Thin Target simulation - beam heating

Particle beam interaction with a thin target has the following aspects:

The ionization energy loss is dominated by the electronic loss. Nuclear contribution reaches several percent for projectile energy of the order of a few keV (protons), and drops to 10^-5 for relativistic energies. As the energy is lost mainly via interaction with target electrons, some of those electrons receive a high energy transfer. Those electrons may escape the target effectively removing part of the energy loss from the targer thermal energy balance. Therefore, in case of thin target, simple use of tabularized dE/dx values leads to overestimation of the target heating.

In order to estimate the real energy deposit in the target material, a Geant4 simulation was performed. The geometry is a simple extended particle source and the target in shape of a very long cyllinder.

The beam energy and the cyllinder diameter were varied. To obtain the results, the following Geant4 settings were used:

The plot below shows target dE/dx defined as the energy loss of the beam particles which must be used to calculate the beam heating. It is different than the actual energy loss as seen by the beam particles and the difference comes from delta electrons. It is interesting to note that the 'tabular' value of dE/dx is reached for targets as thick as 100 mm for 3 GeV protons and 1 meter for 30 GeV protons on carbon target.

The next plot shows energy deposit in the wire for various beam energies and materials (two most popular are Tungsten and Carbon) as a function of wire diameter. It is interesting to note that, above the typical MIP energies, higher energy deposited in the target provokes more 'kick-off electrons cooling', effectively making the energy deposition independent on impacting particles energy.