TabulatedMaterial
A metatype exposing the tabulations of a material.
Attributes
A TabulatedMaterial is a special instance of a Material for which physical properties relevant for the transport have been pre-computed (tabulated), e.g. the energy loss of the projectile. In addition to the base attributes of a Material it has the following extra attributes:
Name | Type | Description |
---|---|---|
name | string |
Name of the material used e.g. when referring to from a Medium. |
physics | Readonly | The Physics instance this TabulatedMaterial belongs to. |
table | Readonly | Material tabulations (see below). |
composite | boolean |
Flag indicating if the instance is a composite material (true ) or a base one (false ). |
materials | CompositeMaterials or nil |
For composite materials the CompositeMaterials table contains the mass fractions of the base materials indexed by name. |
Note
All attributes are Readonly, the base Material ones as well as the extra tabulated ones. There is one exception though. For composite materials the mass fractions of the base materials can be modified (see CompositeMaterials).
table
The table attribute contains the physics tabulations organized in three
sub-tables corresponding to the three energy loss modes: 'csda'
, 'detailed'
and 'hybrid'
. The available tabulations are summarized below, where it must be
understood that mode stands for one of csda, detailed or hybrid. E.g.
table.csda.energy_loss
returns the tabulation of the continuous energy loss
for the CSDA mode. More detailed explanations of the various physical quantities
are also provided hereafter.
Name | Type | Description |
---|---|---|
(mode).energy_loss | Readonly | Continuous Energy Loss (CEL) per unit grammage, \frac{dE}{dX}, in \text{GeV} \cdot \text{m}^2 \cdot \text{kg}^{-1} (see below). |
(mode).kinetic_energy | Readonly | Tabulated projectile kinetic energies, E, in \text{GeV}. |
(mode).grammage | Readonly | Total grammage for CEL, X, in \text{kg} \cdot \text{m}^{-2} (see below). |
(mode).proper_time | Readonly | Total proper time for CEL, \tau, assuming a uniform density, in \text{kg} \cdot \text{m}^{-2} (see below). |
(mode).cross_section | Readonly | Macroscopic cross-section for DELs, \Sigma, in m2/kg. Available only for detailed and hybrid modes (see below). |
Note
The detailed and hybrid mode use the same tabulations. For convenience both notations can be used. Yet, they actualy refer to the same tables.
energy_loss
The simulation of physics interactions is split into two components: Discrete Energy Losses (DELs) and Continuous Energy Losses (CELs), see Niess et al., 2017 for more details. The splitting is done using a relative cutoff \alpha = 5\%, following Sokalski et al., 2001. The continuous energy loss per unit of grammage, \frac{dE}{dX}, is given as:
with E the projectile kinetic energy, \frac{\partial \sigma}{\partial q} the total Differential Cross Section (DCS), \mathcal{N}_A Avogadro number and A the molar mass of the target material.
cross_section
The macroscopic cross-section for DELs, \Sigma, is defined per unit mass as:
The macroscopic cross-section is related to the interaction length, \lambda, as:
with \rho the medium density.
grammage
In the absence of DEL, the total grammage path length of the projectile is obtained by integrating its energy loss up to its initial energy, as:
The previous expression can also been used in order to compute the grammage variation, \Delta X, between two DELs as:
where E_0 if the energy after the first DEL and E_1 the energy before the second DEL occurs.
proper_time
For a uniform density and in the absence of DEL, the total proper time of the projectile is obtained by integration similarly to the grammage path length. Per unit mass, it writes:
In order to get the proper time in unit of time one needs to divide the previous expression by \rho c, i.e. the constant medium density, \rho, times the vacuum speed of light, c.
See also
TabulatedMaterial.cross_section
Interpolation of the DELs macroscopic cross section, \Sigma, as function of the projectile kinetic energy, E. See above for more details.
Synopsis
TabulatedMaterial:cross_section(energy)
Arguments
Name | Type | Description |
---|---|---|
energy | number |
Kinetic energy of the projectile, in GeV. |
Returns
Type | Description |
---|---|
number |
The macroscopic cross-section per unit mass, in \text{m}^2 \cdot \text{kg}^{-1} (see above). |
See also
energy_loss, grammage, kinetic_energy, magnetic_rotation, proper_time, scattering_length.
TabulatedMaterial.energy_loss
Interpolation of the Continuous Energy Loss (CEL), \frac{dE}{dX}, as function of the projectile kinetic energy, E. See above for more details.
