Influence of the current profile on the growth rate of m = 1 kink modes in a pure z-pinch

Nycander, Jonas; Wahlberg, Christer

doi:10.1088/0029-5515/24/10/009

Cited by 10 publications

(11 citation statements)

References 5 publications

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“…The present investigation thus generalizes the result of Ref. [12] to the case of a completely arbitrary equilibrium magnetic field. Furthermore, we consider here also the effect of a non-circular plasma cross-section, having particularly the Extrap configuration [7] in mind.…”

Section: Introductionsupporting

confidence: 86%

“…[12], the current profile effect can be related to a single, well known quantity of the plasma column, namely the inductance associated with the axial current where 7 E = 0.5772 ... is Euler's constant, we obtain after some algebra the long wavelength m = 1 dispersion relation of a general screw pinch in the form…”

Section: Profile Effectsmentioning

confidence: 99%

“…After multiplication with r, this equation is readily integrated, giving In the region outside the pinch, r > 1 (vacuum region), the equilibrium magnetic field (also normalized to B^a)) can be written as = -+ B e z r (12) where B e = B z (l). Thus, both B^, and B z are chosen to be continuous at r = 1, implying that the total equilibrium current (including possible azimuthal and axial equilibrium surface currents) is assumed to flow inside the plasma boundary.…”

Section: V-£ =mentioning

confidence: 99%

“…The pressure balance at the perturbed plasma surface then yields the boundary condition (see Ref. [12])…”

Section: V-£ =mentioning

confidence: 99%

“…for ka < 1 (k being the axial wave number of the kink perturbation), we series expand the MHD equations in ka, but let the equilibrium profiles B^r) and B z (r) be arbitrary. In a previous paper [12] this technique was used in a derivation of the long wavelength dispersion relation for kink modes in a pure Z-pinch (B z = 0). The present investigation thus generalizes the result of Ref.…”

Section: Introductionmentioning

confidence: 99%

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Current problems in ball lightning science

Smirnov¹

1990

Sov. Phys. Usp.

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Section: Introductionsupporting

confidence: 86%

Section: Profile Effectsmentioning

confidence: 99%

Section: V-£ =mentioning

confidence: 99%

“…The pressure balance at the perturbed plasma surface then yields the boundary condition (see Ref. [12])…”

Section: V-£ =mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Current problems in ball lightning science

Smirnov¹

1990

Sov. Phys. Usp.

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Kinetic theory of the m = 1 kink instability in Z-pinches

1988

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The kinetic theory of the m = 1 kink instability of a Z-pinch with Bennett profile is presented. The dominant particle trajectories in the equilibrium field are the large excursion betatron orbits. To deal with these orbits, an integral formulation of the stability analysis is adopted. In this case, the dispersion relation is expressed as the determinant of a matrix. In the limit where the electrostatic perturbation is neglected, the eigenmodes are computed numerically from this dispersion relation. Two methods are used to obtain the growth rates, and the computed values agree very well. The Landau damping of the mode is found to be strong enough to stabilize the mode at shorter wavelengths. This may explain the stability of the kink mode in some experiments.

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Effect of paramagnetism on the global stability of straight screw pinches

Wahlberg

1991

Nucl. Fusion

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An analytical expression for the eigenvalue of the global m = 1 kink mode in a straight screw pinch with arbitrary profiles of current density and axial magnetic field is derived in a long wavelength approximation of the incompressible ideal MHD equations. While the influence of the current profile is related to the inductance li of the plasma column, as has been shown previously (Nucl. Fusion 24 (1984) 1357), it is found here that the effect of the axial magnetic field profile can be expressed in terms of the poloidal beta value βp of the pinch. In turn, βp is related to a possible paramagnetism (βp < 1) or diamagnetism (βp > 1) of the plasma. Considering the range of stable eigen-values, the Kruskal-Shafranov condition q(a) > 1, independent of li and βp, is recovered in the tokamak regime Bz, ≫ Bϕ. In the regime Bz ⪅ Bϕ, on the other hand, the stability condition is strongly dependent on both li and βp. Optimal stability conditions in this regime are obtained for li, ≪ 1 (hollow current distribution), βp ≪ 1 (strong paramagnetism) and Bz(a) ≪ Bϕ(a) (low q(a)). In this case, wavelengths of up to fourteen times the plasma radius become stable, and also the growth rates of the unstable wavelengths are considerably reduced as compared to the situation with li, βp ∼ 1 and Bz ∼ Bϕ, or compared to the growth rates obtained in the tokamak regime. The results obtained are consistent with recent experimental observations in ‘ultra low q’ discharges.

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Influence of the current profile on the growth rate of m = 1 kink modes in a pure z-pinch

Abstract: An expression for the growth rate of longwavelength m = 1 kink modes in a z-pinch with arbitrary current profile is derived. The ideal-MHD-equations for an incompressible fluid are used. The result is compared with calculations based on specific models of the current distribution.

Cited by 10 publications

References 5 publications

Current problems in ball lightning science

Current problems in ball lightning science

Kinetic theory of the m = 1 kink instability in Z-pinches

Effect of paramagnetism on the global stability of straight screw pinches

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