scholarly journals Nonlinear Problems of Equilibrium Charge State Transport in Hot Plasmas

2020 ◽  
Author(s):  
Vladimir A. Shurygin
Keyword(s):  
Charge State ◽  
Particle Transport ◽  
Local Equilibrium ◽  
Transport Coefficients ◽  
Nonlinear Problems ◽  
Kolmogorov Equation ◽  
Atomic Data ◽  
Theoretical Interpretation ◽  
Atomic Processes ◽  
Equilibrium Charge

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.

scholarly journals Nonlinear Problems of Equilibrium Charge State Transport in Hot Plasmas

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 324
Author(s):  
Vladimir A. Shurygin
Keyword(s):  
Charge State ◽  
Particle Transport ◽  
Strong Dependence ◽  
Kolmogorov Equation ◽  
Theoretical Interpretation ◽  
Partial Density ◽  
Atomic Processes ◽  
Density Profiles ◽  
Carbon Impurity ◽  
Equilibrium Charge

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 simultaneously a unit phase volume, the characteristic scales (in space and time) of local equilibrium, and a comprehensive solution for the simplest nonlinear relations between transport and atomic processes. The space-time relationships between the equilibrium constant, transport rates, density distributions, and impurity confinement time are found. The subsequent direct calculation of the total and partial density profiles and the transport coefficients of argon impurity showed a strong dependence of the 2D CS equilibrium and transport on the atomic structure of ions. A model for recovering the recombination rate profiles of carbon impurity was developed basing on the CS equilibrium conditions, the derived relationships, the data about density profiles, plasma parameters and ionization rates.

Local Equilibrium Evaluation of Thermal Transport Coefficients in Simple Liquids

1968 ◽  
Vol 48 (2) ◽  
pp. 951-953 ◽  
Author(s):  
J. Misguich ◽  
G. Nicolis ◽  
J. A. Palyvos ◽  
H. Ted Davis
Keyword(s):  
Thermal Transport ◽  
Local Equilibrium ◽  
Transport Coefficients ◽  
Simple Liquids

Diffusion in Materials with Ionic and Electronic Disorder

1990 ◽  
Vol 210 ◽  
Author(s):  
Joachim Maier
Keyword(s):  
Ionic Conduction ◽  
Diffusion Theory ◽  
Local Equilibrium ◽  
Transport Coefficients ◽  
Electrochemical Techniques ◽  
Chemical Diffusion ◽  
Tracer Diffusion ◽  
Internal Defect ◽  
Concentration Cell ◽  
The Individual

AbstractBesides some necessary reviewing of conventional diffusion theory, this paper deals with the modification of the mass and charge transport equations originating from the occurence of internal defect-chemical reactions (especially valence changes of the defects) which can be considered to be in local equilibrium. It is shown how the phenomenological transport coefficients for chemical diffusion, tracer diffusion and ionic conduction depend on the individual defect diffusivities under such general conditions. Moreover, the evaluation formulae of well-known electrochemical techniques such as Wagner-Hebb polarization and concentration cell experiments have to be modified. Application is made to the influence of trapping effects in doped SrTi03, to the valence changes in YBa2Cu3O6+x as well as to the mixed conduction in orthorhombic PbO.

Equilibrium charge-state distributions for 16O ions at 20–65 MeV

1975 ◽  
Vol 124 (2) ◽  
pp. 317-319 ◽  
Author(s):  
David J. Weber ◽  
Norton M. Hintz ◽  
D. Dehnhard
Keyword(s):  
Charge State ◽  
Equilibrium Charge ◽  
Charge State Distributions

scholarly journals Study on the electron configuration and the average equilibrium charge-state of highly charged Kr13+ ion

2014 ◽  
Vol 488 (13) ◽  
pp. 132034
Author(s):  
Cexiang Mei ◽  
Xiaoan Zhang ◽  
Yongtao Zhao ◽  
Jieru Ren ◽  
Xianming Zhou ◽  
...  
Keyword(s):  
Charge State ◽  
Electron Configuration ◽  
Equilibrium Charge

scholarly journals Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
A. Zocco ◽  
P. Xanthopoulos ◽  
H. Doerk ◽  
J. W. Connor ◽  
P. Helander
Keyword(s):  
Temperature Gradient ◽  
Temperature Dependence ◽  
Local Equilibrium ◽  
Acta Math ◽  
Theoretical Interpretation ◽  
Ion Temperature ◽  
Temperature Ratio ◽  
Ion Temperature Gradient ◽  
First Case ◽  
Unstable Solutions

