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Hi all! This is from: Tough SF: Cold, Laser-Coupled Particle Beams
I hope it can help you build more exciting SciFi worlds.
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.
I hope it can help you build more exciting SciFi worlds.
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.