10.66 MATTER—A Coulomb-scattering and energy-absorbing element simulating material in the beam path.

A Coulomb-scattering and energy-absorbing element simulating material in the beam path.
Parallel capable? : yes
GPU capable? : yes
Back-tracking capable? : no

A Coulomb-scattering and energy-absorbing element simulating material in the beam path.

This element is based on section 3.3.1 of the Handbook of Accelerator Physics and Engineering, specifically, the subsections Single Coulomb scattering of spin- particles, Multiple Coulomb scattering through small angles, and Radiation length. There are two aspects to this element: scattering and energy loss.

Scattering. The multiple Coulomb scattering formula is used whenever the thickness of the material is greater than 0.001X_o, where X_o is the radiation length. (Note that this is inaccurate for materials thicker than 100X_o.) For this regime, the user need only specify the material thickness (L) and the radiation length (XO).

For materials thinner than 0.001X_o, the user must specify additional parameters, namely, the atomic number (Z), atomic mass (A), and mass density (RHO) of the material. Note that the density is given in units of kg∕m³. (Multiply by 10³ to convert g∕cm³ to kg∕m³.) In addition, the simulation parameter PLIMIT may be modified.

To understand this parameter, one must understand how elegant simulates the thin materials. First, it computes the expected number of scattering events per particle, E = σ_T nL = , where n is the number density of the material, L is the thickness of the material, K₁ = ()², and K₂ = , with r_e the classical electron radius and α the fine structure constant. The material is then broken into N slices, where N = E∕P_limit. For each slice, each simulation particle has a probability E∕N of scattering. If scattering occurs, the location within the slice is computed using a uniform distribution over the slice thickness.

For each scatter that occurs, the scattering angle, θ is computed using the cumulative probability distribution F(θ > θ_o) = . This can be solved for θ_o, giving θ_o = . For each scatter, F is chosen from a uniform random distribution on [0,1].

Energy loss. There are two ways to compute energy loss in materials, using a simple minded approach and using the bremsstrahlung cross section. The latter is recommended, but the former is kept for backward compatibility.

• To enable bremsstrahlung simulation, simply set NUCLEAR_BREMSSTRAHLUNG=1. Note that the energy loss is not correlated with the scattering angle, which is not entirely physical but should be reasonable for large numbers of scattering events.
• To use the simplified approach:
  • Set ENERGY_DECAY=1. Energy loss simulation is very simple. The energy loss per unit distance traveled, x, is = -E∕X_o. Hence, in traveling through a material of thickness L, the energy of each particle is transformed from E to Ee^-L∕X_o.
  • Optionally, set ENERGY_STRAGGLE=1. Not recomemnded. Exists only for backward compatibility. This adds variation in the energy lost by particles. The model is very, very crude and not recommended. It assumes that the standard deviation of the energy loss is equal to half the mean energy loss. This is an overestimate, we think, and is provided to give an upper bound on the effects of energy straggling until a real model can be developed. Note one obvious problem with this: if you split a MATTER element of length L into two pieces of length L/2, the total energy loss will not not change, but the induced energy spread will be about 30% lower, due to addition in quadrature.

Slotted absorber. If the WIDTH and SPACING parameters are set to non-zero values, then a slotted absorber is simulated. The number of slots is by default infinite, but can be limited by setting N_SLOTS to a positive value; in this case, the slot array is centered about the transverse coordinate given by the CENTER parameter.

Note that the simulation contains a simplification in that particles cannot leave or enter the material through the side of the slot. I.e., if a particle is inside (outside) the material when it hits the front face of the object, it is assumed to remain inside (outside) until it has passed the object. For long objects, breaking the simulation up into multiple MATTER elements is suggested if a slotted arrangement is being simulated.

One-sided scrapers. One sided scrapers may be modeled using the SCRAPER element. It uses the same material-modeling algorithm as described here.