Possible non-explicit relation between radau_gauss_grid and special_wfb_lorentz options

[David Dickinson]

In doing some testing of the response matrix I was calculating the relative difference between the collisional and collisionless response matrices in a range of cases. I found that with default settings in my test case this peaked at around 0.025. When I tried switching to the old radau_gauss_grid = .false. option this difference shot up to ~4. It seems that setting special_wfb_lorentz = .true. allows the difference to drop back to ~0.025 (and indeed the difference in this case is almost identical to the default case). This seems to suggest that these two choices are (perhaps unsurprisingly) linked and we should perhaps default as special_wfb_lorentz = .not. radau_gauss_grid?

I’ve not looked into the code yet so this task is here to remind me to look and for us to have discussion.

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[David Dickinson]

I’d guess that @Michael Hardman might have some insight on this and @Colin Malcolm Roach may also have some thoughts.

[Michael Hardman]

I think this may be explained by the fact that radau_gauss_grid gives weight to the wfb as if it was a passing particle, and special_wfb = .false. means that the wfb is treated like every other particle in the pitch angle solve. If special_wfb = .true., wfb is unphysically deleted from the pitch-angle solve at theta = +-Npi. I think if special_wfb = .false. and radau_gauss_grid = .false. then the wfb weight needs to be introduced into the pitchangle scheme in an ad-hoc way. Maybe this makes a huge numerical error. Could you try with "lorentz_scheme_old"?

[David Dickinson]

Thanks, that makes sense.

For both flags false the lorentz_scheme = ‘old’ option only makes a ~10% difference to the ~4 difference with collisionless.

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I suppose it’s also interesting to note that the relative difference for the two collisionless response matrices with and without radau_gauss_grid can also be significant (5). The maximum absolute difference is ~1e-4 whilst the maximum absolute value is close to 2. The relative difference is coming out so large because the absolute difference peaks where the absolute value is small.