Collisional equipartition rate for a magnetized pure electron plasma

Abstract

The collisional equipartition rate between the parallel and perpendicular velocity components is calculated for a weakly correlated electron plasma that is immersed in a uniform magnetic field. Here, parallel and perpendicular refer to the direction of the magnetic field. The rate depends on the parameter κ̄=(b̄/rc)/, where rc=(T/m)1/2/Ωc is the cyclotron radius and b̄=2e2/T is twice the distance of closest approach. For a strongly magnetized plasma (i.e., κ̄≫1), the equipartition rate is exponentially small (ν∼exp[−5(3πκ̄)2/5/6]). For a weakly magnetized plasma (i.e., κ̄≪1), the rate is the same as for an unmagnetized plasma except that rc/b̄ replaces λD/b̄ in the Coulomb logarithm. (It is assumed here that rc<λD; for rc>λD, the plasma is effectively unmagnetized.) This paper contains a numerical treatment that spans the intermediate regime κ̄∼1, and connects onto asymptotic results in the two limits κ̄≪1 and κ̄≫1. Also, an improved asymptotic expression for the rate in the high-field limit is derived. The present theoretical results are in good agreement with recent measurements of the equipartition rate over eight decades in κ̄ and four decades in the scaled rate ν/nv̄b̄2, where n is the electron density and v̄=(2T/m)1/2.

Adiabatic Cooling of Antiprotons

“…For B ¼ 0, a classic treatment [18] gives a p À e À collision rate 10 6 times larger than p for our plasmas. The rate for collisions that couple radial and axial energy is suppressed when a strong B is added along the trap axis [19]. Even with the predicted suppression by a factor of 10 3 , the axial-radial collision rate is much faster than p , with a time constant shorter than 0.01 s for even our lowest temperatures.…”

A laser-cooled, high density positron plasma

“…This is because for a strongly magnetized plasma the perpendicular kinetic energy is constrained by a many-particle adiabatic invariant [23]. This modifies the particle distribution function (which is what we measure in Fig.…”

A Laser-cooled Positron Plasma

“…Second, an increase of a few dB in the applied microwave power above this threshold was sufficient to rapidly annihilate the positrons, presumably through excitation of the positrons to a least a few volts energy where positronium formation with background gas atoms could take place. The significant excitation of the positron cyclotron motion was probably necessary because of the weak coupling between the positron cyclotron and 9 Be + ion motions, and the low rate of energy transfer between the positron cyclotron and axial energies in the high magnetic field of our trap [29]. Other potential sources of broadening include the relativistic mass shift (∼10 kHz for each 300 K in energy), first-order Doppler broadening from positron motion within the trap, and magnetic field instability and inhomogeneity.…”

“…In addition the positron cyclotron motion is collisionally coupled to the positron axial motion, but this coupling becomes exponentially weak when the Larmor radius is less than the distance of closest approach (the strongly magnetized regime). This energy transfer rate has been carefully studied [29] and for a 10 9 cm −3 positron plasma is ∼10 Hz for T ∼10 K. Therefore we expect T ⊥ to be greater than 10 K and to be greater than T which is cooled by Coulomb collisions with the laser-cooled 9 Be + ions.…”

“…We emphasize that this temperature limit is only for positron motion parallel to the magnetic field. For a strongly magnetized plasma the perpendicular kinetic energy is constrained by a many-particle adiabatic invariant [29]. This modifies the particle distribution function with the result that the Debye length is determined by T not T ⊥ [36].…”