7.3. Two Stream Instability (PIC, Poisson’s Equation)
This tutorial considers a one-dimensional (1D) setup of the so-called two-stream instability (TSI) using PICLas. The TSI is a key phenomenon in plasma physics, occurring when two counter-flowing and interpenetrating streams of charged particles, such as electrons and ions, travel with different (opposite) velocities. This relative motion induces perturbations that grow exponentially, leading to the amplification of plasma waves and potentially resulting in turbulent behaviour.
In PICLas, this process can be simulated with the electrostatioc PIC-Poisson solver. The setup simulates two electron streams moving with opposite velocities \(\nu_{1}\)=\(-\nu_{2}\) of identical densities \(n_{1}\)=\(n_{2}\), interacting with each other, leading to an instability that generates a fluctuating electric field. The particle phase-space plot at the end of the simulation results in an eye-like structure.
Begin the tutorial, by copying the pic-poisson-TSI directory from the tutorial folder in the top level directory of the piclas repository to a separate location
cp -r $PICLAS_PATH/tutorials/pic-poisson-TSI .
cd pic-poisson-TSI
where the variable PICLAS_PATH contains the path to the location of the piclas repository.
7.3.1. Mesh Generation with HOPR (pre-processing)
In a first step, the mesh file in HDF5 format is created. The mesh files used by piclas are created by supplying an input file hopr.ini with the required information for a mesh that has either been created by an external mesh generator or directly from block-structured information in the hopr.ini file itself. Here, a block-structured grid is created directly from the information in the hopr.ini file. To create the .h5 mesh file, run
hopr hopr.ini
This creates the mesh file two_stream_instability_mesh.h5 in HDF5 format. The size of the simulation domain is set to [\(4\pi\times0.03\times0.03\)] m\(^{3}\) and is defined by the single block information in the line, where each node of the hexahedral element is defined
Corner = (/0.,0.,0.,,12.566370614359,0.,0.,,12.566370614359,0.03,0.,,0.,0.03,0.,,0.,0.,0.03,,12.566370614359,0.,0.03,,12.566370614359,0.03,0.03,,0.,0.03,0.03/)
The number of mesh elements for the block in each direction can be adjusted by changing the line
nElems = (/801,1,1/) ! number of elements in each direction (x,y,z)
Each side of the block has to be assigned a boundary index, which corresponds to the boundaries defined in the next steps
BCIndex = (/5,3,2,4,1,6/)
The field boundaries can directly be defined in the hopr.ini file (contrary to the particle boundary conditions, which are defined in the parameter.ini). Periodic boundaries always have to be defined in the hopr.ini.
!=============================================================================== !
! BOUNDARY CONDITIONS
!=============================================================================== !
BoundaryName = BC_periodicx+ ! Periodic (+vv1)
BoundaryType = (/1,0,0,1/) ! Periodic (+vv1)
BoundaryName = BC_periodicx- ! Periodic (-vv1)
BoundaryType = (/1,0,0,-1/) ! Periodic (-vv1)
BoundaryName = BC_periodicy+ ! Periodic (+vv2)
BoundaryType = (/1,0,0,2/) ! Periodic (+vv2)
BoundaryName = BC_periodicy- ! Periodic (-vv2)
BoundaryType = (/1,0,0,-2/) ! Periodic (-vv2)
BoundaryName = BC_periodicz+ ! Periodic (+vv3)
BoundaryType = (/1,0,0,3/) ! Periodic (+vv3)
BoundaryName = BC_periodicz- ! Periodic (-vv3)
BoundaryType = (/1,0,0,-3/) ! Periodic (-vv3)
VV = (/12.566370614359 , 0. , 0./) ! Displacement vector 1 (x-direction)
VV = (/0. , 0.03 , 0./) ! Displacement vector 2 (y-direction)
VV = (/0. , 0. , 0.03/) ! Displacement vector 3 (z-direction)
In this case, a fully periodic setup is chosen by defining periodic boundaries on all six sides of the block, reflecting each positive and negative Cartesian coordinate. In \(x\)-direction,
BoundaryName = BC_periodicx+ ! Periodic (+vv1)
BoundaryType = (/1,0,0,1/) ! Periodic (+vv1)
BoundaryName = BC_periodicx- ! Periodic (-vv1)
BoundaryType = (/1,0,0,-1/) ! Periodic (-vv1)
where for each of the six boundaries, a name BoundaryName and a type BoundaryType must be defined (in this order).
