# Publications by Alexander Schekochihin

## Disruption of sheet-like structures in Alfvénic turbulence by magnetic reconnection

Monthly Notices of the Royal Astronomical Society Oxford University Press **468** (2017) 4862-4871

We propose a mechanism whereby the intense, sheet-like structures naturally formed by dynamically aligning Alfv´enic turbulence are destroyed by magnetic reconnection at a scale ˆλ D, larger than the dissipation scale predicted by models of intermittent, dynamically aligning turbulence. The reconnection process proceeds in several stages: first, a linear tearing mode with N magnetic islands grows and saturates, and then the X-points between these islands collapse into secondary current sheets, which then reconnect until the original structure is destroyed. This effectively imposes an upper limit on the anisotropy of the structures within the perpendicular plane, which means that at scale ˆλD the turbulent dynamics change: at scales larger than ˆλD, the turbulence exhibits scale-dependent dynamic alignment and a spectral indexapproximately equal to −3/2, while at scales smaller than ˆλD, the turbulent structures undergo a succession of disruptions due to reconnection, limiting dynamic alignment, steepening the effective spectral index and changing the final dissipation scale. The scaling of ˆλD with the Lundquist (magnetic Reynolds) number SL⊥ depends on the order of the statistics being considered, and on the specific model of intermittency; the transition between the two regimes in the energy spectrum is predicted at approximately ˆλD ∼ SL⊥^−0.6 . The spectral index below ˆλD is bounded between −5/3 and −2.3. The final dissipation scale is at ˆλη,∞ ∼ SL⊥^−3/4, the same as the Kolmogorov scale arising in theories of turbulence that do not involve scale-dependent dynamic alignment.

## A statistical model of three-dimensional anisotropy and intermittency in strong Alfvénic turbulence

Monthly Notices of the Royal Astronomical Society Oxford University Press **466** (2016) 3918-3927

We propose a simple statistical model of three-dimensionally anisotropic, intermittent, strong Alfv\'enic turbulence, incorporating both critical balance and dynamic alignment. Our model is based on log-Poisson statistics for Elsasser-field increments along the magnetic field. We predict the scalings of Elsasser-field conditional two-point structure functions with point separations in all three directions in a coordinate system locally aligned with the direction of the magnetic field and of the fluctuating fields and obtain good agreement with numerical simulations. We also derive a scaling of the parallel coherence scale of the fluctuations, $l_\parallel \propto \lambda^{1/2}$, where $\lambda$ is the perpendicular scale. This is indeed observed for the bulk of the fluctuations in numerical simulations.

## Experimental determination of the correlation properties of plasma turbulence using 2D BES systems

Plasma Physics and Controlled Fusion IOP Publishing **59** (2017) 044008-

A procedure is presented to map from the spatial correlation parameters of a turbulent density field (the radial and binormal correlation lengths and wavenumbers, and the fluctuation amplitude) to correlation parameters that would be measured by a beam emission spectroscopy (BES) diagnostic. The inverse mapping is also derived, which results in resolution criteria for recovering correct correlation parameters, depending on the spatial response of the instrument quantified in terms of point-spread functions (PSFs). Thus, a procedure is presented that allows for a systematic comparison between theoretical predictions and experimental observations. This procedure is illustrated using the Mega-Ampere Spherical Tokamak BES system and the validity of the underlying assumptions is tested on fluctuating density fields generated by direct numerical simulations using the gyrokinetic code GS2. The measurement of the correlation time, by means of the cross-correlation time-delay method, is also investigated and is shown to be sensitive to the fluctuating radial component of velocity, as well as to small variations in the spatial properties of the PSFs.

## Supergranulation and multiscale flows in the solar photosphere Global observations vs. a theory of anisotropic turbulent convection

