AN EXAMPLE OF A PLASMA DISCHARGE, EXTERNALLY DRIVEN,
IN WHICH THE PLASMA EDGE CONTROLS THE FINAL STATE

The objective is to show a whole plasma device where the behavior of the plasma edge region (consisting of the sheath, pre-sheath, wall charge), plus external drive (applied to the walls), dominates and dictates the final state of the device.

The model is a planar plasma diode, 1d3v, with a core, sheath, wall charge (done with PIC, ES Poisson solver), solved self-consistently (kinetically) with the external circuit (Kirchhoff's laws solver) (Ref. is JV et al., 1993) [We have also done this magnetized, with the applied B field at a small angle to the plates, and in 2d3v, ES and EM, making plasma surface-wave discharges. In this area we have a report by Xu (1992), and 3 Ph.D. theses, by Cooperberg (1997), Bowers (2001),and Qiu (2001)].

A key part to the solution is obtaining the contributions to the wall surface charge both from the plasma (induced) and also from the external circuit (current). The Poisson-Kirchhoff equations are solved together in order to obtain the self-consistent solution, all at the same time step. (Totally integrated.)

The example to be shown starts with an argon plasma at p = 3 mT, Te = 2eV, cool ions, RF driven by 7 volts at 81 MHz. Initially the plasma appears capacitive to the source, but, as it is weakly driven, the electrons and ions decay; it never becomes a capacitive discharge. However, the sheath width increases steadily at sound velocity and then explosively [like 1/(to - t)^a], "locking in" when the sheath edge reaches the plasma density where the edge plasma frequency equals the drive frequency.

The series resonance has set in. V is now in phase with I, a change of state, from capacitive to resistive, with most action in the sheath.

The plasma descriptors increase remarkably: mid (plasma) potential to 35 volts (greatly amplified); reactive power to real power; current; KE of both electrons and ions; the J.E heating jumps up by 10, mostly in the sheath. The decay of the particle number now becomes a growth, and a diffusive density profile begins to set in.

The real physics changes are in the sheath. The core heats up and diffuses but otherwise remains quite benign during all of these changes.

A full fusion reactor simulation would be much more complex, with many more processes, with surface charges and surface currents in the walls, and several kinds of drives. Seeking "full integration", self-consistency, is most desirable.

Reference: "Simultaneous potential and circuit solution for 1d bounded plasma particle simulation codes" by J.P. Verboncoeur, M.V. Alves, V. Vahedi, C. K. Birdsall, J. Comp. Phys., Vol. 104, pp. 321-328, 1993.