Spatial and temporal distribution of a 1-MeV proton microbeam guided through a poly(tetrafluoroethylene) macrocapillary

We present computer simulations about the spatial and temporal evolution of a 1-MeV proton microbeam transmitted through an insulating macrocapillary with the length of 45 mm and with the inner diameter of 800 {\mu}m. The axis of the capillary was tilted to 1{\deg} relative to the axis of the incident beam, which ensured geometrical nontransparency. The simulation is based on the combination of stochastic (Monte Carlo) and deterministic methods. It involves (1) random sampling of the initial conditions, according to distributions generated by the widely used and freely available computer software packages, SRIM and WINTRAX, (2) the numerical solution of the governing equations for following the classical trajectory of the projectiles, and (3) the description of the field-driven charge migration on the surface and in the bulk of the insulator material. We found that our simulation describes reasonably all of our previous experimental observations, indicating the functionality and reliability of the applied model. In addition, we found that at different phases of the beam transmission, different atomic processes result in the evolution of the beam distribution. First, in a scattering phase, the multiple small angle atomic scattering dominates in the beam transmission, resulting in an outgoing beam into a wide angular range and in a wide energy window. Later, in a mixed phase, scattering and guiding happens simultaneously, with a continuously increasing contribution of guiding. Finally, in the phase of the stabilized, guided transmission, a quadrupolelike focusing effect is observed, i.e., the transmitted beam is concentrated into a small spot, and the transmitted protons keep their initial kinetic energy.