Reduced magnetohydrodynamic theory of oblique plasmoid instabilities

Baalrud, S. D.; Bhattacharjee, A.; Huang, Y.-M.

doi:doi:10.1063/1.3678211

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The three-dimensional nature of plasmoid instabilities is studied using the reduced magnetohydrodynamic equations. For a Harris equilibrium with guide field, represented by B_o = B_potanh(x/λ) math

+B_zo

, a spectrum of modes are unstable at multiple resonant surfaces in the current sheet, rather than just the null surface of the poloidal field B_yo(x) = B_potanh(x/λ), which is the only resonant surface in 2D or in the absence of a guide field. Here, B_po is the asymptotic value of the equilibrium poloidal field, B_zo is the constant equilibrium guide field, and λ is the current sheet width. Plasmoids on each resonant surface have a unique angle of obliquity θ ≡ arctan(k_z/k_y). The resonant surface location for angle θ is x_s = λarctanh(μ), where μ = tanθB_zo/B_po and the existence of a resonant surface requires |θ|<arctan(B_po/B_zo). The most unstable angle is oblique, i.e., θ ≠ 0 and x_s ≠ 0, in the constant-ψ regime, but parallel, i.e., θ = 0 and x_s = 0, in the nonconstant-ψ regime. For a fixed angle of obliquity, the most unstable wavenumber lies at the intersection of the constant-ψ and nonconstant-ψ regimes. The growth rate of this mode is γ_max/Γ_o ≃ SL1/4(1-μ⁴)^1/2, in which Γ_o = V_A/L, V_A is the Alfvén speed, L is the current sheet length, and S_L is the Lundquist number. The number of plasmoids scales as N~SL3/8(1-μ²)^-1/4(1+μ²)^3/4.

Article Outline

INTRODUCTION
REDUCED MHD EQUATIONS
BOUNDARY LAYER ANALYSIS
1. Outer region
2. Inner region
LINEAR GROWTH RATE
NUMERICAL EIGENMODE SOLUTIONS
SUMMARY

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KEYWORDS and PACS

Keywords

plasma instability, plasma magnetohydrodynamics, plasma transport processes

PACS

52.35.Py

Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.30.Cv

Magnetohydrodynamics (including electron magnetohydrodynamics)
52.25.Fi

Transport properties

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1063/1.3678211

PUBLICATION DATA

ISSN

1070-664X (print)

1089-7674 (online)

Publisher

$abstract.society.value is a Member of CrossRef

American Institute of Physics

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