# Publications by Alexander Schekochihin

## Generation of magnetic field by combined action of turbulence and shear

Physical Review Letters **100** (2008)

The feasibility of a mean-field dynamo in nonhelical turbulence with a superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of the magnetic field at scales much larger than the outer scale of the turbulence is found. The characteristic scale of the field is lB̄S-1/2 and the growth rate is γS, where S is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows. © 2008 The American Physical Society.

## Model Collision Operators for Numerical Gyrokinetics

THEORY OF FUSION PLASMAS **1069** (2008) 233-+

## Kinetic simulations of magnetized turbulence in astrophysical plasmas

Physical Review Letters **100** (2008)

This Letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic- and electric-field energy spectra show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfvén waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfvén waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind. Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale. © 2008 The American Physical Society.

## A model of turbulence in magnetized plasmas: Implications for the dissipation range in the solar wind

JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS **113** (2008) ARTN A05103

## Linearized Model Fokker-Planck Collision Operators for Gyrokinetic Simulations, II. Numerics

Phys. Plasmas **16** (2008) 072107-

## Nonlinear growth of firehose and mirror fluctuations in astrophysical plasmas

Physical Review Letters **100** (2008)

In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, ÎB/Bâ1, on a time scale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas. © 2008 The American Physical Society.

## Numerical demonstration of fluctuation dynamo at low magnetic prandtl numbers

Physical Review Letters **98** (2007)

Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm 1 and small magnetic Prandtl number Pm 1. The dependence of the critical Rmc for dynamo on the hydrodynamic Reynolds number Re is obtained for 1 Re 6700. In the limit Pm 1, Rmc is about 3 times larger than for the previously well-established dynamo at large and moderate Prandtl numbers: Rmc 200 for Re 6000 compared to Rmc∼60 for Pm 1. It is not yet possible to determine numerically whether the growth rate of the magnetic energy is Rm1/2 in the limit Rm→, as it should be if the dynamo is driven by the inertial-range motions at the resistive scale. © 2007 The American Physical Society.

## Dissipation-scale turbulence in the solar wind

AIP Conference Proceedings **932** (2007) 3-8

We present a cascade model for turbulence in weakly collisional plasmas that follows the nonlinear cascade of energy from the large scales of driving in the MHD regime to the small scales of the kinetic Alfvén wave regime where the turbulence is dissipated by kinetic processes. Steady-state solutions of the model for the slow solar wind yield three conclusions: (1) beyond the observed break in the magnetic energy spectrum, one expects an exponential cut-off; (2) the widely held interpretation that this dissipation range obeys power-law behavior is an artifact of instrumental sensitivity limitations; and, (3) over the range of parameters relevant to the solar wind, the observed variation of dissipation range spectral indices from -2 to -4 is naturally explained by the varying effectiveness of Landau damping, from an undamped prediction of -7/3 to a strongly damped index around -4. © 2007 American Institute of Physics.

## Instability of current sheets and formation of plasmoid chains

Physics of Plasmas **14** (2007)

Current sheets formed in magnetic reconnection events are found to be unstable to high-wavenumber perturbations. The instability is very fast: its maximum growth rate scales as S1/4vA/LCS, where LCS is the length of the sheet, vA the Alfvén speed, and S the Lundquist number. As a result, a chain of plasmoids (secondary islands) is formed, whose number scales as S3/8. © 2007 American Institute of Physics.

## Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence

Journal of Fluid Mechanics **575** (2007) 111-120

This paper examines the consistency of the exact scaling laws for isotropic magnetohydrodynamic (MHD) turbulence in numerical simulations with large magnetic Prandtl numbers Pm and with Pm. The exact laws are used to elucidate the structure of the magnetic and velocity fields. Despite the linear scaling of certain third-order correlation functions, the situation is not analogous to the case of Kolmogorov turbulence. The magnetic field is adequately described by a model of a stripy (folded) field with direction reversals at the resistive scale. At currently available resolutions, the cascade of kinetic energy is short-circuited by the direct exchange of energy between the forcing-scale motions and the stripy magnetic fields. This non-local interaction is the defining feature of isotropic MHD turbulence. © 2007 Cambridge University Press.

## Scaling laws, nonlocality and structure in isotropic magnetohydrodynamic turbulence

Advances in Turbulence XI - Proceedings of the 11th EUROMECH European Turbulence Conference (2007) 76-78

## Interplanetary and interstellar plasma turbulence

PLASMA PHYSICS AND CONTROLLED FUSION **49** (2007) A195-A209

## FLR effects in nonlinear tearing mode reconnection

33rd EPS Conference on Plasma Physics 2006, EPS 2006 **2** (2006) 1444-1447

## Future magnetic field studies using the Planck surveyor experiment

Astronomische Nachrichten **327** (2006) 626-631

The Planck mission will permit measurements of the polarization of the cosmic microwave background and of polarized foregrounds such as our own Galaxy with an unprecedented combination of accuracy and completeness. This will provide information on cosmological and galactic magnetic fields. The latter can be studied in detail via nearly Faraday-rotation free synchrotron and polarized dust emission. Methods are discussed to extract physically relevant information on the magnetic turbulence from Planck data and other measurements. © 2006 WILEY-VCH Verlag GmbH & Co. KGaA.

