The Drift Diffusion Interface

The interface (

), found under the branch (

), solves for the electron density and mean electron energy for any type of plasma. A wide range of boundary conditions are available to handle secondary emission, thermionic emission, and wall losses.

When this physics interface is added, these default nodes are also added to the — , (the default boundary condition), and . Then, from the toolbar, add other nodes that implement, for example, boundary conditions and velocity. You can also right-click to select physics features from the context menu.

The is the default physics interface name.

The is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the field. The first character must be a letter.

The default (for the first physics interface in the model) is dd.

Select the or , or check boxes as needed and select the model for the — (default), or .

Select the check box to specify the electron mobility, diffusivity, energy mobility and energy diffusivity in reduced form. The neutral number density is then specified in the node. The electron transport properties are computed from the reduced transport properties using:

where Nn is the user-defined neutral number density.

	It is sometimes more convenient to use reduced transport properties, since they can be output from The Boltzmann Equation, Two-Term Approximation Interface.

Select the check box to automatically compute the tensor form of the electron mobility, diffusivity, energy mobility and energy diffusivity when a static magnetic field is present. In this case the magnetic flux density is specified in the Drift Diffusion Model feature.

Select the check box to add an additional term to the definition of the electron current due to gradients in the electron diffusivity. If the diffusivity is a constant then including this does not affect the solution. It is only necessary to include this term if the electron diffusivity is a function of the electron temperature, and there are significant gradients in the electron temperature.

Select (default) to solve the mean electron energy equation self-consistently with the continuity, momentum, and Poisson’s equations, and to use the mean electron energy to parameterize transport and source coefficients. This is the most numerical demanding option to find the mean electron energy because of the strong coupling between the mean electron energy and the electromagnetic fields.

If is selected it is assumed that transport and source coefficients are well parameterized through the reduced electric field (E/Nn). The relation between the reduced electric field and the mean electron energy needs to be provided in the section in the node. When using the local field approximation the fluid equation for the mean electron energy is not solved, which reduces significantly the complexity of the numerical problem. The local field approximation is valid in a situation where the rate of electron energy gain from the electric field is locally balanced by the energy loss rate. When this condition is met the electrons are said to be in local equilibrium with the electric field and the electron mean properties can be expressed as a function of the reduced electric field.

Select to fix the mean electron energy to its initial value. This can be useful in some situations because the strong coupling between the mean electron energy and the electromagnetic fields is removed. This allows for non-self-consistent models to be created quickly, since problems where the mean electron energy is fixed are easier to solve numerically.

To display this section, click the button (

) and select in the dialog box.

If the is set to or then the solver can run into difficulties when the species mass fractions approach zero. The check box (selected by default) adds an additional source term to the rate expression for each species. In the ζ text field, enter a tuning parameter for the source stabilization. The default value is 1. This value is usually good enough. If the plasma is high pressure (atmospheric) then it can help to lower this number to somewhere in the range of 0.25–0.5. For information on stabilization see Stabilization.

Select — , (the default) to solve the equations in logarithmic form, ,, or. The Log formulation solves for the log of the dependent variables, ensuring that the mass fraction of any of the species is never lower than zero. This makes it more numerically stable but increases the nonlinearity of the equation system, and as such the model might take slightly longer to solve. The linear formulation solves the equations in the original form.

The dependent variables (field variables) are the and . The name can be changed but the names of fields and dependent variables must be unique within a model. The physical meanings of and change depending on the formulation used. For example, when log formulations are used, is the logarithm of the electron density; whereas for other cases, it is the electron density