Temperature Equilibration and Three-Body Recombination in Strongly Magnetized Pure Electron Plasmas

Two properties of a weakly correlated pure electron plasma that is immersed in a uniform magnetic field are calculated. The strength of the magnetic field is determined by the dimensionless parameter r_{ce }/b, wherer_{ce } = sqrt{k_{B}T_ {e}/m_{e}}/Omega_ {ce}is the cyclotron radius and b = e^{2}/k_{B}T _{e} is the classical distance of closest approach. The first property examined is the collisional equipartition rate between the parallel and perpendicular velocity components. Here, parallel and perpendicular refer to the direction of the magnetic field. For a strongly magnetized plasma (i.e., r_{ce}/b << 1), the equipartition rate is exponentially small (~ exp[ {-}2.34(b/r_{ce}) ^{2/5}]). For a weakly magnetized plasma (i.e., r _{ce}/bgg 1), the rate is the same as for an unmagnetized plasma except that r _{ce}/b replaces lambda _{D}/b in the Coulomb logarithm. (It is assumed here that r_{ce}<lambda _{D}; for r_{ce }>lambda_{D}, the plasma is effectively unmagnetized.) Presented is a numerical treatment that spans the intermediate regime r _{ce}/b~ 1, connects on to asymptotic results in the two limits r_ {ce}/b<< 1 and r_ {ce}/bgg 1 and is in good agreement with experiments. Also, an improved asymptotic expression for the rate in the high field limit is derived. Secondly, the three-body recombination rate for an ion introduced into a cryogenic electron plasma in the high field limit is calculated. An ensemble of plasmas characterized by classical guiding center electrons and stationary ions is described with the BBGKY hierarchy. Under the assumption of weak electron correlation, the hierarchy is reduced to a master equation. Insight to the physics of the recombination process is obtained from the variational theory of reaction rates and from an approximate Fokker -Planck analysis. The master equation is solved numerically using a Monte Carlo simulation, and the recombination rate is determined to be 0.070(10)n_sp{e }{2}v_{e}b^5 per ion, where n_{e} is the electron density andv_{e } = sqrt{k_{B}T_ {e}/m_{e}}is the thermal velocity. Also determined by the numerical simulation is the transient evolution of the distribution function from a depleted potential well about the ion to its steady state.