Transport in a toroidally confined pure electron plasma

O’Neil and Smith [T.M. O’Neil and R.A. Smith, Phys. Plasmas 1, 8 (1994)] have argued that a pure electron plasma can be confined stably in a toroidal magnetic field configuration. This paper shows that the toroidal curvature of the magnetic field of necessity causes slow cross-field transport. The transport mechanism is similar to magnetic pumping and may be understood by considering a single flux tube of plasma. As the flux tube of plasma undergoes poloidal E×B drift rotation about the center of the plasma, the length of the flux tube and the magnetic field strength within the flux tube oscillate, and this produces corresponding oscillations in T∥ and T⊥. The collisional relaxation of T∥ toward T⊥ produces a slow dissipation of electrostatic energy into heat and a consequent expansion (cross-field transport) of the plasma. In the limit where the cross section of the plasma is nearly circular the radial particle flux is given by Γr=1/2ν⊥,∥T(r/ρ0)2n/(−e∂Φ/∂r), where ν⊥,∥ is the collisional equipartition rate, ρ0 is the major radius at the center of the plasma, and r is the minor radius measured from the center of the plasma. The transport flux is first calculated using this simple physical picture and then is calculated by solving the drift-kinetic Boltzmann equation. This latter calculation is not limited to a plasma with a circular cross section.