Alternative formulation of time step

[David Dickinson]

The basic time step in GS2 involves :

1. first finding g_p, the distribution function taking the potentials as constant in time
2. find the change in potentials using g_p and the response matrix.
3. Form the fields at the next time step
4. solve for the full new distribution function using the current and new fields.

It is also possible to replace steps 3 and 4 with simply solving for the change in the distribution g_c and then adding this to g_p.

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Branch experimental/alternative_advance_formulation gives a simple example of this alternative approach.

This is mostly intended as a brief note to record this option. I don’t currently have any strong argument why one form should be preferred over the other in terms of either performance or numerical stability. The original form is likely more elegant.

[David Dickinson]

As the current branch only implements this for field_option = 'local' the test suite doesn’t exercise this approach for all cases. However, if one forces field_option = 'local' for all tests then the test suite still passes.