Diffusive-convective model of impurity transport in quasi-stationary plasma: criticism and alternative

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In studies of impurity transport in quasi-stationary hot plasma, the initial kinetic equation and the diffusive-convective transport model take into account ionization and recombination as “sources and sinks” of particles. Due to the incompatible representation of the radial dynamics and charge kinetics of impurity charge states, this approach and the results obtained appear to be out of system. The basis for their systematic criticism is the ideas of the theory of random processes proposed by M.A. Leontovich in 1935 as a theoretical alternative to the gas-kinetic equation. In this case, the charge-radial transport of an impurity in a quasi-stationary plasma is defined as a syncretic vector random Markov process of charge state transport. Its coupling (ergodicity) in a two-dimensional Markov system excludes “sources and sinks” from it in principle, and the relaxation convergence is directed to the formation of equilibrium invariant density profiles. The impurity equilibrium and density profiles are specified by a system of invariant functions that provide analysis of any types of density profiles observed in experiments. Modeling of radial profiles of helium, boron and carbon impurities allows us to find variants of their transformation from accumulation in the center to concentration near the plasma edge, transport coefficients and systematic connection with plasma parameters.

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V. Shurygin

National Research Center “Kurchatov Institute”

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Email: Shurygin_VA@nrcki.ru
俄罗斯联邦, Moscow

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2. Fig. 1. General shapes of impurity density profiles observed in tokamak and stellarator plasmas: (a) impurity accumulation in the central region; (b) nearly flat profiles; (c) hollow with impurity accumulation near the edge. Data in the figures: (a) – Не (dashed line) (DIII - D [58]), C (solid line) and O (dots) (TEXT [59]), Ar (short dashed line JET #52136 [44]), Ni (dotted dots JET #74354 [56]); (b) He (dashed line, DIII - D [58]), C (solid curve DIII - D # 180520 [60], B (dots, ASDEX Upgrade # 37112 [61]), Ar (short dotted line JET #53048 [44]), Ni (dash-dotted line, JET #58149 [62]); (c) He (dashed line LHD, t = 4.07 s [63], C (solid line, L - mode ITB in LHD [34], Al (dash-dotted line, HL-2A, ECRH, t = 601 ms, [64]), Ar (fine dotted line, JET #52146 [65]).

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3. Fig. 2. Simulation (a–e, curves – measurements, symbols – simulation) and analysis (g–j) of the density profiles of He, B, and C impurities included in the general systems of invariant functions (for the selected pairs of impurities): reduced ionization and recombination rate profiles. Measured impurity density profiles: (a) – C (TFTR, RS, t = 2.7 s [79]) and B (ASDEX Upgrade, #25832, 5 MW NBI + 2 MW ECH, [80]); (b) – B (ASDEX Upgrade 5 MW NBI, #25832 [80]) and B (Alcator C - Mod, = 0.36 s [81]), (c) – B (ASDEX Upgrade, #34021 [82]) and B (ASDEX Upgrade, #30368 [4]); (d) – C (DIII - D, t = 2.0 s [6]) and B (ASDEX Upgrade, #38541, 2.5 MW NBI + 2.1 MW ECH [82]); (e) – He (TFTR, RS, t = 2.5 s [79]) and C (LHD, L - mode, t = 1.83 s [34]); (e) – C (LHD, ITB, t = 2.23 s [34]) and He (LHD, t = 4.07 s [63])

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4. Fig. 3. Sequence of invariant equilibrium density profiles included in the corresponding systems of invariant equilibrium functions – profiles of reduced ionization and recombination rates. Impurity density profiles are designated in the figure as follows: 1 – Не (ASDEX Upgrade, #30368, t = 4.39 s [4]); 2 – He (TFTR, RS, t = 2.55 s [79]); 3 – He (TFTR, RS, t = 2.5 s [79]); 4 – С (LHD, L - mode, t = 1.83 s [34]); 5 – С (LHD, ITB, t = 2.03 s [34]); 6 – В (Alcator C - Mod, ∆ t = 0 s [81]); 7 – 10 – C (LHD, ITB, t = 4.64/4.74/4.84/4.94 s [83]).

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