Laser Propagation in vacuum

The goal of this tutorial is to run your first simulation with Smilei. The following points will be addressed:

  • How to prepare an input file

  • How to check your input file using the test mode

  • How to access your simulation results

  • Get familiar with the Courant-Friedrich-Lewy (CFL) condition.

Physical configuration

Download the input file laser_propagation_2d.py. Note that this file is written in the python language.

Read through this file and try to understand the contents of the Main(...) and LaserGaussian2D(...) blocks. You can obtain details on the meaning of all keywords in this documentation page. Note that all units are normalized according to these conventions.

A Gaussian (in both space and time) laser pulse enters in the simulation box from the xmin side and propagates through the box.

Setup the tutorial

As explained in the setup page, you should make a new directory to run your simulation. This directory should contain the input file that you just downloaded and the executables smilei and smilei_test.

Checking your input file in test mode

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 laser_propagation_2d.py

This test mode does the same initialization as the normal mode but does not enter the PIC loop. It provides you with a log (what appears on your screen). What does this log tells you? Do you spot any ERROR message?

If you did spot an ERROR, can you correct it? If so, correct it, and try again!

Once you have no more ERROR message. Do you get WARNING messages?

Running the simulation

Once your simulation input file is correct, you can run the simulation.

./smilei laser_propagation_2d.py

Before going to the analysis of your simulation, check the output on the screen (the log).

  • What did change compared to the test mode?

  • Did your run complete correctly?

  • 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 the python post-processing package happi. To do so, open a new terminal window, and start ipython:

ipython

From ipython, import the happi module:

import happi

Get basic info on the simulation

Open the simulation that you have just run:

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

Warning

Use the correct path to the simulation folder.

See what is available from the simulation:

S.namelist.  # then press <tab>

When pressing <tab>, ipython display the content of the simulation. You can explore all these items. They should all be exactly the same as the ones that were defined earlier in the namelist laser_propagation_2d.py.

Check laser using Scalar

Read the namelist again and spot the line where the Scalar diagnostic has been defined. You may get more information on this diagnostic on this page.

Obtain a list of Scalar diagnostics:

S.Scalar()

Open the Uelm scalar and plot:

diag = S.Scalar('Uelm')
diag.plot()

This scalar represents the electromagnetic energy in the box. The plot we just obtained should represent its evolution with time.

More Scalar diagnostics

Check the evolution of the total energy in the simulation box:

S.Scalar('Utot').plot()

Check the evolution of the energy balance in the simulation box:

S.Scalar('Ubal').plot()

You can also compare the last two quantities on the same plot:

happi.multiPlot(
    S.Scalar('Utot', label="Total energy"),
    S.Scalar('Ubal', label="Balance")
    )

Plot laser using Field

Read the namelist again and spot the line where the Field diagnostic has been defined.

Open the Ey field and plot:

diag = S.Field(0, "Ey")
diag.slide(vsym=1)

This new function slide() makes a sliding bar to explore the time-evolution of the simulation.

Now, open the field with an average, and compare to the previous profile. The following calculates the laser amplitude envelope using "Ey**2+Ez**2". Then, using the argument average, it makes an average of this envelope for x close to 0 and y at 100.

S.Field(0, "Ey**2+Ez**2", average={"x":[0,7],"y":100}).plot()

Compare the laser profile with the theory

We are going to overlay the previous plot of the laser profile with the theoretical laser profile.

Get the Laser block from the namelist:

laser = S.namelist.Laser[0]

laser

Note that the laser is an object of type <Smilei Laser>.

See what is available in this laser object:

laser.  # then press <tab>
        # This should display all info on the laser

laser.time_envelope

Note that this quantity is a python function: what function is it? Some help is available here.

To plot the laser profile as a function of time, a list of times is necessary. In the following, we use the package numpy to generate a list of times from 0 to the end of the simulation, separated by the timestep.

from numpy import array, arange
tstop = S.namelist.Main.simulation_time # simulation final time
tstep = S.namelist.Main.timestep        # simulation timestep
times = arange(0., tstop, tstep)

You may type times in order to see what is the list of times that we have created.

Now, we execute the laser.time_envelope function on each of the times that we just created. We obtain a list of values of the laser envelope corresponding to each time.

laser_profile = array([laser.time_envelope(t) for t in times])

Plot the profile using the matplotlib package:

%pylab
plot( times+5, laser_profile**2 / 2 )

Testing the CFL condition

Now change the input file and increase the time-step e.g. using \(\Delta t = 0.95\,\Delta x\).

Re-run Smilei and check the total energy and/or energy balance.

What is going on?