NonNeutral Plasma Physics and Antihydrogen

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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
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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.

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Recipe

• Take 104 antiprotons (pbars). Cool to several
  Kelvin.
• Take 10-100 million positrons. Cool to several
  Kelvin.
• Mix, keeping species cold and confined.

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Apparatus
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Apparatus

• Surko-style positron accumulator.
• Antiprotons delivered by CERNs 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.

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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.

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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.

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Temperature Requirements

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

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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.

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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.

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Plasma Temperatures

• Parallel and perpendicular temperatures decouple
  at low temperatures in strong magnetic fields
  (ONeil et al.)
• Decoupling occurs because of separation-of-timesca
  les the cyclotron period is much shorter than
  the collision time.

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Ultimate Parallel Temperature

• Electron perpendicular energy cools to 4.2K, the
  temperature of the electrons surroundings.
• Electron parallel energy decouples and hangs at
  6-7K.

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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 coupledand
  are decoupled from the electron perpendicular
  temperature.
• In principle, the pbars should cool to 6-7K.

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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.

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Do the Leptons Really Cool to 4.2K?
Radiation Spectrum

• Total intensity differs by 107.
• 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 ONeil, and Dan Dubin
for helpful discussions.
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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 achieved50
  of the Hbars would be trappable.

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Will Supercooled pbars Stay Cold?

• The electron perpendicular temperature will
  quickly rethermalize.
• Other degrees of freedom are protected by
  ONeils adiabatic invariant.
• Since the collision periods below 4.2K is
  thousands of seconds, the anti-protons will stay
  cold.

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

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Conclusions

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

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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 aficionadosFor 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.

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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

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