Cadarache 2012 1 Max-Planck-Institut für Plasmaphysik K. Behringer A few comments on Opacity Calculations Using ADAS214 Cadarache, 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
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1 Max-Planck-Institut für Plasmaphysik Cadarache 2012 K. Behringer A few comments on Opacity Calculations Using ADAS214 Cadarache, Sept. 2012 K. Behringer.
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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
Cadarache 2012 K. Behringer 3
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
Cadarache 2012 K. Behringer 4
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)
Cadarache 2012 K. Behringer 5
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
Cadarache 2012 K. Behringer 6
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
Cadarache 2012 K. Behringer 7
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!
Cadarache 2012 K. Behringer 8
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
Cadarache 2012 K. Behringer 9
ADAS214 input – excited state factors
Cadarache 2012 K. Behringer 10
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).
Cadarache 2012 K. Behringer 11
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-----------------
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.