Generalized kinetic description of a plasma in an arbitrary field‐aligned potential energy structure

Abstract

Abstract. We present a general solution to the collisionless Boltzmann (Vlasov) equation for a free-flowing plasma along a magnetic field line using Liouville's theorem, allowing for an arbitrary field-aligned potential energy structure including nonmonotonicities. The constraints of the existing collisionless kinetic transport models are explored, and the need for a more general approach to the problem of self-consistent potential energy calculations is described. Then a technique that handles an arbitrary potential energy distribution along the field line is presented and discussed. For precipitation of magnetospherically trapped hot plasma, this model yields moment calculations that vary by up to a factor of 2 for various potential energy structures with the same total potential energy drop. The differences are much greater for the high-latitude outflow scenario, giving order of magnitude variations depending on the shape of the potential energy distribution. Self-consistent calculations for the photoelectron-driven polar wind are compared with previous results, and it is shown that even a photoelectron concentration of 0.03% at the base of the simulation (500 km) will cause the potential energy distribution to violate the constraints of the existing models.

Current–voltage relationship

“…Khazanov et al (1998) and Liemohn and Khazanov (1998) generalized the expressions of the particle flux and current density for an arbitrary potential distribution and for five different VDFs (Lorentzian, bi-Lorentzian, Maxwellian, bi-Maxwellian and bi-Maxwellian loss cone distribution). For nonmonotonic potential energies, the current-voltage relationship becomes a non-linear function of V. The global distribution of the potential energy has to be known in advance below the altitude considered to calculate the moments of the VDF and the net current densities carried by the electrons and ions.…”

“…the general formula for the current density obtained by Khazanov et al (1998) and Liemohn and Khazanov (1998) is, using the same notations:…”

Heating of the sunlit polar cap ionosphere by reflected photoelectrons

“…Khazanov et al [1998] generalized the work of Khazanov et al [1997] to allow for arbitrary potential profiles, including nonmonotonicities. According to Khazanov et al [1998], the results of Khazanov et al [1997] hold at low and moderate photoelectron concentrations, but the generalized model produces substantially different potential profiles and more outflow compared to the Khazanov et al [1997] model when the photoelectron fraction at 500 km is 0.03% or higher. For the reference simulation in Figure 1 the photoelectron fraction at 500 km is 0.0143%, and thus, this simulation lies comfortably in the classical polar wind regime.…”

Mechanisms of ionospheric mass escape

“…Such waves may exist in the ion resonant frequency range, or may nonresonantly power outflows via the ponderomotive effect [Khazanov et al, 1998;Guglielmi and Lundin, 2001]. As important as these effects may well be, they remain problematic to derive from global magnetospheric simulations, owing to the inherent time resolution or other limitations of such models.…”