Andres working on this now
JOREK Physics Models
Reduced MHD:
model 600 is the workhorse for reduced MHD as it allows users to combine the different physics ($v_\parallel$, separate $T_e$ and $T_i$, fluid neutrals, fluid impurities, …) they wish to keep in their simulations at compile time. The variables that are always present in model 600 are:
| Variable | Symbol | variable number |
|---|---|---|
| Poloidal magnetic flux: | $\psi$ | 1 |
| Velocity stream function: | $u$ | 2 |
| Toroidal current density: | $zj$ | 3 |
| Vorticity: | $\omega$ | 4 |
| Mass density: | $\rho$ | 5 |
| Temperature: | $T$ or $T_i$ | 6 |
When $v_\parallel$ is used, it is always var_vpar=7.
For model 600, the variable numbers are assigned at compile time.
In addition to model 600, there are older, legacy, reduced MHD models shown below. However, new developments are not necessarily included in these models and, as such, users are suggested to use model 600.
| Model | Description | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| model199 | No parallel flows | $\psi$ | $u$ | $j$ | $\omega$ | $\rho$ | $T$ | ||||
| model303/333 | Parallel flows | $\psi$ | $u$ | $j$ | $\omega$ | $\rho$ | $T$ | $v_{\vert\vert}$ | |||
| model305 | ECCD 1 current model | $\psi$ | $u$ | $j$ | $\omega$ | $\rho$ | $T$ | $v_{\vert\vert}$ | $J_{ECCD}$ | ||
| model306 | ECCD 2 current model | $\psi$ | $u$ | $j$ | $\omega$ | $\rho$ | $T$ | $v_{\vert\vert}$ | $J_{EC1}$ | $J_{EC2}$ | |
| model400 | Parallel flows; separate $T_e$ and $T_i$ | $\psi$ | $u$ | $j$ | $\omega$ | $\rho$ | $T_i$ | $v_{\vert\vert}$ | $T_e$ | ||
| model500/501/555 | Parallel flows and neutral/impurity density | $\psi$ | $u$ | $j$ | $\omega$ | $\rho$ | $T$ | $v_{\vert\vert}$ | $\rho_{n/imp}$ |
Full MHD
| Model | Variables: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| model710 | $A_3$ | $A_R$ | $A_Z$ | $u_R$ | $u_Z$ | $u_\phi$ | $\rho$ | $T$ | ||
| model711 | $A_3$ | $A_R$ | $A_Z$ | $u_R$ | $u_Z$ | $u_\phi$ | $\rho$ | $Ti$ | $Te$ | |
| model712 | $A_3$ | $A_R$ | $A_Z$ | $u_R$ | $u_Z$ | $u_\phi$ | $\rho$ | $Ti$ | $Te$ | $\rho_n$ |
Refer also to the page about Notation Conventions.
Derivations by Emmanuel Franck et al.
Table of contents
- Reduced MHD models
- Tokamak Full MHD
- Stellarator Reduced MHD
- Magnetic Vector Potential
- Current Expression
- Vorticity Expression
- Stream Function and Electric Potential Expression
- The j x B Term Expression
- The v x B Term Expression
- The Continuity Equation Expression
- The Poloidal Flux Equation Expression
- The Diamagnetic Vorticity Expression
- Derivation of the Parallel Momentum Equation
- Weak-Form Resistive Term in Full MHD