## Computational Research Projects

### Secondary Electron Emission Effects on Sheath Existence and Stability

#### Michael Campanell

Debye sheaths are universal features of plasma-material interaction. My work is on the PIC simulation and theoretical analysis of secondary electron emission (SEE) effects on sheaths. It is well known for a plasma contacting a wall that when "secondary" electrons are emitted, more plasma electrons must reach the wall in order to balance the (fixed) ion flux; this reduces the sheath potential and enhances losses. But in bounded plasmas, secondaries accelerated away by the sheath form beams that can strike other surfaces or reflect back to the emitting surface. This substantially alters the current balance compared to treatments that consider one wall. SEE can also cause instability or "collapse" of the sheath if the derivative of the net electron flux with respect to the sheath potential is positive. At high temperatures, it is possible for the plasma electrons to eject more than one secondary on average. In this case, a classical sheath cannot exist. Simulations show that an "inverse" sheath may appear, in which the surface charge is positive and secondaries are pulled back to the surface to maintain zero current.

Advisor: Igor Kaganovich

### Symplectic Integration of Guiding Center Orbits

#### Lee Ellison

As tokamak discharges extend longer (currently several seconds), accurate numerical modeling requires long-term fidelity. A typical discharge can involve millions of particle transit times. It then becomes critical how one discretizes the equations of guiding center motion. Symplectic integrators establish good long-term behavior by exactly preserving a symplectic structure and bounding oscillations in energy error for all simulation time. A Lagrangian expression exists for guiding center motion in an arbitrary magnetic and electric field, however, the coordinates are non-canonical, making implementation of standard symplectic integrators difficult. Recently, a purely variational approach to developing symplectic integrators has emerged, allowing a symplectic algorithm even in non-canonical coordinates. At present, a fully three-dimensional code has been developed for symplectically integrating guiding center orbits in an arbitrary electric and magnetic field. Future work includes adaptive-step integration, applications in more complicated configurations, and studying problems where long-term fidelity is crucial.

Advisors: Hong Qin and Bill Tang