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The genesis of the ion axial velocity distribution function (VDF) is analyzedfor collisionless Hall thruster discharges. An analytical form for the VDF isobtained from the Vlasov equation, by applying the Tonks-Langmuir theory in thethruster channel, under the simplifying assumptions of monoenergetic creationof ions and steady state. The equivalent set of 1D unsteady anisotropic momentequations is derived from the Vlasov equation, and simple phenomenologicalclosures are formulated, assuming a polynomial shape for the ions VDF. Theanalytical results and the anisotropic moment equations are compared tocollisionless PIC simulations, employing either a zero heat flux (Euler-likeequations) or the polynomial-VDF closure for the heat flux. The analytical ionVDF and its moments are then compared to experimental measurements.

Collisionless ion modeling in Hall thrusters: analytical axial velocity distribution function and heat flux closures