## Proceedings of the International School of Physics "Enrico Fermi.", Volume 25 |

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Page 159

Part A consists mainly of extracts from the paper «

a plane sheet pinch », written in collaboration with M. N. Rosenblttth and J.

Killeen. The complete paper is available by request. Part B discusses some of the

material on collisionless sheet-pinch instabilities and related instabilities in

references [2] and [3]. An excellent generalization of some of this material was

given in the seminar by I). Pfirsch (see also ref. [4]). The purpose of presenting

the material of ...

Part A consists mainly of extracts from the paper «

**Finite**-resistivity instabilities ofa plane sheet pinch », written in collaboration with M. N. Rosenblttth and J.

Killeen. The complete paper is available by request. Part B discusses some of the

material on collisionless sheet-pinch instabilities and related instabilities in

references [2] and [3]. An excellent generalization of some of this material was

given in the seminar by I). Pfirsch (see also ref. [4]). The purpose of presenting

the material of ...

Page 160

The analysis for the plane current layer is particularly significant in the high-

conductivity limit, since the problem then separates into the analysis of two

regions: 1) a narrow central region, where

motions of field and fluid, and where geometric curvature may be neglected; 2)

an outer region, where field and fluid are coupled, as in the infinite-conductivity

case, and where generalizations to nonplanar geometry can be introduced as

desired. In Section 2 of ...

The analysis for the plane current layer is particularly significant in the high-

conductivity limit, since the problem then separates into the analysis of two

regions: 1) a narrow central region, where

**finite**conductivity permits relativemotions of field and fluid, and where geometric curvature may be neglected; 2)

an outer region, where field and fluid are coupled, as in the infinite-conductivity

case, and where generalizations to nonplanar geometry can be introduced as

desired. In Section 2 of ...

Page 179

(86) may provide guide-lines for the full Vlasov-equation stability analysis, and

that conversely the Vlasov-equation analysis will shed light on the role of

gyro-radius effects in the hydromagnetic

CES P. Furth, J. Killeen and M. N. Rosenbluth: Phys. Fluids 6, 459 (1963). P.

Furth: Suppl. ft'ucl. Fusion, 169 (1962) Part I. K. Neil: Phys. Fluidn, 5, 14 (1962).

Pfirscii: MikroinstabilUdten vom Spiegeltyp in inhomogenen Plasmen (Max-

Planck Inst.

(86) may provide guide-lines for the full Vlasov-equation stability analysis, and

that conversely the Vlasov-equation analysis will shed light on the role of

**finite**-gyro-radius effects in the hydromagnetic

**finite**-resistivity problem. R E V V, REN'CES P. Furth, J. Killeen and M. N. Rosenbluth: Phys. Fluids 6, 459 (1963). P.

Furth: Suppl. ft'ucl. Fusion, 169 (1962) Part I. K. Neil: Phys. Fluidn, 5, 14 (1962).

Pfirscii: MikroinstabilUdten vom Spiegeltyp in inhomogenen Plasmen (Max-

Planck Inst.

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### Contents

Lezioni | 1 |

carrier mass | 159 |

hydrodynamique an voisinage dun axe magnetique | 214 |

Copyright | |

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### Common terms and phrases

adiabatic invariant amplitude approximation assumed Boltzmann equation boundary conditions boundary layer calculated cathode charge coefficient collision components consider const constant contraction corresponds courbe critère current density Debye length derived differential equations diffusion discharge dispersion relation distribution function double adiabatic theory eigenvalue electric field electromagnetic waves electrons and ions electrostatic energy principle equations of motion equilibrium expand experimental F(co finite fluid theory frequency given Hence inertia-limited instability integral interaction ionized Kruskal l'axe magnétique lignes limit linear theory lowest order magnetic field Maxwell's equations mode negative ions nonlinear obtain Ohm's law parameter particle perturbation Phys plasma oscillations Plasma Physics Poisson's equation potential pressure problem quantities radial region satisfied saturation current self-adjointness solution solving stabilité stability surface temperature thermal tion transverse wave values vanish variables vector velocity Vlasov equation waves in plasmas zero zero-order