Drift kinetic fluid particle methods for magnetized Vlasov emission equilibria

A Vlasov equilibrium previously developed¹ for steady state emission into a magnetized gap in coaxial geometry is equipped with electron, ion and neutral surface emission rules that accurately support the solution profiles. These algorithms are formulated in terms of novel drift kinetic fluid particle (DKFP) methods that conserve number, momentum, and enthalpy to machine precision. The cathode boundary conditions are those of a perfect conductor that emits a electron flux radially, azimuthally, and axially. The anode boundary conditions are those of a perfectly absorbing conductor. The cathode carries a fixed current and the radial gap is set to a fixed voltage. The angular momentum of emitted electrons around the cathode is found to materially change the orbit turning points. When energy conserving solutions are examined it is found that axial velocities must remain bounded above by a well defined function of radius, magnetic field, and voltage. A fully nonlinear and self consistent Vlasov-Poisson problem is formulated and solved for the space charge distribution implied by the Vlasov equilibrium. Moments of the Vlasov distribution then determine the shunt impedance of the gap and the criteria for "warm" magnetic insulation of the coaxial line. The DKFP emission scheme must then benchmark to these profiles in the gap if it is to resolve these steady state properties. The theory limits to Ottinger's critical current magnetization picture for cold electrons, but shows a properly non-singular behavior in the electron density profile at the radial turning points and so properly reduces the enhancement of ion flux across the gap.