liquid hydrogen coolant per second is the ‘ammunition’. The accelerator can fire for one hour with 180.7 kg of hydrogen on-board or for a full day (delivering 864 GJ) with 4.3 tons. Cesium consumption is negligible, at just 55 micrograms per second. At this scale, the entire accelerator assembly would have a power density of 2.89 kW/kg. When more advanced technologies are included, such as better heat pumps or lighter radiators, the figure increases even further. For the rest of this post, we will use three designs: Modern Accelerator Output: 10 MW Divergence: 40.5 nanoradians Beam velocity: 18,900 km/s Total mass: 3.45 tons. The modern accelerator is built out of existing components as described above. The biggest contributors to the device’s mass are the cavities and the RF power source. Huge Accelerator Output: 500 MW Divergence: 16.7 nanoradians Beam velocity: 18,900 km/s Total mass: 203 tons. Some design changes made sense at a larger scale. Better radiators in the form of ‘wire radiators’ show benefits when 185 MW of waste heat must be removed from the RF generators. At smaller scales, the support structure needed to handle the 1 mm thick carbon fiber wires makes them uninteresting. The SRF cavities are heated significantly more by 500 MW of input power. Ejecting a huge load of hydrogen is wasteful at this scale, so a closed loop solution using 65.6 tons of heat pumps and 8.2 tons of nylon radiators operating at 300 K was selected. It ends up more mass efficient than open loop cooling after 8.8 hours of operation. A larger set of lens was also used, with 0.25 m width. Together, a power density of 2.46 kW/kg (even with +25% for other equipment) is achieved and the beam can be focused to a spot 33.4 cm wide at 10,000 km distance. Advanced Accelerator Output: 1000 MW Divergence: 3.9 nanoradians Beam velocity: 48,270 km/s Total mass: 131.2 tons In the advanced accelerator, we assume some technological progress has taken place. The RF power source is more efficient, at 85%, which increases its power density to 18.6 kW/kg. Heat pump technology moves to using superconducting electric motors to drive Brayton cycle compressors, increasing their power density to 5 kW/kg, which in turn allows them to be used to increase the temperature of all waste heat. The heat from RF generator and the SRF cavities is pumped up to 600 K, which allows for a very lightweight bubble membrane radiator to be used. Stronger materials can also allow for lighter SRF cavities, reducing them to 50 kg/m. We can therefore use a longer accelerator (50 m long at 33 MV/m) and a larger lens (1m wide). Adding on improvements to the ion source, we end up with an overall power density of 7.6 kW/kg and the ability to focus a 48,270 km/s beam to a spot just 39 cm wide at a distance of 50,000 km. The particle beam cannot be bent after neutralization, and it becomes very hard to steer it using electromagnetic optics after it has reached high energies near the end of the accelerator. A reasonable configuration of all these components is to have a fixed ion source and low energy accelerator stages, and a moving high energy stage topped with a neutralizer. It would resemble a turret. Power transmission and propulsion The ability to focus a beam of high velocity particles onto a small spot over long distances has applications in transmitting power or spacecraft propulsion. For power transmission, you need a beam accelerator and a receiver, separated by the distance you want to cross. The beam accelerator is as described above. The receiver has three parts. The first part is the beam stripper, most likely a metal foil. A neutral beam cannot be converted into electricity without turning it back into a charged beam. After passing through the stripper, the beam becomes a plasma of electrons and ions. This plasma travels into the next part: the beam optics. Electromagnetic lenses (for relativistic beams) or electrostatic optics (for slow beams) attempt to brake and bend the beam. The effect on the lighter electrons is much greater than on the heavy ions, which leads to the electrons slowing down more and bending away from the main ion beam. Once separated from its electrons, the ions are directed through the third part: the beam recuperator. It works like an accelerator in reverse and is a commonly proposed for use in fusion reactors to convert alpha products: instead of using electric fields to accelerate particles, it slows them down and converts its energy into electricity. Direct energy conversion turns kinetic energy into electric energy with no intermediate steps. ‘Travelling Wave’ or ‘Inverse Cyclotron’ direct energy converters have a maximum efficiency of over 90% and can handle high particle energies. Similar power density is expected at either end of the power transmission, with RF generators replaced by power processing units at the receiving end. A direct conversion receiver works best over distances where the beam does not spread too much. A very wide beam would have to be handled by equally large beam optics, which become very heavy when scaled up. For example, the Huge Accelerator would produce a beam about 1 meter wide at a distance of 60,000 km. The Advanced Accelerator achieves this at a distance of 256,000 km. These are more than sufficient for carrying power between spacecraft, such as a booster mothership and a cargo tug, but not enough to transmit power over the distances between moons or planets. Increasing the transmission distance by a factor 10 would require beam optics over 100 times larger and heavier. A different way of converting beam power into electricity can used to unlock the longer distances. When a particle beam intersects a gas, collisions between the beam and gas molecules turn kinetic energy into heat. A tube of gas can be used as a beam target, with the beam entering through a thin window of dense metal. The beam loses its energy by travelling through the gas, which is converted into heat with an efficiency approaching 100%. The hot gas is then used to power turbomachinery, much like a modern power reactor. After passing through