The boundary name can be chosen by the user and may be used again in the parameter.ini.
The first “1” in BoundaryType corresponds to the type “periodic” and the last entry, here, either “1” or “-1” corresponds to the
first periodic vector that is defined via VV=(/12.566370614359 , 0. , 0./) that handles periodicity in the x-direction and gives the
orientation on the boundary for the vector. Note that each periodic boundary must have one positive and one negative corresponding
boundary for the same periodic vector.
7.3.2. PIC Simulation with PICLas
Install piclas by compiling the source code as described in Chapter Installation, specifically described under Section Compiling the code. Always build the code in a separate directory located in the piclas top level directory. For this PIC tutorial, e.g., create a directory build_poisson_Leapfrog by running
cd $PICLAS_PATH
where the variable PICLAS_PATH contains the path to the location of the piclas repository.
If the piclas repository is located in the home directory, runlasma Wave
cd /home/$(whoami)/piclas
and the create the build directory, in which the compilation process will take place
mkdir build_poisson_Leapfrog
and the directory structure, which can be viewed via
ls -l
should look like this
build_poisson_RK3
cmake
CMakeListsLib.txt
CMakeListsMachine.txt
CMakeLists.txt
CONTRIBUTORS.md
docs
LICENCE.md
README.md
REFERENCE.md
REGGIE.md
regressioncheck
share
SpeciesDatabase.h5
src
tools
tutorials
unitTests
Always compile the code within the build directory, hence, navigate to the build_poisson_Leapfrog directory before running cmake
cd build_poisson_Leapfrog
For this specific tutorial, make sure to set the correct compile flags
PICLAS_EQNSYSNAME = poisson
LIBS_USE_PETSC = ON
PICLAS_TIMEDISCMETHOD = Leapfrog
using the ccmake (gui for cmake) or simply run the following command from inside the build directory
cmake ../ -DLIBS_USE_PETSC=0N -DPICLAS_EQNSYSNAME=poisson -DPICLAS_TIMEDISCMETHOD=Leapfrog
to configure the build process and run
make -j
afterwards to compile the executable. For this setup, the Poisson solver is used with the Leapfrog time discretization method. An overview over the available solver and discretization options is given in Section Solver settings. To run the simulation, the piclas binary is used and to visualise the resulting .h5 output files, the post-processing too piclas2vtk is required to convert them into the standard .vtu format.
To avoid having to use the absolute file path of the executables, an alias or a symbolic link may be created. To create a symbolic link within the directory of the tutorial, run
ln -s $PICLAS_PATH/build_poisson_Leapfrog/bin/piclas
ln -s $PICLAS_PATH/build_poisson_Leapfrog/bin/piclas2vtk
where the variable PICLAS_PATH contains the path to the location of the piclas repository.
If the piclas repository is located in the home directory, the two commands
ln -s /home/$(whoami)/piclas/build_poisson_Leapfrog/bin/piclas
ln -s /home/$(whoami)/piclas/build_poisson_Leapfrog/bin/piclas2vtk
can directly be executed without needing to modify them.
Always check where piclas is located before running the commands to ensure that the correct solver settings have been compiled into the executable.
