@RadiationModel¶
This module determines how the angular dependence of the emitted radiation should be treated. We can conveniently express the position of an observer relative to the emitting particle using a spherical coordinate system \((r, \theta, \phi)\). Since the direction in which the observer is located relative to the emitter is fully determined by the two angles \(\theta\) and \(\phi\), and since the amount of radiation emitted towards an observer is independent of how far away the observer is located, we can speak of the angular distribution of emitted radiation.
To not assume anything about the angular distribution of the emitted radiation, the (angdist) should be used. It accounts for the full angular distribution of all types of radiation, and is therefore also somewhat heavier to run.
Directed radiation, such as bremsstrahlung and synchrotron radiation, are almost exactly emitted along the velocity vector of the emitting particle, with an angular spread that is proportional to \(\gamma^{-1}\), where \(\gamma\) denotes the relativistic factor. As an approximation, we may therefore assume that all radiation is emitted exactly along the velocity vector of the particle. We refer to this approximation as the cone approximation, and it is implemented in the (cone) module. It corresponds to assuming
where \(\frac{\mathrm{d} P}{\mathrm{d}\Omega}\) is the angular distribution of radiation (see the synthetic radiation diagnostic equation on the page about @Radiation), \(P_0\) is the total amount of emitted radiation (possibly in a limited wavelength range), \(\delta\) is a Dirac delta function, \(\hat{\boldsymbol{v}}\) denotes the direction of motion of the particle and \(\hat{\boldsymbol{n}}\) the unit vector pointing out the direction along which the particle is being observed.
The cone model is significantly faster to run than the (angdist) model, and can produce accurate results if the energies of the emitting particles are sufficiently high.
Finally, we may also assume that the emitted radiation is independent of the two angles \(\theta\) and \(\phi\) and that the radiation is emitted uniformly in all directions. A special radiation model has been implemented for this case, called (isotropic), which is primarily used for benchmarking purposes and producing pretty images.
Available models¶
| Model | Description |
| (angdist) | No approximations. Consider full angular distribution of radiation. |
| (cone) | Cone approximation. All radiation emitted exactly along velocity vector. |
| (isotropic) | Isotropically emitted radiation. |