(numerical)¶

This module provides a way for the user to specify an arbitrary phase space distribution function \(f(r, p, \xi)\).

Summary of options¶

Option	Description
`numerical flippitchsign`	If true, flips the sign of the particle pitch.
`numerical interptype`	Interpolation method to use.
`numerical logarithmize`	Whether or not to interpolate in the logarithm of the distribution function.
`numerical name`	Name of file containing numerical distribution function.

Example configuration¶

The following example configures a SOFT numerical distribution function:

@DistributionFunction ourDistributionFunction (numerical) {
    name = "/path/to/distribution.mat";
}

File layout¶

The format for numerical distribution functions in SOFT is such that a set of momentum-space distribution functions are specified at a number of radii. The file therefore contains two levels – a top-level where the radial grid is specified along with the number of radial points nr, and nr groups (HDF5) or structs (MAT), each containing the momentum-space distribution function corresponding to a particular point on the radial grid.

The following variables must/may be present in the top-level of the distribution function file:

Variable	Required	Description
`r`	Yes	(Dimensionful) minor radius (one-dimensional).
`type`	No	Type of distribution function (must be `distribution/soft`)

Additionally, on the top-level, nr (number of points in r) number of groups/structs named rX must be present, each containing the variables:

Variable	Required	Description
`f`	Yes	Distribution function \(f(r, p, \xi)\) of size \(n_\xi \times n_p\).
`p`	Yes	Momentum grid vector (one-dimensional).
`xi`	Yes	Pitch (cosine of pitch angle) grid vector (one-dimensional).

Note

In f, the “inner” dimension (i.e. last index in C/C++/Python, first index in Matlab/Fortran) must be p. In memory, the layout of the array should be:

f(p0,xi0)  f(p1,xi0)  f(p2,xi0) ... f(pN,xi0)  f(p0,xi1)  f(p1,xi1) ...

All options¶

flippitchsign¶

Default value:	`no`
Allowed values:	`yes` or `no`

If yes, transforms \(f(p,\xi)\to f(p,-\xi)\). This is useful in case the distribution function is defined in an inconsistent way (i.e. if a positive parallel electric field accelerates particles in the anti-parallel direction).

name¶

Default value:	Nothing
Allowed values:	Any valid file name

Name of the file containing the distribution function.

interptype¶

Default value:	`cubic`
Allowed values:	`cubic` or `linear`

SOFT interpolates in the given distribution function to evaluate it at arbitrary points on the phase space grid. A linear interpolation scheme is always used to interpolate in the radial coordinate, but interpolation in the momentum coordinates (\(p\) and \(\xi\)) can either be done using bi-linear or bi-cubic splines.

logarithmize¶

Default value:	`no`
Allowed values:	`yes` or `no`

If yes, interpolates in the logarithm of the distribution function instead of in the distribution function directly. This can aid in fitting sharply decaying ditsribution functions.