A bounce-averaged ion Fokker–Planck code for Penning fusion devices Original Research Article

A bounce-averaged Fokker–Planck code (BAFP) has been developed and tested. BAFP implements a multi-dimensional, energy-conservative, time-implicit solution of the Fokker–Planck equation in two velocity and one spatial dimensions. A Jacobian-free, Newton–Krylov solver efficiently inverts the time-implicit equations. Bounce averaging removes the fast time scale for motion of trapped ions, so low-collisionality ion systems can effectively be treated. BAFP has been applied to ion dynamics in virtual-cathode spherical inertial electrostatic (IEC) fusion devices, which employ a spherical cloud of electrons to create a kV electrostatic well to confine and spherically focus ions. Here, Penning-type IEC devices are studied. Steady-state ion distribution functions obtained with BAFP in operating limits of interest are presented, and show that a variety of steady-state equilibriums are possible in these systems.