7.3.2.1. Overview
The simulation setup is defined in parameter.ini. The process of the TSI corresponds to a transfer of initial transversal velocities \(\nu_{tr,x}(t=0)=\nu_{1}(t=0)\), into thermal velocities \(\nu_{th,x}\). The transversal velocity in x-direction is computed as
which in term is used to compute the thermal velocity in x-direction as
The initial velocity \(\nu_{tr,x}\) is computed as
For a specific electron number density, the (cold) plasma frequency of the system is
which is the frequency with which the charge density of the electrons oscillates, where \(\varepsilon_{0}\) is the permittivity of vacuum, \(e\) is the elementary charge, \(n_{e}\) and \(m_{e}\) are the electron density and mass, respectively. For a standard explicit PIC method, the plasma frequency yields the smallest time step that has to be resolved numerically. The Debye length
where \(\varepsilon_{0}\) is the permittivity of vacuum, \(k_{B}\) is the Boltzmann constant, \(e\) is the elementary charge and \(T_{e}\) and \(n_{e}\) are the electron temperature and density, respectively, gives a spatial resolution constraint. The restriction on the spatial resolution is the number of elements (and polynomial degree \(N\)) that are required to resolve the physical properties of the PIC simulation. If the temporal and/or spatial constraints are violated, the simulation cannot not yield physical results and might result in a termination of the simulation.
The physical parameters for this test case are summarized in Table 7.2.
Property |
Value |
|---|---|
electron mass \(m_{e}\) |
\(\pu{9.1093826E-31 kg}\) |
electron charge \(q_{e}\) |
\(\pm\pu{1.60217653E-19 C}\) |
ion mass \(m_{i}\) |
\(\pu{1.672621637E-27 kg}\) |
ion charge \(q_{i}\) |
\(\pm\pu{3.20435306E-19 C}\) |
7.3.2.2. Numerical setup
The general numerical parameters (defined in parameter.ini) are set via
! =============================================================================== !
! DISCRETIZATION
! =============================================================================== !
N = 2 ! Polynomial degree of the DG method (field solver)
! =============================================================================== !
! MESH
! =============================================================================== !
MeshFile = two_stream_instability_mesh.h5 ! Relative path to the mesh .h5 file
! =============================================================================== !
! General
! =============================================================================== !
ProjectName = two_stream_instability ! Project name that is used for naming state files
ColoredOutput = F ! Turn ANSI terminal colors ON/OFF
doPrintStatusLine = T ! Output live of ETA
TrackingMethod = TriaTracking
where, among others, the polynomial degree \(N\), the path to the mesh file MeshFile, project name and the option to print the ETA
to the terminal output in each time step.
The temporal parameters of the simulation are controlled via
! =============================================================================== !
! CALCULATION
! =============================================================================== !
ManualTimeStep = 1e-10 ! Fixed pre-defined time step only when using the Poisson solver. Maxwell solver calculates dt that considers the CFL criterion
tend = 1e-6 ! Final simulation time
Analyze_dt = 1E-8 ! decrease analyze_dt for better resolution of fish eye
IterDisplayStep = 1000 ! Number of iterations between terminal output showing the current time step iteration
TimeStampLength = 13 ! Reduces the length of the timestamps in filenames for better postprocessing
where the time step for the field and particle solver is set via ManualTimeStep, the final simulation time tend, the time
between restart/checkpoint file output Analyze_dt (also the output time for specific analysis functions) and the number of time
step iterations IterDisplayStep between information output regarding the current status of the simulation that is written to std.out.
The format of the restart/checkpoint files, which are created every time the simulation time reaches a multiple of
Analyze_dt, is set via TimeStampLength = 13, the names of the output files are shortened for better postprocessing.
This is done, because some visualisation tools might otherwise incorrectly group the files when opening a complete set of output files.
The remaining parameters are selected for the field and particle solver as well as run-time analysis.
7.3.2.2.1. Boundary conditions
As there are no walls present in the setup, all boundaries are set as periodic boundary conditions for the field as well as the particle solver. The particle boundary conditions are set by the following
! =============================================================================== !
! PARTICLE Boundary Conditions
! =============================================================================== !
Part-nBounds = 6 ! Number of particle boundaries
Part-Boundary1-SourceName = BC_periodicx+ ! Name of 1st particle BC
Part-Boundary1-Condition = periodic ! Type of 1st particle BC
Part-Boundary2-SourceName = BC_periodicx- ! ...
