Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

S. D. Baalrud; A. Bhattacharjee; Y. M. Huang; K. Germaschewski

doi:10.1063/1.3633473

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

S. D. Baalrud, A. Bhattacharjee, Y. M. Huang, K. Germaschewski

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39 Scopus citations

Abstract

A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth d_η S _L^-1/2 √L_VA/γ, where S_L is the Lundquist number, L, the length of the current sheet, _A, the Alfvén speed, and , the growth rate. Modifications to a recent resistive MHD analysis N. F. Loureiro, Phys. Plasmas 14, 100703 (2007) arise when collisions are sufficiently weak that d_η is shorter than the ion skin depth d_i ≡ c/ω_pi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (d _i/L)^6/13S_L^7/13 v_A/L and the number of plasmoids as (d_i/L)^1/13S_L ^11/26, compared to S_L^1/4 v_A/L and S^3/8, respectively, in resistive MHD.

Original language	English (US)
Article number	092108
Journal	Physics of Plasmas
Volume	18
Issue number	9
DOIs	https://doi.org/10.1063/1.3633473
State	Published - Sep 2011
Externally published	Yes

All Science Journal Classification (ASJC) codes

Condensed Matter Physics

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10.1063/1.3633473

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title = "Hall magnetohydrodynamic reconnection in the plasmoid unstable regime",

abstract = "A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth dη S L-1/2 √LVA/γ, where SL is the Lundquist number, L, the length of the current sheet, A, the Alfv{\'e}n speed, and , the growth rate. Modifications to a recent resistive MHD analysis N. F. Loureiro, Phys. Plasmas 14, 100703 (2007) arise when collisions are sufficiently weak that dη is shorter than the ion skin depth di ≡ c/ωpi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (d i/L)6/13SL7/13 vA/L and the number of plasmoids as (di/L)1/13SL 11/26, compared to SL1/4 vA/L and S3/8, respectively, in resistive MHD.",

author = "Baalrud, {S. D.} and A. Bhattacharjee and Huang, {Y. M.} and K. Germaschewski",

note = "Funding Information: The authors gratefully acknowledge conversations with Dr. Brian Sullivan and Dr. Will Fox. This research was supported in part by an appointment to the U.S. Department of Energy Fusion Energy Postdoctoral Research Program administered by the Oak Ridge Institute for Science and Education (S.D.B.) and DOE Grant No. DE-FG02-07ER46372, NSF Grant Nos. ATM-0802727, ATM-0903915, and AGS-0962698, and NASA Grant Nos. NNX09AJ86G and NNX10AC04G.",

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AU - Baalrud, S. D.

AU - Bhattacharjee, A.

AU - Huang, Y. M.

AU - Germaschewski, K.

N1 - Funding Information: The authors gratefully acknowledge conversations with Dr. Brian Sullivan and Dr. Will Fox. This research was supported in part by an appointment to the U.S. Department of Energy Fusion Energy Postdoctoral Research Program administered by the Oak Ridge Institute for Science and Education (S.D.B.) and DOE Grant No. DE-FG02-07ER46372, NSF Grant Nos. ATM-0802727, ATM-0903915, and AGS-0962698, and NASA Grant Nos. NNX09AJ86G and NNX10AC04G.

PY - 2011/9

Y1 - 2011/9

N2 - A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth dη S L-1/2 √LVA/γ, where SL is the Lundquist number, L, the length of the current sheet, A, the Alfvén speed, and , the growth rate. Modifications to a recent resistive MHD analysis N. F. Loureiro, Phys. Plasmas 14, 100703 (2007) arise when collisions are sufficiently weak that dη is shorter than the ion skin depth di ≡ c/ωpi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (d i/L)6/13SL7/13 vA/L and the number of plasmoids as (di/L)1/13SL 11/26, compared to SL1/4 vA/L and S3/8, respectively, in resistive MHD.

AB - A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth dη S L-1/2 √LVA/γ, where SL is the Lundquist number, L, the length of the current sheet, A, the Alfvén speed, and , the growth rate. Modifications to a recent resistive MHD analysis N. F. Loureiro, Phys. Plasmas 14, 100703 (2007) arise when collisions are sufficiently weak that dη is shorter than the ion skin depth di ≡ c/ωpi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (d i/L)6/13SL7/13 vA/L and the number of plasmoids as (di/L)1/13SL 11/26, compared to SL1/4 vA/L and S3/8, respectively, in resistive MHD.

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Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

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