Numerical methods in the simulation of gas-based detectors

Abstract

aftermath of the second world war to solve numerical problems in atomic physics and to calculate ballistic trajectories. Computers are ubiquitous in particle physics laboratoria since the 1960s. CERN for instance installed its first computer in 1958, a vacuum-tube Ferranti Mercury which was replaced in 1960 by an IBM 709 [1]. In the years 1962-1967, Johannes Ranft used these computers to develop the first versions of Fluka to simulate hadron cascades. M. Veltman, during a stay at SLAC in 1963-1964, wrote the first versions of the symbolic manipulation program Schoonschip [2, 3], which was to prove useful in 1971. A first version of the Geant detector simulation program came soon after (1974, CERN), followed by the MNCP neutrons, γ and electron program (1977, LANL), and the EGS electron and γ shower simulation (1978, SLAC). Calculations for gas-based detectors have 3 main components: ionisation, field calculation and charged particle transport. In the following, we sketch the development of some computer programs that simulate each of these. No attempt is made to be complete.

Electron transparency of a Micromegas mesh

“…The flux argument assumes that electrons actually follow the electric field, and thus neglects diffusion. To assess the impact of diffusion we have also calculated the transparency using microscopic electron tracking [5,6]. This technique tries to reproduce electron transport at the molecular level.…”

“…These measurements are sensitive to electron transport at the micron-scale, and thus test the Magboltz-based [4] microscopic tracking algorithms in Garfield [5,6] as well as the field calculation methods.…”

New approach to 3D electrostatic calculations for micro-pattern detectors

“…Most of the existing electrostatic codes are based on a finite differences or finite element methods [12, 13] which find a potential values on a grid of points in volume respecting the given boundary conditions on electrodes. Besides the fact that such solutions are not solutions to the Maxwell equations [14] there is another problem that the grid of points has to be terminated artificially somewhere in space [15], introducing an arbitrary parameter into calculations. Moreover, an impractically fine density of grid points is required in order to achieve accurate values of the electric field around corners and edges of electrodes.…”

Simulations of electron avalanches in an ultra-low-background proportional counter

“…Enhancements were also made to the script to include the midpoints of the second-order tetrahedra that could be used for more accurate interpolations in G++. As noted by Veenhof [20], FEM programs have drawbacks associated with solving non-linear fields. In particular, the use of tetrahedral elements will most likely lead to a discontinuous electric field on tetrahedra boundaries.…”