Boltzmann-Fokker-Planck model for the electron distribution function in the Earth's ionosphere

Abstract Using Boltzmann-Fokker-Planck methods and the diffusion approximation, we derive coupled non-linear equations for the first two angular moments of the electron distribution function in the Earth's ionosphere. The theory includes a phenomenological treatment of photionization of the neutral species by an externally produced photon flux; electron-ion recombination; electronneutral particle attachment; elastic, excitation, deexcitation, and ionizing electron-neutral particle collisions; and elastic electron-electron and electron-ion collisions. At high and low energies, we obtain approximate analytic solutions for the steady-state electron distribution function. Under certain conditions we also obtain the standard continuous slowing-down formulae for the steady-state electron distribution function in the diffusion approximation.

[1]  M. McElroy,et al.  ELECTRON TEMPERATURES IN THE IONOSPHERE , 1963 .

[2]  N. F. Sir Mott,et al.  The theory of atomic collisions , 1933 .

[3]  R. Cicerone,et al.  Photoelectron fluxes in the ionosphere computed by a Monte Carlo Method , 1971 .

[4]  Siegfried Bauer,et al.  Physics of Planetary Ionospheres , 1973 .

[5]  T. Holstein.  Energy Distribution of Electrons in High Frequency Gas Discharges , 1946 .

[6]  K. Takayanagi,et al.  Velocity distribution of ionospheric low-energy electrons , 1974 .

[7]  A. Nagy,et al.  Concerning the influence of elastic scattering upon photoelectron transport and escape , 1970 .

[8]  J. Nisbet,et al.  THE RECOMBINATION COEFFICIENT OF THE NIGHTTIME F LAYER /NASA GRANT NSG-134-61/ V. 68, NO. 4 , 1963 .

[9]  R. Stolarski,et al.  Thermalization and transport of photoelectrons - A comparison of theoretical approaches. , 1973 .

[10]  J. Geisler,et al.  EXCHANGE OF ENERGY BETWEEN THE IONOSPHERE AND THE PROTONOSPHERE , 1965 .

[11]  A. Dalgarno.  Inelastic collisions at low energies , 1969 .

[12]  J. Nisbet.  FACTORS CONTROLLING THE SHAPE OF THE UPPER F REGION UNDER DAYTIME EQUILIBRIUM CONDITIONS , 1963 .

[13]  E. A. Mason,et al.  FORMAL KINETIC THEORY OF TRANSPORT PHENOMENA IN POLYATOMIC GAS MIXTURES , 1963 .

[14]  M. Bachynski,et al.  The Particle Kinetics of Plasmas , 1966 .

[15]  K. Takayanagi,et al.  Elementary processes involving electrons in the ionosphere , 1970 .

[16]  J. Geisler,et al.  Ionospheric temperatures at sunspot minimum , 1965 .