1 Max-Planck-Institut für Plasmaphysik Cadarache 2012 K. Behringer A few comments on Opacity...

Cadarache 2012 1

Max-Planck-Institutfür Plasmaphysik

K. Behringer

A few comments on

Opacity Calculations Using ADAS214Cadarache, Sept. 2012

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

Cadarache 2012 K. Behringer 2

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 Tg)

in technical Plasmas (neutral H, He, Ar ….. in arcs also ions)

in divertor plasmas (neutral H, He)

→ here mainly neutral He

P8

A

cg

gn)( jk

4

j

kjabsorption coefficient

Doppler profile: gkjj19 T/fn1008.1)0( K,nm,m,m 31


line escape factor

)(

')'(exp)()(0

P

ddbL

L

b b

0

5

10

15

20

25

30

35

40

45

50

422,1 422,3 422,5 422,7 422,9 423,1 423,3

wavelength [nm]

inte

nsity

[arb

.un

its]

w = 0.06 nm /1023 m-3

0.1 nm, 1022 m-3

Ca I 4s2 1S - 4s4p 1P

b

L

b

line

b

tL

L

d

dddPlP

0

0

)(

')()'(exp)()(

b

L0


absorption of greenhouse gases

brightness temperature:

blackbody ceiling approached from above!

),()( brTTBL O3

CO2

surface temperature

temperature in 19.6 km

measurementfrom 19.6 km altitude(stratosphere)


population escape factor

......mk

mk,kmk,mk

k AnXnn e ....),()(1

1mk line

mk,km,m

km,m

ddL

hAnAn

the collisional-radiative particle balance is modified by absorption:

population escape factor

b

L2 a x


escape factors in the ASDEX Upgrade divertor

0 5 10 15 20 25

0.1

10-4

[pm]

P [pm-1]

10-5

10

1001000

0.01

10-3

1

wD / wH = 5

Doppler-Holtsmark

wD = 5.4 pm

parameter = (0) b

0.01 100.1 1 100 100010-3

10-2

0.1

1

p

wD / wH = 5

Doppler-Holtsmarkcylinder

parabolic emission profile

(0) b

10-3

sphere

disk

L L L L

(0): line centre

ne = 41020 m-3

nH = 31019 m-3

ionisation and recombination coefficients are also affected


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!


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


ADAS214 input – excited state factors


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 ni = ne (not the case in mixture plasmas).


output of my off-line program (in part)

C 06-04-2012 escape factor programC 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-03 1.00e-06)C m = 4, te = 3.50 eV, tg = 500.00 K, l = 6 cm, na (or nion) = 1.00e+15 cm-3C KB He microwave 10Pa, 3.5 eV, metastables according to ADAS208, M o'M ionisation lines C----------------------------------------------------------------------------C level= 2; Te= 3.5 2.15e+11 fraction/Boltz= 2.15e-04 2.07e-02C level= 3; Te= 3.5 1.99e+10 fraction/Boltz= 1.99e-05 7.21e-03C level= 4; Te= 3.5 7.28e+10 fraction/Boltz= 7.28e-05 3.24e-03C level= 5; Te= 3.5 1.71e+10 fraction/Boltz= 1.71e-05 2.45e-03C level= 6; Te= 3.5 2.13e+08 fraction/Boltz= 2.13e-07 4.69e-05C -----------------d:\adas\henew\1.00e+15\p0435_1E12.1E4; ne= 1.00e+12-----------------

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) -------------- 1.00D+00 | 1.19D-05 1.00D+00 | 7.46D-07 1.00D+00 | 1.37D-06 1.30D+00 | 6.94D-06 1.30D+00 | 4.61D-07 1.30D+00 | 1.12D-06 1.50D+00 | 5.41D-06 1.50D+00 | 3.66D-07 1.50D+00 | 1.01D-06 1.80D+00 | 5.76D-06 1.80D+00 | 4.08D-07 1.80D+00 | 1.27D-06 2.00D+00 | 8.90D-06 2.00D+00 | 6.61D-07 2.00D+00 | 2.12D-06 2.30D+00 | 2.09D-05 2.30D+00 | 1.65D-06 2.30D+00 | 5.51D-06 2.50D+00 | 3.57D-05 2.50D+00 | 2.90D-06 2.50D+00 | 9.93D-06 2.80D+00 | 7.02D-05 2.80D+00 | 5.94D-06 2.80D+00 | 2.10D-05 3.00D+00 | 1.02D-04 3.00D+00 | 8.90D-06 3.00D+00 | 3.19D-05 3.50D+00 | 2.16D-04 3.50D+00 | 2.00D-05 3.50D+00 | 7.29D-05


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 m2/s, 1 cm, tau = 210-6 sDiffusion 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 10-4 – 10-6 s.

important at low electron densities.

D6

a 2


helium 388.9 nm, 2s - 3p 3S - 3P°, Te = 3 eV, nHe = 1015 cm-3

n [cm ]10 101010 12 14

-3e

10

10-13

-12

X [cm /s]3

th ick, 10 s-4

th in, 10 s-4

th in, 10 s-5

th ick, 10 s-5

th in, no diffusionT = 3 eVe

triplet system!


neutral helium, “Boltzmann plot”

20 21 22 23

10 -10

10 -9

-8

10 -7

10 -6

10 -5

10 -4 T e = 4,0 eV

m -3

= 1,61x10 21 mn e = 1017

n Hep = 10 Pa

2 3 P

2 1 P

2 1 S2 3 S

3 3 S3 3 P

3 3 D

3 1 S

3 1 P3 1 D

-3

A D A S (op t. th in ) m easu rem en t

A D A S

n /m g n H em

E [eV ]

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


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 defaultsome 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

1 Max-Planck-Institut für Plasmaphysik Cadarache 2012 K. Behringer A few comments on Opacity...

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