@Radiation¶

This tool calculates various radiation quantities, including radiation images, spectra and Green’s functions. It is the tool to use for studying bremsstrahlung and synchrotron radiation.

The basic purpose of the @Radiation tool is to evaluate various forms of the radiation diagnostic integral [2].

(1)¶\[I = \int \Theta\left( \frac{\boldsymbol{r}}{r} \right) \frac{\boldsymbol{r}\cdot\hat{\boldsymbol{n}}}{r^3} \frac{\mathrm{d}I(\boldsymbol{x},\boldsymbol{p},\boldsymbol{r})}{\mathrm{d}\Omega} f(\boldsymbol{x},\boldsymbol{p})\,\mathrm{d}\boldsymbol{p}\,\mathrm{d} V\,\mathrm{d} A.\]

where \(I\) denotes a general radiation quantity (e.g. radiation power, spectral power, etc.), \(\Theta\) is the field-of-view step function, \(\boldsymbol{r}\) is a vector from the particle to the detector, \(\hat{\boldsymbol{n}}\) is the detector surface normal vector, \(\mathrm{d}I/\mathrm{d}\Omega\) is the angular distribution of radiation and \(f(\boldsymbol{x},\boldsymbol{p})\) is the distribution function. The integral is taken over all of momentum space (indicated by the differential \(\mathrm{d}\boldsymbol{p}\)), real space (indicated by the volume element \(\mathrm{d}V\)), and the detector surface (indicated by \(\mathrm{d} A\)).

To simplify the computation, SOFT evaluates the above integral in guiding-center coordinates. Using these coordinates, the radiation diagnostic integral (1) can be written

\[I = \int\Theta\left( \frac{\boldsymbol{r}}{r} \right) \frac{\boldsymbol{r}\cdot\hat{\boldsymbol{n}}}{r^3} \frac{\mathrm{d}I(\boldsymbol{X},\boldsymbol{p},\boldsymbol{r})}{\mathrm{d}\Omega} f(\rho,p_\parallel,p_\perp)\,J\,\underbrace{\mathrm{d}p_\parallel\mathrm{d}p_\perp\mathrm{d}\zeta}_{\mathrm{d}\boldsymbol{p}} \,\underbrace{\mathrm{d}\rho\mathrm{d}\tau\mathrm{d}\phi}_{\mathrm{d}\boldsymbol{X}}\,\mathrm{d} A.\]

where now \(\boldsymbol{X}\) denotes the guiding-center position, \(p_\parallel\) and \(p_\perp\) are the particle momenta in the directions parallel and perpendicular respectively to the magnetic field, \(\zeta\) is the gyro angle, \(\rho\) is the maximum major radius visited by a guiding-center along its orbit, \(\tau\) is the time along the orbit of the guiding-center and \(\phi\) is the toroidal angle.

[1]	Hoppe et al., 2018, “SOFT: a synthetic synchrotron diagnostic for runaway electrons”. Nuclear Fusion 58 (2), 026032 doi:10.1088/1741-4326/aa9abb.

[2]	Hoppe, 2019, “Simulation and analysis of radiation from runaway electrons”. Licentiate thesis Available online.

Summary of options¶

Option	Description
`@Radiation detector`	Specifies which detector configuration to use
`@Radiation ignore_trapped`	Discards all trapped orbits
`@Radiation model`	Specifies which radiation model to use
`@Radiation ntoroidal`	Toroidal resolution parameter
`@Radiation output`	Specifies which output module(s) to use
`@Radiation torthreshold`	Parameter for Toroidal optimization
`@Radiation torquad`	Quadrature rule to use when evaluating toroidal integral
`@Radiation wall_opacity`	Specifies the wall “opacity”

Example configuration¶

The @Radiation is merely the parent of a set modules which together produce the desired simulation output. As such, we must specify both the detector, the radiation model and output type. An example configuration of a @Radiation module, along with its required sub-modules, is:

@Radiation rad {
    detector     = det;
    model        = cone;
    ntoroidal    = 7500;
    output       = image topview;
}

@Detector det {
    aperture     = 0.006;
    direction    = 0, 1, 0;
    position     = 0, 1.7, 0;
    vision_angle = 1.25 fov;
    spectrum     = 440e-9, 790e-9, 40;
}

@RadiationModel cone (cone) {
    emission = synchrotron;
}

@RadiationOutput image (image) {
    pixels = 600;
    output = "myimage.mat";
}

Available sub-modules¶

There are three types of sub-modules that must be configured for the @Radiation module. In addition to a @Detector, one radiation model must specified as well as at least one output module.

