A p r i o r i incorporation of ballistic and heating effects in a four-moment approach to the Boltzmann equation

A new four-moment method for the approximate solution of the Boltzmann equation is considered. It is based on a systematic expansion of the distribution function in Hermite polynomials that accounts a priori for ballistic and heating effects. The closure relation for the fourth moment, the ‘‘quadratic energy density,’’ is tested using numerically exact solutions of the coupled Boltzmann–Poisson equations for the n+nn+ diode in the constant relaxation time approximation. It is shown that the present expansion converges faster than expansions that do not account a priori for heating and drift of the electrons. The quality of the expansion is also discussed in relation to the value of the relaxation time.