The threshold for the resonant destabilisation of ion-temperature-gradient (ITG) driven instabilities that render the modes ubiquitous in both tokamaks and stellarators is investigated. We discover remarkably similar results for both confinement concepts if care is taken in the analysis of the effect of the global shear ${\hat{s}}$. We revisit, analytically and by means of gyrokinetic simulations, accepted tokamak results and discover inadequacies of some aspects of their theoretical interpretation. In particular, for standard tokamak configurations, we find that global shear effects on the critical gradient cannot be attributed to the wave–particle resonance destabilising mechanism of Hahm & Tang (Phys. Plasmas, vol. 1, 1989, pp. 1185–1192), but are consistent with a stabilising contribution predicted by Biglari et al. (Phys. Plasmas, vol. 1, 1989, pp. 109–118). Extensive analytical and numerical investigations show that virtually no previous tokamak theoretical predictions capture the temperature dependence of the mode frequency at marginality, thus leading to incorrect instability thresholds. In the asymptotic limit ${\hat{s}}\unicode[STIX]{x1D704}\ll 1$, where $\unicode[STIX]{x1D704}$ is the rotational transform, and such a threshold should be solely determined by the resonant toroidal branch of the ITG mode, we discover a family of unstable solutions below the previously known threshold of instability. This is true for a tokamak case described by a local ${\hat{s}}-\unicode[STIX]{x1D6FC}$ local equilibrium, and for the stellarator Wendelstein 7-X, where these unstable solutions are present even for configurations with a small trapped-particle population. We conjecture they are of the Floquet type and derive their properties from the Fourier analysis of toroidal drift modes of Connor & Taylor (Phys. Fluids, vol. 30, 1987, pp. 3180–3185), and to Hill’s theory of the motion of the lunar perigee (Acta Math., vol. 8, 1886, pp. 1–36). The temperature dependence of the newly determined threshold is given for both confinement concepts. In the first case, the new temperature-gradient threshold is found to be rather insensitive to the temperature ratio $T_{i}/T_{e}$, at least for $T_{i}/T_{e}\lesssim 1$, and to be a growing function of the density gradient scale for $T_{i}/T_{e}\gtrsim 1$. For Wendelstein 7-X, the new critical temperature gradient is a growing function of the temperature ratio. The importance of these findings for the assessment of turbulence in stellarators and low-shear tokamak configurations is discussed.

scholarly journals Charge equilibrium of fast heavy ions traversing through gaseous media

1984 ◽  
Vol 2 (4) ◽  
pp. 477-483
Author(s):  
S. Karashima ◽  
T. Watanabe
Keyword(s):  
Charge State ◽  
Hydrogen Gas ◽  
Electron Loss ◽  
Equilibrium Conditions ◽  
Equilibrium Charge ◽  
Gas Target ◽  
Gaseous Media ◽  
Ion Ranges ◽  
Non Local ◽  
Made In

The charge distribution of an incident ion as a function of projectile velocity, its range and its average equilibrium charge are studied theoretically. The calculations are made only for an atomic hydrogen gas target. The charge of the ion is determined by the equilibrium between electron loss from the ion and electron capature from a hydrogen atom to the ion. The charge states of the ions are calculated in two cases; to assume a local balance condition for electron loss and capture and to solve a rate equation for the charge state fraction function under non-local balance conditions, both only taking into account single electron loss and capture processes. In the calculations we use empirical formulae for electron loss and capture cross section by making some simplifications. Calculations for the charge state fraction as functions of ion ranges under non-equilibrium conditions have been carried out in the cases of Ne, Ar, and Xe ions. Calculations for the charge state under local balance conditions have been made in the cases of C, Ne, Ar, Kr, I, and U ions.

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