Generalized universal instability: transient linear amplification and subcritical turbulence

Landreman, Matt; Plunk, G. G.; Dorland, W.

doi:10.1017/s0022377815000495

Cited by 19 publications

(27 citation statements)

References 46 publications

(184 reference statements)

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“…Thus, in the experimental instance that we have considered, ion-scale turbulence in MAST in the presence of flow shear is subcritical and so tokamak plasmas join a plethora of neutral fluid systems where the transition to turbulence depends strongly on the (size of) initial perturbation (Trefethen (Salwen et al 1980;Trefethen et al 1993), but still able to transition to a nonlinear, turbulent state; a similar situation arises in Keplerian shear flows believed to exist in accretion disks (Riols et al 2013). Recent theoretical work, involving very simple models, suggested that this may also be possible in plasmas (Newton et al 2010;Schekochihin et al 2012;Landreman et al 2015), as did simulations of simplified tokamak equilibria (Barnes et al 2011a;Highcock et al 2010Highcock et al , 2011Highcock et al , 2012, but ours appears to be the first demonstration of subcritical ion-scale turbulence in a specific, experimentally diagnosed tokamak plasma.…”

Section: Subcritical Turbulencementioning

confidence: 99%

Transition to subcritical turbulence in a tokamak plasma

et al. 2016

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Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.Comment: 16 pages, 5 figures, accepted to Journal of Plasma Physic

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Section: Subcritical Turbulencementioning

confidence: 99%

Transition to subcritical turbulence in a tokamak plasma

et al. 2016

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“…This has reinvigorated the exploration of universal modes, with Ref. 25 exploring its role in subcritical turbulence and Ref. 26 investigating these modes in general geometries.…”

Section: Introductionmentioning

confidence: 99%

Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

2018

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A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on k = 0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k ⊥ ρ i ∼ 1 and vanish in the long wavelength k ⊥ → 0 limit. This work also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ = β/[2(1 + β)]C s /|L p | with C 2 s = p 0 /ρ 0 for k ⊥ → 0 and is universally unstable for 1/L p = 0. We show the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p 0 + B 2 0 /(8π) = constant, which renders the assumption B 0 = 0 inconsistent if p 0 = 0. a)

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“…There is also a growing interest in the subcritical transition to turbulence in tokamak plasmas (e.g. Landremann, Plunk & Dorland 2015; van Wyk et al. 2016) and the non-modal consequences of shearing on microinstabilities (e.g.…”

Section: Introductionmentioning

confidence: 99%

The non-modal onset of the tearing instability

MacTaggart¹

2018

J. Plasma Phys.

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We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. This possibility increases as the Lundquist number $S$ increases. In particular, we find evidence, numerically, that the maximum possible transient growth, measured in the $L_{2}$-norm, for the classical set-up of current sheets unstable to the TI, scales as $O(S^{1/4})$ on time scales of $O(S^{1/4})$ for $S\gg 1$. This behaviour is much faster than the time scale $O(S^{1/2})$ when the solution behaviour is dominated by the tearing mode. The size of transient growth obtained is dependent on the form of the initial perturbation. Optimal initial conditions for the maximum possible transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities.

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Generalized universal instability: transient linear amplification and subcritical turbulence

Cited by 19 publications

References 46 publications

Transition to subcritical turbulence in a tokamak plasma

Transition to subcritical turbulence in a tokamak plasma

Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

The non-modal onset of the tearing instability

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