The Wisconsin Plasma Astrophysics Laboratory

Forest, C. B.; Flanagan, K.; Brookhart, Matthew; Clark, Michael; Cooper, C. M.; Désangles, Victor; Egedal, J.; Endrizzi, Douglass; Khalzov, Ivan; Li, Hui; Miesch, Mark S.; Milhone, Jason; Nornberg, M. D.; Olson, Joseph; Peterson, Ethan; Roesler, F. L.; Schekochihin, A. A.; Schmitz, O.; Siller, Robert; Spitkovsky, Anatoly; Stemo, Aaron; Wallace, John; Weisberg, David B.; Zweibel, Ellen G.

doi:10.1017/s0022377815000975

Cited by 62 publications

(48 citation statements)

References 78 publications

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“…No inverse transfer is possible in HD, even if α = 4, contrary to earlier claims [15]. The experimental realization of initial conditions with α = 2 could be challenging for wind tunnels, but may well be possible in plasma experiments [33]. …”

Section: Figs 4(d) and (F)mentioning

confidence: 79%

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

2017

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We perform numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence. We classify our time-dependent solutions by their evolutionary tracks in parametric plots between instantaneous scaling exponents. We find distinct classes of solutions evolving along specific trajectories toward points on a line of self-similar solutions. These trajectories are determined by the underlying physics governing individual cases, while the infrared slope of the initial conditions plays only a limited role. In the helical case, even for a scale-invariant initial spectrum (inversely proportional to wavenumber k), the solution evolves along the same trajectory as for a Batchelor spectrum (proportional to k 4 ). [7], galaxy clusters [8], and the early Universe [9,10]. In the latter case, cosmological magnetic fields generated in the early Universe provide the initial source of turbulence, which leads to a growth of the correlation length by an inverse cascade mechanism [11], in addition to the general cosmological expansion of the Universe. In the last two decades, this topic has gained significant attention [12]. The time span since the initial magnetic field generation is enormous, but it is still uncertain whether it is long enough to produce fields at sufficiently large length scales to explain the possibility of contemporary magnetic fields in the space between clusters of galaxies [13].In this Letter, we use direct numerical simulations (DNS) of both hydrodynamic (HD) and magnetohydrodynamic (MHD) decaying turbulence to classify different types by their decay behavior. The decay is characterized by the temporal change of the kinetic energy spec- * Electronic address: brandenb@nordita.org † Electronic address: tinatin@andrew.cmu.edu trum, E K (k, t), and, in MHD, also by the magnetic energy spectrum, E M (k, t). Here, k is the wavenumber and t is time. In addition to the decay laws of the energies E i (t) = E i (k, t) dk, with i = K or M for kinetic and magnetic energies, there are the kinetic and magnetic integral scales,We quantify the decay by the instantaneous scaling exponents p(t) ≡ d ln E/d ln t and q(t) ≡ d ln ξ/d ln t. Thus, we study the decay behaviors by plotting p(t) vs. q(t) in a parametric representation. The pq diagram turns out to be a powerful diagnostic tool. Earlier work [8,14,15] has suggested that the decay behavior, and thus the positions of solutions in the pq diagram, depend on the exponent α for initial conditions of the form E ∼ k α e −k/k0 , where k 0 is a cutoff wavenumber. Motivated by earlier findings [2,11] of an inverse cascade in decaying MHD turbulence, Olesen considered the time-dependent energy spectra E(k, t) to be of the form [15]where ξ(t) ∝ t q , with q being an as yet undetermined scaling exponent, and ψ is a function that depends on the dissipative and turbulent processes that lead to a departure from a powerlaw at large k. Moreover, the slope ψ ′ ≡ dψ/dκ with κ = kξ must vanish for κ → 0. This turns out to be a critical restriction. Olesen then makes use of the f...

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Section: Figs 4(d) and (F)mentioning

confidence: 79%

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

2017

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“…The recently launched Magnetospheric Multiscale (MMS) Mission is known to be capable of probing such scales [62], and observational results in these regimes have also been recently published [68]. We also note that probing such scales may also become feasible in the laboratory, such as the WiPAL [115]. Thus, in the coming years, it is likely that a thorough understanding of the physics at these scales will be necessary.…”

Section: Discussionmentioning

confidence: 95%

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

2017

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Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range-this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.

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“…This may be productively pursued using a 3D LF code (as in Sharma et al 2006Sharma et al , 2007 or using Braginskii MHD. Overall, although many questions remain, both the limit  d b -B B 0 1 2 itself and the strong dominance of magnetic over kinetic energy are robust, appearing across a variety of models. Given the stringent nature of the amplitude limit and the interesting implications for high-β magnetized turbulence in weakly collisional plasmas, we anticipate a range of future applications to heliospheric, astrophysical, and possibly laboratory (Forest et al 2015, Gekelman et al 2016 plasmas.…”

Section: Future Workmentioning

confidence: 99%

Amplitude limits and nonlinear damping of shear-Alfvén waves in high-beta low-collisionality plasmas

2017

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This work, which extends Squire et al. [ApJL, 830 L25 (2016)], explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-β plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, "interrupting" the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional "Braginskii" regime, for both standing and traveling waves. The focus is on simplified models in one dimension, on scales much larger than the ion gyroradius. The effect has interesting implications for the physics of magnetized turbulence in the high-β conditions that are prevalent in many astrophysical plasmas.

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The Wisconsin Plasma Astrophysics Laboratory

Cited by 62 publications

References 78 publications

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

Amplitude limits and nonlinear damping of shear-Alfvén waves in high-beta low-collisionality plasmas

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