Eirene code calculations for the CX spectra of TJ-II

1. Eirene code calculations for the CX spectra of TJ-II • (or ‘Close Encounters of the Third Kind with Eirene’) • J. Guasp, A. Salas, etc… • Index • 1. Introduction • 2. Experimental data • 3. Fitting Eirene parameters • 3.1 Case of a single ion population • 3.2 Case of two populations • 4. Case with gas puffing • 5. Conclusions and NNET (Next Next Step) • Ciemat. January 12th 2007

2. Introduction • Up to now, in the Eirene calculations using TJ-II experimental data there have been three Phases: • 1st Phase: He lines emissivity. First using only relative values, later with absolute calibration. Good fit if the shape of the profiles is modified near the border, strong sensitivity to these modifications. Poster. • 2nd Phase: H emission (in H, of course), only relative values without absolute calibration. Good fit in the case without gas puffing, but without global level. Strong anisotropy due to the effect of the limiter. Seminars by Eduardo de la Cal and by myself. • 3rd Phase: CX spectra (in H), with and without gas puffing. Present seminar. • Weather and Authorities permitting, more Phases will be perpetrated in the near future(NNET).

3. Introduction • The experimental data for the CX spectra come from two detectors, both located at  = 85º (sector A8), whose viewing chords cross the plasma. For the 100_44 configuration the maximum proximities to the magnetic axis are s= 0.16 for theTop chord and s= 0.09 for the Bottom chord. Five energy measurements have been taken for each chord. • First we have analyzed shot #14579, without puffing and with a line-averaged density of 0.61x1013 cm-3 at the time of the Thomson Scattering profiles measurement. Top Bottom

4. Experimental data • The plots shown represent, as usual, the variable y  ln (Flux/E1/2) vs the energy E. Theoretically, in the case of a single ion population, the plots should be almost straight lines: • y = ln { A. [E1/2. exp-(2E/3Ti)] / E1/2 } = ln (A) - 2E/3Ti . • The experimental data for the spectra (red points and lines) suggest the possible presence of two populations with different ion temperatures, or at least this possibility can not be clearly excluded. • Indeed, one population fits give the following results (blue lines): • Top chord: Ti= 110.1 eV, with Max. diff. = +1.5% and  = 1.2% • Bottom chord: Ti = 113.9 eV, with Max. diff. = +2.1% and  = 1.7% • I.e., the maximum difference is 2% .

5. Experimental data • On the other hand, if two populations are considered, then the fit is much better (< 0.6%): • y = ln { A. [ (1-f2). E1/2. exp-(2E/3Ti1) + f2. E1/2. exp-(2E/3Ti2) ] /E1/2 } . • For the Top chord: 1stPopulation: 92.2%, Ti = 68.7 eV, • 2ndPopulation: 7.8%, Ti= 148.1 eV, • with Max. diff. = +0.51%,  = 0.42% • For the Bottom chord: 1stPopulation: 91.3%, Ti = 72.5 eV, • 2ndPopulation: 8.7%, Ti = 178.1 eV, • with Max. diff. = +0.55%,  = 0.52%

6. Eirene fits • I.e., the “logaritmic-linear” fits, purely mathematical (here Eirene is not used at all), give a maximum deviation with respect to the experimental data of 2% in the case of a single ion population and of less than 1% for two populations. Of course this does not demonstrate, at all, the reality of the two ion populations (it could be instead a simple numerical artifact) but as the possibility can not be clearly excluded, we are forced to include that case in the analysis. • These fits have been made separately for each chord, while with Eirene the fit is conjoint (both at the same time, since for each run the code uses a prescribed set of ion temperature distributions for the plasma). Moreover, the CX neutrals come from several chord points with different densities an temperatures, there is a statistical dispersion inherent in the Montecarlo method, there are many other parameters, etc., etc. • Therefore, one should not reasonably expect that the fits with Eirene should reach the same precision as the previous ones. Thus, we will feel satisfied as soon as we approach deviations of order 2% for a single ion population and 1% for two populations. • For the Eirene calculations the number of trajectories followed has been 4.8x106 (200000 per PE with 24 PE’s). A single run for a typical case takes some 12 min (on Fenix). Of course, to perform fits or parameter scans many runs for different cases must be made. • Let us see the results:

7. Eirene fits. One population • For a fit with a single population (thick line) the result is: • Maximum difference: -2.7% for the Top chord and +2.7% for the Bottom chord with  = 1.7%. • The result of the calculation for the manometer signal is 21.7% below the corresponding value in the TJ-II database (well inside the statistical incertitude for that measurement). • Moreover,Ti(0) = 113 eV (114 eV in the “logarithmic - linear” fit).

