Standard Form of Source Terms

The remaining problem is to evaluate the terms (2.12) for all collision processes to be considered. Due to the special notation chosen here, however, these terms are already exactly in the format to which Monte Carlo kinetic particle transport codes can be applied directly. The probabilistic formulation is particularly suitable for these procedures. We refer to standard literature on Monte Carlo methods for linear transport, such as [19]. Here it is only important to note that one may write equation (2.12) as linear functional of the neutral particle distribution function /  

From the above consideration one can furthermore infer that the detector functions gA are always of the form 

depends on the W-kernels introduced above, but in general stands for terms of the form r (wrei) Crei- v1 is a cross-section, appropriately weighted by factors [1 — cosl(0)], l = 1, 2,. .., if the efficiency of exchange of quantity A in a collision depends on the scattering angle 0 in this way (as, e.g., in case of elastic neutral particle - ion collisions, see Sect. 2.2.4). In case of inelastic collision processes a is simply the total cross-section, denoted r° (if no confusion with the weighting exponent l = 1, 2. is possible) or a1. In principle the detector functions qa must be obtained by numerical integration and tabulated for the parameters of the relevant distribution functions fa. 

However, a much more tractable form can be derived, strongly reducing the number of parameters in these data tables. The first step follows from the fact, that consistent with the fluid approximation for the charged particles a we can make the assumption of a near Maxwellian distribution 

V and vT stands for any element of tensors v v... v (any rank, i.e., any number of factors in this outer product). We may even omit the shift vector 

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