a compressor, turbine and radiator, the cooler gas is returned to the beaming tube. The best type design is one where the particle accelerates the heaviest particles possible to velocities just high enough so that they reach high charge states when striking the metal window. Heavy particles disperse the least and slow down the quickest when travelling through a gas, which keeps the transmission range high and the beaming tube short. A high charge state also helps them to slow down faster. An ideal ion is Uranium 238, which has a high mass, low ionization energy and low radioactivity. The beaming tube should be filled with a high molar weight gas with a low heat capacity. The high molar weight allows for a higher density (kg/m^3) to slow down the beam in a shorter distance, while the low heat capacity allows for the gas to heat up to high temperatures to improve thermodynamic efficiency. Iodine is a good example, as it is sufficiently dense even at high temperatures (1.2 kg/m^3 at 10 atm pressure and 2500 K temperature in the form of the molecule I2) while being not as rare and expensive as Xenon nor likely to condense in the radiators (it boils at 457 K). Efficiency of the beaming tube power transmission design suffers due to the intermediate thermodynamic step for converting beam energy into kinetic energy. If the beaming tube is 90% efficient, the Brayton turbomachinery 60% efficient and the alternator and power handling steps 90% efficient, the overall efficiency is 48.6%. Power generators seeking the highest possible power density will have a higher temperature Brayton cycle that minimizes radiator size but cuts into efficiency even further, down to 24.3% perhaps. This is roughly the efficiency of solar power. The beaming tube power generator can operate at extreme distances away from the power source, does not rely on the sun and can achieve overall high power density. A dedicated power source would use the extra equipment required to reduce the divergence of its heavy ion beam to the lowest possible value, roughly equal to that caused by the neutralization disturbance. For a 1000 MeV Uranium 238 beam, this can be as low as 0.45 nanoradians. A 20 m beaming tube would intercept 100% of this beam at a distance of 22 million km. Another way to use a particle beam is to bounce it off a magnetic field in a propulsion system known as the ‘mag-sail’. The slower the particle beam, the better the thrust per watts of the propulsion. The efficiency falls as the ratio of mag-sail velocity to beam velocity increases, but it can be ignored for interplanetary trips. For example, a 100 MW beam of 0.3 C particles would deliver 2.2 Newtons of thrust to a stationary mag-sail (45.5 MW/Newton), but a 0.01 C beam would deliver 66.6 Newtons (1.5 MW/Newton). The main advantage of mag-sails is that they can create huge reflecting field areas using lightweight conducting coils. Mag-sails prefer the use of lighter particles that are more easily reflected by magnetic fields after they are ionized, but this tends to negatively affect divergence. Using Zubrin’s estimates, superconducting coils that can handle 1000 MA/m^2 of current can produce a magnetic field of 1 Tesla in a bubble nearly 500 m in diameter using loops massing just 10 tons. This mag sail is large enough to fully intercept a 1 nrad beam at distance of 250 million km or 1.7 AU. It could potentially catch 15.7% of a nanoradian beam across the 4.2 AU distance that separated Earth from Jupiter. A 20 ton spaceship with a 10 ton magsail riding a 1 GW beam of heavy particles at a velocity of 0.01 C would accelerate at a rate of 22.2 mm/s^2. This is enough to cross the distance between Earth and Jupiter in about 17.6 weeks. The field area can be further boosted by ejecting plasma, as is done by the M2P2 Mini-Magnetospheric Plasma Propulsion system. We can also imagine a Particle Beam Thermal Rocket engine, where the beam is used to directly heat propellant. This is similar to the Laser Thermal Rocket engine. Instead of optical mirrors, a stripping foil with bending magnets behind it can direct a particle beam into a reaction chamber filled with propellant. Particle beams can efficiently heat up propellant without the need for seeding particles, allowing for pure hydrogen gas to be used for maximal exhaust velocity. They can also ionize a good portion of the propellant gases, allowing for electromagnetically confined propellant that can reach very high temperatures without touching the chamber walls. The main disadvantage is that a Particle Beam Thermal Rocket cannot work in an atmosphere. Weaponry and damage mechanics The ability of particle accelerators to focus their output onto a small area at a great distance has an obvious application as a weapon system. First of all, how does a particle beam deal damage? The ‘Report to the American Physical Society of the study group on science and technology of directed energy weapons’ is the golden reference for its section on Neutral Particle Beam weapons. Two damage mechanisms prevail for the heavy ion particle beams discussed so far: radiation dose and volumetric heating. High energy particles are considered as penetrating radiation. They do not deposit all of their energy on a target’s surface, but travel through a certain depth of matter before stopping. The depth depends on the properties of the beam and density of the target material. All energies discussed in this post are more than enough completely strip any electrons from an impacting particle. In fact, the target material acts like a 100% effective stripper. This is why the particles from a neutral hydrogen beam will be referred to as protons, and why previously neutral particles are described as ion in the following sections. The main way that particles lose energy when traversing matter is due to collisions with the electrons surrounding atoms in the matter. The equation that governs how far a particle penetrates into matter is based on that effect: Penetration depth: 0.00331 * E^1.74 / (Z^2 * A^0.74 * D)) Penetration depth will be in centimetres. E is the particle energy in