Eirene calculations for H  emissivity in TJ-II with and without gas puffing

1. Eirene calculations for H emissivity in TJ-II with and without gas puffing J. Guasp, A.Salas, E. de la Cal, et al. Contents H detection chords. Best fit. Neutral profiles. Case with puffing 5. Conclusions. Ciemat. June 2006

2. 1. H detection chords Vertical projection of the 1st chord, passing near the 2nd limiter. The other 10 chords have the same origin but are shifted vertically, the last one cross the magnetic axis.

3. 1. H detection chords Chord dz(cm) smin 1 0.64 0.89 2 1.95 0.76 3 3.27 0.69 4 4.59 0.57 5 5.91 0.48 6 7.23 0.39 7 8.55 0.27 8 9.86 0.18 9 11.2 0.11 10 12.5 0.08 11 13.8 0.0 __________________________ 12 ----- 0.0 13 ----- 0.14 Toroidal cut at  = -155º showing the plasma cross section, the 2nd limiter and the projection of the 1st chord, the closest point to the magnetic axis has s = 0.89 and is very near the limiter position. There are in total 11 chords, sharing a common origin, that are on the same vertical plane. The closest plasma radius reached by these chords appears in the table above and goes from 0.89 (1st) up to the axis (11th).

4. 2. Best fit For the calculations a pure H, ECRH discharge, without gas puffing, was chosen (#14605). It had, at the moment of TS measurement (1120 ms), a line average density of 5.9x1012 cm-3, the two limiters were placed at -35.2 cm, the particle confinement time estimated at 5 ms and the width of the SOL at 1 cm for the density and 2 cm for the temperatures. The recycling coefficient was taken as 1. In the Eirene code the default set of reactions for H and H2 were taken. A total of 2.4 million of trajectories were followed (100000 by PE with 24 PEs) producing an statistical incertitude of ~ 2%. As no absolute values were given for the 11 H signals, the relative values with respect to the 1st chord (the most external one and the closest to the limiter) were taken as experimental data to fit, with an incertitude of ~20% (10% for the original signals). The fit procedure was done in the same way than with the He lines calculations: the shape of the profiles near the border was modified (this time including also the ion temperature, not measured, as well at the border as at the center), of course the energy of the H+ ions emerging from the plasma and hitting the wall was calculated internally as in the He case and, this time, as the limiters were very close to some of the signal chords, the proportion of particles intercepted by the limiters (variable fraclim in the PREPROC program) was included also. The H ratios were insensible to the rest of parameters.

5. 2. Best fit After many trials a satisfactory fit was found, with a visible modification of the density profile at border (changing from 1.08x1012 cm-3 to 1.3 9%) and a lesser one, smoothing the profile, for the electron temperature (changing from 36 eV to 39 7%). The ion temperature was 108 eV (18%) at center and 23 eV (40%) at border.

6. 2. Best fit In this best fit, the maximum difference between the Eirene results and the experimental H ratios was of -17.5% at the 2nd chord, followed by the 4th one with -17.3% and the 8th with +16.5%, all the other chords had a difference lesser than 15%. The relative RMS deviation was of 14.3%. In consequence the fitting can be considered as satisfactory.

7. 3. Neutral profiles The surface averaged radial profiles for the neutral population ( H atoms in black, H2 molecules in red) are shown in the plot above. The H2 density at plasma border is 2.3x1010 cm-3, the value at magnetic axis is 6.8x105: a ratio border/center greater than 34000. The shape is clearly not exponential (exponential fit average difference ~20%) but rather gaussian (7%). Penetration length is 0.13 of average plasma radius (~2.4 cm) For the H atoms: border value 5.8x109, central 1.7x109, ratio 3.5: much lower. The exponential fit differs in 13%, better than the gaussian (27%), penetr. is 0.6 (~ 11 cm).

8. 3. Neutral profiles The neutral densities along the two extreme chords are represented above. The left plot corresponds to the chord closest to the limiter (1st one) whose influence is evident, the H2 density reaching more than 2.2x1012 cm-3, the atomic density is one order of magnitude lesser. The right plot corresponds to the last chord (11th one) that crosses the magnetic axis, the limiter effect is not visible, any more, in the molecular density that concentrates at plasma border, this time with only 1.3x1011 at maximum and negligible values near the axis. The atom population is more uniformly distributed but the limiter effect is yet visible.

9. 3. Neutral profiles Two more neutral distributions along chords are represented here. The left one corresponds to an intermediate H chord (6th, with dz = 7.2 cm and smin = 0.39), where the effect of the limiter is still very visible for the H atomic population, but is lost for the molecular one. The right plot corresponds to a supplementary chord (the 12th one), not included in the H signals, that goes from the limiter to the magnetic axis. In this chord the penetration length for the atoms is 4.5 cm, a gaussian fit for the first part of the profile (left of the s = 0 point) gives a relative RMS deviation of 12%, while for an exponential fit it is 15%. For the molecules these values are 2.4 cm, 6% and 28%.

10. 4. Case with gas puffing A very similar discharge (#14616), but this time with gas puffing injection, coming from the 2nd limiter surface, has been analysed. This time there are two separated sources: the H+ ions coming from the plasma, that are treated as before, and the H2 molecules coming from the gas puffing. The gas puffing intensity was, at most, ~ 1020 H2 molecules/sec, and this new parameter was included in the search. The average emission energy of these molecules (with maxwellian distribution) was taken as 0.026 eV, fixed, there were very small sensitivity to this paremeter. As before the default Eirene reaction data for H and H2 were used. But, up to now, NO satisfactory fit has been found.

11. 4. Case with gas puffing The least worst fit found up to now, had a maximum difference between the Eirene results and the experimental H ratios of +24.8% at the 6th chord, -23.9% at the 5th and -18.3% at the 2nd one. The relative RMS deviation was of 11%. Clearly not a satisfactory fit at all. In particular the 2nd and 5th chords were extremelyrigid to all intended changes in any parameter. The main parameter values were: eneb = 2.5x1012 cm-3 (6%) almost double than for the case without puffing. Teb = 22 eV (7%) 23% lesser and flxpuff = 0.50x1020 molec/s ( 19%)

12. 4. Case with gas puffing In reason of the lack of agreement we tried to change, artificially, the emission energy of the H ions playing with the sheath potential factor (fsheath parameter), usually taken as 2.8 times of the Te at border. Nevertheless the improvement was minimal: the maximum difference only decreased from -25% up to -24.7 when fsheath changed from 2.8 to 1.15 (39%), a change that is inside the statistical uncertainty margins (~2%) Of course the existence of a better fit can not be excluded but, to me, it seems rather improbable. The neutral profile behaviours along the chords are similar to the case with puffing but with much higher values for the neutral densities, one order of magnitude, mainly near the limiter.

13. 5. Conclusions A search for the Eirene parameters that produce agreement between the experimental data for the ratio of the H emission in a TJ-II discharge without gas puffing has been done. Optimal values, inside the given experimental errors and statistical incertitude of the calculations, have been found (maximal difference ~-17%, average ~14%) and the corresponding neutral profiles obtained and analysed. Instead, in the case with puffing, no good agreement has been found with the default Eirene reactions (maximal difference greater than ~30%) even if the emission atom energy has been allowed to change artificially. The resulting neutral profiles along the chords have similar behaviour than in the former case but with much higher densities.