Part-Boundary2-Condition = periodic ! ...
Part-Boundary3-SourceName = BC_periodicy+ ! ...
Part-Boundary3-Condition = periodic ! ...
Part-Boundary4-SourceName = BC_periodicy- ! ...
Part-Boundary4-Condition = periodic ! ...
Part-Boundary5-SourceName = BC_periodicz+ ! ...
Part-Boundary5-Condition = periodic ! ...
Part-Boundary6-SourceName = BC_periodicz- ! ...
Part-Boundary6-Condition = periodic ! ...
Part-nPeriodicVectors = 3 ! Number of periodic boundary (particle and field) vectors
Part-FIBGMdeltas = (/12.56637061435917295 , 0.03 , 0.03/) ! Cartesian background mesh (bounding box around the complete simulation domain)
Part-FactorFIBGM = (/801., 1. , 1./) ! Division factor that is applied t the "Part-FIBGMdeltas" values to define the dx, dy and dz distances of the Cartesian background mesh
where, the number of boundaries Part-nBounds (6 for a 3D cuboid domain) is followed by the names of
the boundaries (given by the hopr.ini file) and the type periodic.
Furthermore, the periodic vectors must be supplied and the size of the Cartesian background mesh Part-FIBGMdeltas, which can be
accompanied by a division factor (that is the number of background cells) in each direction given by Part-FactorFIBGM.
Here, the size and number of cells of the background mesh correspond to the actual mesh.
7.3.2.2.2. Field solver
The settings for the field solver (HDGSEM) are given by
! =============================================================================== !
! Field Solver: HDGSEM
! =============================================================================== !
IniExactFunc = 0 ! Initial field condition. 0: zero solution vector
PrecondType = 10 ! Direct numerical method
For this tutorial the PETSc solver is used where a multitude of different numerical methods to solve the resulting system of linear
equations is given by the implemented PETSc library are available.
The direct solver of PETSc is used by setting PrecondType=10.
The parameter IniExactFunc sets the initial solution of the field solver and a value of zero means that the electric potential is
initialised with zero everywhere.
The PIC parameters for interpolation (of electric fields to the particle positions) and deposition (mapping of charge properties from particle locations to the grid) are selected via
! =============================================================================== !
! PIC: Interpolation/Deposition
! =============================================================================== !
PIC-DoInterpolation = T ! Activate Lorentz forces acting on charged particles
PIC-DoDeposition = T ! Activate particle charge deposition
PIC-Deposition-Type = cell_volweight_mean ! Linear deposition method
Electro(-magnetic) forces that act on charged particles and accelerate these are activated by setting PIC-DoInterpolation=T.
The deposition of charges to the grid, which is required to consider source terms in the field solver, is activated via PIC-DoDeposition=T.
For charge and current deposition, PIC-Deposition-Type = cell_volweight_mean is selected.
Note that current deposition is only performed as post-processing output when using the Poisson solver in PICLas, as this solver
only required the charge deposition as input source terms.
The different available deposition types are described in more detail in Section Charge and Current Deposition.
7.3.2.2.3. Particle solver
The numerical scheme for tracking the movement of all particles throughout the simulation domain can be switched by
! =============================================================================== !
! Particle Solver
! =============================================================================== !
TrackingMethod = refmapping ! [INT/STR] Define Method that is used for tracking of particles:
! refmapping (1): reference mapping of particle position with (bi-)linear and
! bezier (curved) description of sides.
! tracing (2): tracing of particle path with (bi-)linear and bezier (curved)
! description of sides.
! triatracking (3): tracing of particle path with triangle-aproximation of
! (bi-)linear sides.
The number of particle species Part-nSpecies that are used in the simulation (created initially or during the simulation time
through chemical reactions) defines the number of subsequent parameters that will be defined in the parameter input file
! =============================================================================== !
! PARTICLE Emission
! =============================================================================== !
