# Publications by Alexander Schekochihin

## Editorial Special issue: Macroscopic randomness in astrophysical plasmas: The legacy and vision of Ya. B. Zeldovich

JOURNAL OF PLASMA PHYSICS **81** (2015) ARTN 391810403

## Fluctuation-dissipation relations for a plasma-kinetic Langevin equation

JOURNAL OF PLASMA PHYSICS **81** (2015) ARTN 305810104

## Non-linear mirror instability

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **447** (2015) L45-L49

## Refined critical balance in strong Alfv,nic turbulence

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **449** (2015) L77-L81

## INTERMITTENCY AND ALIGNMENT IN STRONG RMHD TURBULENCE

ASTROPHYSICAL JOURNAL **807** (2015) ARTN 39

## Gas density fluctuations in the Perseus Cluster: clumping factor and velocity power spectrum

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **450** (2015) 4184-4197

## Fluctuation-dissipation relations for a plasma-kinetic Langevin equation

Journal of Plasma Physics **81** (2015)

© 2014 Cambridge University Press. A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation relations are derived. The kinetic fluctuation-dissipation relation reduces to the standard fluid one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation relations for the perturbations of the distribution function are derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.

## Developed turbulence and nonlinear amplification of magnetic fields in laboratory and astrophysical plasmas.

Proceedings of the National Academy of Sciences of the United States of America National Academy of Sciences **112** (2015) 8211-8215

The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe.

## THE RELATION BETWEEN GAS DENSITY AND VELOCITY POWER SPECTRA IN GALAXY CLUSTERS: QUALITATIVE TREATMENT AND COSMOLOGICAL SIMULATIONS

ASTROPHYSICAL JOURNAL LETTERS **788** (2014) ARTN L13

## Editorial: The Way Forward for JPP

JOURNAL OF PLASMA PHYSICS **80** (2014) 131-131

## Models of magnetic field evolution and effective viscosity in weakly collisional extragalactic plasmas

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **440** (2014) 3226-3242

## Erratum: "Correlations at large scales and the onset of turbulence in the fast solar wind" (2013, ApJ, 778, 177)

Astrophysical Journal **782** (2014)

## Turbulent heating in galaxy clusters brightest in X-rays.

Nature **515** (2014) 85-87

The hot (10(7) to 10(8) kelvin), X-ray-emitting intracluster medium (ICM) is the dominant baryonic constituent of clusters of galaxies. In the cores of many clusters, radiative energy losses from the ICM occur on timescales much shorter than the age of the system. Unchecked, this cooling would lead to massive accumulations of cold gas and vigorous star formation, in contradiction to observations. Various sources of energy capable of compensating for these cooling losses have been proposed, the most promising being heating by the supermassive black holes in the central galaxies, through inflation of bubbles of relativistic plasma. Regardless of the original source of energy, the question of how this energy is transferred to the ICM remains open. Here we present a plausible solution to this question based on deep X-ray data and a new data analysis method that enable us to evaluate directly the ICM heating rate from the dissipation of turbulence. We find that turbulent heating is sufficient to offset radiative cooling and indeed appears to balance it locally at each radius-it may therefore be the key element in resolving the gas cooling problem in cluster cores and, more universally, in the atmospheres of X-ray-emitting, gas-rich systems on scales from galaxy clusters to groups and elliptical galaxies.

## Turbulent amplification of magnetic fields in laboratory laser-produced shock waves

NATURE PHYSICS **10** (2014) 520-524

## Firehose and Mirror Instabilities in a Collisionless Shearing Plasma

PHYSICAL REVIEW LETTERS **112** (2014) ARTN 205003

## Suppression of local heat flux in a turbulent magnetized intracluster medium

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY **440** (2014) 1153-1164

## Comparison of BES measurements of ion-scale turbulence with direct gyro-kinetic simulations of MAST L-mode plasmas

Plasma Physics and Controlled Fusion **56** (2014)

Observations of ion-scale (kyρi 1) density turbulence of relative amplitude 0.2% are available on the Mega Amp Spherical Tokamak (MAST) using a 2D (8 radial × 4 poloidal channel) imaging beam emission spectroscopy diagnostic. Spatial and temporal characteristics of this turbulence, i.e., amplitudes, correlation times, radial and perpendicular correlation lengths and apparent phase velocities of the density contours, are determined by means of correlation analysis. For a low-density, L-mode discharge with strong equilibrium flow shear exhibiting an internal transport barrier in the ion channel, the observed turbulence characteristics are compared with synthetic density turbulence data generated from global, non-linear, gyro-kinetic simulations using the particle-in-cell code NEMORB. This validation exercise highlights the need to include increasingly sophisticated physics, e.g., kinetic treatment of trapped electrons, equilibrium flow shear and collisions, to reproduce most of the characteristics of the observed turbulence. Even so, significant discrepancies remain: an underprediction by the simulations of the turbulence amplitude and heat flux at plasma periphery and the finding that the correlation times of the numerically simulated turbulence are typically two orders of magnitude longer than those measured in MAST. Comparison of these correlation times with various linear timescales suggests that, while the measured turbulence is strong and may be 'critically balanced', the simulated turbulence is weak. © 2014 IOP Publishing Ltd.

## Local dependence of ion temperature gradient on magnetic configuration, rotational shear and turbulent heat flux in MAST

NUCLEAR FUSION **54** (2014) ARTN 042003

## Correlations at large scales and the onset of turbulence in the fast solar WIND

Astrophysical Journal **778** (2013)

We show that the scaling of structure functions of magnetic and velocity fields in a mostly highly Alfvénic fast solar wind stream depends strongly on the joint distribution of the dimensionless measures of cross helicity and residual energy. Already at very low frequencies, fluctuations that are both more balanced (cross helicity ∼0) and equipartitioned (residual energy ∼0) have steep structure functions reminiscent of "turbulent" scalings usually associated with the inertial range. Fluctuations that are magnetically dominated (residual energy ∼-1), and so have closely anti-aligned Elsasser-field vectors, or are imbalanced (cross helicity ∼1), and so have closely aligned magnetic and velocity vectors, have wide "1/f" ranges typical of fast solar wind. We conclude that the strength of nonlinear interactions of individual fluctuations within a stream, diagnosed by the degree of correlation in direction and magnitude of magnetic and velocity fluctuations, determines the extent of the 1/f region observed, and thus the onset scale for the turbulent cascade. © 2013. The American Astronomical Society. All rights reserved.