Limitations on the step size

The routine GMULOF called by GPHYSI creates and fills a table of NEK1 values corresponding to the ELOW values containing the smaller of the upper limits for the step imposed by the three continuous processes: energy loss, multiple scattering and bending of the track induced by the magnetic field.

Continuous energy loss can introduce an upper limit on the step via the variable DEEMAX, an argument to the GSTMED routine. During tracking the value of DEEMAX for the current medium is stored in the common /GCMATE/. DEEMAX is the maximum fraction of kinetic energy which a particle can lose in a step due to continuous ionisation ( ). The limitation on the step size coming from DEEMAX is:

$step\; \le \{DEEMAXdE/dx\}$

Multiple scattering as well can limit the step size, see [PHYS325]. The limitation is given as:

$step\; \le min(\; T$_Bethe, 10  X₀)

where $X$₀ is the radiation length and $T$_Bethe is the maximum step for which the Molière approximation is valid (see [PHYS325]).

Another upper limit on the step size comes from the magnetic field. The bending of the particle trajectory in the magnetic field may be limited by the TMAXFD argument to the GSTMED routine. During tracking the value of TMAXFD for the current medium is stored in the common /GCMATE/.

A lower limitation on the tracking step is not generally imposed. There is, however, a protection against the step being reduced to a very small value by continuous processes. In particular multiple scattering at low energies (< 1 MeV) can impose a very small tracking step with serious consequences on the tracking time. To avoid this, a lower limit on the step imposed by continuous processes is introduced: STMIN. The meaning of STMIN is the following: below 1 MeV the stopping range is usually small. If the stopping range becomes smaller than STMIN, the constraint imposed by the multiple scattering is ignored and the minimum is taken between the reduced stopping range (the distance the particle has to travel to reach its threshold energy) and STMIN itself. In this sense STMIN is no more than a tracking accelerator for stopping particles.

Another limitation on the step size which is imposed by the tracking routines during transport is the STEMAX parameter of GSTMED which sets an absolute upper limit to the size of a step for each tracking medium.