KAHIBARO
11.3. Angular Distributions
Table of Contents
Directional sources
Angular distributions in the General Particle Source (GPS) control how particles are emitted in direction. For directional sources you want most or all particles to travel along a specific direction, with only a small angular spread if desired.
The simplest directional GPS source is a mono-directional pencil beam. In a macro you specify the particle direction with the GPS angle commands. The most direct way is to set a direction vector:
/gps/ang/type direction
/gps/ang/direction 0 0 1Here the direction vector is along the positive $z$ axis. Every primary particle will be fired parallel to this axis. The vector components follow the usual Geant4 convention, $x, y, z$, and the vector is normalized internally. Any nonzero vector is accepted, but it is good practice to give a unit vector to avoid confusion.
You can also define the direction using angular coordinates, which is useful when you think in terms of polar and azimuthal angles. For example:
/gps/ang/type iso
/gps/ang/maxtheta 5 deg
/gps/ang/mintheta 0 deg
/gps/ang/maxphi 360 deg
/gps/ang/minphi 0 deg
/gps/ang/rot1 1 0 0
/gps/ang/rot2 0 1 0
With this configuration you get a cone around the reference axis. The GPS uses two perpendicular vectors, given by /gps/ang/rot1 and /gps/ang/rot2, to define a local coordinate system. Within this system $\theta$ is the angle away from the reference axis and $\phi$ is the angle around that axis.
A typical narrow beam with small angular divergence can be defined using a cone:
/gps/ang/type cos
/gps/ang/mintheta 0 deg
/gps/ang/maxtheta 2 deg
/gps/ang/minphi 0 deg
/gps/ang/maxphi 360 deg
The cos type gives a $\cos(\theta)$ distribution inside the given angular range, which concentrates more particles close to the central direction. If you instead use:
/gps/ang/type beam2dyou create a beam with a specified divergence in one or two transverse directions. This is useful when you want a realistic beam spot that is narrow in one plane but wider in the other.
For strongly directional sources you often choose small values of maxtheta so that the maximum deflection from the central axis is only a few degrees or less. If maxtheta approaches $90^\circ$ you move away from a narrow beam into a more spread out source, which may or may not match your physical setup.
When selecting a directional distribution you should think about the physical beam you want to model. A pencil beam for testing detector geometry might be perfectly collimated with a single direction vector. A realistic accelerator beam or collimated gamma source usually has a finite angular spread that you can approximate with a cone or cos-type distribution.
For a strictly uni-directional GPS source use
/gps/ang/type direction and set exactly one direction vector, for example /gps/ang/direction 0 0 1.
For a finite angular spread around this direction use a cone with mintheta at $0$ and a small maxtheta, combined with a suited angular type such as cos.
Isotropic sources
Isotropic sources emit particles uniformly in all directions. In GPS you achieve this by telling the angular generator to sample directions uniformly over the unit sphere or over a spherical segment.
A fully isotropic point source is defined using:
/gps/ang/type iso
/gps/ang/mintheta 0 deg
/gps/ang/maxtheta 180 deg
/gps/ang/minphi 0 deg
/gps/ang/maxphi 360 degThis configuration makes the direction vector equally likely to point into any solid angle in $4\pi$. The GPS takes care of sampling the angles with the correct probability density. Internally the polar angle distribution is proportional to $\sin\theta$, so the density is uniform over the sphere rather than uniform in $\theta$.
You can also create a half-isotropic source, for example emitting only into a hemisphere. If you place a source on a boundary and want all particles to go into one side of the geometry, you can set:
/gps/ang/type iso
/gps/ang/mintheta 0 deg
/gps/ang/maxtheta 90 deg
/gps/ang/minphi 0 deg
/gps/ang/maxphi 360 deg
This emits particles inside a cone that covers a hemisphere. By changing the mintheta and maxtheta values you can restrict the isotropic emission to a spherical cap. By restricting minphi and maxphi you can further limit the emission to a sector, for example only into one quadrant.
For isotropic emission around an arbitrary axis you still use iso but define the local coordinate system with /gps/ang/rot1 and /gps/ang/rot2. These commands choose the reference orientation of the spherical coordinates. Although a fully isotropic distribution is independent of the axis, a restricted angular range, for example a hemisphere, will depend on which direction you select as the polar axis.
Isotropic GPS sources are very useful for simulating uncollimated radioactive sources, cosmic background approximations, or diffuse radiation fields when you are not interested in a specific incoming direction. They are also practical when you want to estimate detector acceptance averaged over all possible orientations.
A fully isotropic GPS source over $4\pi$ solid angle is obtained with
/gps/ang/type iso and the ranges
mintheta = 0 deg, maxtheta = 180 deg, minphi = 0 deg, maxphi = 360 deg.
Any restriction on these four angles changes the source from fully isotropic to partially isotropic inside the chosen angular region.
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