In this example we show the required steps to set up an inductively coupled plasma (ICP) simulation. The simulation model is a so called µRIT - a small scaled, RF excitated ion thruster using Xenon as propellent. The example setup is similar to the model of an µRIT as shown in Robert Henrich et. al. at IEPC 2015 ¹⁾.

The zip-archive for this example contains two mesh files 'RIT-1.msh' and 'RIT-1_coils.msh' as seen in figure 1. The latter is derived from the former by commenting out all physical domains beside the coil's skin surface and both facesides from corresponding 'RIT-1.geo' geometry file.

Figure 1: Geomtry mesh with coil for PIC-MC simulation (left) and separated coil mesh for BEM computation (right).

Due to the skin effect the coil current can be described as surface current. We can use the BEM solver to compute such a field by applying Laplace boundary conditions to the coil's physical surfaces. The accordant parameter file 'RIT-1_0p83P_0p08W.bem' looks like this:

Domains = [1];
 
Boundary coils_i = {icodec = 1; type = "neumann";   val = 0; domain = 0; neighbourdomain = 0;};
Boundary coils_p = {icodec = 2; type = "dirichlet"; val =+1; domain = 0; neighbourdomain = 0;};
Boundary coils_n = {icodec = 3; type = "dirichlet"; val =-1; domain = 0; neighbourdomain = 0;};

There is only one domain and no interfaces defined. Hence, 'domain' and 'neighbourdomain' have no relevance here and can stay zero. You start the BEM solving process on 20 CPU cores by entering:

rvmmpi -bem 20 RIT-1_0p83P_0p08W.par

Since version 2.4.2.2. there is a switch in the parameter file's 'Additional switch' section:

ICP_SOURCE = 1;

Please uncomment it to improve performance of BEM solver when used for ICP source computation only. After the solving process a file 'BEM_icp_source_field.pos' is available in the project folder (see figure 2).

Figure 2: Resulting potential distribution 'BEM_Dirichlet.pos' (left) and derived gradient field 'BEM_icp_source_field.pos' (right).

The mesh for PIC-MC simulation must include the coil on which the vector field from previous BEM computation is applied. This is done by the reaction entry 'add_icp_source(“filename”, frequency)'. Move the file 'BEM_icp_source_field.pos' to where the parameter file resides, otherwise 'filename' must include the project folder e.g., 'RIT-1_0p83P_0p8W/BEM_icp_source_field.pos'. The second parameter 'freqency' defines the excitation frequency. The coil has been defined as fully transparent membrane here only because it is outside the discharge chamber and thus, coil-particle interactions must not be considered:

Border coils_i = {
  icodec      =   4;                          # Codec number from meshfile
  type        = "membrane";                   # Membrane for convenience
  T           = PAR.T0;                       # Wall temperature
  reactions: {
    Transparent_Membrane;                   # Fully transparent membrane
    # Load vector field from file with excitation frequency of 5 MHz
    add_icp_source("BEM_icp_source_field.pos", 5e6); 
  };                                          
};

As for the other parameters e.g., applied power, time step width or particle weighting, they follow the same rules as with CCP simulation. Other then the aforementioned procedure there are no additional switches or settings to be taken into account. The simulation is started with the command:

rvmmpi -picmc 10 RIT-1_0p83P_0p08W.par

Using the discharge parameters found in the IEPC paper (0.085 Watt @ 5 MHz) the ICP simulation converged after approximately 30 RF cycles. As seen in Figure 3, results from the Fraunhofer IST PIC-MC software are in relatively good agreement with the reference from IEPC proceedings paper. However, the coil slope related plasma density asymmetry is much less pronounced. This might be related to differing geometry and / or parameter settings.

Figure 3: Electron density in 1/m³ at y-z plane and x-y plane from Gießen PIC-MC software (top) and accordant results from Fraunhofer IST PIC-MC software (bottom).