8. Eirene fits. One population • Density of neutrals, magnetic surface average. • H atoms: border density = 3.1x109 cm-3, central density = 1.0x109 cm-3, ratio = 3.0, penetr = 0.69 (12.3 cm) • H2 molecules: border density = 9.7x109 cm-3, central density = 3.2x105 cm-3, ratio = 29600, penetr = 0.21 ( 3.9 cm) • As is usually the case, molecules predominate clearly in the plasma border but they practically disappear below s ~ 0.4. On the contrary, atoms are less abundant in the border but they penetrate the plasma deeply.

9. Eirene fits. One population • Neutral distribution along the CX Top and Bottom chords. The green vertical lines indicate the plasma limits. The horizontal lines correspond to the values of the surface average densities at the plasma border (previous figure). • As usual, the density of molecules is very large near the VV wall (left and right side of each figure) and specially near the HC (right side of the first figure, 2.3x1010 cm-3 for the molecules, 4x109 for the atoms). The atoms are distributed more uniformly. The poloidal asymmetry is obvious in the first figure. • In these chords so central and so far from the limiters their effect is not discernible.

10. Eirene fits. One population • Distributions of neutrals along a chord going from the limiter to the HC crossing the magnetic axis (left), and along another chord tangent to the limiter (right). • It may be seen that the density of molecules at the limiter (5x1011 cm-3) is much higher than the surface average density at the border (~ 50 times higher). The same happens with the atoms (6x1010 cm-3 at the limiter, ~ 20 times higher than at the border). • The poloidal asymmetry is obvious for the first chord, and the “toroidal” one is spectacular for the second chord.

11. Eirene fits. Two populations • In the case of two populations the fit is much better (although it might perhaps be improved). • Maximum difference: -1.3% for the Top chord and +1.3% for the Bottom chord with  = 0.94%. • The central ion temperature for the first population (87%) is 85 eV (somewhat high) and for the second population (13%) it is 176 eV. The values for these temperatures in the “logarithmic-linear” fit were73 and 178 eV. • The neutral densities are slightly higher (3.8% H, 3.6% H2) than in the previous case. • The manometer signal is now 18.1% below the experimental value. • The shapes of the plasma radial profiles are fairly similar to those of the previous case.

12. Case with gas puffing • Subsequently we have also analyzed shot #14567, with an average density somewhat higher (0.64x1013 cm-3). This discharge has gas puffing. • In the case of one ion population the fit is somewhat better: • +2.0% for the Bottom chord, -1.9% for the Top chord, with  = 1.3%. • The neutral densities are now higher than those of shot #14579 (+28% H, +31% H2). • Surprisingly (?) the manometer signal differs only -0.5% from the experimental value !!!??? • Ti(0) is 113 eV (as in shot #14579) (110 eV in the “logarithmic-linear” fit). • The puffing rate is 29 A (~ 0.9x1020 molecules/seg). • In the case of two ion populations the fit is very good: • -0.80% for the Top chord, +0.75% for the Bottom chord, with  = 0.48%. • The neutral densities are somewhat higher than in the case of one population • (+16% H, +14% H2) and almost 50% higher than those of shot #14579 with one population. • The manometer signal is now 23% above the experimental value. • The central temperatures are 75 eV (90.7%) and 166 eV (9.3%) (73 and 174 in the “linear” fit) • The puffing rate is now 32 A (~ 1020 molecules/seg). • In all the cases the plasma radial profiles are quite similar, the dependence on the values and shape at the border seems to be weak, except perhaps in the case with puffing (few CX chords and too central ??).

13. Conclusions and Next Next Step • The fits performed with Eirene to the CX experimental data give reasonable results, both with one and with two possible ion populations, and also with or without gas puffing (although these results might perhaps still be improved, but remember that eachindividual case takes about 12 min). • It is very likely that the relative centrality and the scarce number of CX chords might be responsible for the lack of sensitivity to the shape and values of the density and temperature profiles at the border, at least in the case without puffing (??). • When using only H emission lines the results obtained were also reasonable (at least in the case with no gas puffing). • NNET: • For all these reasons I hereby decree that the NNET shall comprise some combination of both cases (CX and H). Since the evidence for two ion populations is not very strong we will consider the case of a single ion population only. • Therefore we should find some discharge of the 2006 campaign (either without NBI or with Scattering Thomson measurements taken before NBI) with both CX and H data and repeat the calculations. It would be best to have a typical (???) case without gas puffing and another one with it and, preferably, with signals usually included in the TJ-II Database … • A. M. TJ-IID. G.