## Astrophysical gyrokinetics: Basic equations and linear theory

ASTROPHYSICAL JOURNAL **651** (2006) 590-614

## Turbulence, magnetic fields, and plasma physics in clusters of galaxies

Physics of Plasmas **13** (2006)

Observations of galaxy clusters show that the intracluster medium (ICM) is likely to be turbulent and is certainly magnetized. The properties of this magnetized turbulence are determined both by fundamental nonlinear magnetohydrodynamic interactions and by the plasma physics of the ICM, which has very low collisionality. Cluster plasma threaded by weak magnetic fields is subject to firehose and mirror instabilities. These saturate and produce fluctuations at the ion gyroscale, which can scatter particles, increasing the effective collision rate and, therefore, the effective Reynolds number of the ICM. A simple way to model this effect is proposed. The model yields a self-accelerating fluctuation dynamo whereby the field grows explosively fast, reaching the observed, dynamically important, field strength in a fraction of the cluster lifetime independent of the exact strength of the seed field. It is suggested that the saturated state of the cluster turbulence is a combination of the conventional isotropic magnetohydrodynamic turbulence, characterized by folded, direction-reversing magnetic fields and an Alfván-wave cascade at collisionless scales. An argument is proposed to constrain the reversal scale of the folded field. The picture that emerges appears to be in qualitative agreement with observations of magnetic fields in clusters. © 2006 American Institute of Physics.

## Fast growth of magnetic fields in galaxy clusters: A self-accelerating dynamo

Astronomische Nachrichten **327** (2006) 599-604

We propose a model of magnetic-field growth in galaxy clusters whereby the field is amplified by a factor of about 108 over a cosmologically short time of ∼ 108 yr. Our model is based on the idea that the viscosity of the intracluster medium during the field-amplification epoch is determined not by particle collisions but by plasma microinstabilities: these give rise to small-scale fluctuations, which scatter particles, increasing their effective collision rate and, therefore, the effective Reynolds number. This gives rise to a bootstrap effect as the growth of the field triggers the instabilities which increase the Reynolds number which, in turn, accelerates the growth of the field. The growth is explosive and the result is that the observed field strength is reached over a fraction of the cluster lifetime independent of the exact strength of the seed field (which only needs to be above ∼ 10-15 G to trigger the explosive growth). © 2006 WILEY-VCH Verlag GmbH & Co. KGaA.

## Microstability physics as illuminated in the spherical tokamak

Plasma Physics and Controlled Fusion **47** (2005)

Spherical tokamaks (STs) have attractive features for fusion, and there is considerable interest in understanding their transport properties which depend on the underlying microinstabilities. STs are capable of operation with low magnetic fields and exhibit large inhomogeneity in the toroidal magnetic field. These factors strongly affect particle dynamics and the potency of magnetic perturbations, which correspondingly impact on the microstability properties of STs. This paper reviews previous microstability studies in ST plasma configurations and presents gyrokinetic microstability calculations for a range of ST equilibria, using the gyrokinetic code GS2. Microstability properties of L-mode and H-mode equilibria, from the MAST experiment at Culham, are compared. In MAST the shearing rates of equilibrium E × B flows usually exceed the growth rates of microinstabilities with k⊥ρi < 1 (including ion temperature gradient, ITG, driven drift waves) and are generally smaller than the growth rates of shorter wavelength modes with k ⊥ρi > 1 (electron temperature gradient, ETG, driven drift waves). Electromagnetic effects are significant at mid-radius in these MAST equilibria, where the local β ≥ 0.1. At k ⊥ρi < 1, strongly electromagnetic modes dominate over ITG instabilities, and these modes are found to have tearing parity in the H-mode plasma and twisting parity in the L-mode plasma. Numerical experiments have been carried out to assess the properties of the tearing parity modes and to probe the underlying physical drive mechanism. At shorter wavelengths the electromagnetic effects can significantly stabilize the ETG instabilities. Nonlinear electron scale microturbulence calculations for two surfaces of a MAST H-mode plasma suggest that significant electron heat transport can be carried via this mechanism. In an extremely high β ST equilibrium, which has been proposed as the basis of a conceptual ST power plant, electrostatic instabilities are fully stabilized, but tearing parity modes are predicted to be unstable over-wide range of length scales. © 2005 IOP Publishing Ltd.

## X-point collapse and saturation in the nonlinear tearing mode reconnection

Physical Review Letters **95** (2005)

We study the nonlinear evolution of the resistive tearing mode in slab geometry in two dimensions. We show that, in the strongly driven regime (large Δ′), a collapse of the X point occurs once the island width exceeds a certain critical value ∼1/Δ′. A current sheet is formed and the reconnection is exponential in time with a growth rate ∞η1/2, where η is the resistivity. If the aspect ratio of the current sheet is sufficiently large, the sheet can itself become tearing-mode unstable, giving rise to secondary islands, which then coalesce with the original island. The saturated state depends on the value of Δ′. For small Δ′, the saturation amplitude is ∞Δ′ and quantitatively agrees with the theoretical prediction. If Δ′ is large enough for the X-point collapse to have occurred, the saturation amplitude increases noticeably and becomes independent of Δ′. © 2005 The American Physical Society.

## Nonlinear tearing mode reconnection

32nd EPS Conference on Plasma Physics 2005, EPS 2005, Held with the 8th International Workshop on Fast Ignition of Fusion Targets - Europhysics Conference Abstracts **1** (2005) 193-196