Synopsis
TabulatedMaterial:energy_loss(energy, (mode))
Arguments
Name | Type | Description |
---|---|---|
energy | number |
Kinetic energy of the projectile, in GeV. |
mode | string |
Energy loss mode, one of 'csda' , 'detailed' or 'hybrid' . Defaults to 'csda' . |
Returns
Type | Description |
---|---|
number |
The continuous energy loss per unit grammage, in \text{GeV} \cdot \text{m}^2 \cdot \text{kg}^{-1} (see above). |
See also
cross_section, grammage, kinetic_energy, magnetic_rotation, proper_time, scattering_length.
TabulatedMaterial.grammage
Interpolation of the total grammage path length, X, as function of the projectile initial kinetic energy, E. See above for more details.
Synopsis
TabulatedMaterial:grammage(energy, (mode))
Arguments
Name | Type | Description |
---|---|---|
energy | number |
Initial kinetic energy of the projectile, in GeV. |
mode | string |
Energy loss mode, one of 'csda' , 'detailed' or 'hybrid' . Defaults to 'csda' . |
Returns
Type | Description |
---|---|
number |
The total grammage path length, in \text{kg} \cdot \text{m}^{-2} (see above). |
See also
cross_section, energy_loss, kinetic_energy, magnetic_rotation, proper_time, scattering_length.
TabulatedMaterial.kinetic_energy
Interpolation of the projectile initial kinetic energy, E, as function of its total grammage path length, X. See above for more details.
Synopsis
TabulatedMaterial:kinetic_energy(grammage, (mode))
Arguments
Name | Type | Description |
---|---|---|
grammage | number |
Total grammage path length, in \text{kg} \cdot \text{m}^{-2}. |
mode | string |
Energy loss mode, one of 'csda' , 'detailed' or 'hybrid' . Defaults to 'csda' . |
Returns
Type | Description |
---|---|
number |
The projectile initial kinetic energy, in GeV (see above). |
See also
cross_section, energy_loss, grammage, magnetic_rotation, proper_time, scattering_length.
TabulatedMaterial.magnetic_rotation
Interpolation of the total rotation angle of the projectile direction, \Theta, due to a constant magnetic field, B, as function of its initial kinetic energy, E. For a uniform magnetic field and medium density, \rho, if no DELs occur the rotation angle is related to the total proper time, \tau, as:
with q (m) the projectile electric charge (rest mass). See above for more details on how the proper time is computed.
Synopsis
TabulatedMaterial:magnetic_rotation(energy)
Arguments
Name | Type | Description |
---|---|---|
energy | number |
Initial kinetic energy of the projectile, in GeV. |
Note
The magnetic rotation is only available for the CSDA mode.
Returns
Type | Description |
---|---|
number |
Total rotation angle, in \text{rad} \cdot \text{kg} \cdot \text{m}^{-3} \cdot \text{T}^{-1}. Multiply by the constant magnetic field, B, and divide by the uniform medium density, \rho, in order to get the angle in radians. |
See also
cross_section, energy_loss, grammage, kinetic_energy, proper_time, scattering_length.
TabulatedMaterial.proper_time
Interpolation of the total proper time, \tau, as function of the projectile initial kinetic energy, E. See above for more details.
Synopsis
TabulatedMaterial:proper_time(energy, (mode))
Arguments
Name | Type | Description |
---|---|---|
energy | number |
Initial kinetic energy of the projectile, in GeV. |
mode | string |
Energy loss mode, one of 'csda' , 'detailed' or 'hybrid' . Defaults to 'csda' . |
Returns
Type | Description |
---|---|
number |
The total proper time, in \text{kg} \cdot \text{m}^{-2} (see above). |
See also
cross_section, energy_loss, grammage, kinetic_energy, magnetic_rotation, scattering_length.
TabulatedMaterial.scattering_length
Compute the first transport path length for Coulomb Multiple Scattering (MS), \lambda, as function of the projectile kinetic energy, E. The first path length is related to the standard deviation of the MS angle as:
with X the grammage path length. See Fernández-Varea et al., 1993, for more details.
Synopsis
TabulatedMaterial:scattering_length(energy)
Arguments
Name | Type | Description |
---|---|---|
energy | number |
Kinetic energy of the projectile, in GeV. |
Returns
Type | Description |
---|---|
number |
The Coulomb MS first path length, in \text{kg} \cdot \text{m}^{-2}. |
See also
cross_section, energy_loss, grammage, kinetic_energy, magnetic_rotation, proper_time.