Progress on Numerical Simulations Trapped nonneutral plasmas are systems subject to relatively few physical laws, yet exhibiting a startling variety of intriguing behaviors. If the plasma is treated as a charged fluid, for example, the charge distribution creates an electric field. The velocity of flow is altered by the resulting Coulomb forces as well as by viscous damping and by pressure gradients. The altered velocity pattern in turn causes changes in density. Looping through these three gives the time evolution.
In the example presented below, a computer simulation in two dimensions is shown. The simulation space is subdivided into 39 x 81 cells. Periodic boundary conditions are applied. The four rectangles, top to bottom, show density, electric potential, x and y components of velocity. The false color pattern is rescaled for each frame so the 161 colors span lowest to highest values linearly, with black as midpoint, red through purple rising to the maximum and purple through red again in falling to the minimum.
The initial condition has uniform flow in the x direction (left-to-right). A 5 cell rod of negative charge is fixed left of center to represent the "beam". To reduce the size of the initial transient as the positive "plasma" fluid Debye-screens itself from the beam charge, a 25 cell neutralizing bump on an otherwise uniform plasma density surrounds the beam. For OCP confinement, a fixed uniform background charge is added to ensure overall neutrality within the space.
As the simulation proceeds, the fluid dragging past the fixed obstacle generates a detached soliton-like wave packet which travels faster than the fluid velocity. The motion is followed as the packet returns from the left to collide with the fixed beam-plasma dipole, proceeds around again with an added node to suffer a second collision.
Between collisions, the region near the beam stabilizes, and the drag force of beam on plasma is relatively steady.
Caution - this is work in progress and further checking needs to be done to verify the correctness of some of the details. It is displayed in its present form as an indicator of the level of complexity accessible to such fluid-in-cell simulations.
This animated gif image is 383 kb in length, and so may take some time to download via modem. It should repeat when viewed by a conforming Browser. The first 4 frames show the initial condition, the first step in potential, and then in velocity, and then the next complete cycle. The time interval between the next 35 frames is fixed, except for the pause before repeating.
The left button below returns you to the plasma site, while the right button takes you further afield (to home page of R. E. Pollock).