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We present computer simulations about the spatial and temporal evolution of a1-MeV proton microbeam transmitted through an insulating macrocapillary withthe length of 45 mm and with the inner diameter of 800 {\mu}m. The axis of thecapillary was tilted to 1{\deg} relative to the axis of the incident beam,which ensured geometrical nontransparency. The simulation is based on thecombination of stochastic (Monte Carlo) and deterministic methods. It involves(1) random sampling of the initial conditions, according to distributionsgenerated by the widely used and freely available computer software packages,SRIM and WINTRAX, (2) the numerical solution of the governing equations forfollowing the classical trajectory of the projectiles, and (3) the descriptionof the field-driven charge migration on the surface and in the bulk of theinsulator material. We found that our simulation describes reasonably all ofour previous experimental observations, indicating the functionality andreliability of the applied model. In addition, we found that at differentphases of the beam transmission, different atomic processes result in theevolution of the beam distribution. First, in a scattering phase, the multiplesmall angle atomic scattering dominates in the beam transmission, resulting inan outgoing beam into a wide angular range and in a wide energy window. Later,in a mixed phase, scattering and guiding happens simultaneously, with acontinuously increasing contribution of guiding. Finally, in the phase of thestabilized, guided transmission, a quadrupolelike focusing effect is observed,i.e., the transmitted beam is concentrated into a small spot, and thetransmitted protons keep their initial kinetic energy.

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