Transport equations and gradient instabilities in a high pressure collisional plasma

Mikhaǐlovskiǐ, A. B.; Tsypin, V. S.

doi:10.1088/0032-1028/13/9/009

Cited by 96 publications

(116 citation statements)

References 3 publications

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“…(24). Like the ∇⋅ r q || − 3 r n⋅∇ r q || ⋅ r n term, they have small coefficients, but are formally of the same order as the remaining terms previously obtained by Mikhailovskii and Tyspin [4][5][6]. Indeed, the r q || ⋅∇T and q || 2 are exactly of the same form and so can be combined to write t π || = ( r n r n − 1 3…”

Section: Ion Viscosity and Collisional Perpendicular Ion Heat Fluxmentioning

confidence: 73%

“…The solution for f 2 contains terms of order δ 2 and δ ∆ ; the order ν/Ω perpendicular viscosity corrections will be evaluated by a moment approach in the next section. Our solution differs from that of Mikhailovskii and Tsypin [4][5][6] who use a polynomial approximation for f 2 that neglects terms involving L 2…”

Section: Ion Formulationmentioning

confidence: 93%

“…The preceding results are well known [1][2][3][4][5][6]; however, the solution of Eq. (11) for f 2 that follows is new so we present a few more details.…”

Section: Ion Formulationmentioning

confidence: 99%

“…, and using the orthogonality relations for the Legendre and generalized Laguerre polynomials to show d 3 ∫ w r w r w r w r wL j (5/2) (x 2 )f 0 = 0 , we find the Mikhailovskii and Tyspin [4][5][6] result for the gyro-viscosity, namely,…”

Section: Ion Viscosity and Collisional Perpendicular Ion Heat Fluxmentioning

confidence: 99%

“…Mikhailovskii and Tsypin [4][5][6] realized that this ordering is not the one of most interest in many practical situations in which the flow is weaker and on the order of the ion diamagnetic heat flux divided by the pressure. In their drift ordering the ion flow velocity is assumed to be on the order of the diamagnetic drift velocity -the case of interest for most magnetic confinement and fusion devices in general, and the edge of many tokamaks in particular.…”

Section: Introductionmentioning

confidence: 99%

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A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy

2004

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Short mean free path descriptions of magnetized plasmas have existed for almost 50 years so it is surprising to find that further modifications are necessary. The earliest work adopted an ordering in which the flow velocity was assumed to be comparable to the ion thermal speed. Later, less well known studies extended the short mean free path treatment to the normally more interesting drift ordering in which the pressure times the mean flow velocity is comparable to the diamagnetic heat flow. Such an ordering is required to properly retain the temperature gradient terms in the viscosity that arise from the gyrophase dependent and independent portions of the distribution function. Our treatment corrects the expressions for the parallel and perpendicular collisional ion viscosities found in these later treatments which used an approximate truncated polynomial expression for the distribution function and neglected the non-linear piece of the collision operator due to its bi-linear form. The modified parallel and perpendicular ion viscosities contain additional terms quadratic in the heat flux. In addition, we solve for the electron parallel and gyro-viscosities which were not considered by previous drift ordered treatments. As in all drift orderings we assume the collision frequency is small compared to the cyclotron frequency. However, we permit the perpendicular scale lengths to be much less than the parallel ones as is the case in many magnetic confinement applications. As a result, our description is valid for turbulent and collisional transport, and also allows stronger poloidal density and temperature variation in a tokamak than the standard Pfirsch-Schlüter ordering.

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Section: Ion Viscosity and Collisional Perpendicular Ion Heat Fluxmentioning

confidence: 73%

Section: Ion Formulationmentioning

confidence: 93%

“…The preceding results are well known [1][2][3][4][5][6]; however, the solution of Eq. (11) for f 2 that follows is new so we present a few more details.…”

Section: Ion Formulationmentioning

confidence: 99%

Section: Ion Viscosity and Collisional Perpendicular Ion Heat Fluxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy

2004

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On the Maxwellian Regimes of the Electron Component in the Plasmachemical Reactors of Beam‐Plasma Type

Mikhaǐlovskiǐ

1983

Contrib Plasma Phys

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Transport Equations of Plasma in a Curvilinear Magnetic Field

Mikhaǐlovskiǐ

Tsypin²

1984

Contrib Plasma Phys

100

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The problem of transport equations of a collisional plasma in a curvilinear magnetic field is studied. Two main approaches to this problem are presented: that based on using the Boltzmann kinetic equation and the drift kinetic equation approach. In the frame of the first approach a multimoment transport equation set is found which is more general than the transport equation sets of Braginskii and Grad. The tensor equations of this set are described in an arbitrary curvilinear coordinate system. This allow to use these equations in problems of a plasma confined in toroidal magnetic configurations. Simplification of the multimoment transport equation set in the case of high magnetic field is performed. In the frame of the drift kinetic equation approach, a generalization of the drift transport equations derived earlier by the authors (Zh. Eksp. Teor. Fiz. 83 (1982) 139) is given.

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Transport equations and gradient instabilities in a high pressure collisional plasma

Cited by 96 publications

References 3 publications

A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy

A drift ordered short mean free path description for magnetized plasma allowing strong spatial anisotropy

On the Maxwellian Regimes of the Electron Component in the Plasmachemical Reactors of Beam‐Plasma Type

Transport Equations of Plasma in a Curvilinear Magnetic Field

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