MeV Z is the particle charge state. A is the particle molar mass in g/mol. D is the target material’s density in g/cm^3 We can see that more energetic and lighter particles would penetrate the most, with protons being the best at traversing matter. In fact, any other particle than a proton is unlikely to penetrate significant lengths of any material due to 1/Z^2 factor. A helium particle would gain 2 positive charges after impact while weighing 4 times more than a hydrogen particle. For the same energy, it penetrates 11.15 times less material than a hydrogen particle. This get much worse for heavier particles, with Cesium penetrating 112,817 times less than hydrogen. We can safely ignore the penetrating effects of anything other than protons. The penetration depth equation does not account for the changes in how protons interact with electrons at energy levels greater than 10 GeV. The energy transfer from a proton to an electron increases rapidly beyond 1 GeV, which makes penetration rates fall below the expected values. At even higher energies, the protons cause multiple neutrons to be knocked out of the shielding material for every incident particle and can even create muons and pions… these are additional energy loss mechanisms that further affect penetration. The shielding table from a CERN lecture empirically confirms that proton penetration rises more slowly for energies higher than 3 GeV. In other words, proton penetration at 3 GeV is the most efficient, but it can be increases further. Another complication is that shielding full of hydrogen, such as water or plastic, is much more effective than the equation would suggest for the same g/cm^2 values. From this table, we find a 29% discrepancy between the penetration depth calculated for 250 MeV protons (49 cm) and the value measured (38 cm). It can all be summarized by the relative effectiveness of shielding materials: We can see that water is again about 30% more effective than aluminium at great shielding amounts. Surprisingly, there are materials even more effective than water but are not liquid hydrogen, such polyethylene and lithium hydride requiring 45% less shielding than aluminium. Considering all these complications, it is best to simply use the data collected in the physics databases made online by the National Institute for Standards and Technology. Using those databases, we will produce charts for the penetration of protons of 100 MeV to 10 GeV into polyethylene, water, carbon, steel, tungsten, lead and uranium. Polyethylene: Polyethylene has a density of 0.94 g/cm^3 so a 250 MeV proton would go through 38 cm and a 3 GeV one would go through 13 meters. Water is 1 g/cm^3 so the y-axis can be read in centimeters. 250 MeV protons go through 35.7 cm and 3 GeV through 12.47 meters. Graphite can have a density of 1.5 to 2.3 g/cm^3. Amorphous carbon has 2 g/cm^3 and diamond has 3.5 g/cm^3. For this graphite specifically, 250 MeV protons go through 24.9 cm and 3 GeV through 8.7 meters. We use iron at 7.84 g/cm^3 to simulate steel. 250 MeV go through 6.92 cm and 3 GeV protons go through 2.31 meters. Tungsten at 19.3 g/cm^3 is interesting as it is dense, temperature resistant and strong. It stops 250 MeV protons within 3.7 cm and 3 GeV protons within 1.21 meters. Lead is disappointing as it requires 6.6 cm for 250 MeV protons and 2.08 meters for 3 GeV protons. Uranium is great as it stops 250 MeV protons within 4.6 cm and 3 GeV after 1.3 meters, but there is the danger of significant secondary radiation in the form of neutrons. The energy of a proton is not deposited continuously throughout the penetration depth. As the particle slows down, the material becomes more effective at slowing it down further. At a certain point, usually for protons of less than 100 MeV, material stopping power increases very rapidly up to a maximum at 1 MeV. The Bragg peak is situated in this region . The heavier the particle, the narrower and sharper the Bragg peak is. More importantly, the Bragg curves indicate that shielding that is too thin to fully absorb a beam let through a lot more radiation than what you’d expect, up to 40% of a 250 MeV proton or 3% of a 3 GeV proton. Whatever passes through the radiation shielding is fully absorbed by people or electronics. People and electronics do not like being hit by high energy particles. One rad of radiation is 0.01 J of particle energy per kg of matter. Sickness, nausea, anaemia and immunodeficiency is caused by 3 J/kg. 30 J/kg is enough to kill within a day after incapacitating the person. 300 J/kg kills most people on the spot, and no-one can survive 750 J/kg. The full effects and calculations of radiation doses are given on the Atomic Rockets website. The only saving grace here is that when the highest energy protons encounter very thin or no shielding, they don’t slow down at all keep on going through the walls, people and electronics before exiting without losing much of their energy. This is the reason behind NASA stating that aluminium walls on their spacecraft makes Galactic Cosmic Ray radiation worse by causing them to release more of their energy in people. A completely unshielded human modelled as a 30 g/cm^2 target would absorb only 10% of a 1 GeV proton or 0.7% of a 10 GeV proton. However, particle beams can be tailored to deal maximum damage. An over-penetrating beam can easily be detected leaving the target from the other side. The particle energy would then be adjusted so that the Bragg peak sits inside people or electronics. A large portion of the beam’s energy would then be released in the most damaging manner. This is used to a good end in proton radiation therapy: 250 MeV protons deposit most of their energy in the center of a person. Weaponized protons would designed to have at most 250 MeV left over after passing through shielding to prevent over-penetration. Insufficient shielding against weaponized radiation beams will be deadly in short order. A 100 MW accelerator shooting 1 GeV protons with a divergence of 0.1 urad, facing shielding that lets through 100 MeV of energy per particle, would cause immediately