  AA numerical code, labeled InCa4D, used for simulating CPU-efficiently the
guiding of charged beam particles through insulating straight nano or macro
capillaries, is presented in detail. The paper may be regarded as a walk
through the numerical code, where we discuss how we compute the charge
deposition and charge dynamics at the interfaces of a straight capillary and
how we compute the electric field with imposed boundary conditions. The latter
add surface polarization charges at the dielectric interfaces and free charges
at conducting interfaces. Absorbing boundary conditions allow for a leakage
current. As a result, the electric field in InCa4D yields accurate relaxation
rates and decay rates for both cases, namely where the outer surface of the
straight capillary is covered by a grounded conducting paint or not.
Eventually, we show how we sample the initial conditions of the inserted beam
particles and how we evaluate CPU-efficiently the particles' trajectory,
allowing to compute typically $10^6$ trajectories in about two hours on a
modern CPU.
