Particle Source¶

MULASSIS uses the G4GeneralParticleSource (GPS) for specification of the primary incident particle. It is a very powerful tool that allows the user to control of all aspects of the incident particle definition: particle type, energy, position and directional distributions. In this section we will show the GPS is used in the context of MULASSIS only. Please refer to [R23] for a complete set of instructions.

Particle definition¶

The type of incident particle species can be specified with the command /gps/particle, e.g.

PreInit> /gps/particle proton
PreInit>

The user can list the names of potential primary particles with the standard Geant4 command /particle/list

PreInit> /particle/list
/particle/list
                 B+,                 B-,                 B0,                Bc+
                Bc-,                Bs0,                 D+,                 D-
                 D0,                Ds+,                Ds-,         GenericIon
                He3,              J/psi,           N(1440)+,           N(1440)0
           N(1520)+,           N(1520)0,           N(1535)+,           N(1535)0
           N(1650)+,           N(1650)0,           N(1675)+,           N(1675)0
           N(1680)+,           N(1680)0,           N(1700)+,           N(1700)0
           N(1710)+,           N(1710)0,           N(1720)+,           N(1720)0
           N(1900)+,           N(1900)0,           N(1990)+,           N(1990)0
           N(2090)+,           N(2090)0,           N(2190)+,           N(2190)0
           N(2220)+,           N(2220)0,           N(2250)+,           N(2250)0
...
...
...
          xi(1530)-,          xi(1530)0,          xi(1690)-,          xi(1690)0
          xi(1820)-,          xi(1820)0,          xi(1950)-,          xi(1950)0
          xi(2030)-,          xi(2030)0,                xi-,                xi0
              xi_b-,              xi_b0,              xi_c+,              xi_c0

PreInit>

Generic ions can be used as incident particle in MULASSIS, e.g.,

Idle> /gps/particle ion
Idle> /gps/ion 26 56 -2 0

We see here that ions are defined in two steps: first the /gps/particle ion command declares that the incident particle type is “ion”, then the /gps/ion command is used to specify the nature of the ion. The four parameters of the /gps/ion command are:

the atomic number (Z);

the nucleon number (A);

the charge (Q) in units of electron charge;

and the excitation energy (E) in MeV.

The first three quantities for the definition of the ion are integers, the fourth one is a real number.

Energy distribution¶

The GPS provides many built-in options that define the incident particle energy. Some of the commonly used energy distributions are described below, and fall into three basic categories:

Mono-energetic distribution;

Parameterised functions, where the differential energy flux versus energy takes the standard functional form (linear, power-law, exponential, etc.);

User-defined spectrum, where the user provides a series of data points of the integral or differential flux versus energy.

Mono-energetic distribution¶

Mono-energetic particles are defined with the command /gps/energy, e.g.
PreInit> /gps/energy 100 MeV
Two parameters are required: the energy and the units.

Linear distribution¶

The linear distribution takes the form:

\(y = A E + B\)

The energy E is expressed in MeV, and the default values for A and B are 1.0 and 0.0 respectively. The minimum and the maximum energy range must also be specified, e.g.
Idle> /gps/ene/type Lin
Idle> /gps/ene/gradient 1.0
Idle> /gps/ene/intercept 0.0
Idle> /gps/ene/max 100 MeV
Idle> /gps/ene/min 10 MeV
The above commands define the primary paricle energy spectrum follows a linear distribution, gradient as 1 and intercept at 0, between 10 and 100 MeV.

Power-law distribution¶

The power law distribution takes the form:

\(y = A E^{alpha}\)

In this case, the user must define the exponent alpha (the default value is -1.0). The constant A is arbitrarily, i.e., it does not need to be defined since the overall spectrum intensity is defined by the Normalisation Factor applied to the results. The minimum and maximum energy has to be defined as well, e.g.
Idle> /gps/ene/type Pow
Idle> /gps/ene/alpha -2
Idle> /gps/ene/max 100 MeV
Idle> /gps/ene/min 10 MeV
The above commands define the primary paricle follows power-law energy distribution with index of -2, between the 10 to 100 MeV energy range.

Exponential distribution¶

The exponential distribution takes the form:

\(y = A e^{-E/E_0}\)

The exponent \(E_0\) has to be defined (the default value is 1.0 MeV). As in the previous case, the value of the constant A is arbitrarily, i.e., it does not need to be defined since the overall spectrum intensity is defined by the Normalisation Factor applied to the results. Again, the minimum and maximum energy of the spectrum has to be given, e.g.
Idle> /gps/ene/type Exp
Idle> /gps/ene/ezero 5.0
Idle> /gps/ene/max 100 MeV
Idle> /gps/ene/min 10 MeV
The command /gps/ezero takes one double parameter only. The input number is assumed to be in units of MeV and positive for a monotonically decreasing spectrum.

