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RRC Kurchatov Institute, Moscow, Russia
FAST CODES
FOR MODELING THE FUSION
PLASMAS RADIATIVE PROPERTIES
V.S. Lisitsa
IAEA CCN meeting, Vienna, Sept. 27-28, 2010
A survey of current status and applications of fast
codes
Why do we need the simplified fast atomic codes?
1) Incorporation as the blocks into integrated plasma modeling (on
the basis of transport code ASTRA, B2-EIRENE, etc.)
2) Account of new plasma effects: turbulent fluctuation of plasma
parameters (especially for edge and divertor plasmas);
3) Estimation of atomic effects for complex ions (RR and DR for
complex ion with account of core polarization effects);
4) Universal representation of plasma radiative properties with
multi-electron impurity ions.
General approach - quasiclassical methods
V.A.Astapenko, L.A.Bureyeva, V.S.Lisitsa Review of Plasma Physics, 2003,
v.23, pp.1-206.
L.A. Bureyeva et al. Phys. Rev.A, v.65032702 (2002)
V.I. Kogan, A.B. Kukushkin, V.S. Lisitsa, Phys. Rep., v.213,1 (1992)
1. nl-KINRYD, n,l collisional-radiative kinetics of
Rydberg atomic states
Goal:
Estimation of contribution of heavy atom impurities to the charge
exchange recombination spectroscopy (CXRS) in tokamak
plasmas (including the CXRS of core plasma in ITER)
Motivation:
• The number of atomic energy states in two dimensional (nl)
kinetics is rather large for direct computing of DR and CX
spectroscopy,
• 2D radiative-collisional cascade is well described by
quasiclassical kinetic model (without cut-off procedure, typical
for numerical solving of kinetic equations system).
M.B. Kadomtsev, M.G. Levashova, V.S. Lisitsa, JETP 106 (2008) 635-649
nl-population distribution function in С5+ ion
Population distribution function of bound atomic electron in С5+ as a
function of principal (nZ) and orbital (lZ) quantum numbers for charge
exchange
of С 6+ on diagnostic beam of Hydrogen atoms per one ion of С 5+ and
one atom of Hydrogen
Hydrogen atoms in the ground state H0(n
= 1)
Ne=1014 cm-3,
Te=15 keV
Excitation rates for a 100-keV hydrogen beam
Element
Transition
Excitation rates (n=1)
ns, 10–14 m3/s
Excitation
rates H(n=2)
ns,
10–14 m3/s
DINA [3]
ADAS [3]
nl-KINRYD
nl-KINRYD
He+
4–3
0.102
0.088
0.077
0.016
C5+
8–7
0.609
0.688
0.574
0.124
O7+
10–9
0.091
0.025
S.N. Tugarinov, M.B. Kadomtsev, M.G. Levashova, V.S. Lisitsa, N.N. Nagel,
36th EPS Conference on Plasma Phys. Sofia, June 29 - July 3, 2009 ECA
Vol.33E, P-5.214 (2009)
User:
ITER CXRS diagnostics , S.Tugarinov et al. (TRINITI, Russia)
2. Fast code for Bremsstrahlung + Radiative
Recombination spectra
ESMEABRR = (Electron + Static Many-Electron Atom)
Goals:
• Estimations of background radiation for Thomson scattering
diagnostics in ITER.
• Estimation of contribution of impurities to continuous spectrum
in divertor and edge tokamak plasmas (including ITER divertor
diagnostics tasks)
Semi-analytic description of Bremsstrahlung and radiative recombination cross
sections for collisions of quasiclassical electrons with a static many electron
atoms and ions (from neutral atom to fully stripped).
Users:
• ITER Divertor Thomson Scattering diagnostics, E.Mukhin et al. (Ioffe, Russia)
• ITER Edge Physics and Plasma-Wall Interactions Section (ITER).
Gaunt factor g for electron Bremsstrahlung on neutral atoms
Thomas-Fermi model
Z – nucleus electric charge
E- incident electron energy
Classical “rotational“ approximation
for high 
The universal classical functions g0() and g1(e) (curves) compared with the
corresponding (replotted) results of the numerical quantum calculations s)
[Lee C.M., Kissel L., Pratt R.H., Tseng H.K. Phys.Rev., 1976]
V.I. Kogan, A.B. Kukushkin, Sov. Phys. JETP, 60 (1984) 665.
V.I. Kogan, A.B. Kukushkin, V.S. Lisitsa, Phys. Rep., 213 (1992) 1.
3. Fast quasiclassical code for radiative and
EMEARCP =recombination
(Electron + Many-Electron
with Core
dielectronic
rates forAtom
many-electron
Polarization).
ions with core
polarization effects
Goal: recombination rates of electrons in collision with complex
ions (the input atomic data – energy levels and oscillator
strengths are needed)
Application: ionization balance in divertor and edge plasmas
V.A.Astapenko, L.A.Bureyeva, V.S.Lisitsa Review of Plasma Physics, 2003,
v.23, pp.1-206.
L.A. Bureyeva et al. Phys. Rev.A, v.65032702 (2002)
Enhanced R-factor for radiative recombination with
core polarization effects
Enhanced factor R averaged over coronal equilibrium for the
temperature 500 eV for different heavy ions: 1 – W, 2 – Mo, 3 – Fe.
