1 dimensional particle-in-cell code

Files description

• parameters.py - simulation & plasma parameters

• generation.py - various function to generate plasma

• cycle.py - basic [backwards]weighting and solution functions

• main.py - the main part containing the whole p-i-c cycle and data export

• plotter.py - for creating animation from data exported to .dat files

• helpers.py - progress-bar and timing functions

Simulation

The program can be started by calling python main.py. Make sure to modify output paths in main.py and input in parameters.py:

NAME = ‘input_value_name’

This NAME determines what primary configuration is used:

• ’plasma_fluc’ - simple plasma fluctuations (see video)
• ’two-stream’ - two-stream instability (uniform distribution) (see video)
• ’two-stream_r’ - two-stream instability (random distribution) (see video)
• ’four-stream’ - "four-stream" instability (kind of) (see video)
• ’beam_instability’ - beam instability (see video)

Plotting

Plotter works distinctly by calling python plotter.py. To simply view the animation comment out anim.save(…) leaving plt.show(). To save the animation, make sure to put ffmpeg codecs from here to your /usr/local/bin/ directory (necessary for OS X).

Experimenting with various inputs

Feel free to create your own plasma generation functions. Add the NAME parameter for it in parameters.py and add the elif case in main.py.

The only thing you need to keep in mind, is to keep the overall charge density neutral. You can check that by doing

numpy.sum(density(particles)[:-1])

[:-1] here is because of the periodic boundary conditions and density[NODES - 1] equals to density[0].

Particles can be movable, i.e., particle.mv = True, or permanently nailed in place, particle.mv = False.

Particle class

This class contains the info about particles.

It accepts:

• pos: position
• vel: velocity
• omegaP: plasma frequency
• QoverM: charge-to-mass ratio
• move: True if particle is movable, False if it’s not

It contains:

• particle.x and particle.v: [accepts float] logical position and velocity of the particle

• particle.qm: [accepts float] charge/mass ratio for the particle

• particle.q: particle charge determined by the equation

  self.q = omega_p**2 * (1 / qm) * eps_0 * (L / N)

  • omega_p is the given plasma frequency
  • eps_0 is the vacuum permittivity (set to be 1)
  • L / N is the number density of particle specie

• particle.mv: [accepts bool] the particle is either movable or not

Further reading

• Birdsall, C. K., & Langdon, A. B., 1991, Plasma Physics via Computer Simulation, The Adam Hilger Series on Plasma Physics, edited by C. Birdsall & A. Langdon. Adam Hilger, Bristol, England (ISBN: 0-07-005371-5)
• Hockney, R. W., & Eastwood, J. W., 1988, Computer Simulation Using Particles, Bristol: Hilger (ISBN: 978-0852743928)