To increase the number of unstable modes with UPIC, there are two ways to go. One way is to increase the system length, this will improve the resolution in space and increase the number of unstable modes within the same interval. Another way to go is to decrease the drift velocity, because the instability occurs within the range of , decreasing will increase the number of unstable modes in the same range of .
In the previous simulation, modes 1-3 are unstable. In this case, we double the size of the simulation and reduce the drift velocity by a factor of 1.8 (from 9 to 5). So in this case, modes 1-11 are unstable w.r.t. the two-stream instability. In this example, we will see how well the simulation agrees with theory when there are a large number of unstable modes.
The simulation parameters are:
- The length of the plasmas is 256 grids
- The simulation will run for a time 60 , stepsize is 0.2 , so the simulation has 300 timesteps.
- The simulation uses particles.
- Beam velocity for each beam is (which provides a small amount of noise to trigger the instability).