SpECTRE
v2024.05.11
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Things related to the initial (seed) magnetic field that can be superposed on GRMHD initial data. More...
Classes | |
class | InitialMagneticField |
The abstract base class for initial magnetic field configurations. More... | |
class | Poloidal |
Poloidal magnetic field for GRMHD initial data. More... | |
class | Toroidal |
Toroidal magnetic field for GRMHD initial data. More... | |
Functions | |
bool | operator!= (const Toroidal &lhs, const Toroidal &rhs) |
Things related to the initial (seed) magnetic field that can be superposed on GRMHD initial data.
In many cases we assign magnetic fields in terms of the vector potential, which can be computed as
\begin{align*} B^i & = n_a\epsilon^{aijk}\partial_jA_k \\ & = \frac{1}{\sqrt{\gamma}}[ijk]\partial_j A_k, \end{align*}
where \([ijk]\) is the total anti-symmetric symbol.
For example, in the Cartesian coordinates,
\begin{align*} B^x & = \frac{1}{\sqrt{\gamma}} (\partial_y A_z - \partial_z A_y), \\ B^y & = \frac{1}{\sqrt{\gamma}} (\partial_z A_x - \partial_x A_z), \\ B^z & = \frac{1}{\sqrt{\gamma}} (\partial_x A_y - \partial_y A_x). \end{align*}
variables
function. This is so that multiple magnetic fields can be superposed. Each magnetic field configuration does a +=
to make this possible.