Transport in partially degenerate, magnetized plasmas. Part 2. Numerical calculation of transport coefficients

1999 ◽  
Vol 62 (2) ◽  
pp. 129-144 ◽  
Author(s):  
S. R. BROWN ◽  
M. G. HAINES
Keyword(s):  
Classical Limit ◽  
Transport Coefficients ◽  
Collision Operator ◽  
Plasma Phys ◽  
Low Energy ◽  
Magnetized Plasma ◽  
Linear Electron ◽  
Discrete Ordinate ◽  
Electron Collisions ◽  
Polynomial Expansions

The modified Fokker–Planck collision operator for partially degenerate electrons was derived in an earlier paper [J. Plasma Phys.58, 577 (1997)]. This is now employed to study linear electron transport for a partially degenerate, magnetized plasma. Because polynomial expansions can yield incorrect transport coefficients owing to lack of resolution of the small fraction of low-energy unmagnetized electrons, a numerical discrete-ordinate scheme is employed. The inclusion of electron–electron collisions advances the model beyond that of Lee and More, and in the classical limit agrees with the results of Epperlein and Haines.

Anomalous transport due to long-lived fluctuations in plasma Part 1. A general formalism for two-time fluctuations

1976 ◽  
Vol 16 (2) ◽  
pp. 193-227 ◽  
Author(s):  
John A. Krommes ◽  
Carl Oberman
Keyword(s):  
Classical Theory ◽  
Test Particle ◽  
Initial Conditions ◽  
Superposition Principle ◽  
Transport Coefficients ◽  
Collision Operator ◽  
Magnetized Plasma ◽  
Constructive Proof ◽  
Fluid Viscosity ◽  
Image Position

A general formalism for describing two-time fluctuations in magnetized plasma is presented. Two-time expectations of one-body operators (phase functions) are written in terms of the phase space density autocorrelation functionwhere δN is the fluctuation in the singular Klimontovich microdensity. It is shown that is the first member of a set of two-time quantitieswhich collectively obeys the linearized BBGKY cumulant hierarchy in the (Xi, t) variables, with initial conditions successively smaller in the plasma parameter . We study in detail the case of fluctuations in thermal equilibrium, although the general formalism holds also for the non-equilibrium case. To lowest order in εP, Γ obeys the linearized Vlasov equation. From this are recovered all of Rostoker's results for fluctuations excited by Cherenkov emission and absorbed by Landau damping, as well as a constructive proof of the test particle superposition principle. To first order, Γ obeys (in the Markovian approximation) the linearized Balescu-Guernsey-Lenard equation. For frequencies and wavenumbers in the hydrodynamic regime, the velocity moments of Γ obey linearized fluid equations with classical transport coefficients (i.e. essentially those computed by Braginskii in the 3-D case). It has been found that the classical theory is in disagreement with certain computer and laboratory experiments performed in strong magnetic fields. This defect is attributed to the absence in the classical theory of contributions to the collision operator, hence transport coefficients, of fluctuations long-lived on the Vlasov scale. Analogous difficulties arise in the theory of hydrodynamics in neutral fluids. To improve the plasma theory, a renormalization of the two-time hierarchy is proposed which sums selected terms from all orders in εP and thus treats the hydrodynamic fluctuations self-consistently. The resulting theory retains appropriate fluid conservation laws, thereby avoiding erroneous results encountered in certain diffusing orbit theories, when the fluid viscosity is indiscriminantly replaced by the test particle diffusion coefficient. In order to explain the results of the computer simulations, the theory is applied in part 2 to the problem of anomalous hydrodynamic contributions to the transport coefficients.

Anomalous transport coefficients in a magnetized turbulent plasma

1982 ◽  
Vol 28 (2) ◽  
pp. 193-214 ◽  
Author(s):  
Qiu Xiaoming ◽  
R. Balescu
Keyword(s):  
Transport Coefficients ◽  
Collision Operator ◽  
Turbulent Plasma ◽  
Anomalous Transport ◽  
Weak Turbulence ◽  
Dissipative Effects ◽  
Dependent Transport ◽  
Two Fluid ◽  
Two Fluid Plasma

In this paper we generalize the formalism developed by Balescu and Paiva-Veretennicoff, valid for any kind of weak turbulence, for the determination of all the transport coefficients of an unmagnetized turbulent plasma, to the case of a magnetized one, and suggest a technique to avoid finding the inverse of the turbulent collision operator. The implicit plasmadynamical equations of a two-fluid plasma are presented by means of plasmadynamical variables. The anomalous transport coefficients appear in their natural places in these equations. It is shown that the necessary number of transport coefficients for describing macroscopically the magnetized turbulent plasma does not exceed the number for the unmagnetized one. The typical turbulent and gyromotion terms, representing dissipative effects peculiar to the magnetized system, which contribute to the frequency-dependent transport coefficients are clearly exhibited.

Accurateab initiotreatment of low-energy electron collisions with ethylene

1991 ◽  
Vol 66 (21) ◽  
pp. 2728-2730 ◽  
Author(s):  
B. I. Schneider ◽  
T. N. Rescigno ◽  
B. H. Lengsfield ◽  
C. W. McCurdy
Keyword(s):  
Low Energy ◽  
Energy Electron ◽  
Electron Collisions ◽  
Low Energy Electron

scholarly journals Theory of the tertiary instability and the Dimits shift within a scalar model

2020 ◽  
Vol 86 (4) ◽  
Author(s):  
Hongxuan Zhu ◽  
Yao Zhou ◽  
I. Y. Dodin
Keyword(s):  
Turbulent Transport ◽  
Plasma Phys ◽  
Magnetized Plasma ◽  
Radial Coordinate ◽  
Flow Shear ◽  
Zonal Flows ◽  
Drift Wave ◽  
Zonal Velocity ◽  
Instability Growth ◽  
Traditional Paradigm

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in a magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry–Horton system has been proposed by St-Onge (J. Plasma Phys., vol. 83, 2017, 905830504) as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$ , where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U'' \doteq {\rm d}^2 U/{\rm d} x^2 $ . Then, depending on $U''$ , the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $| {\rm d} U / {\rm d} x |$ . Our analytic predictions are in agreement with direct numerical simulations of the modified Terry–Horton system.

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