ASTRONOMY & ASTROPHYSICS **599** (2017) ARTN A69

## Symmetry breaking in MAST plasma turbulence due to toroidal flow shear

PLASMA PHYSICS AND CONTROLLED FUSION **59** (2017) ARTN 034002

## Constraints on dynamo action in plasmas

Journal of Plasma Physics Cambridge University Press **82** (2016) 905820601-

Upper bounds are derived on the amount of magnetic energy that can be generated by dynamo action in collisional and collisionless plasmas with and without external forcing. A hierarchy of mathematical descriptions is considered for the plasma dynamics: ideal MHD, visco-resistive MHD, the double-adiabatic theory of Chew, Goldberger and Low (CGL), kinetic MHD, and other kinetic models. It is found that dynamo action is greatly constrained in models where the magnetic moment of any particle species is conserved. In the absence of external forcing, the magnetic energy then remains small at all times if it is small in the initial state. In other words, a small “seed” magnetic field cannot be amplified significantly, regardless of the nature of flow, as long as the collision frequency and gyroradius are small enough to be negligible. A similar conclusion also holds if the system is subject to external forcing as long as this forcing conserves the magnetic moment of at least one plasma species and does not greatly increase the total energy of the plasma (i.e., in practice, is subsonic). Dynamo action therefore always requires collisions or some small-scale kinetic mechanism for breaking the adiabatic invariance of the magnetic moment.

## Transition to subcritical turbulence in a tokamak plasma

JOURNAL OF PLASMA PHYSICS **82** (2016) ARTN 905820609

## Arithmetic with X-ray images of galaxy clusters: effective equation of state for small-scale perturbations in the ICM

Monthly Notices of the Royal Astronomical Society Oxford University Press **463** (2016) 1057-1067

We discuss a novel technique of manipulating X-ray images of galaxy clusters to reveal the nature of small-scale density/temperature perturbations in the intracluster medium (ICM). As we show, this technique can be used to differentiate between sound waves and isobaric perturbations in Chandra images of the Perseus and M87/Virgo clusters. The comparison of the manipulated images with the radio data and with the results of detailed spectral analysis shows that this approach successfully classifies the types of perturbations and helps to reveal their nature. For the central regions (5–100 kpc) of the M87 and Perseus clusters, this analysis suggests that observed images are dominated by isobaric perturbations, followed by perturbations caused by bubbles of relativistic plasma and weak shocks. Such a hierarchy is best explained in a ‘slow’ active galactic nuclei feedback scenario, when much of the mechanical energy output of a central black hole is captured by the bubble enthalpy that is gradually released during buoyant rise of the bubbles. The ‘image arithmetic’ works best for prominent structure and for data sets with excellent statistics, visualizing the perturbations with a given effective equation of state. The same approach can be extended to faint perturbations via cross-spectrum analysis of surface brightness fluctuations in X-ray images in different energy bands.

## A stringent limit on the amplitude of alfvénic perturbations in high-beta low-collisionality plasmas

Astrophysical Journal Letters IOP Publishing **830** (2016) L25-

It is shown that low-collisionality plasmas cannot support linearly polarized shear-Alfvén fluctuations above a critical amplitude δB⊥/B0 ∼ B-1/2, where β is the ratio of thermal to magnetic pressure. Above this cutoff, a developing fluctuation will generate a pressure anisotropy that is sufficient to destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, interrupting the fluctuation before any oscillation. The magnetic field lines rapidly relax into a sequence of angular zig-zag structures. Such a restrictive bound on shear-Alfvén-wave amplitudes has far-reaching implications for the physics of magnetized turbulence in the high-β conditions prevalent in many astrophysical plasmas, as well as for the solar wind at ∼1 au where β ≳ 1.

## Polarization of thermal bremsstrahlung emission due to electron pressure anisotropy

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **461** (2016) 2162-2173

## Thermal conduction in a mirror-unstable plasma

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **460** (2016) 467-477

## Suppression of phase mixing in drift-kinetic plasma turbulence

Physics of Plasmas AIP Publishing **23** (2016) 1-5

Transfer of free energy from large to small velocity-space scales by phase mixing leads to Landau damping in a linear plasma. In a turbulent drift-kinetic plasma, this transfer is statistically nearly canceled by an inverse transfer from small to large velocity-space scales due to “anti-phase-mixing” modes excited by a stochastic form of plasma echo. Fluid moments (density, velocity, temperature) are thus approximately energetically isolated from the higher moments of the distribution function, so phase mixing is ineffective as a dissipation mechanism when the plasma collisionality is small.