Part-nSpecies = 3 ! Number of particle species
The creation (sometimes labelled emission or initialisation) of particles at the beginning or during the simulation
is controlled via the following parameters. Here, the parameters for the electrons are shown, however, the parameters for the ions
are set analogously and included in the supplied parameter.ini.
For each species, the mass (Part-SpeciesX-MassIC), charge (Part-SpeciesX-ChargeIC) and weighting factor (Part-SpeciesX-MacroParticleFactor)
have to be defined.
! -------------------------------------
! Electrons 1
! -------------------------------------
Part-Species1-ChargeIC = -1.60217653E-19 ! Electric charge of species #1
Part-Species1-MassIC = 9.1093826E-31 ! Rest mass of species #1
Part-Species1-MacroParticleFactor = 2.4e5 ! Weighting factor for species #1
Part-Species1-nInits = 1 ! Number of initialization/emission regions for species #1
The number of initialization sets is defined by Part-Species1-nInits, where each initialization set is accompanied
by a block of parameters that starts from Part-Species1-Init1-SpaceIC up to Part-Species1-Init1-VeloVecIC and are preceded by the
corresponding -InitX counter. In this example we have a single initialization set per species definition.
The Part-Species1-Init1-SpaceIC = sin_deviation flag defines the type of the initialization set, here, the distribution the particles
equidistantly on a line and sinusoidally dislocates them (representing an initial stage of a plasma wave in 1D).
Each type of the initialization set might have a different set of parameters and an overview is given in Section
Particle Initialization & Emission.
Part-Species1-Init1-ParticleNumber = 100000 ! Number of simulation particles for species #1 and initialization #1
Part-Species1-Init1-maxParticleNumber-x = 100000 ! Number of simulation particles in x-direction for species #1 and initialization #1
Part-Species1-Init1-SpaceIC = sin_deviation ! Sinusoidal distribution is space
Part-Species1-Init1-BasePointIC = (/0.0 , 0.015 , 0.015/)
Part-Species1-Init1-velocityDistribution = constant ! Constant velocity distribution
Part-Species1-Init1-maxParticleNumber-y = 1 ! Number of particles in y
Part-Species1-Init1-maxParticleNumber-z = 1 ! Number of particles in z
Part-Species1-Init1-MWTemperatureIC = 0.72429730341e23
Part-Species1-Init1-Amplitude = 0.004 ! Specific factor for the sinusoidal distribution is space
Part-Species1-Init1-WaveNumber = 0.5 ! Specific factor for the sinusoidal distribution is space
Part-Species1-Init1-VeloIC = 1.06e8 ! Velocity magnitude [m/s]
Part-Species1-Init1-VeloVecIC = (/1.,0.001,0.001/) ! Normalized velocity vector
The extent of dislocation is controlled by Part-Species1-Init1-Amplitude, which is only set for the electron species as the ion
species is not dislocated (they remain equidistantly distributed).
The parameter Part-Species1-Init1-WaveNumber sets the number of sine wave repetitions in the \(x\)-direction of the domain.
In case of the SpaceIC=sin_deviation, the number of simulation particles must be equal to the multiplied values given in
Part-Species1-Init1-maxParticleNumber-x/y/z as this emission type allows distributing the particles not only in one, but in all
three Cartesian coordinates, which is not required for this 1D example.
In the same manner, a second stream of electron is defined with only the difference of Part-Species2-Init1-VeloVecIC = (/-1.,0.001,0.001/) and Part-Species2-Init1-Amplitude = -0.004
The ions at rest in the background are defined as well providing a quasi-neutral state.
! ------------------------------------------------------------------------------- !
! Ions 3
! ------------------------------------------------------------------------------- !