lethal doses of 300 J/kg at a distance of over 59,467 km… in one second. If the beam can be held on the target for just one minute, it can be lethal at a distance of 0.46 million km. Electronics do not fare much better. Sensitive devices used in sensors would be even less resistant than people. Electronics can survive a dose of 100 kJ/kg if they are extremely radiation hardened (at the cost of weight and performance). This decreases the lethal distance by a factor 18.25. It should be noted that a 1000 MW beam would terminally irradiate targets in a period 10 times shorter, or at a distance 3.16 times further, than a 100 MW beam. Protecting against such a beam would be of capital importance to having human crews anywhere near a space battle. Armor and defense schemes will be discussed in the next section. If a proton beam does not fully penetrate the shielding, it will have almost all of its energy converted into heat instead. We can use the following equation to determine how much heat energy is deposited per m^3 of shielding material: Volumetric heating rate = BP / ((Divergence * D)^2 * 3.142*Penetration)) The heating rate is in W/m^3. BP is Beam power in watts. Divergence is in radians. D is Distance in meters. Penetration is in meters. We can work out that the previous beam (100 MW, 1 GeV protons with a divergence of 0.1 urad), if encountering a thickness of shielding it cannot penetrate from 59,467 km away, would spread its energy over a volume 11.89 m wide and 2.15 m deep in graphite or 0.58 m deep in steel. The volumetric heating is 418.6kW/m^3 in graphite or 1552 kW/m^3 in steel. These figures can be converted into 182 and 197 W/kg respectively. This heating can be ignored for temperature resistant materials such as graphite or steel, but could cause the best radiation shielding materials such as polyethylene or water to fail. What is to be done if the particle beams cannot irradiate their target or cause sufficient volumetric heating? You change the beam properties to maximize volumetric heating. Instead of a lightweight, penetrating particle, you choose a heavy atom with the lowest divergence possible. As we can see from the penetration equation, a higher mass and charge state reduces penetration. Heavy atoms striking solid matter quickly lose most or all of their electrons and achieve a multiply charged state. A 250 MeV Cesium particle would only penetrate a distance of only 1.88 micrometers into graphite or 0.4 micrometers into steel. We will set 63 MJ/kg as the energy needed to vaporize carbon, which happens at a temperature of about 3600 K in vacuum. Steel sublimates at just 873 K in vacuum, requiring 6.3 MJ/kg. We can convert those figures into 144.9 GJ/m^3 for carbon and 54.2 GJ/m^3 for steel. If we divide the beam energy by the multiple of the beam area and the volumetric vaporization energy, we can get a penetration rate. This is the resulting equation: Penetration rate = Beam Power/(Spot Area * VVE) Beam P is beam power in Watts SA is the beam Spot Area in m^2, equal to ((Divergence * Distance)^2 * 3.142) VVE is the volumetric vaporization energy in J/m^3. That equation is only useful at shorter ranges, where the beam intensity is rather high. At the shortest ranges (a few hundred km), the beam causes explosive expansion of the target material and gains an even greater penetration rate from the pressure breaking up and excavating more material. At longer ranges, the beam spreads out enough for thermal conduction and blackbody radiation to sap away its power and reduce penetration significantly, or even stop it. For a more accurate result, we would best use this laser damage calculator. While it is designed for laser beams, the extremely low penetration of heavy ions allows the model to carry over accurately. Let’s use the calculator to work the penetration rate of the three accelerator designs described previously against carbon (at 2.1 g/cm^3) and against steel (at 7.87 g/cm^3). Modern Accelerator 100 km= 1.28 m/s in carbon, 2.61 m/s in steel. 1,000 km= 1.47 cm/s in carbon, 3.48 cm/s in steel. 2,000 km= 3.6 mm/s in carbon, 1.09 cm/s in steel. Large Accelerator 100 km= 366 m/s in carbon, 2380 m/s in steel. 1,000 km= 3.75 m/s in carbon, 7.14 m/s in steel. 10,000 km= 4.32 cm/s in carbon, 8.76 cm/s in steel. 50,000 km= 1.66 mm/s in carbon, 3.87 cm/s in steel. Advanced Accelerator 1,000 km= 1930 m/s in carbon, 1440 m/s in steel. 10,000 km= 1.38 m/s in carbon, 2.8 m/s in steel. 100,000 km= 1.58 cm/s in carbon, 3.28 cm/s in steel. 500,000 km= 0.57 mm/s in carbon, 1.47 mm/s in steel. An ideal particle beam weapon would have a high power output, narrow divergence and minimal penetration. This is best done by using heavy particles such as Cesium or Uranium: when they strike the target material, they lose their electrons and acquire a very high charge state. This drastically reduces penetration depth and allows the beam’s energy to be concentrated into a thin layer on the target’s surface. For practical reasons, the beam cannot have too low of a velocity. If particles take 0.33 seconds to reach their target (100 MeV Uranium ions from 3,000 km away), then the target has the option of accelerating in any direction for 0.33 seconds before the beam’s aim can be adjusted. If the target acceleration is 1g, the beam’s position can be moved +/- 0.52 meters before it is adjusted. This might be enough to completely move the beam away from the area it has started burning through and expose fresh surfaces of armor. A target able to spread the beam’s damage across more of their armor surface would take considerably longer to destroy. Pulsed particle beams, just like pulsed lasers, have additional damage mechanisms. They produce pressures by vaporizing target material quickly enough to cause the mechanical failure of surrounding material. A pulse energy great enough to overcome the cratering energy of a material can rip out large chunk of material more efficiently than a continuous beam that if forced to fully vaporize that same material. Weak materials suffer the most from pulsed particle beams. Graphite, for example, takes