Laser Plasma Acceleration

Problem Description

An intense, short laser pulse propagating through a plasma can lead to the separation of electrons and ions capable of producing accelerating electric fields of hundreds of GV/m. VORPAL is capable of simulating laser plasma accelerators (LPA) using several different models; envelope, fluid and full particle-in-cell (PIC) which will be the focus of this study.

Here we look at the full PIC model with a 1 mm long plasma with uniform density of 1.e25 m^-3. The laser wavelength is 800 nm with a waist of 9 μm.

Input File Features

The simulation domain size was chosen such that several RMS intensity pulse lengths and laser pulse lengths are continuously in the domain. The simulation time is set to run until shortly after the pulse leaves the plasma. For the grid spacing, the longitudinal size was determined based on the necessity to resolve the laser wavelength. A Gaussian pulse wave launcher is set as a boundary condition on the z component of the electric field which is launched into an electron species with a density ramp into a uniform species density. The moving window allows for a smaller simulation domain while still allowing the laser pulse to propagate further into the plasma as time increases.

Running the Simulation

Start VorpalComposer and select File -> Clone Example. Highlight Solving Classical Physics Problems and then select Next. Highlight Laser Plasma Accelerators and then select Choose. Create a new folder and then select Choose.

Alternatively, save the VORPAL input file, lpa.pre, and open in VorpalComposer.

The file should be displayed in the right pane of the Setup window. Click on the Save and Process Setup button in the lower right corner. Proceed to the run window as instructed. To run the file, click on the Run button in the lower left corner of the window. You can see the real time output of the run in the right pane.

Running in 2D, this simulation uses around 225,000 cells and nearly 200,000 particles. Run time may take several hours depending on your system.

Viewing the Output

Once instructed after the run has completed, proceed to the Visualize window to view the results. Load in the data files as instructed.

To view the electric field, switch to the Field Analysis tab in the Controls pane. From the Field drop down menu, choose the desired component of the YeeElecField. The laser pulse can be seen in the z (2) component of the field. The wakefield and plasma density can be seen in the SumRhoJ field. The zeroth component of this field corresponds to the charge density for the simulation.

Results

The output of the run shows the z polarized laser pulse in the electric field and the charge density after 1.8 picoseconds.

The z component of the electric field (left) and the charge density (right) at 1.8 picoseconds.

The acceleration of the particles can be seen by viewing the x component of the velocity. To do this, switch to the Phase Space tab in VorpalComposer and set the X-axis variable to plasmaElectrons_0 and the Y-axis variable to plasmaElectrons_2, then click Draw. Here the velocity is displayed as \(\gamma\)*v.

The x component of the velocity for the electrons at 1.8 picoseconds.

Further Experiments

Additional experiments worth investigating are:

• Comparison to the envelope model
• Comparison to the fluid model

References

[1] Cameron G.R. Geddes, Csaba Toth, Jeroen van Tilborg, Eric Esarey, Carl B. Schroeder, David L. Bruhwiler, Chet Nieter, John R. Cary, and Wim Leemans, “High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding”, Nature 431 (2004), p. 538-541.