Part-Species3-ChargeIC = 3.204e-19
Part-Species3-MassIC = 6.69e-27
Part-Species3-MacroParticleFactor = 2.4e5 ! Weighting factor for species #3
Part-Species3-nInits = 1
!Part-Species3-Init1-maxParticleNumber-x = 100000 ! Number of simulation particles in x-direction for species 3
Part-Species3-Init1-maxParticleNumber-y = 1 ! Number of particles in y
Part-Species3-Init1-maxParticleNumber-z = 1 ! Number of particles in z
Part-Species3-Init1-SpaceIC = sin_deviation
Part-Species3-Init1-BasePointIC = (/0.0 , 0.015 ,0.015/)
Part-Species3-Init1-velocityDistribution = constant
Part-Species3-Init1-VeloIC = 0.0
Part-Species3-Init1-VeloVecIC = (/0.,0.,0./)
Part-Species3-Init1-Amplitude = 0.0 ! Specific factor for the sinusoidal distribution is space
Part-Species3-Init1-WaveNumber = 0. ! Specific factor for the sinusoidal distribution is space
7.3.2.2.4. Analysis setup
For run-time analysis, piclas offers a multitude of possible settings to activate.
! =============================================================================== !
! Analysis
! =============================================================================== !
CalcCharge = T ! writes rel/abs charge error to PartAnalyze.csv
CalcPotentialEnergy = T ! writes the potential field energy to FieldAnalyze.csv
CalcKineticEnergy = T ! writes the kinetic energy of all particle species to PartAnalyze.csv
PIC-OutputSource = T ! writes the deposited charge (RHS of Poisson's equation to XXX_State_000.0000XXX.h5)
CalcPICTimeStep = T ! writes the PIC time step restriction to XXX_State_000.0000XXX.h5 (rule of thumb)
CalcPointsPerDebyeLength = T ! writes the PIC grid step restriction to XXX_State_000.0000XXX.h5 (rule of thumb)
CalcTotalEnergy = T ! writes the total energy of the system to PartAnalyze.csv (field and particle)
CalcInternalEnergy = T
CalcTemp = T
CalcVelos = T
Part-LorentzType = 3
CalcTimeAverage = T
CalcPlasmaParameter =T
VarNameAvg = ChargeDensity-Spec01
VarNameAvg = ChargeDensity-Spec02
VarNameAvg = ChargeDensity-Spec03
The function of each parameter is given in the code comments. Information regarding every parameter can be obtained from running the command
piclas --help "CalcCharge"
where each parameter is simply supplied to the help module of piclas. This help module can also output the complete set of
parameters via piclas --help or a subset of them by supplying a section, e.g., piclas --help "HDG" for the HDGSEM solver.
7.3.2.3. Running the code
The command
./piclas parameter.ini | tee std.out
executes the code and dumps all output into the file std.out. To reduce the computation time, the simulation can be run using the Message Passing Interface (MPI) on multiple cores, in this case 8
mpirun -np 8 piclas parameter.ini | tee std.out
If the run is successful, the contents of the working folder should look like this
4.0K drwxrwxr-x 4.0K Jun 28 13:07 ./
4.0K drwxrwxr-x 4.0K Jun 25 23:56 ../
8.0K -rw-rw-r-- 5.8K Jun 28 12:51 ElemTimeStatistics.csv
120K -rw-rw-r-- 113K Jun 28 12:51 FieldAnalyze.csv
4.0K -rw-rw-r-- 2.1K Jun 26 16:49 hopr.ini
8.0K -rw-rw-r-- 5.0K Jun 28 13:07 parameter.ini
156K -rw-rw-r-- 151K Jun 28 12:51 PartAnalyze.csv
32K -rw-rw-r-- 32K Jun 26 16:43 plasma_wave_mesh.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:44 two_stream_instability_State_.000000000.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:45 two_stream_instability_State_000.000000004.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:45 two_stream_instability_State_000.000000008.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:46 two_stream_instability_State_000.000000012.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:47 two_stream_instability_State_000.000000016.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:48 two_stream_instability_State_000.000000020.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:49 two_stream_instability_State_000.000000024.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:50 two_stream_instability_State_000.000000028.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:50 two_stream_instability_State_000.000000032.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:51 two_stream_instability_State_000.000000036.h5
1.6M -rw-rw-r-- 1.6M Jun 28 12:51 two_stream_instability_State_000.000000040.h5
72K -rw-rw-r-- 71K Jun 28 12:51 std.out
Multiple additional files should appear, which are named Projectname_State_Timestamp.h5 and contain the solution vector of the
equation system variables at each interpolation nodes at the given time, which corresponds to multiples of Analyze_dt.
