1 Max-Planck-Institut für Plasmaphysik Cadarache 2012 K. Behringer A few comments on Opacity Calculations Using ADAS214 Cadarache, Sept K. Behringer escape factors for line radiation (pec-files) – or – population simple(r) case: excited state population negligible (only resonance lines optically thick) opacity of excited states (iteration) additional remark: the importance of diffusion summary

2Cadarache 2012 K. Behringer when is opacity important? optical thickness (re-absorption) of line radiation is mainly important at - high lower state densities (→ resonance lines) - high transition probabilities - narrow lines (low T g ) in technical Plasmas (neutral H, He, Ar ….. in arcs also ions) in divertor plasmas (neutral H, He) → here mainly neutral He absorption coefficient Doppler profile:

3Cadarache 2012 K. Behringer line escape factor

4Cadarache 2012 K. Behringer absorption of greenhouse gases brightness temperature: blackbody ceiling approached from above! O3O3 CO 2 surface temperature temperature in 19.6 km measurement from 19.6 km altitude (stratosphere)

5Cadarache 2012 K. Behringer population escape factor the collisional-radiative particle balance is modified by absorption: population escape factor 

6Cadarache 2012 K. Behringer escape factors in the ASDEX Upgrade divertor  (0): line centre n e = 4  m -3 n H = 3  m -3 ionisation and recombination coefficients are also affected

7Cadarache 2012 K. Behringer pec files with optical thickness ADAS214 calculates these escape factors. ADAS214 changes A-values in adf04 files according to population escape factors, subsequent ADAS208 calculations correct the population structure for opacity. however: the reduced A-values are also being used for line emission in the pec output files! This may not be what you want (fortunately line and population factors are similar for the longer plasma dimension). It may be necessary to use the paper.text output and multiply by the proper A-values later!

8Cadarache 2012 K. Behringer lower state densities do we know the lower state densities? resonance lines: yes if excited state population negligible - fortunately often the case lines between excited states? if excited state population matters, iteration is required manual input in ADAS214: default = Boltzmann distribution! cannot input small numbers – are set to zero by program must use tricks

9Cadarache 2012 K. Behringer ADAS214 input – excited state factors

10Cadarache 2012 K. Behringer transitions between excited states run ADAS214 with a first guess of excited state population run ADAS208 to calculate excited state densities use output for ADAS214 – iterate (tedious procedure by hand) input of ADAS208 paper.text densities and output of excited state information in adf04 file provided in my off-line escape factor program – text output of ADAS214 is pretty useless caution: ADAS208 equilibrium population output includes recombination with n i = n e (not the case in mixture plasmas).

11Cadarache 2012 K. Behringer output of my off-line program (in part) C escape factor program C produced with ADASESCV.BAS (V. 31/3/98) from d:\adas\adf04\helium\behringer_he\p04he0.dat and the following data: C parab. case; cyl.; profile#: 1 (underpop: 6.00e e-06) C m = 4, te = 3.50 eV, tg = K, l = 6 cm, na (or nion) = 1.00e+15 cm-3 C KB He microwave 10Pa, 3.5 eV, metastables according to ADAS208, M o'M ionisation lines C C level= 2; Te= e+11 fraction/Boltz= 2.15e e-02 C level= 3; Te= e+10 fraction/Boltz= 1.99e e-03 C level= 4; Te= e+10 fraction/Boltz= 7.28e e-03 C level= 5; Te= e+10 fraction/Boltz= 1.71e e-03 C level= 6; Te= e+08 fraction/Boltz= 2.13e e-05 C d:\adas\henew\1.00e+15\p0435_1E12.1E4; ne= 1.00e ADAS208 output with this file (3.5eV/1e12cm-3): LEVEL = 2 - EQUILIBRIUM POP LEVEL = 3 - EQUILIBRIUM POP LEVEL = 4 – EQUILIBRIUM POP NE (CM-3) 1.00D+12 NE (CM-3) 1.00D+12 NE (CM-3) 1.00D+12 TE (EV) TE (EV) TE (EV) D+00 | 1.19D D+00 | 7.46D D+00 | 1.37D D+00 | 6.94D D+00 | 4.61D D+00 | 1.12D D+00 | 5.41D D+00 | 3.66D D+00 | 1.01D D+00 | 5.76D D+00 | 4.08D D+00 | 1.27D D+00 | 8.90D D+00 | 6.61D D+00 | 2.12D D+00 | 2.09D D+00 | 1.65D D+00 | 5.51D D+00 | 3.57D D+00 | 2.90D D+00 | 9.93D D+00 | 7.02D D+00 | 5.94D D+00 | 2.10D D+00 | 1.02D D+00 | 8.90D D+00 | 3.19D D+00 | 2.16D D+00 | 2.00D D+00 | 7.29D-05

12Cadarache 2012 K. Behringer additional process: diffusion diffusion of metastable particles out of the plasma volume must be taken into account – possibly by an artificial transition probability to the ground state. for a cylindrical plasma with radius a and a parabolic source the confinement time is metastable He in He, 500 K, 1 Pa, D = 8 m 2 /s, 1 cm, tau = 2  s Diffusion and Excitation Transfer of Metastable Helium in Normal Gaseous Helium, R. A. Buckingham and A. Dalgarno, Proc. Roy. Soc. A, 506 (1952) in technical plasma diffusion times are of the order of – s. important at low electron densities.

13Cadarache 2012 K. Behringer helium nm, 2s - 3p 3 S - 3 P°, T e = 3 eV, n He = cm -3 triplet system!

14Cadarache 2012 K. Behringer neutral helium, “Boltzmann plot” He I experiment: ECR discharge, emission spectroscopy, n=2 from absorption (Augsburg University: Berger, Fantz, Dietrich) clear proof of optical thickness rate coefficients pretty well confirmed similar in Haas’ ionisation gauge

15Cadarache 2012 K. Behringer summary  in some plasmas optical thickness of spectral lines is important influences (differently) population and emitted intensities  using ADAS214 and ADAS208, the same escape factors are used for population and pec files – may have to use paper.text files  ADAS214 uses Boltzmann population of excited levels by default some problems to put in low values (→correct code)  when optical thickness between excited levels is really important, iteration of population calculations is required – hard with ADAS214 better text output of ADAS214 desirable  in many plasmas, diffusion of metastable ions must be taken into account – possibly by an artificial transition probability