(connorhastie)¶

When the runaway generation is dominated by the primary (or Dreicer) mechanism, the distribution function is predicted to take the form given by Connor & Hastie [1]:

\[f(p, \xi) = \frac{1}{p\xi}\exp\left[ -\frac{\hat{E}+1}{2(Z_{\rm eff}+1)}\frac{1-\xi^2}{\xi}p \right],\]

where \(p\) is the electron momentum, \(\xi = \cos\theta_{\rm p}\) the electron pitch with respect to the magnetic field, \(\hat{E}\) the electric field strength normalized to the threshold electric field, and \(Z_{\rm eff}\) the plasma effective charge. The threshold electric field \(E_{\rm c}\) is given by

\[E_{\rm c} = \frac{n_ee^3\ln\Lambda}{4\pi\epsilon_0^2 m_ec^2},\]

where \(n_e\) is the electron density, \(e\) the elementary charge, \(\ln\lambda\) the Coulomb logarithm, \(\epsilon_0\) the permittivity of free space, \(m_e\) the electron mass and \(c\) the speed of light in vacuum.

[1]	Connor and Hastie, 1975 “Relativistic limitations on runaway electrons”. Nuclear Fusion 15 (3), 415 doi:10.1088/0029-5515/15/3/007.

Summary of options¶

The following parameters can be set on a Connor-Hastie distribution function.

Option	Description
`connorhastie EHat`	Electric field strength, normalized to the threshold electric field.
`connorhastie Zeff`	Plasma effective charge.
`connorhastie radprof`	Name of configuration block for radial profile.

Example configuration¶

This example illustrates how a Connor-Hastie distribution function can be defined and used in SOFT2 simulations:

# Global parameter specifying which distribution function to use
distribution_function = connor-hastie;

@DistributionFunction connor-hastie (connorhastie) {
    EHat     = 10;            # Electric field strength (normalized to
                              # the Connor-Hastie critical electric field)
    Zeff      = 4;            # Effective plasma charge
}

All options¶

EHat¶

Default value:	None
Allowed values:	Any real number

Electric field strength, normalized to the Connor-Hastie critical electric field (see above).

radprof¶

Default value:	Uniform radial profile
Allowed values:	Name of any defined @RadialProfile

Specifies the radial profile object to use to generate a radial profile.

Zeff¶

Default value:	None
Allowed values:	Any real number

Effective plasma charge.