Renormalization-group analysis on the stability of large-scale electrostatic fluctuations of two-dimensional plasmas

Kim, Chang-Bae

doi:10.1063/1.1645522

Cited by 4 publications

(3 citation statements)

References 9 publications

(8 reference statements)

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“…kρ s > 1 and ξ 0 is a relative measure of the PNC noise with the condition that 0 < ξ 0 < 1, and ŝ is the direction of anisotropy. Parity-conserving anisotropic noise spectrum has been shown to develop anisotropic dissipation of large-scale fluctuations [22,23]. PNC helical noise was considered for helicity injection into the plasmas [19,24].…”

Section: Response Of the Plasmamentioning

confidence: 99%

Generation of plasma flow in noise-driven Hasegawa–Mima model

Kim

2010

Nucl. Fusion

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The presence of macroscopic flows in hot plasmas is of great importance in nuclear fusion experiments. For pedagogical purposes, the spontaneous appearance of the flow is studied using the Hasegawa–Mima equation (HME) driven by external noise. The noise is assumed to model a bath of microscopic-scale turbulence. If the noise has a parity-nonconserving element, it is shown that an advective term associated with a uniform flow is inherently generated in the HME. A renormalization-group approach up to the lowest order is taken in the analysis of the asymptotic state. Parity-conserving noise is shown to lead to the renormalizations of field and viscosity and the critical dimensions are obtained.

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Section: Response Of the Plasmamentioning

confidence: 99%

Generation of plasma flow in noise-driven Hasegawa–Mima model

Kim

2010

Nucl. Fusion

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“…The noise spectrum is modeled to peak at infrared assuming that in the interactions of the turbulent fluctuations p and q, p + q = k and p ≈ q k are important. A parity-conserving anisotropic noise spectrum proportional to k 2−d−δ | k • ŝ| 2 has been shown to develop anisotropic dissipation, not growth, of large-scale fluctuations [16,17]. PNC helical noise was considered for helicity injection into the plasmas [12,18].…”

Section: Destabilizationmentioning

confidence: 99%

Stabilization of large-scale fluctuations in noise-driven plasmas by magnetic field

Kim¹

2008

Plasma Phys. Control. Fusion

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The stability of large-scale fluctuations in plasmas driven by the paritynonconserving (PNC) noise is studied. The noise may model such short-scale turbulence as the drift waves of short wave lengths. It is known that the relative strength of the PNC noise greater than ∼ ln R/R, where R is the ratio of the largest to the smallest scales, destabilizes the plasma. As a result, largescale fluctuations emerge and grow in time. It is shown that a homogeneous magnetic field, which exists either as a result of the growth of large scales or by external means, can stabilize the plasma. The stability diagram of the marginally unstable plasma is plotted in terms of the magnetic Prandtl number P m and the Hartmann number H . It is found that the plasma is stable if P m > (1 + √ 5)/2 in the limit H → 0. In another limit P m → ∞, the finite critical size of the magnetic field (i.e. H c ) is found to exist.

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“…We investigate the properties of incompressible MHD turbulence in three dimensions (3D), in the absence of a mean magnetic field and with a specific type of power-law, random forcing, which we define precisely below; henceforth, we refer to this type of MHD as 3DRFMHD, as opposed to its conventionally forced counterpart, which we refer to as 3DMHD. The motivation for our study arises from the use of such random forcing for field-theoretical studies, initially of fluid turbulence [34,35,36,37,38,39] and subsequently of MHD turbulence [8,40,41,42,43,44,45,46,47]. It is useful, therefore, to examine the statistical properties of 3DRFMHD turbulence by a careful, direct numerical simulation (DNS).…”

Section: Introductionmentioning

confidence: 99%

Direct Numerical Simulations of Three-dimensional Magnetohydrodynamic Turbulence with Random, Power-law Forcing

Sahoo,

Padhan,

Basu

et al. 2020

Preprint

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We present pseudospectral direct-numerical-simulation (DNS) studies of the three-dimensional magnetohydrodynamic (MHD) equations (3DRFMHD) with a stochastic force that has zero mean and a variance ∼ k −3 , where k is the wavenumber, because 3DRFMHD is used in field-theoretic studies of the scaling of energy spectra in MHD turbulence. We obtain velocity and magnetic-field spectra and structure functions and, from these, the multiscaling exponent ratios ζ p /ζ 3 , by using the extended self similarity (ESS) procedure. These exponent ratios lie within error bars of their counterparts for conventional three-dimensional MHD turbulence (3DMHD). We then carry out a systematic comparison of the statistical properties of 3DMHD and 3DRFMHD turbulence by examining various probability distribution functions (PDFs), joint PDFs, and isosurfaces of of, e.g., the moduli of the vorticity and the current density for three magnetic Prandtl numbers Pr M = 0.1, 1, and 10.

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Renormalization-group analysis on the stability of large-scale electrostatic fluctuations of two-dimensional plasmas

Cited by 4 publications

References 9 publications

Generation of plasma flow in noise-driven Hasegawa–Mima model

Generation of plasma flow in noise-driven Hasegawa–Mima model

Stabilization of large-scale fluctuations in noise-driven plasmas by magnetic field

Direct Numerical Simulations of Three-dimensional Magnetohydrodynamic Turbulence with Random, Power-law Forcing

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