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SpECTRE
v2024.04.12
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Computes the stiff part \(\tilde{J}^i_\mathrm{parallel}\) of the generalized electric current density \(\tilde{J}^i\). More...
#include <ElectricCurrentDensity.hpp>
Public Types | |
| using | argument_tags = tmpl::list< Tags::TildeQ, Tags::TildeE, Tags::TildeB, Tags::ParallelConductivity, gr::Tags::Lapse< DataVector >, gr::Tags::SqrtDetSpatialMetric< DataVector >, gr::Tags::SpatialMetric< DataVector, 3 > > |
| using | return_type = tnsr::I< DataVector, 3 > |
Static Public Member Functions | |
| static void | apply (gsl::not_null< tnsr::I< DataVector, 3, Frame::Inertial > * > parallel_tilde_j, const Scalar< DataVector > &tilde_q, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_e, const tnsr::I< DataVector, 3, Frame::Inertial > &tilde_b, double parallel_conductivity, const Scalar< DataVector > &lapse, const Scalar< DataVector > &sqrt_det_spatial_metric, const tnsr::ii< DataVector, 3, Frame::Inertial > &spatial_metric) |
Computes the stiff part \(\tilde{J}^i_\mathrm{parallel}\) of the generalized electric current density \(\tilde{J}^i\).
\begin{align*} \tilde{J}^i_\mathrm{parallel} & = \alpha \sqrt{\gamma} \eta \left[ \frac{(E_lB^l)B^i}{B^2} + \frac{\mathcal{R}(E^2-B^2)}{B^2} E^i \right] \end{align*}
where \(\alpha\) is lapse, \(\gamma\) is the determinant of the spatial metric, \(E^i\) is the electric field, \(B^i\) is the magnetic field, \(\eta\) is the parallel conductivity, and \(\mathcal{R}(x) = \max (x,0)\) is the rectifier function.