about three hundred times less energy to break apart than it takes to completely vaporize it. The penetration rates of a perfect pulsed particle beam can many times greater than a continuous particle beam. Unlike a laser, they can ignore debris and plasma ejected from the target material into the path of the beam, allowing for very high pulse frequencies. Pulsing a beam’s power also allows it to better overcome the losses from thermal conduction or blackbody radiation at very long range. There is also potential for a deeply penetrating, pulsed particle beam to exploit the Bragg peak of a particle to rapidly heat material inside the target’s volume. This would have an effect equivalent to placing dynamite inside a boulder: all of the pulse’s energy will go towards straining the target material and causing shockwaves that crack and shatter the material. Multiple pulses can shake the material apart without having to vaporize it all. The downside is the increased mass penalty from the pulsing equipment, as well as the challenges of producing and accelerating pulsed particle beams. Compressing a bunch of particles into short packets causes heating of the particles and greatly increases divergence. It is worse inside the accelerator because the particles are still charged ions and repel each other. Very strong magnets are needed to handle these packets of ions. You would also need large capacitors to produce and accelerate the peak currents necessary for pulsed operation. Insufficient peak power would just warm up a larger volume of material than a continuous particle beam, making it far less efficient. Defending against particle beams Different approaches are needed to defend against the two main types of particle beam weapon: the penetrating proton beam and the vaporizing heavy ion beam. The simple answer to the penetrating proton beam is to have sufficiently thick radiation shielding. ‘Sufficient’ is hard to judge when everything from the lowest energy 10 MeV accelerator to the kilometer-length 10 GeV beams are possible. It would depend on accelerator technology, how long the engagements last and the degree of automation a space force employs. Better technology allows spaceships to use more powerful accelerators, which produce more penetrating beams. Longer engagements allow for a low dose to accumulate to damaging levels. More automation allows for less radiation-sensitive equipment and personnel to encounter the beams. Even better, good intelligence on the enemy and their equipment. The shielding does not need to be one block of material on the outside of a spaceship. The outermost layers could be just enough to stop lower energy protons. An internal shell would contain more delicate equipment, with an innermost radiation shelter lined with sufficient shielding. The objective is to reduce the surface area the shielding has to cover to reduce the mass penalty of all this shielding. Even with polyethylene, it is 12.22 tons per square meter against 3 GeV beams. When using tungsten, this rises to 23.3 tons per square meter. Simple mass shielding is therefore very bad for spacecraft. In the worst case scenario, a 10 meters diameter ship would need 1,819 ton slab on its nose to prevent radiation coming through. Providing protection for the flanks would be an even greater mass penalty. A lot of research has gone into protecting astronauts from cosmic galactic rays and other particle radiation using electromagnetic fields as a lighter solution. Electrostatic shielding is simple to understand. There are three parts to it: stripper layer, electrostatic plates and backplate. The stripper layer resembles a Whipple shield. Thin layers of metal strip the electrons off an incoming neutral particle. The electrostatic plates are the critical piece. Two conducting plates can built up a large voltage difference.If they are also close together, they produce an electrostatic gradient that can be measured in the megavolts per meter. Sandwiching a dielectric material, the best of which is diamond, in between these plates allows for gradients of up to 1000 MV/m even when allowing for a safety margin. Charged particles travelling through these fields are slowed down. The backplate catches any excess energy from the particles and any secondary radiation they released when crashing through the plates. Using equations for capacitors, we can work out that two plates separated by 1 millimeter, with the gap filled with diamond, maintaining a 10 MV potential in between them, would achieve a voltage gradient of 1 GV/m. The charged plates attract each other with a force per area equivalent to 425 MPa. This force can be handled by most structural materials, such as high strength steel or the diamonds serving as dielectric insulators themselves. The plates are thin compared to the dielectric material in between them, so we can simplify the shielding to a solid stack of dielectric layers. For example, 1 GV/m shielding using diamond would be able to stop 1 GeV protons if it were a meter thick. Diamond has a density of 3510 kg/m^3, so this shielding would mass 3510 kg/m^2. That mass adds another 1.2 GeV worth of protection for a total of 2.2 GeV. Particle beams of less than 2.2 GeV energy will not go through. Particle beams with more than that would have their energy reduced by 2.2 GeV. A particle beam striking the layers of electrostatic shielding would deplete the voltage potential between the charged plates. That potential must be recharged with onboard power. The beams also continuously degrade the charged plates, so they must be replaced eventually. If a 2.2 GeV proton beam with 100 MW of power struck the diamond dielectric shielding described above, then 1 GeV (45.5%) of the beam’s power must be recharged plates and 1.2 GeV (54.5%) will have to be dissipated as heat. As the shielding thickness increases, the protection from the electrostatic charge also increases (1 GV/m over 2 meters is 2 GV) but the contribution from mass shielding only rises by the power ^0.5747. More energetic particles follow the same relationship (a 2 GeV particle is 2^1.74 times