Capacitive 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.
Capacitive Stochastic Heating Model
Select an option from the Stochastic frequency model list — Collisionless (the default), Collisional, Homogeneous, or User defined.Each option determines how the stochastic collision frequency is calculated.
Collisionless
When Collisionless is selected the stochastic collision frequency is defined by
where the electron mean velocity is given by
and the remaining quantities are explained below. Note that the electron temperature cancels in this case. The following quantities need to be provided:
•
Plasma bulk thickness d (SI unit: m): the length of the plasma bulk, excluding the sheath region
•
Edge-to-center density ratio hl (SI unit: 1): the ratio of the plasma density in the sheath region to that at the center of the reactor
•
Voltage amplitude V (SI unit: V): the rf voltage amplitude across a single sheath
•
Adjusting coefficient Ks (SI unit: 1) the default is 0.33
Collisional
When Collisional is selected the stochastic collision frequency is defined by
.
To define the Edge electron temperature Te,s 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.
Additionally enter the following quantities:
•
Plasma bulk thickness d (SI unit: m): the length of the plasma bulk, excluding the sheath region
•
Edge-to-center density ratio hl (SI unit: 1): the ratio of the plasma density in the sheath region to that at the center of the reactor
•
Edges density ns (SI unit: m−3): the plasma density at the interface between the bulk and the sheath region
•
Voltage amplitude V (SI unit: V): the rf voltage amplitude across a single sheath
•
Ion mean-free-path λi (SI unit: m): the ion mean-free-path in the sheath region
•
Adjusting coefficient Ks (SI unit: 1) the default is 0.78
Homogeneous
When Homogeneous is selected the stochastic collision frequency is defined by
.
To define the Edge electron temperature Te,s 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.
Additionally enter the following quantities:
•
Plasma bulk thickness d (SI unit: m): the length of the plasma bulk, excluding the sheath region
•
Adjusting coefficient Ks (SI unit: 1) the default is 0.78
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:
•
Profile width pw (SI unit: m) determines the profile spatial spread.
•
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.