search

MatthewGrim / plasma_physics

0 stars 0 forks source link

Write a resistive tearing mode growth rate solver for circular plasmas #37

Closed MatthewGrim closed 5 years ago

MatthewGrim commented 5 years ago

This issue documents the solution of resistive tearing modes for circular plasmas. The numerical method used is outlined in:

https://aip.scitation.org/doi/pdf/10.1063/1.1694467 https://minds.wisconsin.edu/bitstream/handle/1793/8602/file_1.pdf?sequence=1&isAllowed=y

The theory for this instability is outlined in: Tokamaks - John Wesson, D. J. Campbell

This basically should solve equation 6.8.7 in the same way as outlines in Section 6.9

MatthewGrim commented 5 years ago

The first pass implementation seems to work, but needs to be tested against the original results from:

https://aip.scitation.org/doi/pdf/10.1063/1.1694467

MatthewGrim commented 5 years ago

Currently the solvers give similar results, but clearly have problems at the r=0 condition that prevent a good solution. The ways to solve this problem are to find a series expansion and use this close to the axis, either to extrapolate out to the axis, or to set the initial conditions for the lower solution.

MatthewGrim commented 5 years ago

At this point, the solver has been tested against literature and results compare reasonably with my intuition.

The implementation could be improved by refactoring the normalised and physical solvers into a single code, but I don't see a string argument for doing this right now. For that reason I will close this issue, and if necessary return to re-factor the code when it becomes necessary/desirable.