Non-Neutral Plasma Physics and Antihydrogen Joel Fajans U.C. Berkeley and the ALPHA Collaboration G. Andresen, W. Bertsche, A. Boston, P. D. Bowe, C. L. Cesar, S. Chapman, M. Charlton, M. Chartier, J. Fajans, M.C. Fujiwara, R. Funakoshi, D.R. Gill, J.S. Hangst, R.S. Hayano, R. Hydomako, M.J. Jenkins, L.V. Jørgensen, L. Kurchaninov, N. Madsen, P. Nolan, K. Olchanski, A. Olin, A. Povilus, F. Robicheaux, E. Sarid, D.M. Silveira, J.W. Storey, H. H. Telle, R.I. Thompson, D.P. van der Werf, J. S. Wurtele, and Y. Yamazaki Work supported by NSF and DOE

Antihydrogen Production Antihydrogen (Hbar) was first made at CERN in 2002 by the ATHENA and ATRAP collaborations. (ALPHA is the successor to ATHENA.) Tens of millions of Hbar atoms have been created. None of these atoms were trapped. Ultimate physics goals: –Tests of the Standard model via spectroscopic comparisons of hydrogen and antihydrogen. –Tests of gravitational interactions between matter and antimatter. –Trapped Hbar is required for these tests.

Recipe Take ~10 4 antiprotons (pbars). Cool to several Kelvin. Take million positrons. Cool to several Kelvin. Mix, keeping species cold and confined.

Apparatus

Surko-style positron accumulator. Antiprotons delivered by CERN’s AD ring. Penning-Malmberg trap to capture pbars. 3T solenoidal field for radial confinement. Electrostatic well for axial confinement. 1T Penning-Malmberg trap for mixing. Minimum-B trap for confining neutral, diamagnetic Hbar. An octupole which makes a radial minimum-B. Mirror coils which make an axial minimum-B. Particle detectors.

Non-Neutral Plasma Physics and Antihydrogen Production Antiproton cooling. Antiproton transfer. Positron transfer and recapture. Combined trap physics. Mixing. Plasma parameter manipulation: radius, length, temperature, density. Diagnostics.

How Many Antihydrogen Atoms Can We Trap? Very few: Hbar trap depths are only 1K. Hbar created to date probably has energies of several hundred K. Most of the Hbars are likely to be high-field seekers.

Temperature Requirements We need cold: Positrons to improve the recombination rate and the keep the antiprotons cold during mixing. Electrons to cool the antiprotons.

Particle Cooling Lepton perpendicular energy cools by cyclotron radiation. The electrons are cooled in a 3T field, so their cooling time is about 0.44s. The positrons are cooled in a 1T field, so their cooling time is about 4s. To cool from 1eV to 4.7K takes 4.4s for the electrons and 40s for the positrons.

Coupling Between Degrees of Freedom Define temperatures parallel and perpendicular to the local magnetic field. Only the perpendicular temperature is cooled by cyclotron radiation; the parallel temperature is coupled to the perpendicular temperature by collisions. At high temperatures, the collision frequency scales as T -3/2. The parallel temperature is well coupled to the perpendicular temperature.

Plasma Temperatures Parallel and perpendicular temperatures decouple at low temperatures in strong magnetic fields (O’Neil et al.) Decoupling occurs because of separation-of- timescales; the cyclotron period is much shorter than the collision time.

Ultimate Parallel Temperature Electron perpendicular energy cools to 4.2K, the temperature of the electron’s surroundings. Electron parallel energy decouples and hangs at 6-7K.

How Are the Electron and Antiproton Temperatures Coupled? There is no published theory describing collisions between different mass particles in the low temperature (strongly magnetized) regime. The collision frequencies are different for all combinations of species and parallel and perpendicular energy. For our parameters, the electron parallel temperature, and the antiproton parallel and perpendicular temperatures are well coupled…and are decoupled from the electron perpendicular temperature. In principle, the pbars should cool to 6-7K.

Do the Leptons Really Cool to 4.2K? ALPHA (and ATHENA) has an aperture for positron and electron loading. ATRAP used not to have such an aperture, but does now. 300K infrared light leaks into the trap through this aperture.

Do the Leptons Really Cool to 4.2K? Radiation Spectrum Total intensity differs by Only intensity at cyclotron wavelength matters. Room temperature radiation is brighter by ~100. Leptons probably come into equilibrium with the room temperature radiation leaking into the trap from the aperture, not with the trap walls. ATHENA was unaware of this effect and the 15K temperatures they reported are likely too low. ALPHA now includes a flapper to block this radiation. Thanks to Nat Fisch, Tom O’Neil, and Dan Dubin for helpful discussions.

Supercooling Even with 6-7K pbars, few Hbars would be trapped. We can supercool the pbars below the background temperature by adiabatic expansion. Transferring the pbars from 3T to 1T will supercool their perpendicular energy. Expanding their orbits axially will supercool their parallel energy. Temperatures as low as 0.5K could be achieved…50% of the Hbars would be trappable.

Will Supercooled pbars Stay Cold? The electron perpendicular temperature will quickly rethermalize. Other degrees of freedom are protected by O’Neil’s adiabatic invariant. Since the collision periods below 4.2K is thousands of seconds, the anti-protons will stay cold.

Is the Theory Correct? Interactions with the background radiation field, in the presence of magnetic field inhomogeneities, will break the O’Neil’s adiabatic invariant. (F. Robicheaux)

Influence of Magnetic Inhomogeneities Consider a diamagnetic particle bouncing between magnetic mirrors and exchanging photons with the background radiation field. The mirrors form an axial well whose “spring constant” is a function of the perpendicular energy of the particle. Thus, the spring constant will change as the particle exchanges photons with the background field. This will couple the parallel and perpendicular degrees of freedom.

Conclusions Non-neutral plasmas physics effects are very important in making antihydrogen. We hope to trap antihydrogen this year or next.

How Are the Electron and Antiproton Temperatures Coupled? There is no published theory describing collisions between different mass particles in the low temperature (strongly magnetized) regime. The collision frequencies are different for all combinations of species and parallel and perpendicular energy. The results so far (theory confirmed by particle simulations) The relaxation rate for the electrons’ perpendicular energy is largely unaffected by the addition of collisions with pbars. The pbars perpendicular energy also possess an adiabatic invariant, which comes into play at temperatures scaled by the square root of the mass ratio. This just starts to matter for the pbars at 4.2K in 3T, but the pbar-pbar relaxation rate at these parameters is still high, ~1kHz. For the aficionados…For like-mass collisions, the adiabatic invariant is the perpendicular energy summed over all the particles. For unlike-mass collisions, the adiabatic invariant is the perpendicular energy for each particle individually.

How Are the Electron and Antiproton Temperatures Coupled? Still tentative conclusions: The pbar parallel off of electron parallel scattering rate is unaffected by the strong magnetization. For the model parameters it is on the order of 100Hz at 4.2K. The electron parallel off of pbar parallel scattering rate is affected by the strong magnetization, and equals the pbar parallel off of electron parallel scattering rate. The pbar perpendicular off of electron parallel scattering rate is controlled by the adiabatic invariant, but the adiabatic invariant becomes important at parameters scaled by the mass ratio. It does not matter near 4.2K. Thus the pbar perpendicular off of electron parallel scattering rate is similar to the pbar parallel off of electron parallel scattering rate