DR rates in quasiclassical approximation
6
C3+
5
QDR(n)
4
3
2
1
0
0
20
40
60
80
100
120
n
4
Distribution of DR rates (in units 1012 cm3/s) over n for the C3+ ion at the
electron temperature Te=105 K: solid
curve – universal formula; dotted
line – calculation [3]; long dashed
line- calculation [2]
Mg1+
QDR(n)
3
The same but for the Mg1+ ion: solid
curve – universal formula; dotted line –
calculation [1]
2
1
0
0
30
60
90
120
150
n
Reference
1. K. LaGattuta and Yu. Hahn, Phys. Rev. Lett. V. 51, 558 (1983)
2. D. R. Rosenfeld, Astroph. J. V. 398, 386 (1992)
3. J. Li and Yu. Hahn, Z. Phys. V. D41, 19 (1997)
The ISAN site: http://www.isan.troitsk.ru/
Recombination rates of Fe2+ ion vs. electron temperature
1- total recombination rate
(close coupling S. N. Nahar,
Phys. Rev. A 55, 1980
(1997), 83 atomic states),
2- total radiative
recombination rate
(quasiclassical method with
core polarization effects),
3- radiative recombination
rate ( Kramers approx.),
4- recombination rate (static
core),
5-dielectronic recombination
rate.
4. Line broadening of hydrogen spectral lines
in strongly magnetized plasmas
Unified approach to dynamic and static Stark broadening,
strong Zeeman splitting, etc.
Goals: isotope composition diagnostics in ITER plasma by Balmer
spectroscopic measurements (H-alpha, H-betha spectral lines;
estimations of background radiation for Thomson diagnostics in
ITER Paschen (e.g. P7) spectral line shape)
Method:
Fast numerical codes for line shapes in thermonuclear plasmas
with strong magnetic fields combined with B2-EIRENE data for
plasma parameters distribution along lines of sights.
Users:
• ITER H-alpha diagnostics , A. Medvedev et al. (Kurchatov,
Russia)
• ITER Thomson scattering diagnostics, E.Mukhin et al. (Ioffe,
Russia)
Balmer lines spectra
in magnetized plasmas
Diagnostics D/T ratio in divertor
plasmas
Hb, B = 4 T, Ne = 1014 cm-3, Te = 1 eV
Observation
angle= 90°
_ kinetic method
o molecular
dynamics
Observation
angle = 0°
Ha (B = 2 T and B = 4 T),
Ne = 1015cm−3, Te = 99764 K.
S. Ferri, A. Calisti, C. Mosse et al., Contr.
Plas. Phys. (2010);
Marseille U. + Kurchatov Inst.
Line shape calculations with B2-EIRENE code data for
plasma parameters distribution
Goal: background for Thomson diagnostics in ITER
Users: ITER Divertor Thomson Scattering diagnostics,
E.Mukhin et al. (Ioffe, Russia)
LINES OF SIGHT
Plasma parameters along lines of sight: electron and neutral
(Monte-Carlo modeling –B2- EIRENE code) densities and temperatures.
PLASMA PARAMETERS ALONG CHORDS (B2EIRENE code)
Te
ne
Balmer P7 line shapes for ITER TS chord
0.1
The typical spectral line shape of deuterium Р-7
line across magnetic field in one separate point at
the chord, observed under dome ( ~ 10000 A).
Intensity, a.u.
0.08
0.06
0.04
0.02
0
1.0035
Intensity, photon /(s m 2 sr A)
10
x 10
1.004
1.0045
, A
1.005
15
Blue – static line shape with Zeeman splitting,
Red – with addition of ion dynamics (FFM),
Green – with addition of electron impact
broadening,
Magenta – total line shape, with Doppler
1.0055
1.006 broadening;
4
x 10
Vertical lines mark the position of Zeeman
components.
8
6
  = 4.73 A
4
2
0
1.001
The integral along the chord.
Green line is the contribution of continuum.
1.002
1.003
1.004
, A
1.005
1.006
1.007
1.008
4
x 10
5. Universal radiative-collisional kinetic code,
based on the method of charge screening
constants and quantum defect for arbitrary
chemical elements
(work in progress)
Screening constants + quantum defect method = fast code for
calculations of radiative energy losses of arbitrary impurities in
unstable plasmas et. It was demonstrated the effect of precise
kinetics on radiative energy losses at low temperatures (R.E.H
Clark, J. Abdallah (Jr.),At. Plasma-Material Int. Data for Fusion,
v.11(2003)1).
Just for such plasma parameters the turbulent temperature and
density fluctuations can change strongly the results. To take
turbulent effects into account is more simply by fast kinetics codes
with further comparison with precise kinetics.
Radiative losses of Li-plasma for Ne = 1013 см-3 :
with (solid) and without (dashed) turbulence
6. Conclusions
1. Fast Quasiclassical Codes (FQC) are effective method for
calculations of radiative properties of tokamak plasmas
including ITER conditions.
2. These codes need the support of more complex codes both
atomic ones (energy levels, oscillator strengths) and plasma
modeling codes (B2-EIRENE, transport code ASTRA, etc.)
3. The codes are accessible:
- Kurchatov Institute website (next year);
- RAS Institute of Spectroscopy website;
- semi-analytical formulas from surveys referenced above.