less affected by mass shielding than a 1 GeV particle). This means that the power required to recharge the shielding quickly matches the power of the incoming beam. In other words, radiation protection can become a tug of war between the power of the incoming beams and the power flowing through the shielding. At this point, it might be worthwhile to consider the effects that volumetric heating and electric resistance heating have on the conductivity of the charged plates and therefore power requirements needed to recharge them. High temperature stacked capacitors are a good design inspiration () and it would eventually be necessary to sacrifice some dielectric strength to be able to use liquid dielectric materials that can double as coolant. Despite all those requirements and drawbacks, note that using electrostatic shielding on the front of a 10 m diameter spaceship against 3 GeV protons would not mass more than 300 tons. Deflecting particle beams is a potentially even more efficient solution. If a beam never strikes the spaceship, then only the mass of the deflecting equipment is needed, without any of the shielding. The risk, of course, is if the beam ever overcomes the deflection force and does hit the ship, then it will do so at full strength since it was not slowed down. For magnetic shielding, we use the Larmor radius of an ion. It is the radius of the curvature of an ion’s trajectory through a magnetic field. Because of how the force a magnetic field applies on an ion increases with its velocity, the Larmor radius can be pretty small. We work out that a 10 GeV proton beam can be bent 180 degrees by a magnetic field averaging 1 Tesla within a distance of 35.5 meters, and by a field of 10 Tesla within 3.6 meters. Simple wires on the surface of a spaceship’s armor could project a magnetic field strong enough to deflect even the highest energy particles. A current of 14.5 MA running through a wire is enough to produce a field with a strength of 10 Tesla at a distance of 3.65 meters from the wire. The critical current for superconducting wires is usually 15 MA/m^2, but it is preferable to use the same Niobium-Tin alloy as in SRF accelerators to achieve critical current densities of over 300 MA/m^2. A Niobium-Tin wire handling 14.5 MA would mass about 1600 kg per meter of length (since it loop around to form a coil and needs a safety margin on top of that) to which must be added the mass of cooling, insulating and structural equipment. Each meter of superconducting coil would protect about 7.3 m^2, allowing for a shielding requirement of 213 kg/m^2 for the coils alone, likely 500 kg/m^2 with the additional equipment. If we only expect 3 GeV beams, the shielding requirement would fall to about 170 kg/m^2. This compares favourably with other shielding options. The downside to relying on magnetic deflection is that unexpectedly powerful beams would hit the spaceship with full force, and that the wires themselves are rather vulnerable. A temperature increase could cause them to tear themselves apart or vaporize instantly due to a quench. All momentum from the beam is transmitted directly to the wires, creating uneven stresses that could break them, especially from the hammering of a pulsed beam. Broken wires would leave gaps in the shielding, so a warship would likely have many hundreds of smaller coils that are redundant and easily replaced. A strong magnetic field running through a spaceship is likely to have major deleterious effects. This is why all modern magnetic radiation shielding concepts include the use of another, internal set of coils to create a field-free volume. The internal coils don’t have to be as strong as the external coils as a layer of conductors with very high magnetic permeability, such as nickel or gold, can be included to help the external magnetic field lines take a different path and avoid the protected volume. Electromagnetic shielding only works if the particle beam is ionized before it interacts with the magnetic fields. Turning an incoming neutral beam into a charged beam is therefore of critical importance. There are four potential methods for ionizing at a distance. The first is to use an electron beam. Just like an electron beam can be added to positive ions to neutralize them, another electron beam can be used to create electron/atom impacts to re-ionize them. Since the electron beam leaving the defending ship is travelling in the opposite direction as the incoming particle beam, there is no need for highly energetic electrons: the incoming beam is travelling fast enough to ionize itself with each collision. Even better, the electron beam can be easily steered using electromagnetic optics, allowing it to quickly change target within microseconds and handle multiple incoming beams. There are many challenges though. The electron beam spreads quickly due to electrostatic self-repulsion. This makes it difficult to create the electron densities needed for full ionization within reasonable distances. For example, a 1 GeV 100 MW hydrogen beam with a divergence of 0.1 urad would have a current density of 31.8 mA/m^2 after travelling 10,000 km. A 1 MeV electron beam of the same total current and an initial beam diameter of 10 cm has a doubling distance of just 95 meters. The two beams would have the same current density at a distance just 4.5 km away from the defending spaceship. Increasing the electron energy to 10 MeV increases this distance to about 90 km. The electron beam must be carefully aimed to not be bent off-course by the electromagnetic fields meant to protect the spaceship. This difficulty in using electron beams is compounded by the fact that hydrogen beams are highly relativistic and would only give 4 milliseconds of warning over a distance of 10,000 km at 1 GeV of energy, or 0.12 milliseconds at 10 GeV, after the light signal from their firing arrives. In short, it is very hard to ionize incoming radiation beams using electrons. Ionizing slow, heavy particle beams is a different matter. The current density is usually higher owning to the lower per-particle energies, but the