Time dependent multi-term solution of Boltzmann's equation for magnetised low-temperature plasmas

We present details of the first time dependent multi-term solution of Boltzmann's equation for charged particles in gases under the influence of electric and magnetic fields. A Sonine polynomial representation of the velocity distribution function requires a time dependent weight function to accommodate arbitrary initial conditions and/or time dependent fields. The theory and code are benchmarked against an independent time resolved Monte Carlo simulation for both DC and RF orthogonal electric and magnetic fields. The results support the numerical integrity of the technique