(bessel)¶

This module provides a radial profile that decays according to a zeroth-order Bessel function of the first kind, from a radius \(r_{\rm min}\) to a radius \(r_{\rm max}\) and is zero outside of that radial interval. More precisely, on the interval \(r_{\rm min}\leq r \leq r_{\rm max}\) the radial profile is

\[f_r(r) = J_0\left( \frac{r-r_{\rm min}}{r_{\rm max}-r_{\rm min}} x_0 \right),\]

and it is identically zero everywhere else. Here, \(J_0(x)\) denotes a zeroth-order Bessel function of the first kind and \(x_0\) is its first zero.

This type of radial profile is expected if runaway electrons are radially transported diffusively in the plasma, with a uniform diffusion coefficient.

Summary of options¶

The following parameters can be set on a bessel radial profile.

Option	Description
`radprof-bessel amax`	Normalized minor radius of the outer edge of the electron beam.
`radprof-bessel amin`	Normalized minor radius of the inner edge of the electron beam.
`radprof-bessel rhomax`	Major radius of the outer edge of the electron beam.
`radprof-bessel rhomin`	Major radius of the inner edge of the electron beam.
`radprof-bessel rmax`	Minor radius of the outer edge of the electron beam.
`radprof-bessel rmin`	Minor radius of the inner edge of the electron beam.

Example configuration¶

This example illustrates how a bessel radial profile can be defined and used together with the (avalanche) distribution function in SOFT2 simulations:

# Global parameter specifying which distribution function to use
distribution_function = analytical_avalanche;

@DistributionFunction analytical_avalanche (avalanche) {
    EHat     = 10;            # Electric field strength (normalized to
                              # the Connor-Hastie critical electric field)
    lnLambda = 17;            # Coulomb logarithm
    Zeff      = 4;             # Effective plasma charge

    # Set the radial profile
    radprof   = ourradprof;
}

@RadialProfile ourradprof (bessel) {
    # Set normalized minor radius
    # These settings creates a beam with radius
    # 2/3 of the device minor radius.
    amin = 0;
    amax = 0.67;
}

All options¶

amax¶

amin¶

rhomax¶

rhomin¶

rmax¶

rmin¶

Default value:	`amin = 0` and `amax = 1`.
Allowed values:	Any radial position that is inside the plasma and on the outboard side.

Specifies the inner and outer edges of the electron beam. The prefix (a*, r*, rho*) specifies whether the edge is given in normalized minor radius, regular minor radius or major radius coordinates.