google-deepmind / google-deepmind/torax
Add full "circuit equation" boundary condition on the psi equation
- Dominant language
- Python
- Stars
- 721
- Forks
- 145
- Avg merge
- 2d 14h
- Merged PRs (30d)
- 49
Description
TORAX currently has the "loop voltage" boundary condition,
$$
\left. \frac{\partial \psi}{\partial t} \right\rvert_{\rho=\rho_B} = u(t)
$$
This allows an ad-hoc/approximate method for generating scenarios with prescribed inductive coil contributions (e.g. fully inductive scenarios, where $u(t) = 0$ and the ohmic current is hoped to be small).
For a better representation of solenoid-driven or solenoid-free scenarios, we should instead use the external circuit equation BC,
$$
u_{\rm inductive}(t) = \frac{d}{dt} (L_{\rm external} I_p) + V_{\rm loop}
$$
where $V_{\rm loop} = \left. \frac{\partial \psi}{\partial t} \right\rvert_{\rho=\rho_B} + 2\pi B_0 \mu(\rho_B) \frac{\partial \rho_B}{\partial t}$ (eq 51 and 74 from the ASTRA manual).
Contributor guide
Assessment
This issue has not been assessed yet.