Collisional Contributions to Braginskii Equations

Collisional contributions in the above set of equations due to the elastic Coulomb interactions are the terms Rap and Qap. We now proceed to express more explicitly the source terms Sn[fa] due to atomic and molecular interactions with neutral particles. These result from the collision integrals Can in (2.1). These integrals may be considered separately for each individual collision process, and then summed up. We omit the index labelling a particular type of process in the following discussion. 

The dominant processes to be considered here are inelastic, reactive and even chemical processes, such as formation and breakup of molecules at the surfaces and by volume processes respectively. For large, cold divertor plasmas as currently envisaged for, e.g., ITER, also elastic neutral-ion collisions gain relevance, due to their frictional effects on the plasma flow. 

For all collision processes of interest in the present context a splitting of the collision integral (2.13) into a gain (first term) and a loss (second term) is possible. 

The nine-fold integration for the gain term is over both pre-collision velocities and over the second (all but the first) post-collision velocity. Both pre-collision states are folded with their corresponding distribution function. 

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