multiRegionPlasma

multiRegionPlasma is a program to model electromagnetic field and trajectories of charged particles. It contains five parts:

• multiRegionPlasmaFoam - does computations of fields and particles;
• multiRegionPlasmaTest - demonstration example to model electric and magnetic fields and electron trajectories in simple circular magnetron sputtering system;
• plasmaInitialise - initializes charged particles.
• basic and dsmc are modified OpenFOAM libraries.

License

The program is licensed under GNU General Public License, for details see LICENSE.md.

Running

The program tested on OpenFOAM 2.2.2. If you are using version 2.1.x or older then probably you need to delete file system/surfaceFeatureExtractDict and instead write few lines in the file multiRegionPlasmaTest/Allrun. For example look here.

To begin, copy multiRegionPlasma folder to your working directory. No changes will be made to your original OpenFOAM program.

Program compiling

Make appropriate changes in addresses that contains /home/juris/Desktop/ in such files:

• dsmc/Make/options
• multiRegionPlasmaFoam/Make/options

To compile:

 cd basic
 wmake libso
 cd ../dsmc
 wmake libso
 cd ../plasmaInitialise
 chmod +x Allrun
 ./Allrun
 cd ../multiRegionPlasmaFoam
 chmod +x Allrun
 ./Allrun

Now in the folder /home/juris/OpenFOAM/juris-2.2.0/platforms/ you will find compiled libraries and program.

Demonstrational example

The example multiRegionPlasmaTest uses around 1.5 GB of RAM, its execution takes around one hour (around half is used for the mesh generation).

Geometry processing

If you want just to try the program, you can skip this step.

Geometry and .stl file generation files are located in multiRegionPlasmaTest/geometry.

1. Make appropriate changes to adresses that contains /home/juris/Desktop/ in the file scriptSalome.py.
2. Open Salome and open geometrySalome.hdf. In Geometry module you can see geometry of regions. Note that some flat surfaces are splitted.
3. To cut air region from box and to find surface pairs between two neighbouring regions use script. Do "File->Load Script", then choose scriptSalome.py. This script finds surface pairs, renames them and makes .stl surface mesh (it is not computational mesh). Surface mesh will be saved in the draft folder.
4. To merge these .stl files together use bash script mergeFiles.

cd multiRegionPlasmaTest/geometry chmod +x mergeFiles ./mergeFiles This script will merge all appropriate files together and result will be copied to the folder final. Here you will find surface files that correspond to each region.

5. Copy these region surface meshes to folder constant/triSurface.

Running the example

 cd multiRegionPlasmaTest
 chmod +x Allrun
 ./Allrun

Possible problems during a run

If during test example execution the program produces domain * folders then it means that .stl surface meshes intersect and splitMeshRegions interprets intersections as a separate regions. To solve it try increase change .stl mesh refinement, look scriptSalome.py for details.

If splitMeshRegions produces error then most probably you must increase refinement of blockMesh mesh. Look constant/polyMesh/blockMeshDict.

Changes to make

Particle initialization can be specified in the constant/air/dsmcProperties. Here you can add other species, set superparticles etc. Magnetic permiability dependence can be specified in the constant/wire/muProperties.

Post processing

Open ParaView and open appropriate region file, for example multiRegionPlasmaTest{air}.OpenFOAM. Do not use the command paraFoam, because it will not be able to handle multi-region case. To see particles, open the air region, change time step to bigger value, because initially there are no particles initialized. Then choose lagrangian fields.

Purpose of the program

Program was designed as a part of Bachelor's thesis. The purpose was to create a tool to optimize magnetron sputtering process. OpenFOAM was chosen as a basis because of free availability, open source code and large community. Discussion can be found in the cfd-online forum. BSc work called BSc-work.pdf you can find in the main folder. The work is written in Latvian because of compulsory requirement.

What is done

You can use program Kompare to see the changes made.

General

Pre-processing:

• Geometry export from Salome, .stl file processing.

Electric and magnetic fields:

• Electric field calculation via electric scalar potential.
• Magnetic field calculation via vectorial magnetic potential.
• Hybrid boundary conditions for magnetic vector potential on boundaries between two regions.
• Magnetic permeability dependence on magnetic field strength.
• Open boundary conditions (infinite space) [see 4.2.1].

Particles:

• Particles can be initialized in one or many separate regions.
• Particles of different species (charges, masses etc.).
• Particles can be initialized from any specific boundary (inlet).

Specific

• In basic library added possibility for particle to hit mappedPatch. See basic/particle/particleTemplates.C.
• In dsmc library added fields rhoQ - charge density. See DsmcCloud.C, DsmcCloud.H, DsmcCloudI.H.

PIC is realized in the file DsmcParcel.C. Here the program reads the electric field and uses RK4 to compute particle velocity. Then collects charge from all particles in the cell.

Charge defined in DsmcParcel.H and DsmcParcelI.H

Particles can be initialized from mapped patch, see FreeStream.C.

• plasmaInitialise is based on dsmcInitialise.

• multiRegionPlasmaFoam is based on chtMultiRegionFoam and dsmcFoam. I used ideas of Zhe Huang master thesis to compute magnetic field via magnetic vectorpotential. Idea how to make magnetic permiability dependent from strenght of magnetic field comes from Anja Miehe post in the cfd-online forum.

• multiRegionPlasmaTest is based on snappyMultiRegionHeater and freeSpaceStream.

OpenFOAM additional benefits

• You can run the program in parallel. Modify all decomposeParDict files, these you can find in the folders system and also system/'regionName'.

Magnetron sputtering

To answer the question about handling such problem in OpenFOAM, I will note some unsolved problems in the work.

Appropriate boundary conditions for magnetic vector potential are quite difficult to realize properly. There are some cases when magnetic field vectors are parallel to ferromagnetic surface, in this case boundary conditions are calculated quite wrongly [see page 32]. I came with mixed boundary conditions [see 4.2.4], but even these BC do not solve the problem stated before. I tried other formulations, but solutions diverged.

Magnetic field have gradient on magnet surfaces [compare Fig. 4.25 and 4.26]. I think it is because of curl scheme that is used to compute magnetization currents around magnets.

Simple interpolation scheme was used for PIC (Particle In Cell). OpenFOAM is FVM program that stores fields in cell centers, consequently all charged particles belongs to the total charge in the center of cell. I have not done further studies, but seems that energy is not conserved. Try to avoid large charge gradients in the simulation. I did two and one electron beam simulations and compared results with self-written program in C++ [see 5.3.2]. Red particles are from OpenFOAM, blue - from C++ program that uses particle-particle interaction model.

Possible applications

• Salome script scriptSalome.py and Bash script mergeFiles can be used to generate complicated geometries and export them to the OpenFOAM.
• Heat and mass transfer equations can be added to multiRegionFOAM and rarefied gas dynamics can be studied in complicated geometry cases.

Contact information

Private email: [email protected]

For general questions: http://www.cfd-online.com/Forums/openfoam-solving/126256-multi-region-solver-electric-magnetic-fields-charged-particles.html