## MULTI-SPECIES MEASUREMENTS OF THE FIREHOSE AND MIRROR INSTABILITY THRESHOLDS IN THE SOLAR WIND

ASTROPHYSICAL JOURNAL LETTERS **825** (2016) ARTN L26

## Pressure-anisotropy-driven microturbulence and magnetic-field evolution in shearing, collisionless plasma

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **459** (2016) 2701-2720

## Measures of three-dimensional anisotropy and intermittency in strong Alfvénic turbulence

Monthly Notices of the Royal Astronomical Society Oxford University Press **459** (2016) 2130-2139

We measure the local anisotropy of numerically simulated strong Alfvénic turbulence with respect to two local, physically relevant directions: along the local mean magnetic field and along the local direction of one of the fluctuating Elsasser fields. We find significant scaling anisotropy with respect to both these directions: the fluctuations are ‘ribbon-like’ – statistically, they are elongated along both the mean magnetic field and the fluctuating field. The latter form of anisotropy is due to scale-dependent alignment of the fluctuating fields. The intermittent scalings of thenth-order conditional structure functions in the direction perpendicular to both the local mean field and the fluctuations agree well with the theory of Chandran, Schekochihin & Mallet, while the parallel scalings are consistent with those implied by the critical-balance conjecture. We quantify the relationship between the perpendicular scalings and those in the fluctuation and parallel directions, and find that the scaling exponent of the perpendicular anisotropy (i.e. of the aspect ratio of the Alfvénic structures in the plane perpendicular to the mean magnetic field) depends on the amplitude of the fluctuations. This is shown to be equivalent to the anticorrelation of fluctuation amplitude and alignment at each scale. The dependence of the anisotropy on amplitude is shown to be more significant for the anisotropy between the perpendicular and fluctuation-direction scales than it is between the perpendicular and parallel scales.

## The nature and energetics of AGN-driven perturbations in the hot gas in the Perseus Cluster

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **458** (2016) 2902-2915

## Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence

Journal of Plasma Physics Cambridge University Press **82** (2016) 905820212

A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g., drift-wave turbulence driven by temperature gradients) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating ExB flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. A consistent theory is constructed in which very little free energy leaks into high velocity moments of the distribution, rendering the turbulent cascade in the energetically relevant part of the wave-number space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also in contrast with the linear problem, in which it occurs at the finite rate equal to the Landau-damping rate). The ability of the free energy to stay in the low velocity moments of the distribution is facilitated by the "anti-phase-mixing" effect, whose presence in the nonlinear system is due to the stochastic version of the plasma echo (the advecting velocity couples the phase-mixing and anti-phase-mixing perturbations). The partitioning of the wave-number space between the (energetically dominant) region where this is the case and the region where linear phase mixing wins is governed by the "critical balance" between linear and nonlinear timescales (which for high Hermite moments splits into two thresholds, one demarcating the wave-number region where phase mixing predominates, the other where plasma echo does).

## Turbulent dynamo in a collisionless plasma.

Proceedings of the National Academy of Sciences of the United States of America **113** (2016) 3950-3953

Magnetic fields pervade the entire universe and affect the formation and evolution of astrophysical systems from cosmological to planetary scales. The generation and dynamical amplification of extragalactic magnetic fields through cosmic times (up to microgauss levels reported in nearby galaxy clusters, near equipartition with kinetic energy of plasma motions, and on scales of at least tens of kiloparsecs) are major puzzles largely unconstrained by observations. A dynamo effect converting kinetic flow energy into magnetic energy is often invoked in that context; however, extragalactic plasmas are weakly collisional (as opposed to magnetohydrodynamic fluids), and whether magnetic field growth and sustainment through an efficient turbulent dynamo instability are possible in such plasmas is not established. Fully kinetic numerical simulations of the Vlasov equation in a 6D-phase space necessary to answer this question have, until recently, remained beyond computational capabilities. Here, we show by means of such simulations that magnetic field amplification by dynamo instability does occur in a stochastically driven, nonrelativistic subsonic flow of initially unmagnetized collisionless plasma. We also find that the dynamo self-accelerates and becomes entangled with kinetic instabilities as magnetization increases. The results suggest that such a plasma dynamo may be realizable in laboratory experiments, support the idea that intracluster medium turbulence may have significantly contributed to the amplification of cluster magnetic fields up to near-equipartition levels on a timescale shorter than the Hubble time, and emphasize the crucial role of multiscale kinetic physics in high-energy astrophysical plasmas.

## INEFFICIENT DRIVING OF BULK TURBULENCE BY ACTIVE GALACTIC NUCLEI IN A HYDRODYNAMIC MODEL OF THE INTRACLUSTER MEDIUM

ASTROPHYSICAL JOURNAL **815** (2015) ARTN 41

## Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas

JOURNAL OF PLASMA PHYSICS **81** (2015) ARTN 325810501