Finite-gyroradius effects on m = 1 and m = 2 instabilities of sharp-boundary screw pinches

Lewis, Harry R.; Turner, Leaf

doi:10.1088/0029-5515/16/6/010

Cited by 18 publications

(3 citation statements)

References 8 publications

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“…These modes are not observed for experiments with high-temperature plasmas, as has been explained in terms of finite-Larmor-radius effects. The stability criterion for hab 0 and b 2 -^C bi, using the sharp-boundary model [9,13,14], is…”

Section: Table I Diffuse-profile Correction Factorsmentioning

confidence: 99%

Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

et al. 1978

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Feedback stabilization of the Scyllac 120° toroidal sector is reported. The confinement time was increased by 10-20 us using feedback to a maximum time of 35-45 /us, which is over 10 growth times of the long-wavelength m = I instability. These results were obtained after circuits providing flexible waveforms were used to drive auxiliary equilibrium windings. The resultant improved equilibrium agrees well with recent theory. It was observed that normally stable short-wavelength m = I modes could be driven unstable by feedback. This instability, caused by local feedback control, increases the feedback system energy consumption. An instability involving direct coupling of the feedback 1 = 2 field to the plasma 1 = 1 motion was also observed. The plasma parameters were: temperature, T,. a T, a !©0eV; density, n. a 2 X 10" cm" 1 ; radius, a a 1 cm; and P 2 0.7. Beta decreased significantly in 40 ^s, which can be accounted for by classical resistivity and particle loss from the sector ends.

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Section: Table I Diffuse-profile Correction Factorsmentioning

confidence: 99%

Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

et al. 1978

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“…The t Present address: Department of Electrical Engineering, Cornell University, Ithaca, NY 14853. techniques which we discuss in these papers are based upon the exact linearized equations which are to be solved approximately, rather than on approximations of the linearized equations. Although some success has been achieved already with our techniques (Lewis & Turner 1976;Schwarzmeier, Lewis, Abraham-Shrauner & Symon 1979;Seyler 1979;Seyler & Freidberg 1980), nevertheless further development is required in order to solve a wide range of problems reliably.…”

Section: Introductionmentioning

confidence: 99%

Stability of Vlasov equilibria. Part 1. General theory

1982

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We present a general formulation for treating the linear stability of inhomogeneous plasmas for which at least one species is described by the Vlasov equation. Use of Poisson bracket notation and expansion of the perturbation distribution function in terms of eigenfunctions of the unperturbed Liouville operator leads to a concise representation of the stability problem in terms of a symmetric dispersion functional. A dispersion matrix is derived which characterizes the solutions of the linearized initial-value problem. The dispersion matrix is then expressed in terms of a dynamic spectral matrix which characterizes the properties of the unperturbed orbits, in so far as they are relevant to the linear stability of the system.

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“…This approach has been described in the context of a general discussion of the initialvalue problem for linearized equations which describe plasma systems in which t Present address: Department of Electrical Engineering, Cornell University, Ithaca, NY 14853. there is a collisionless species . Applications of the general formalism have been made to the stability of a plasma column within the framework of the Vlasov-fluid model (Lewis & Turner 1976) and to the stability of large-amplitude Bernstein-Greene-Kruskal equilibria (Schwarzmeier, Lewis, Abraham-Shrauner & Symon 1979). In addition, the basic approach has been used independently in the context of the Vlasov-fluid model to study the stability of a rotating theta-pinch (Seyler 1979), and to investigate the effects of resonant particles on finite Larmor radius stabilization in screw-pinches (Seyler & Freidberg 1980).…”

Section: Introductionmentioning

confidence: 99%

Stability of Vlasov equilibria. Part 2. One non-ignorable co-ordinate

Lewis

Seyler

1982

J. Plasma Phys.

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The solution of the linearized Vlasov equation is given for an arbitrary equilibrium Hamiltonian in which there is only one non-ignorable co-ordinate. The solution written in terms of integrals with respect to time which only extend over the bounce period of an equilibrium orbit in its equivalent one-dimensional potential. A closed-form solution and a solution based on a Fourier expansion are given. Explicit formulae are presented for Cartesian and cylindrical co-ordinates.

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Finite-gyroradius effects on m = 1 and m = 2 instabilities of sharp-boundary screw pinches

Cited by 18 publications

References 8 publications

Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

Feedback stabilization of an ℓ = 0, 1, 2 high-beta stellarator

Stability of Vlasov equilibria. Part 1. General theory

Stability of Vlasov equilibria. Part 2. One non-ignorable co-ordinate

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