Analytical modelling of impurity transport in toroidal devices

Fußmann, G.

doi:10.1088/0029-5515/26/8/001

Cited by 50 publications

(48 citation statements)

References 14 publications

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“… , which provides a correct description of the radial states (layers) with equal plasma volumes. Third, unlike (36), the sets (21) and (34) are linear on n. But the argument 2  appears before the second derivative in the steady state solution of Equation (36), that is, in the confluent hypergeometric equation to be solved (see, for example, in [21,[33][34][35]). Then, to convert the original coefficient before second derivative of linear expression (21) into that of the standard Equation 36…”

Section: Impurity Equilibrium and Transport Coefficientsmentioning

confidence: 99%

“…The confinement time of impurity particles, p  , is conventionally determined by the smallest of the eigenvalues of the divergence operator [33,34], which represents the particle transport in the standard Equation (36). In the proposed matrix case, the analogue of this value, as follows from Formulas (34)(35), is the product Formulas (32)(33). Using this matrix approach, we obtain a relationship between E  and m. Figure 6 shows the calculations of these dependencies From the definition of p  , Formulas (34)(35) and calculations shown in Figure 6, we get, that…”

Section: Impurity Equilibrium and Confinement Timementioning

confidence: 99%

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Nonlinear Problems of Equilibrium Charge State Transport in Hot Plasmas

Shurygin¹

2020

Preprint

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The general coupling between particle transport and ionization-recombination processes in hot plasma is considered on the key concept of equilibrium charge state (CS) transport. A theoretical interpretation of particle and CS transport is gained in terms of a two-dimensional (2D) Markovian stochastic (random) processes, a discrete 2D Fokker-Plank-Kolmogorov equation (in charge and space variables) and generalized 2D coronal equilibrium between atomic processes and particle transport. The basic tool for analysis of CS equilibrium and transport is the equilibrium cell (EC) (two states on charge and two on space), which presents (i) a unit phase volume, (ii) the characteristic scale of local equilibrium, (iii) a comprehensive solution for the simplest nonlinear relations between transport and atomic processes. The approach opens up new perspectives on transport studies: (i) the direct modelling of equilibrium and transport of impurity using the atomic data base, (ii) recovery of the complete recombination rate profile based on knowledge of density profiles and ionization rate profiles, (iii) the local transport analysis, based on the reduction of the equilibrium set to the single EC (in particular, central or edge), (iv) analysis of the reduced transport coefficients (diffusion and convection) on the density profile measurements.

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Section: Impurity Equilibrium and Transport Coefficientsmentioning

confidence: 99%

Section: Impurity Equilibrium and Confinement Timementioning

confidence: 99%

Nonlinear Problems of Equilibrium Charge State Transport in Hot Plasmas

Shurygin¹

2020

Preprint

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“…At the plasma edge of a divertor tokamak we can re-write ffiffiffiffiffiffi ffi D ? p / ffiffiffiffiffi s k p =s p according to [12]. Furthermore we assume that the effective particle confinement time is approximately close to the global energy confinement time s Ã p ¼ s E .…”

Section: Extrapolation To Itermentioning

confidence: 99%

Highly radiating type-III ELMy H-mode with low plasma core pollution

Rapp¹,

Baar²,

Fundamenski³

et al. 2009

Journal of Nuclear Materials

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“…32 The transport equation for q is formally obtained from Eqs. 32 The transport equation for q is formally obtained from Eqs.…”

Section: A Charge State Dynamicsmentioning

confidence: 99%

Analytical approach to impurity transport studies: Charge state dynamics in tokamak plasmas

Shurygin

2006

Physics of Plasmas

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Ionization and recombination of plasma impurities govern their charge state kinetics, which is imposed upon the dynamics of ions that implies a superposition of the appropriate probabilities and causes an impurity charge state dynamics. The latter is considered in terms of a vector field of conditional probabilities and presented by a vector charge state distribution function with coupled equations of the Kolmogorov type. Analytical solutions of a diffusion problem are derived with the basic spatial and temporal dimensionless parameters. Analysis shows that the empirical scaling DA∝ne−1 [K. Krieger, G. Fussmann, and the ASDEX Upgrade Team, Nucl. Fusion 30, 2392 (1990)] can be explained by the ratio of the diffusive and kinetic terms, DA∕(nea2), being used instead of diffusivity, DA. The derived time scales of charge state dynamics are given by a sum of the diffusive and kinetic times. Detailed simulations of charge state dynamics are performed for argon impurity and compared with the reference modeling.

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Analytical modelling of impurity transport in toroidal devices

Cited by 50 publications

References 14 publications

Nonlinear Problems of Equilibrium Charge State Transport in Hot Plasmas

Nonlinear Problems of Equilibrium Charge State Transport in Hot Plasmas

Highly radiating type-III ELMy H-mode with low plasma core pollution

Analytical approach to impurity transport studies: Charge state dynamics in tokamak plasmas

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