If something goes wrong during the simulation, an output message should be displayed that is also written to the log file std.out
indicating what caused the crash.
A successful simulation should display the following lines at the end of the output:
--------------------------------------------------------------------------------------------
Sys date : 03.07.2021 14:34:26
PID: CALCULATION TIME PER TSTEP/DOF: [ 4.03465E-05 sec ]
EFFICIENCY: SIMULATION TIME PER CALCULATION in [s]/[Core-h]: [ 4.16179E-07 sec/h ]
Timestep : 1.0000000E-10
#Timesteps : 1.0000000E+04
WRITE STATE TO HDF5 FILE [two_stream_instability_State_000.000001000.h5] ... DONE [ 0.06 sec ] [ 0:00:00:00 ]
#Particles : 3.0000000E+05 Average particles per proc : 3.7500000E+04 Min : 3.1914000E+04 Max : 4.0600000E+04
WRITE TIME AVERAGED STATE AND FLUCTUATIONS TO HDF5 FILE... DONE [ 0.01 sec ] [ 0:00:00:00 ]
--------------------------------------------------------------------------------------------
#Particles : 3.0000000E+05 (peak) Average (peak) : 3.7500000E+04 Min : 2.1633000E+04 Max : 1.1188400E+05
============================================================================================
PICLAS FINISHED! [ 1081.47 sec ] [ 0:00:18:01 ]
============================================================================================
7.3.3. Visualization (post-processing)
To visualise the solution, the State-files (landau_damping_State….h5) must be converted into a format suitable for ParaView, VisIt or any other visualisation tool. The conversion if done using the program piclas2vtk, which is found at the same location as the piclas executable. The parameters for piclas2vtk are also defined in the parameter.ini file under
! =============================================================================== !
! piclas2vtk
! =============================================================================== !
NVisu = 6! Polynomial degree used for the visualization when the .h5 file is converted to .vtu/.vtk format. Should be at least N+1
VisuParticles = T ! Activate the conversion of particles from .h5 to .vtu/.vtk format. Particles will be displayed as a point cloud with properties, such as velocity, species ID, etc.
where NVisu is the polynomial visualization degree on which the field solution is interpolated.
Depending on the used polynomial degree N and subsequently the degree of visualization NVisu, which should always be higher than
N, the resulting electric potential \(\Phi\) and its derivative, the electric field strength E might show signs of oscillations.
Additionally, the flag VisuParticles=T activates the output of particle position, velocity and species to the vtk-files.
Running the command
./piclas2vtk parameter.ini plasma_wave_State_000.000000*
to generate the corresponding vtk-files, which can then be loaded into the visualisation tool.
The thermal and drift velocity plots can be viewed, for example with ParaView, by opening PartAnalyze.csv in the
Line Chart View. The graphs are depicted in Fig. 7.5.
Fig. 7.5 Transfer of transversal to thermal velocity over time.
To visualise the probability distribution function (PDF) in ParaView, a script is located in the tools folder of the piclas
repository under piclas/tools/paraview/pdf/511.
This is done by selecting Tools → Manage Plugins → Load New → pdf_paraview511.xml.
After loading the script, ensure that the Auto Load feature in the list of plugins is selected for the PDF to avoid loading the script
every time ParaView is opened.
Then load the particle file, for example, two_stream_instability_visuPart_000.000000000.vtu and apply the
Probability Distribution Function 5.11 (piclas) filter to this file.
This can be done by searching the feature directly in ParaView with the shortcut keys CTRL+SPACE.
Also adjust the spatial extent by setting xMaxto 12.566, that is \(4\pi\), which is the length of the domain in this tutorial.
An animation can be created from the collection of output files and is shown in Fig. 7.6.
Fig. 7.6 Temporal evolution of the PDF of the two-stream instability setup.