Neutrals
Several neutral models are implemented with Soledge3X:
- A simple fluid model (diffusive)
- A coupling to the kinetic code EIRENE
The (crude) fluid model
Directly implemented in soledge3x is a fluid neutral model that aims at providing a rough description of the particle source and energy losses due to recycling, sputtering and radiation by neutrals. For each element, a single diffusive equation for the neural species is solved: $$\frac{\partial n_n}{\partial t} = \vec{\nabla}\cdot\left( D_n \vec{\nabla} n_n \right) - n_e n_n \langle \sigma v \rangle_{iz} + n_e n \langle \sigma v \rangle_{rec} + S_{puff} $$ where
- $n_n$ is the neutral density
- $D_n$ is the neutral diffusivity
- $\langle \sigma v \rangle_{iz}$ (resp. $\langle \sigma v \rangle_{rec}$) is the ionization (resp. recombination) cross section.
- $S_{puff}$ is a source of neutrals due to gas puff injections
The boundary conditions on the wall control the recycling and sputtering. A net flux of atoms $\phi^{inward}_{n_n,wall}$ is emitted from the wall as $$\phi^{inward}_{n_n,wall} = \sum_{ions, neutrals} R \phi^{outward}_{n,wall}$$ where $\phi^{outward}_{n,wall}$ is the incident flux of plasma or neutrals on the wall, and $R$ can be either seen as a recycling coefficient or as a sputtering yield depending on the incident species.
On the plasma side:
- one retrieve the ionization/recombination sources in the particle balance of the singly charged ions: $$S_n = n_e n_n \langle \sigma v \rangle_{iz} - n_e n \langle \sigma v \rangle_{rec}$$
- Associated to this gain/loss of particles is a source of parallel momentum (neutrals are assumed to get born with the same velocity as ions). Charge exchange losses are also accounted: $$S_{v_\parallel} = S_n \times v_\parallel - n_e n_n \langle \sigma v \rangle_{cx} v_\parallel$$
- Ion energy losses can be computed the same way (one assumes neutrals temperature is a fraction $R_\mathcal{E}$ of the ions temperature): $$S_{\mathcal{E}_i} = \left( R_\mathcal{E} n_e n_n \langle \sigma v \rangle_{iz} - n_e n \langle \sigma v \rangle_{rec} \right) \times \left( \frac{3}{2} T_i + \frac{1}{2} m_i v_\parallel^2 \right) - \frac{1}{2} m_i v_\parallel^2 n_e n_n \langle \sigma v \rangle_{cx}$$
- Electron energy losses associated to nucleus-electron binding energy and radiation processes are computed as $$S_{\mathcal{E}_e} = - \sum_{neutrals} \left( n_e n_n \langle \sigma v \rangle_{iz} [ E_{iz} + PLT(T_e) ] + n_e n \langle \sigma v \rangle_{rec} PRB(T_e) \right)$$ where $PLT(T_e)$ is the energy loss by radiation in the ionization process (line emission [bound to bound electron]) and $PRB(T_e)$ is the energy loss by radiation in the recombination process (continuum [free to bound electron + free to free electron (Bremsstrahlung)]).
Coupling with EIRENE
The Soledge3X code has been coupled to EIRENE via an interface called STYX. The purpose of the interface is:
- to perform the interpolations between the plasma grid based on quadrangles (in 2D, toroidally extruded in 3D) and the EIRENE grid based on triangles (in 2D, toroidally extruded in 3D)
- to interpolate plasma fluxes and plasma parameters on the wall
- to setup EIRENE according to a simplified input file for neutrals.
EIRENE provides a flexible kinetic description of neutrals involving an arbitrary number of physical or chemical reactions including molecule dissociation, collisions with plasma ions, ionization, photon emission or absorption… EIRENE computes mass, momentum and energy sources resulting from the complex collisions and ionization of neutral species. It requires a background plasma and impinging fluxes of plasma on the wall. The neutrals history are computed with a Monte-Carlo algorithm from their birth on the wall (recycling or sputtering) or in volume (plasma recombination) up to their ionization by the plasma. During their “life”, neutrals can undergo several events such as elastic collision with the plasma (charge exchange) or collision with the wall. The coupling scheme between Soledge3X and EIRENE is summarized on the figure below showing input/output provided by each code to one another.
The EIRENE grid based on triangles in generated by the Soledge3X-EIRENE mesh tool. It can be extended outside the grid used to solve the plasma (for instance, beyond the first wall components to simulate neutral transport up to the pumps).
