Kinetic equilibrium solution to the Vlasov equation in a cylindrical geometry*

We present a 1D kinetic model in a cylindrical geometry that predicts the plasma potential, density, and electron/ion temperature profiles across dipolarization fronts (DFs) in the near-Earth plasma sheet consistent with space measurements and laboratory experiments. Recent high-resolution observations by NASA’s Magnetoshperic Multi-Scale (MMS) satellites have revealed large density gradients across the DF maintained by an ambipolar electric field. The free energy introduced by the electric field can drive the waves (whistlers, electron holes, and broadband electrostatic turbulence, etc.) observed by MMS. Recent experiments at the Naval Research Lab’s space chamber have reproduced the conditions in a DF layer with small scale gradients and the associated emissions. Traditional fluid and magnetohydrodynamic descriptions of DFs begin to breakdown on the ion gyro scale, creating the need for a kinetic model that captures kinetic equilibrium on such small scales. This model utilizes a particle distribution function that we construct from constants of motion, including energy, parallel momentum, and guiding center position, and generates a self-consistent electrostatic potential across the DF layer consistent with the plasma density profile.