Collisionless plasma modeling in an arbitrary potential energy distribution

Abstract

A new technique for calculating a collisionless plasma along a field line is presented. The primary feature of this new ion-exospheric model is that it can handle an arbitrary ͑including nonmonotonic͒ potential energy distribution. This was one of the limiting constraints on the existing models in this class, and these constraints are generalized for an arbitrary potential energy composition. The formulation for relating current density to the field-aligned potential as well as formulas for density, temperature, and energy flux calculations are presented for several distribution functions, ranging from a bi-Lorentzian with a loss cone to an isotropic Maxwellian. A comparison of these results with previous models shows that the formulation reduces to the earlier models under similar assumptions.

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:…”

“…General formulas for bi-Maxwellian with loss-cone and bi-Lorentzian with loss cone were also calculated in Liemohn and Khazanov (1998). Current-voltage relationships for different types of VDF in monotonic potential energy PÀP 0 40 are summarized in Bostro¨m (2003).…”

A kinetic exospheric model of the solar wind with a nonmonotonic potential energy for the protons

“…[8] In this section we describe how to calculate the main macroscopic quantities (density, field-aligned flux, parallel and perpendicular pressures, and energy flux) of the protons and electrons in the solar wind by integrating their velocity distribution functions (VDF) for the case of a global potential energy of the protons with a maximum at a distance r m and an exobase level r 0 located below r m . These integrations can equivalently be performed in the velocity space [Lemaire et Scherer, 1971b, hereafter LS71] or in the [E, M] space [Khazanov et al, 1998]. The dimensionless total potential energy of a particle is defined by y(r) = mf g þZeV r ð Þ kT 0 , where T 0 is the plasma temperature at r 0 , assumed to be identical for protons and electrons.…”

Coronal heating and solar wind acceleration for electrons, protons, and minor ions obtained from kinetic models based on kappa distributions

“…Such models have been developed and applied to the ion‐exospheres [ Pierrard and Lemaire , ], the solar wind [ Maksimovic et al ., ; Zouganelis et al ., ], the solar corona [ Pierrard and Lamy , ], the terrestrial ionosphere and plasma sheet [ Khazanov et al ., ], the polar wind of the Earth [ Pierrard and Lemaire , ; Tam et al ., ] and other planets like Jupiter and Saturn [ Pierrard , ], some satellites like the Io torus [ Meyer‐Vernet et al ., ], the terrestrial auroral regions [ Pierrard et al ., ], the plasmasphere [ Pierrard and Borremans , ], and the radiation belts [ Pierrard and Borremans , ] among many others. They have been generalized to arbitrary potential energy distributions [ Liemohn and Khazanov , ; Lamy et al ., ]. Suprathermal electrons generate large ambipolar electric fields along open magnetic flux tubes in stellar coronae and in planetary ionospheres and thus contribute significantly to solar and stellar wind accelerations, outflow from planetary ionospheres, and possibly even exoplanetary atmospheric loss.…”