@MagneticField¶

The magnetic field module defines a magnetic field and domain (walls) to use in the simulation. For setting up a quick simulation, the analytical magnetic field can be used to generate a magnetic field with circular flux surfaces. For more advanced applications, SOFT2 is able to take numeric 2D magnetic fields as input.

The type of the magnetic field to load is specified as a secondary type of the block (i.e. in parenthesis after the block name). At the moment, two different types of magnetic fields are available: analytical and numeric.

More details about the magnetic field in SOFT2 can be found on the page Magnetic fields.

Relating safety factor and current profile¶

The safety factor type current has been derived from the current density

\[\boldsymbol{j} = \sigma_I\hat{\boldsymbol{\varphi}}j(r) = \sigma_I\hat{\boldsymbol{\varphi}} j_0\left[ 1 - \left(\frac{r}{r_0}\right)^{q_{a2}} \right],\]

where \(j_0\) is the central current density and \(r_0\) is the plasma radius (see Magnetic fields for details about the notation). The corresponding safety factor is

\[q(r) = \frac{q_0}{1 - \frac{2}{n+2}\left( \frac{r}{r_0} \right)^{q_{a2}}}.\]

From this, the plasma current \(I\) can be related to the central safety factor \(q_0\equiv q(0)\):

\[I = \frac{2\pi B_0}{\mu_0 q_0 R_{\rm m}} r_0^2 \left( 1 - \frac{2}{n+2} \right),\]

or conversely

\[q_0 = \frac{2\pi B_0}{\mu_0 R_{\rm m} I} r_0^2 \left( 1 - \frac{2}{n+2} \right),\]

where \(\mu_0\approx 4\pi\times 10^{-7}\,\text{H/m}\) is the vacuum permeability. With \(B_0\), \(\mu_0\), \(R_{\rm m}\) and \(r_0\) in SI units, and the total plasma current in mega-ampere, the central safety factor can be computed from

\[q_0 = \frac{5n}{n+2} \frac{B_0 r_0^2}{R_{\rm m} I}.\]

Summary of options¶

Option	Type	Description
`analytical B0`	analytical	Magnetic field strength (on-axis) of analytical magnetic field
`analytical Rm`	analytical	Major radius of analytical magnetic field
`analytical zm`	analytical	Vertical position of magnetic axis
`analytical rminor`	analytical	Minor radius of analytical magnetic field
`analytical sigmaB`	analytical	Toroidal field direction of analytical magnetic field
`analytical sigmaI`	analytical	Current direction of analytical magnetic field
`analytical qtype`	analytical	Safety factor type: `current`, `constant`, `linear`, `qudratic` or `exponential`
`analytical qa1`	analytical	First safety factor parameter of analytical magnetic field
`analytical qa2`	analytical	Second safety factor parameter of analytical magnetic field
`numeric filename`	numeric	Name of file containing numeric magnetic field
`numeric filetype`	numeric	Override filetype of file containing numeric magnetic field

Example configuration¶

The following defines an analytical magnetic field, similar to Alcator C-Mod:

magnetic_field = analytical-field;

@MagneticField analytical-field (analytical) {
    B0     = 5.0;
    Rm     = 0.68;
    rminor = 0.22;
    qtype  = quadratic;
    qa1    = 3.0;
    qa2    = 1.0;
}

An example of a numeric magnetic field:

magnetic_field = numeric-field;

@MagneticField numeric-field (numeric) {
    filename = "/path/to/magnetic-field.mat";
    # SOFT will automatically identify the
    # above file as a 'MAT' file, due to its
    # '.mat' filename extension.
}

Common settings¶

analytical¶

B0¶

Default value:	None
Allowed values:	Any positive real number

The magnetic field strength on-axis (in Tesla).

Rm¶

Default value:	None
Allowed values:	Any positive real number (greater than `analytical rminor`)

The tokamak major radius (in meters).

zm¶

Default value:	`0`
Allowed values:	Any real number

The vertical position of the magnetic axis.

rminor¶

Default value:	None
Allowed values:	Any positive real number (less than `analytical Rm`)

The tokamak minor radius (in meters).

sigmaB¶

sigmaI¶

Default value:	`cw`
Allowed values:	`cw` / `-`, or `ccw` / `+`

Sign of the toroidal field component (sigmaB) and plasma current (sigmaI). The value cw corresponds to the toroidal component being oriented in the clock-wise direction, when seen from above the tokamak, while ccw corresponds to the toroidal component being oriented in the counter clock-wise direction, when seen from above.

Instead of specifying the direction, the sign may be given directly as either - (clock-wise) or + (counter clock-wise).

qa1¶

qa2¶

Default value:	1.0
Allowed values:	Any real number

Constants used to define the safety factor. See analytical qtype for details about how exactly they affect the different safety factor.

qtype¶

Default value:	None
Allowed values:	`constant`, `exponential`, `linear`, `quadratic`

Specifies the radial dependence of the safety factor. The functional forms for the various options are given in terms of the normalized minor radius \(a\) (normalized to the value of rminor) in the table below. The constants \(q_{a1}\) and \(q_{a2}\) are specified using the analytical qa1 and analytical qa2 options.

qtype	Functional form
current	\(q(a) = q_{a1}/\left( 1-\frac{2}{n+2}a^{q_{a2}} \right)\)
constant	\(q(a) = q_{a1}\)
linear	\(q(a) = q_{a1} a + q_{a2}\)
quadratic	\(q(a) = q_{a1} a^2 + q_{a2}\)
exponential	\(q(a) = e^{q_{a1}} + q_{a2}\)

numeric¶

filename¶

Default value:	None
Allowed values:	String

Specifies the name of the file that contains the magnetic field to load.

filetype¶

Default value:	Auto-determine filetype based on filename
Allowed values:	`h5`, `hdf5`, `mat`, `out`, `sdt`

Overrides the filetype of the given file. Usually SOFT tries to determine which filetype a given file is of based on its filename extension. By explicitly setting this option, this check is overriden allows you to use non-standard filename extensions for the input file.