FAST CODES FOR MODELING THE FUSION

PLASMAS RADIATIVE PROPERTIES

V.S. Lisitsa

IAEA CCN meeting, Vienna, Sept. 27-28, 2010

RRC Kurchatov Institute, Moscow, Russia

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)

A survey of current status and applications of fast codes

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

1.  nl-KINRYD, n,l collisional-radiative kinetics of Rydberg atomic states

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

Ne=1014 cm-3, Te=15 keV

Hydrogen atoms in the ground state H0(n = 1)

nl-population distribution function in С5+ ion

Element Transition Excitation rates (n=1) , 10–14 m3/s

Excitation rates H(n=2) , 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)

Excitation rates for a 100-keV hydrogen beam

User: ITER CXRS diagnostics , S.Tugarinov et al. (TRINITI, Russia)

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).

2. Fast code for Bremsstrahlung + Radiative Recombination spectra

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.

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]

Thomas-Fermi modelZ – nucleus electric charge E- incident electron energy

Classical “rotational“ approximation for high

Gaunt factor g for electron Bremsstrahlung on neutral atoms

EMEARCP = (Electron + Many-Electron Atom with Core Polarization). 

 

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)

3. Fast quasiclassical code for radiative and dielectronic recombination rates for many-electron

ions 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.

Enhanced R-factor for radiative recombination with core polarization effects

020 40 60 80 100 1200

n

1

2

3

4

5 C3+

6Q

DR

(n)

Distribution of DR rates (in units 10-

12 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]

0 30 60 90 120 1500

n

1

2

3

Mg1+

4

QD

R(n

)

Reference1. 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/

The same but for the Mg1+ ion: solid curve – universal formula; dotted line – calculation [1]

DR rates in quasiclassical approximation

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.

Recombination rates of Fe2+ ion vs. electron temperature

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)

4. Line broadening of hydrogen spectral linesin strongly magnetized plasmas

H(B = 2 T and B = 4 T), Ne = 1015cm−3, Te = 99764 K.

H, B = 4 T, Ne = 1014 cm-3, Te = 1 eV

Observation angle = 0°

Observationangle= 90°

Balmer lines spectrain magnetized plasmas

S. Ferri, A. Calisti, C. Mosse et al., Contr. Plas. Phys. (2010); Marseille U. + Kurchatov Inst.

Diagnostics D/T ratio in divertor plasmas

o molecular dynamics

_ kinetic method

Goal: background for Thomson diagnostics in ITER

Users: ITER Divertor Thomson Scattering diagnostics, E.Mukhin et al. (Ioffe, Russia)

Line shape calculations with B2-EIRENE code data for plasma parameters distribution

Plasma parameters along lines of sight: electron and neutral (Monte-Carlo modeling –B2- EIRENE code) densities and temperatures.

LINES OF SIGHT

PLASMA PARAMETERS ALONG CHORDS (B2-EIRENE code)

Te ne

Balmer P7 line shapes for ITER TS chord

The integral along the chord.Green line is the contribution of continuum.

1.0035 1.004 1.0045 1.005 1.0055 1.006

x 104

0

0.02

0.04

0.06

0.08

0.1

Inte

nsity

, a.u

.

, A

1.001 1.002 1.003 1.004 1.005 1.006 1.007 1.008

x 104

0

2

4

6

8

10x 10

15

Inte

nsity

, pho

ton

/(s

m

2 sr A

)

, A

= 4.73 A

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).

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 broadening;Vertical lines mark the position of Zeeman components.

(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.

5. Universal radiative-collisional kinetic code, based on the method of charge screening

constants and quantum defect for arbitrary chemical elements

Radiative losses of Li-plasma for Ne = 1013 см-3 : with (solid) and without (dashed) turbulence

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.

6. Conclusions