Guiding center atoms: Three-body recombination in a strongly magnetized plasma

TLDR

The plasma is strongly magnetized, with the electron cyclotron radius far smaller than the classical distance of closest approach, defining the regime studied. The authors model the recombination process by treating the ion–electron system as guiding‑center atoms, reducing the BBGKY hierarchy to a master equation under weak electron correlations and analyzing it with variational reaction‑rate theory and an approximate Fokker–Planck approach. Numerical Monte‑Carlo solution of the master equation yields a recombination rate of 0.070(10) n_e^2 v_e^5 per ion and reveals the transient evolution of the ion’s potential‑well distribution toward steady state.

Abstract

The three-body recombination rate is calculated for an ion introduced into a magnetically confined, weakly correlated, and cryogenic pure electron plasma. The plasma is strongly magnetized in the sense that the cyclotron radius for an electron rce=(kBTe/me)1/2/Ωce is small compared to the classical distance of closest approach b=e2/kBTe, where Te is the electron temperature and Ωce=eB/mec is the electron cyclotron frequency. Since the recombination rate is controlled by a kinetic bottleneck a few kBTe below ionization, the rate may be determined by considering only the initial cascade through states of electron-ion pairs with separation of order b. These pairs may be described as guiding center atoms since the dynamics is classical and treatable with the guiding center drift approximation. In this paper, an ensemble of plasmas characterized by 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)n2eveb5 per ion, where ne is the electron density and ve=(kBTe/me)1/2 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.