Implemented Coordinates and Forces

Implemented Spatial Coordinates

These structs define what spatial coordinates are used when solving transport equations.

The currently implemented spatial coordinates include:

Coordinates	Coordinate Struct	Comment
Cartesian Minkowski	Cartesian()	Standard $x,y,z$ flat Minkowski spacetime
Cylindrical Minkowski	Cylindrical()	Standard $\rho ,\vartheta ,z$ flat Minkowski spacetime
Spherical Minkowski	Spherical()	Standard $r,\theta ,\psi$ flat Minkowski spacetime

Global to Local Rotation

By default the local ortho-normal basis of momentum is aligned to the local coordinate directions. For Cartesian and Cylindrical spatial coordinates, the momentum-space polar axis is aligned to the $z$ spatial coordinate direction, with the $\varphi =0$ direction aligned to the spatial $x$ ($rho$) direction. For Spherical spatial coordinates, the polar axis is instead aligned with the $x$ ($r$) direction with $\varphi =0$ aligned to the $y$ ($\theta$) direction.

These default directions may be edited by defining global_to_local_rotation a NTuple{3,Float64} containing three angles (radians normalised by $\pi$) $(\alpha ,\beta ,\gamma )$, which give an $z-x-z$ rotation of the local bases vectors. This can be used to specify the local magnetic field direction with respect to the spatial coordinate bases vectors.

Implemented Forces

These structs define which forces to include when solving the transport equations and depend on the spatial coordinates of the system.

The currently implemented forces include:

External Force	Force Struct	Implemented Spatial Coordinates	Implemented Momentum Space Anisotropies
Ricci Rotation coefficients	CoordinateForce()	Cartesian(), Cylindrical(), Spherical()	N/A
Lorentz Force (Uniform and Orthogonal $E$ and $B$ Fields)	ExB()	Cartesian()	N/A
Synchrotron Radiation Reaction	SyncRadReact()	Cartesian(), Cylindrical(), Spherical()	Ani(),Axi(),Iso()
Grad B. Force due to 1/z B Field	InvGradB()	Cylindrical()	N/A