Inductive Stochastic Heating
The Capacitive Stochastic Heating feature introduces an additional contribution to the electron collision frequency for momentum transfer νm to accounts for stochastic heating effects. An effective collision frequency
is then used to calculate the electron mobility
where νs is the stochastic collision frequency, sp is a profile specifying where the stochastic collision frequency is applied, and as is the anisotropy vector associated with the stochastic collision frequency. Further theoretical background on this theory can be found in Ref. 3.
Inductive Stochastic Heating Model
Select an option from the Stochastic frequency model list — Vahedi (the default), Lieberman, or User defined. Each option determines how the stochastic collision frequency is calculated.
Vahedi
When Vahedi is selected the stochastic collision frequency is defined by
where the regime of validity is defined using
where δ is the skin depth, ω is the angular frequency, and is the electron mean velocity. The stochastic frequency branch is selected from the α regime list, with the following options: Low (the default), Middle, or High.
The following quantities need to be provided:
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Frequency f (SI unit: Hz): excitation frequency of the inductive power source.
•
Electron temperature Te (unit: eV): choose an option from the list — Local (the default) or User defined. If Local is selected the local space dependent value for the electron temperature is used.
•
Electron density ne (SI unit: m−3): choose an option from the list — Local (the default) or User defined. If Local is selected the local space dependent value for the electron density is used.
Lieberman
When Lieberman is selected the stochastic collision frequency is defined by
with
where Ei is the exponential integral
The following quantities need to be provided:
•
Frequency f (SI unit: Hz): excitation frequency of the inductive power source.
•
Electron temperature Te (unit: eV): choose an option from the list — Local (the default) or User defined. If Local is selected the local space dependent value for the electron temperature is used.
•
Electron density ne (SI unit: m−3): choose an option from the list — Local (the default) or User defined. If Local is selected the local space dependent value for the electron density is used.
The skin depth regime is selected from the Skin depth model list, with the following options: Collisionless (the default), Collisional, or Anomalous.
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If Collisionless is selected the skin depth is defined as
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If Collisional is selected, choose an option from the list — Local (the default) or User defined. If Local is selected the local collision frequency for momentum transfer is used. In this case the skin depth is defined as
•
If Anomalous is selected, specify the Anomalous factor. In this case the skin depth is defined as
User defined
When User defined is selected, specify a value in the Stochastic collision frequency field to manually set the collision frequency.
Spatial Distribution
If Collisionless, Collisional, or Homogeneous is selected, a Gaussian profile is defined using the following parameters:
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Profile width pw (SI unit: m) determines the profile spatial spread.
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Peak distance from the boundary pd (SI unit: m) specifies the location of the profile peak relative to the selected boundary.
The reference boundary for pd is set via the subfeature Boundary Selection for Stochastic Heating. This profile modulates the spatial distribution of the stochastic collision frequency, enabling localized application of stochastic heating within the plasma domain.
Stochastic Frequency Anisotropy
The Stochastic frequency anisotropy (SI unit: 1) allows to define in which direction the stochastic collision frequency is to be applied.