grmhd::AnalyticData::InitialMagneticFields Namespace Reference

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)

Detailed Description

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*}

Warning

The magnetic field classes assume the magnetic field is initialized, both in size and value, before being passed into the variables function. This is so that multiple magnetic fields can be superposed. Each magnetic field configuration does a += to make this possible.