10.65 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

Parameter Name Units Type Default


L M double0.0


LEFFECTIVE M double0.0

effective length (used if L=0)

XO M double0.0

radiation length


If nonzero, then particles will lose energy due to material using a simple exponential model.


Use simple-minded energy straggling model coupled with ENERGY_DECAY=1?


Model energy loss to nuclear bremsstrahlung? If enabled, set ENERGY_DECAY=0 to disable simpler model.


If non-zero, electron recoil during Coulomb scattering is included (results in energy change).

Z long 0

Atomic number

A AMU double0.0

Atomic mass

RHO KG∕M3 double0.0



Pressure. Used with temperature and atomic mass to compute density for ideal gas.


Temperature. Used with pressure and atomic mass to compute density for ideal gas.


Atoms per gas molecule.

PLIMIT double0.05

Probability cutoff for each slice

WIDTH M double0.0

Full width of slots. If 0, no slots are present.

SPACING M double0.0

Center-to-center spacing of slots. If 0, no slots are present.

MATTER continued

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

Parameter NameUnitsType Default


TILT RADdouble0.0

Tilt of slot array about the longitudinal axis.

CENTER M double0.0

Position of center of slot array in rotated frame.

N_SLOTS long 0

Number of empty slots in material. If <=0, an infinite array is assumed.

START_PASS long -1

If non-negative, pass on which to start interaction with beam.

END_PASS long -1

If non-negative, pass on which to end interaction with beam.


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-12 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 0.001Xo, where Xo is the radiation length. (Note that this is inaccurate for materials thicker than 100Xo.) For this regime, the user need only specify the material thickness (L) and the radiation length (XO).

For materials thinner than 0.001Xo, 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 = σT nL =  K π3nL
K221+K2-*π2-, where n is the number density of the material, L is the thickness of the material, K1 = (2Zre
 β2γ)2, and K2 = α2Z23-
(βγ)2, with re the classical electron radius and α the fine structure constant. The material is then broken into N slices, where N = E∕Plimit. 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 > θo) = K (π2-θ2)
π22(K2+θo2o)-. This can be solved for θo, giving θo = ∘ (1-F)K-π2
  -K2+F-2π2-. 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.

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.