What happens if two electron beams move through each other in opposite directions? es1 is a numerical simulation to answer this and similar questions.
es1 is a one dimensional simulation of the interaction between two (infinitely long) charged beams moving in opposite directions. The observed behavior for e- e- is commonly known as the two-stream instability. The algorithm for es1 was created long ago (~1970) by A. Bruce Langdon and is fully documented in the book Plasma Physics by C. K. Birdsall and A. Bruce Langdon, McGraw-Hill, 1985. The implementation first on a PC and now the iPhone was done by T. Lasinski.
The opening view is a phase space plot of velocity versus position for the e- e- simulation. The two beams will gradually evolve into a rotating donut shape which is characteristic of the instability. The energy versus time plot (see diagnostics) shows the evolution of the field energy. Initially it grows exponentially; it turns over and levels out once the system becomes non-linear, just as the donut forms.
Input parameters for the two beams can be changed. Suggested parameters are provided for five simulations:
1. two stream instability. The app starts up with the parameters for e- e- interaction.
2. e+ e- instability. The behavior is quite different.
3. weak-beam ion instability. One of the beams has a mass 1000 times the other and is at rest.