User-defined spectrum¶

In GPS the primary particle spectrum can be defined by the user as a simple point-wise energy distribution. The example below shows such a distribution:
/gps/particle  proton
/gps/ene/type Arb
/gps/hist/type arb
/gps/hist/point   1.000000E-01   8.776200E+03
/gps/hist/point   1.500000E-01   6.437500E+03
/gps/hist/point   2.000000E-01   4.478800E+03
/gps/hist/point   3.000000E-01   2.323000E+03
/gps/hist/point   4.000000E-01   1.331700E+03
/gps/hist/point   5.000000E-01   7.876900E+02
/gps/hist/point   6.000000E-01   5.485200E+02
/gps/hist/point   7.000000E-01   3.942600E+02
/gps/hist/point   1.000000E+00   2.033200E+02
/gps/hist/point   1.500000E+00   8.657400E+01
/gps/hist/point   2.000000E+00   5.196400E+01
/gps/hist/point   3.000000E+00   2.282500E+01
/gps/hist/point   4.000000E+00   1.309500E+01
/gps/hist/point   5.000000E+00   7.961600E+00
/gps/hist/point   6.000000E+00   5.435900E+00
/gps/hist/point   7.000000E+00   3.819900E+00
/gps/hist/point   1.000000E+01   2.107100E+00
/gps/hist/point   1.500000E+01   1.000300E+00
/gps/hist/point   2.000000E+01   6.717800E-01
/gps/hist/point   3.000000E+01   4.573100E-01
/gps/hist/point   4.000000E+01   4.016600E-01
/gps/hist/point   5.000000E+01   3.667800E-01
/gps/hist/point   6.000000E+01   3.441200E-01
/gps/hist/point   7.000000E+01   3.156100E-01
/gps/hist/point   1.000000E+02   2.373700E-01
/gps/hist/point   1.500000E+02   1.415400E-01
/gps/hist/point   2.000000E+02   8.335100E-02
/gps/hist/point   3.000000E+02   3.139600E-02
/gps/hist/point   4.000000E+02   7.424200E-04
/gps/hist/inter  Lin
The /gps/ene/type Arb command declares that the energy distribution will follow a user defined point-wise distribution and the following command /gps/hist/type arb prepares a histogram internally ready to receive the data points. The command /gps/hist/point allows the user to supply the data points in terms of energy and probability. The energy of each data point must be in units of MeV, and the data point must be in ascending order in terms of energy. The minimum and maximum energies are defined by the first and the last entry, respectively. The final command gps/hist/inter Lin means GPS will use linear interpolation to generate the random energy point.

By default, the input user-defined spectra are assumed for be differential in energy. The user can use the command:
/gps/ene/diffspec F
to define the point-wise spectrum as integral in energy.

Positional distribution¶

No user input is required for defining the positional distribution of the incident particle in MULASSIS. The incident particles all have the same incident position on the outer surface of layer 1. This is equivalent to have a uniform distribution over the whole incident surface, because of the symmetry in the geometry setup.

Angular distribution¶

The angular distribution in MULASSIS/GPS is the directional distribution of the incident particles in respect of the incident surface. For a isotropic radiation, which most space radiation sources can be considered as, the incident particle angular distribution is cosine-law, as the effective area is reduced by the cosine term of the incident angle hence the term “cosine-law”. The cosine-law distribution is true whether the incident surface is flat, such as slab geometry, or curved, like the spherical case. For both slab and spherical geometry, the maximum incident angle is \(\pi/2\).

The command /gps/ang/type selects the angular distribution. The options are:

iso: isotropic distribution. Used for simulating radiation emitted isotropically from a point, such as a radioactive source.

cos: cosine-law distribution. Used to simulate most space radiation incidence.

planar: directional parallel beam.

beam1d: 1d (axis symmetric) accelerator beam.

beam2d: 2d accelerator beam.

user: user-defined distribution as functions of zenith and azimuth.

For iso and cos distribution, the user can further specify the minimum and maximum in zenith and azimuth angles of the distribution.
Idle> /gps/ang/type cos
Idle> /gps/ang/mintheta 0 deg
Idle> /gps/ang/maxtheta 90 deg
The example above shows the selection of cosine-law distribution with the incident (zenith) angles restricted to 0-90 degrees.

Note

An angle of 0 indicates a direction normal to the geometry surface and propagating into the first layer.

Mulassis/ml-v02-00/r342