Summary of numerical results
Well behaved equilibria exist regardless of the boundary conditions
In the limit of small Debye length (cold plasma), the electrostatic potential becomes nearly constant on magnetic surfaces, except near the edge, where it is determined by the boundary conditions.
In the limit of large Debye length (hot plasma), the density becomes nearly constant on magnetic surfaces, whereas the electrostatic potential is determined by the boundary conditions
Large Debye length limit is trivial. Small Debye length limit is challenging numerically. We are limited to 0<a/?D
- e?/Te varies by 100 in domain - corresponds to 50 orders of magnitude in exp(e?/Te)!!!! Numerical roundoff errors are magnified unacceptably
- Even in the limiting cases, n and e?/Te are perfectly well behaved
- Fix: Renormalization (take out large factors)? Future work.