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MATTER

A Coulomb-scattering and energy-absorbing element simulating material in the beam path.
Parallel capable? : yes
Parameter Name Units Type Default Description
L $M$ double 0.0 length
LEFFECTIVE $M$ double 0.0 effective length (used if L=0)
XO $M$ double 0.0 radiation length
ENERGY_DECAY   long 0 If nonzero, then particles will lose energy due to material using a simple exponential model.
ENERGY_STRAGGLE   long 0 Use simple-minded energy straggling model coupled with ENERGY_DECAY=1?
NUCLEAR_BREMSSTRAHLUNG   long 0 Model energy loss to nuclear bremsstrahlung? If enabled, set ENERGY_DECAY=0 to disable simpler model.
ELECTRON_RECOIL   long 0 If non-zero, electron recoil during Coulomb scattering is included (results in energy change).
Z   long 0 Atomic number
A $AMU$ double 0.0 Atomic mass
RHO $KG/M^3$ double 0.0 Density
PLIMIT   double 0.05 Probability cutoff for each slice
GROUP   string NULL Optionally used to assign an element to a group, with a user-defined name. Group names will appear in the parameter output file in the column ElementGroup





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- ${\rm\frac{1}{2}}$ 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 $0.001 X_o$, where $X_o$ is the radiation length. (Note that this is inaccurate for materials thicker than $100 X_o$.) For this regime, the user need only specify the material thickness (L) and the radiation length (XO).

For materials thinner than $0.001 X_o$, 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 $kg/m^3$. (Multiply by $10^3$ to convert $g/cm^3$ to $kg/m^3$.) 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 = \sigma_T n L = \frac{K_1
\pi^3 n L}{K_2^2 + K_2*\pi^2} $, where $n$ is the number density of the material, L is the thickness of the material, $K_1 = (\frac{2 Z
r_e}{\beta^2 \gamma})^2$, and $K_2 = \frac{\alpha^2
Z^\frac{2}{3}}{(\beta\gamma)^2}$, with $r_e$ the classical electron radius and $\alpha$ 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, $\theta$ is computed using the cumulative probability distribution $F(\theta>\theta_o) = \frac{K_2 (\pi^2 - \theta_o^2)}{\pi^2 (K_2 +
\theta_o^2)}$. This can be solved for $\theta_o$, giving $\theta_o = \sqrt{\frac{(1-F)K_2\pi^2}{K_2 + F \pi^2}}$. 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.


next up previous
Next: MAXAMP Up: Element Dictionary Previous: MATR
Robert Soliday 2014-06-26