Two-Stream Instability (twoStreamT.pre)

Keywords:

electromagnetics, two-stream instability

Problem Description

The two-stream instability is a rapidly growing collision-less plasma instability arising from small charge imbalances. A local imbalance leads to the acceleration or deceleration of particles in its vicinity, which in turn leads to an even stronger imbalance. One setup that allows to easily observe the instability is two counter-streaming beams of identical charge in a periodic system. The advantage of this configuration is that the generated plasma wave becomes a standing wave, thus allowing to easily observe the formation of the phase space vortices.

In this example, we use two electron streams. At \(t=0\) the streams have drift velocities of magnitude \(7.78 \times 10^6\) m/s. In order to accelerate the onset of the instability, the two particle beams are given a small sinusoidal perturbation in velocity space.

This simulation can be performed with a VSimBase license.

Opening the Simulation

The Two-Stream Instability example is accessed from within VSimComposer by the following actions:

  • Select the NewFrom Example… menu item in the File menu.
  • In the resulting Examples window expand the VSim for Basic Physics option.
  • Expand the Basic Examples (text-based setup) option.
  • Select Two-Stream Instability (text-based setup) and press the Choose button.
  • In the resulting dialog, create a New Folder if desired, and press the Save button to create a copy of this example.

The basic variables of this problem should now be alterable via the text boxes in the left pane of the Setup Window, as shown in Fig. 163.

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Fig. 163 Setup Window for the Two-Stream Instability example.

Input File Features

The simulation setup consists of an electromagnetic field and two particle species, one for each of the two counter propagating electron particle streams. Each electron stream is given a drift velocity and an additional velocity perturbation. For diagnostic purposes there is also output for species momentum, species energy and field energy histories.

The input file allows one to choose the average beam velocities and the amplitude of modulation. The number of particles per cell (PPC), dimensionality, length of the simulation and length of a time step can also be modified from the key parameters window.

Running the Simulation

After performing the above actions, continue as follows:

  • Proceed to the Run Window by pressing the Run button in the left column of buttons.
  • To run the file, click on the Run button in the upper right corner of the window. You will see the output of the run in the right pane. The run has completed when you see the output, “Engine completed successfully.” This is shown in Fig. 164.
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Fig. 164 The Run Window at the end of execution.

Visualizing the Results

After performing the above actions, continue as follows:

  • Proceed to the Visualize Window by pressing the Visualize button in the left column of buttons.

To view the instability in phase space:

  • Select the Phase Space option from the Data View menu.
  • In the Plot 1 box, change the X-axis to electrons0_x, the Y-axis to electrons0_ux, and Color to Red.
  • Click the Enable Second Plot box.
  • In the Plot 2 box, change the X-axis to electrons1_x, the Y-axis to electrons1_ux and Color to Blue.
  • Click the DRAW button at the bottom
  • Move the Dump slider over to dump number 100.
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Fig. 165 Visualization of the two-stream instability developing in particle phase space.

Further Experiments

Look at the histories to see how the plasma waves exchange energy with fields and each other as the instability develops.

Change the average velocity and velocity modulation and see how the speed at which the instability sets in depends on the modulation.

To calculate the density of the particles in the simulation switch the key parameters to

  1. VBAR = 7.78e3
  2. PPC = 10. (note that decimal point is important here)
  3. NDIM = 2

Then after the simulation has completed go to the Analyze Window, select ptclNumDensity from the drop down menu, input twoStreamT for the baseName and electrons0 for the speciesName and hit run. This process is detailed further in VSim In Depth