reaction time is measured in tenths of a second instead of milliseconds. For example, a 250 MeV beam of Cesium particles would take 0.529 seconds to cross 10,000 km, while light takes 0.033 seconds, giving a heads up of 0.495 seconds. The slower beams can also be forced to suffer electrostatic bloom even over the short distances the electrons operate on. Fully ionizing an incoming 250 MeV cesium beam would cause it to reduce in intensity 16 times before it crosses 1.5 kilometers. Having that warning time means that a second method is made possible: metal screens can be positioned between the beam and the ship. This screen would act as a foil stripper and efficiently strip electrons from the heavy particles. It does not have to be a large screen, as a cloud of chaff will work equally well. These metal screens work well against radiation beams if they are a few millimeters thick. They can ionize heavy beams with only a few micrometers of thickness but will destroy themselves in doing so.These screens can be moved into place by ‘interceptor drones’ or shot into position out of coilguns. These foil screens are very vulnerable to being swept away by even weak laser beams. They would have to be released at the last possible moment, and be replaced quickly. The third method is to use a plasma screen. A plasma acts somewhat like a foil stripper, except that a much greater thickness of plasma is needed to ionize a beam because the plasma is much less dense than a solid target. This paper suggests that 1 kg/m^2 of plasma is enough to ionize 4.2 GeV Uranium ions, which is more than enough for the other beams discussed here. Plasma screens of such density cannot be extended more than few meters to tens of meters away from the source of a containing magnetic field, so they can only serve to ionize incoming beams. They have the advantage of being easy to replenish. A particle beam travelling through a relatively dense plasma will emit a lot of light and appear like a lightning bolt. The fourth option is an ionizing laser. A laser can react the quickest to an incoming beam. Ultraviolet lasers work to directly ionize atoms with every encounter between a photon and an outer electron of a neutral particle. The relativistic doppler shift from an incoming beam works to the laser’s advantage by shortening the wavelength the neutral particles encounter down to the 90-100 nm optimum for ionizing hydrogen. The only difficulty with ionizing lasers is that they have to work quickly against very low interaction probabilities due to the small ionization cross-sections, which means high laser power is needed. We can estimate that GWs are needed for relativistic hydrogen beams and tens of MWs for slower heavy beams. It should be noted that there is always the option to move out of the way of a particle beam. Slower particle beams that take several tenths of a second to reach their target or correct their aim would create an opportunity to accelerate the spaceship randomly, in any direction, to frustrate the attacker’s efforts to keep the beam focused on one spot or even the hit the spaceship at all. In half a second, a 1g acceleration can allow a spaceship to ‘jink’ by 1.22 meters. This is enough to prevent most beams from staying focused on the same spot. A full study of these anti-particle beam, ionization-at-a-distance concepts and other defensive measures merits its own post. Lasers vs Particle Beams Lasers have been the best contender for long range power transmission, propulsion and weaponry in science fiction and the real world. Their ability to deliver energy to a narrow spot far away comes mainly from advances in laser technology allowing for the efficient production of short wavelength beams. However, we are suggesting the particle beams can produce beams with even shorter ‘wavelengths’ and with even greater efficiency. Their optics are much harder to damage than the mirrors of a laser and can have great effective ranges even when firing through small opening in armor. Using current technology, they are likely to have the upper hand in terms of power density too. From a power transmission standpoint, particle beams can allow for very high efficiency at very long ranges. Propulsion such as mag-sails also benefit from a better thrust per watt than lasers. There are many advantages to a particle beam weapon instead of a laser weapon too. On top of the increase in potential beam intensities, they heat up armor material from the inside, leading to massively better penetration rates. When used as a radiation weapon, they can knock out electronics and crews from very long range as well. While they are immune to damage reducing techniques such as reflective surfaces, and the danger of radiation beams can be greatly reduced by using appropriate shielding, it is still a powerful tool if it imposes on any enemy ship to have several meters of armor or superconducting wires all through its hull as a minimum requirement to enter battle. Deploying a more penetrating beam due to technological advances could suddenly render older warships with insufficient shielding obsolete. The shielding requirements also impose a minimum scale to the warships being deployed. Smaller warships would have a bigger proportion of their mass dedicated to shielding, making them less effective on a ton per ton basis compared to larger warships. The smallest vehicles suffer the most, with cheap massed missile swarms becoming irrelevant due to the ability of a radiation beam to disable them in seconds. There are plenty of secondary benefits and uses to particle beams. Their development as part of the Strategic Defense Initiative focused on using them to discriminate between warheads and decoys. That same ability can be used to identify targets using penetrating beams that exit the other side carrying information on what they passed through. Particle beams could also counter stealth. When energetic particles strike a solid target, they release secondary radiation in form of gamma rays, as well as neutrons and X-rays. These signals do not care about the temperature and albedo of