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 Γ r =1/2ν⊥,∥ T(r/ρ0)2 n/(−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.