Thermal plasma

The goal of this tutorial is to get familiar with:

  • the Species block that allows you to define a particle species,

  • the ParticleBinning diagnostics to obtain particle energy spectra,

  • the problem of numerical heating and the necessity to correctly resolve the electron dynamics in explicit PIC codes.

Physical configuration

Download the input file thermal_plasma_1d.py.

An infinite electron-ion plasma is let free to evolve in a 1D cartesian geometry with periodic boundary conditions.

Check input file and run the simulation

The first step is to check that your input file is correct. To do so, you will run (locally) Smilei in test mode:

./smilei_test thermal_plasma_1d.py

If your simulation input file is correct, you can now run the simulation. Before going to the analysis of your simulation, check your log and/or error output.

Check what output files have been generated: what are they?

Preparing the post-processing tool

Let’s now turn to analysing the output of your run with happi. To do so, open an ipython session:

ipython

In ipython, import the happi package:

import happi

then open your simulation:

S = happi.Open('/path/to/the/simulation')

Warning

Use the correct simulation path.

You are now ready to take a look at your simulation’s results.

The Field diagnostics using happi.multiPlot

To have a quick access at your data and check what is going on, you will plot the electron and ion densities together with the electrostatic field \(E_x\).

First, prepare the data:

# minus the electron density
ne = S.Field(0,'-Rho_eon', label="e- density")

# ion density
ni = S.Field(0,'Rho_ion', label="ion density")

# Ex field
ex = S.Field(0,'Ex', label="Ex field", vmin=-0.25,vmax=2)

You may plot all these quantities independently using ex.plot() or ex.slide(), but you can also use the multiSlide function of happi:

happi.multiSlide(ne,ni,ex)

The ParticleBinning diagnostics

Now, have a look at the ParticleBinning diagnostics in the input file. What kind of data will this diagnostic provide?

You can compare the results at the beginning and at the end of the simulation:

Nt = S.ParticleBinning(0).getTimesteps()[-1] # the last timestep
f_initial = S.ParticleBinning(0, data_log=True, timesteps=0 , label="initial")
f_final   = S.ParticleBinning(0, data_log=True, timesteps=Nt, label="final")
happi.multiPlot(f_initial, f_final)

What can you conclude?

Effect of spatial resolution

Have a look at the total energy and energy balance in your simulation (remember the Utot and Ubal scalars). Note the level of energy imbalance at the end of this simulation for which the spatial resolution is equal to the Debye Length (\(\Delta x = \lambda_{\rm De}\)).

Increase your spatial resolution to \(\Delta x = 16 \times \lambda_{\rm De}\). Run the simulation again, and check the energy imbalance at the end of the simulation. What do you observe? Can you check the electron spectrum at the beginning and end of the simulation? What is going on?

Finally, increase your spatial resolution to \(\Delta x = 2\,c/\omega_{pe} = 2\,c\lambda_{\rm De}/v_{\rm th}\) (you will need to extend your simulation box size to have enough cells). Check the evolution of the total energy. What do you observe?