Single particle colliders use particles that have a known spatial wavefunction and thus extremely low emittance (ΔxΔp~ħ/2).
- - - [Physics] - - -
// Planck energy scale
Original idea came from investigating the ultimate limits of colliders at the F3iA meeting in 2016. Sufficient control over the spatial position of about 1012 particles of 10-6 EPlanck would allow a black hole to be formed, which would in turn evaporate via Hawking radiation to give near-Planck-energy particles.
This would require exotic laser acceleration at near the Schwinger limit. Other physics effects such as synchrotron radiation would also tend to disperse the particle positions unless compensated for, some outline methods for this are given in an IPAC'18 paper and talk.
// Nuclear energy scale
An example that can be realised with closer to present-day technology is a single particle collider at a few MeV, in which two or more nuclei are momentarily confined to within the nuclear radius of 10-14m. This would result in a high probability of fusion reactions, including those with three or more input products, which might give access to high-density processes seen in supernovae and neutron star collisions. Beam colliders have trouble making more than 2-way collisions because the bunches of nuclei are diffuse relative to the nuclear radius. Nuclei on the island of relative stability may be accessible using these processes, for instance Przybylski's Star contains short-lived actinides theorised to be from such an element. Other unusual configurations of nuclear matter may be produced using this process as it allows each nucleus to be placed in a defined (rather than random) location.
- - - [Components] - - -
For the nuclear energy scale single particle collider, the main components would be (briefly):
- Ion source trap: using laser Doppler cooling and perhaps other methods to cool one or more ions to near zero temperature
- Acceleration column likely DC for stability, but would ultimately require an RF chirp to produce the minimal longitudinal wavefunction size at the interaction region
- Magnetic and electrostatic adjustable multipoles for precise beam control
- Suspension and vibration isolation system of the vacuum chamber: this would increase in capability as experiments proceed until the positional stability is similar to that of mirrors in gravitational wave observatories (near the nuclear size)
- Detector: can detect nuclei from Rutherford scattering processes during machine tuning, and fusion products
- - - [Simulations] - - -
// 2D simulations of interaction point
Transverse simulations of the particle wavefunction approaching the interaction point, including spherical aberration etc. (no paraxial approximation made). The wavefunction is treated as a classical distribution while its size is large enough that diffractive effects are insignificant. A series of multipoles is allowed before the interaction point in each direction, while an optimiser adjusts them to minimise the size of the colliding wavefunction. First part of animations show the effect of the optimisation process on the wavefunction spatial distribution, while zooming in as necessary. Finally the propagation towards the interaction point is shown as an animation.
Five multipole elements on each side are allowed, up to 20-pole.
Four elements, up to 16-pole (no zooming).
Three elements, up to 24-pole.
Three elements, up to dodecapole (result only).
Two elements, up to octupole (result only).
Two elements, up to quadrupole (result only). This shows the strength of aberration without correction.
- - - [Future Work] - - -
This page is really just a placeholder for the above animations, but for context, further steps that need to be done are listed below:
- The above animations only get to a few times 10-6m foci, while much smaller (~10-14m) are needed. The scaling with increasing number of parameters and multipole order seems favourable, but the optimisation also becomes more complicated as more variables are added. This is because the opening angle is large, around 0.3 radians, producing very high orders of aberration (smaller opening angles are possible with higher energies but these move away from the optimum for nuclear fusion cross-sections).
- The interaction point needs to be modelled three-dimensionally, including the longitudinal phase space plane. It is likely that a 2D optimisation like that above would eventually become limited by the "hourglass effect" and bench length being too long. This needs the acceleration column and possible RF chirping to be added.
- Initial condition and extraction from the ion trap should be included.
- A realistic detector and operational collision tune-up algorithm should be simulated, using signals from sub-optimal collisions to improve the interaction point, by contrast with the above animations in which an optimiser has complete knowledge of the final wavefunction shape. One important technique is to gradually reduce from ~109 particles with a large and forgiving interaction point, down towards 1 particle, while achieving gradually better tolerances and tuning. An important result is that the event rate of a space-charge-limited interaction point is constant with number of particles in each bunch, providing a measurable signal at all stages of this process.
- Designs of the suspension/isolation system including how to preserve this stability with the required laser and electrical feedthroughs.