the target material. Randomly sweeping the surrounding volume of space with low powered radiation beams could reveal the position of cryogenically-cooled spaceships. Of course, the stealth ships are able to use electromagnetic shielding to ward off these beams, but the act of ionizing an incoming beam so that it is deflected by a magnetic field creates distinctive but more diffuse and inaccurate signals of its own. Finally, while humans are soft targets that want to stay away from particle beams, it might be interesting to keep them nearby. The use of heavy particle beams to damage the exterior of a warship and then disabling it using a radiation attack would mean that there is a high chance of battles ending with most spaceships on either side mostly intact. Sending in a repair crew to swap out the sensitive electronics and computers of disabled warships could be the difference between losing a battle and winning a war. With all this in mind, we cannot dismiss lasers either. Lasers have utility and advantages that would want them in use alongside particles beams instead of one or the other. Lasers are hard pressed to produce the ‘wavelengths’ of particle beams, but they can compensate for it by using large and lightweight mirrors. These mirrors can be tens of meters in diameter, allowing for extreme effective ranges. The range of a laser can be further extended by the use of laser weapon webs. Relaying a beam from one mirror to another is not a feat that particles beams can replicate. Always travelling at C, lasers experience light-lag at distances exceeding 300,000 km. Slower particle beams suffer from the light-lag equivalent at shorter distances, with heavy particles having the worst of it even over distances of a few thousand kilometers. The need for a moving turret to change a neutral particle beam’s direction makes it slow to switch target. Lasers only need to rotate a mirror. Phased array lasers can shift their output electronically, within microseconds, which makes them much better options for point defense. Lasers are also modular and divisible, so a single laser generator can split its beam into multiple channels or supplement a group of generators working together. They have the extra utility of allowing moderated responses (warning shots and low grade heating) and working in or through the upper atmosphere of planets. High energy particle beams meant for space are completely ineffective below about 150 km altitude around Earth. Lasers are much easier to pulse than particle beams. We have devices that work on the scale of femtoseconds. Frequency doubling or tripling also makes them very useful for blinding sensors across many wavelength bands. Lasers and particle beams will in practice cover for each other’s weaknesses. Lasers would start an engagement with their extreme range, but then particle beams are used to degrade an opponent’s reflective surfaces so that they can deal damage. Particle beams can quickly destroy the fragile mirrors of lasers being used for ‘counter-beaming’, in which they try to send laser beams back up an optics train to damage the internal components. Lasers in turn can wipe away metal foil screens and bypass electromagnetic defenses to start heating up the armor, perhaps causing the superconducting wires to fail. Having an ultraviolet laser with several tens to hundred of megawatts of power in addition to a particle beam weapon gives more offensive options as well as defensive ones: the laser can ionize enemy particle beams at a distance, or burn channels through plasma screens to allow your own particle beams to get through. What’s next? This has taken a long time to prepare! Many scientists and researchers have contributed their knowledge, with help from the ToughSF community on twitter, G+ and our Discord. The next steps are to respond to comments and then do a further study of the capabilities of protection mechanisms against particle beams, as well as a look into the more advanced techniques for creating and handling the, such as beam cooling, plasma wakefield accelerators and beam condensation.
  10. MatterBeam

    Probabilistic overheating

    Hi! I want to propose an idea to people who make DangIt! (@linuxgurugamer) , Deadly Reentry (@Starwaster) and others. What if, every second, heating created a chance that the part will explode or fail? For example, at 50% of the maximum temperature, there is a very low probability. At 95% of the maximum temperature, there is a high probability. At 110% of the maximum temperature, the probability is nearly certain. We can do a bit of maths. The part is expected to fail within a minute at 100% temperature - so we give the probability per second calculation something like 0.926118. After 60 'trials', the probability of the part failing at least once rises to 99%. If we have a part at 80% temperature that we expect to fail within 10 minutes, we can use a probability of 0.992354. It can be upgraded. Parts can be given increased reliability by changing that probability factor. Literal randomness is added to the game. Pushing the part to the limit is a gamble that sometimes pays off. Going 2450K on a 2400K part doesn't always mean that it simply explodes in that instant. Running your nuclear engine for hours at just under the critical temperature won't work either. just like in real life. What do you think?
  11. OH. MY. GOD. The art is incredible - you've really raised the bar. There is nothing to fault with the tactical plan and I really liked how you approached this. All I can ask is that it go on for longer, but maybe the next project will have some of that!
  12. Great work, @SaturnianBlue! From the looks of it, going through battles in KSP will be very time consuming and you'll struggle more with the bugs than the enemy... Also, it seems to me that more maneuverable spacecraft that can keep their noses pointed at a moving target is quite important. Perhaps large side thrusters near the nose?
  13. A combination of in-game maneuvers and look-alike space warships, but written/artistic battles would be amazing! I want more of your art.