A multi term Boltzmann equation analysis of non-conservative electron transport in time-dependent electric and magnetic fields

A multi term technique for solving the Boltzmann equation has been developed to investigate the time-dependent behavior of charged particle swarms in an unbounded neutral gas under the influence of spatially uniform time-dependent electric and magnetic fields. The hierarchy resulting from a spherical harmonic decomposition of the Boltzmann equation in the hydrodynamic regime is solved numerically by representing the speed dependence of the phase-space distribution function in terms of an expansion in Sonine polynomials about a Maxwellian velocity distribution at an internally determined time-dependent temperature. This technique avoids restrictions on the electric and magnetic field amplitudes and frequencies and/or the charged particle to neutral molecule mass ratio traditionally associated with many investigations. The variation of the electron transport coefficients with electric and magnetic field strengths, field frequency, phase difference between the fields and angle between the fields is addressed using physical arguments for certain model and real gases.