In the edge and particularly the SOL of fusion devices, the plasma is strongly coupled to neutral gas. Because it is neutral, it has fundamentally different dynamics than the plasma. And additionally, the interaction between different species and charge states requires the consideration of plasma-gas chemistry.
The following is taken from Zholobenko 2021.
A simple plasma consisting of one ion species and the corresponding neutral atoms are considered, ignoring molecules. They interact via three reactions, electron impact ionization and recombination, and charge exchange (CX), In a homogeneous plasma, the dynamics of the ion-neutral reactions is described by the following set of rate equations: The above equations can alternatively be derived from the integration of Krook collision operators [Wersal2017]. We have used here the neutral gas density , the momentum density and thermal energy density . The rate coefficients for ionization and recombination are obtained from collisional-radiative (CR) models, the results being available in public Amjuel or OPEN-ADAS data bases. The same is true for electron cooling rate coefficients \cite[chap.~6]{Zholobenko2018FZJ}, whereby it must be noted that the recombination cooling rate becomes negative below 1 eV. This is because three-body recombination heats up the plasma. Therefore, the database stores the always positive radiation rate coefficient due to recombination instead, and we compute eV . For charge exchange, the simple formula from Helander 1994 can be used, which makes the rather robust assumption that the cross section is constant, i.e. it does not depend on impact energy -- but does not assume an exactly Maxwellian velocity distribution for the electrons, performing a more elaborate closure.
In the momentum balance, we have applied the usual approximation and assume that momentum is exchanged similarly in both elastic and inelastic collisions. Therefore, momentum is simply exchanged between ions and neutrals at each collision, while electrons are scattered from the heavier species (including in elastic collisions with the rate coefficient ). While electron scattering in this approximation does not conserve energy, it is usually dissipative as . However, the process is very inefficient due to the small electron mass, and therefore it will be henceforth simply neglected setting , although this might require reconsideration in a detached divertor with .
Similarly, ion and neutral thermal energy is simply exchanged due to collisions. While momentum dissipation is negligible for electrons, their thermal energy dissipation due to inelastic ionization and recombination is important. Firstly, during ionization thermal energy of the electron fluid is depleted to increase the bound electrons energy (internal atom energy) to the continuum level. Secondly, the neutral atoms are constantly excited and emit energy by spontaneous emission due to electron impact, radiating electron thermal energy away. Both is taken into account by the electron cooling rate coefficients.
In a non-homogeneous plasma, the rate equations \eqref{eq:rate-n}-\eqref{eq:rate-pressurei} can be added to the right-hand side of the Braginskii equations as source terms. We employ the usual approximation , setting as we only consider pure deuterium reactions \eqref{reac:iz} and \eqref{reac:cx}. Further, the ion-neutrals momentum exchange is considered in the drift-reduction, yielding an additional ion drift term , . In summary, we obtain the following source terms:
It is a common approach to assume that the charge exchange reaction mixes the velocity space structure of ions and neutrals so efficiently that their temperature is essentially equal. For simplicity, we make the same assumption for the parallel velocity. We then only require an equation for the evolution of the neutrals density to complete the system, which we obtain from [TODO: add references] as with the diffusion coefficient Thereby, is the neutral gas sound velocity, the neutrals mass and the charge exchange frequency. The diffusivity is limited such that the resulting particle flux does not exceed sound speed, which otherwise happens in low density regions far from the recycling area, like the top of the device.