Add full "circuit equation" boundary condition on the psi equation

[theo-brown]

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).

[Theminacious]

Hi @theo-brown , I’d like to take this issue. I’ll work on replacing the existing loop-voltage BC with the full external circuit equation for ψ, following ASTRA’s formulation.
Please assign it to me — any guidance on where the current BC is implemented would help.

[jcitrin]

@Theminacious thank you for your enthusiasm to contribute. However due to the intricate nature of this issue, we prefer that it is carried out with someone that has established domain expertise and access to an additional high-fidelity simulator for verification. Just added a new label to communicate this.

[Theminacious]

Thanks for the clarification, @jcitrin — completely understand.

I’ll step back from implementing it for now, but I’d love to follow the discussion and help where I can (e.g., documentation, validation, or smaller related tasks). If there is any sub-task or preliminary work that doesn’t require full simulator access, I’d be happy to contribute.

Please keep me in the loop — I’m very interested in contributing.