Speaker
LAURA BANDIERA
(FE)
Description
An algorithm for the numerical calculation of the radiation spectrum based on the direct integration of the Baier Katkov (BK) formula is introduced. Since the coherent effects in the process of radiation emission in crystals appear when the angle between particle trajectories and crystal planes or axes is small and at ultra-relativistic energies the radiation angle 1/gamma is much smaller than unity, we can simplify the BK formula for radiated energy by using the small-angle approximation.
The basis of the algorithm is to start from a classical trajectory. The electron/positron
trajectory can be build with any of the Monte Carlo code available based on the integration of particle trajectories under the continuum potential approximation, thus solving the classical equation of motion through numerical integration. In principle, the BK formula should be integrated along the whole particle trajectory. Nevertheless, at very-high energy it may happen that the total probability of radiation exceeds unity, which means that multiple photon emission may occur. With the aim of simulating multiple photon emission, the classical trajectory can be divided into some intermediate-lengths, in a similar way as implemented by Artru [1], who was the first that treated both multiple coherent and incoherent radiation.
Such algorithm has already been implemented in two different software [2,3], which
generate the classical trajectories also taking into account the contribution of incoherent
scattering with nuclei and electrons. In both cases, the presented method demonstrated
its capability in predicting the experimental spectra of radiation in bent crystals for
different beam energies, from sub-GeV [3,4] to hundreds of GeV [2,5]. Such algorithm can be easily adapted to other Monte Carlo softwares to predict the radiation generated by ultrarelativistic electrons/positrons in crystalline structures.
Primary authors
LAURA BANDIERA
(FE)
Prof.
Victor Tikhomirov
(Research Institute for Nuclear Problems)
Co-author
Enrico Bagli
(FE)
