Measured electron beam parameters and their standard deviation as well as radiator and collimator properties
are the basic input for calculations based on the Monte Carlo technique.
Starting from a given number of electrons Ne, depending on the desired statistical accuracy,
a certain set of physical values are chosen randomly in parameter space.
First the direction of an incident electron
with energy E0 impinging at
on the radiator
is chosen from the beam energy
distributions, which are assumed
to be of Gaussian shape with known parameters
The mean polar angle deviation
from the incident direction depend via
Molières theory on the depth z of the bremsstrahl process in the radiator,
which is chosen randomly from a homogenous distribution within the radiator thickness zR.
To calculate the coherent bremsstrahlung for this particular electron the lattice has to be
rotated into its coordinate system, involving a transformation of the crystal angles .
The total transversal electron deflection
due to multiple scattering and beam divergence
and the transformation of the crystal
axis in the electron system
is calculated (eq. A5c and fig. 2).
Then a lattice vector is chosen uniformly in reciprocal space
with the Miller indices h,k,l,
is calculated with these parameters
and the photon momentum
is transformed back in the lab system.
The resulting cross section is differential in photon energy k and angle, which is
the azimuthal ()
in coherent bremsstrahlung and is the polar angle (
in the incoherent case.
As an example the polarisation for a rectangular collimator compared to a circular one,
both producing the same tagging efficiency, is shown in fig. 3.