Level-resolved radiative recombination rate is overwritten by total radiative recombination rate in `ch_load_2ion_rates`

[wtbarnes]

When constructing the two-ion model, the level-resolved radiative recombination rates from the rrlvl files are added to the appropriate places in the radiative recombination matrix,

chianti-idl/level_population/ch_load_2ion_rates.pro

Lines 271 to 273 in 6641fae

	log_rr=interpol(alog10(rrec.rate[ii,*]), alog10(rrec.temp), alog10(t[ind2]) >0.)
	rr[ind2, n1+rrec.initial_level[ii]-1, rrec.final_level[ii]-1]=$
	10.^log_rr

Notably, this can include level-resolved ground-ground transitions, i.e. (n1,0) in the rate matrix is nonzero.

Additionally, the total radiative recombination rate of the recombining ion is used to calculate ground-ground rate,

chianti-idl/level_population/ch_load_2ion_rates.pro

Lines 297 to 316 in 6641fae

	tot_rr= total(rr[*, n1, 1:*],3)
	;; if verbose then begin
	;; print,'Total RR :', rr_rate_ground
	;; print,'Total RR from level-resolved:', tot_rr
	;; end
	if min(rr_rate_ground- tot_rr) lt 0 then begin
	print, 'ERROR ! the total of the level-resolved RR rates is greater than the total !?? '
	print, 'total level-resolved RR rates: ', arr2str(string(tot_rr,format='(e8.2)'),/trim)
	print, 'total RR rates: ',arr2str(string(rr_rate_ground,format='(e8.2)'),/trim)
	rr[*, n1, 0]= ( rr_rate_ground- tot_rr) > 0.
	wait,3
	endif else rr[*, n1, 0]= rr_rate_ground- tot_rr

However, this is inserted into the matrix in such a way that overwrites the level-resolved ground-ground transition that was added above. Why is this? Is there a particular reason that the total rate is not added to the level-resolved rate?

[pryoung]

Sorry for the delay in getting to this. For these two-ion models, the total recombination rate from the +1 ion must be consistent with that used for the ion balance calculation. The sum of the level-resolved rates should be less that the total recombination rate since the CHIANTI model only has a limited set of atomic levels. Therefore we need to insert the difference into the level balance equations. This is done by setting the n1->0 recombination to the difference. The difference between the total rate and sum of the level-resolved rates is calculated by not including the level-resolved n1->0. Thus when the n1->0 rate is replaced, the total of the level-resolved rates then matches the total rate. You can see this at lines 274-278 in the ch_load_2ion_rates code:

; PRY, 15-Mar-2019
; I've changed the sum in the 3rd dimension from 0:* to 1:* as
; the ground transition shouldn't be included.
;
tot_rr= total(rr[, n1, 1:],3)

An alternative would have been to sum all of the level-resolved rates, including the n1->0 rate. This difference could then be added to the existing n1->0 rate. This is exactly equivalent to the current IDL implementation, since the original n1->0 rate is canceled by the n1->0 rate included in the sum of the level-resolved rates.