Output sub-modules¶

Radiation output modules are specified with the block type @RadiationOutput. The secondary type of the block (in parentheses after the block name) determines which type of output the block configures. The available secondary types of @RadiationOutput are

Module name	Output description
(green)	Green’s/weight functions
(image)	Camera images
(space3d)	3D maps of radiation
(spectrum)	Radiation spectra
(topview)	Tokamak topviews of radiation

Radiation model sub-modules¶

Radiation model modules are specified with the block type @RadiationModel. The secondary type of the block (in parentheses after the block name) determines which type of model the block configures. The available secondary types of @RadiationModel are

Module name	Model description
(angdist)	Full angular (and spectral) distribution of radiation
(cone)	Special model for approximating directed radiation
(isotropic)	Special model for perfectly isotropic radiation

Toroidal optimization¶

Options¶

detector¶

Default value:	Nothing
Allowed values:	Name of any @Detector configuration block

Specifies the name of the configuration block to use for setting the properties of the detector.

ignore_trapped¶

Default value:	No (include trapped orbits)
Allowed values:	`yes` and `no`

Since trapped runaway electrons are rare, calculations can sometimes be sped up, and numerical issues avoided, by discarding trapped orbits. In particular, SOFT has problems calculating the guiding-center Jacobian numerically for trapped orbits, and so including trapped orbits can yield unphysical results if one is not careful.

model¶

Default value:	Nothing
Allowed values:	Name of any radiation model configuration block

Specifies the name of the configuration block to use for setting the radiation model to use. The radiation model basically specifies how the angular distribution of radiation is handled. SOFT can take the full angular distribution of radiation into account, but usually, for synchrotron radiation, the approximative model known as the “cone model” is often used instead. A list of available radiation models can be found above, under the section Radiation model sub-modules.

ntoroidal¶

Default value:	`3500`
Allowed values:	Any positive integer

Number of toroidal sections to divide the tokamak into. This is the resolution parameter for the toroidal integral in the radiation diagnostic integral evaluated by the @Radiation tool.

output¶

Default value:	Nothing
Allowed values:	List of names of radiation output module configuration blocks

List of names of configuration blocks setting the properties of the output modules to use.

The @Radiation tool only facilitates the computation of various radiation quantities (such as images and spectra). The actual evaluation of these quantities, as well as subsequent generation of output files, are handled by the corresponding “radiation output” modules. A full list of available radiation output modules can be found above under the section Output sub-modules.

torthreshold¶

Default value:	`0`
Allowed values:	Any real value between or equal to `0` and `1`

Threshold for neglecting the integrand when using the maximize quadrature to evaluate the toroidal integral. The integration stops as soon as the value of the integrand is a fraction torthreshold of the maximum integrand value seen so far.

For the cone model, this parameter can safely be set to 0. When used together with the models that take the full angular distribution into account, this parameter should be set to a value greater than 0 (yet less than 1).

torquad¶

Default value:	`maximize`
Allowed values:	`maximize`, `trapz`

Determines which quadrature rule to use for evaluating the toroidal integral. The trapz quadrature is a simple trapezoidal rule. The maximize rule is based on the trapezoidal rule, but uses an optimization algorithm to determine which parts of space that will contribute with radiation. The maximize quadrature is often between a factor 25-100 faster than the regular trapezoidal rule.

wall_opacity¶

Default value:	`semi`
Allowed values:	`opaque`, `semi`, `transparent`

Sets the “opacity” level of the wall. If opaque, all walls are fully accounted for, and radiation is not allowed to pass the wall. Conversely, when set to transparent, walls are not accounted for, and the tokamak appears to be transparent, effectively allowing radiation to pass through walls unaffected.

The setting semi is a middle-ground, where only wall segments located at a radius less than the tokamak major radius are accounted for. This means that the tokamak central column is correctly accounted for, while the camera is allowed to be located outside the tokamak wall without radiation being blocked from it. This setting is a way of emulating diagnostic ports in which the radiation diagnostic may be somewhat retracted behind the regular tokamak wall boundary level.