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Better conversion from electric field to vector potential? #322

Open MaxThevenet opened 2 weeks ago

MaxThevenet commented 2 weeks ago

The conversion between (scalar) electric field $E$ and vector potential $A$ should be

$E = - \frac{\partial A}{\partial t}$.

Assuming

$E = \Re[\mathcal{E}e^{-i\omega_0t}]$ and $A = \Re[\mathcal{A}e^{-i\omega_0t}]$

that should read

$\frac{\partial \mathcal{A}}{\partial t} -i\omega_0\mathcal{A} = \mathcal{E}$.

In the current implementation at https://github.com/LASY-org/lasy/blob/0529779df849daa096e9de3fcfdfc7362ae272cc/lasy/utils/laser_utils.py#L494 we neglect the time derivative (first LHS term), which may be too rough in some cases. A more accurate option, e.g., solving in $\omega$ space, could be useful in some cases.