# Publications by Alexander Schekochihin

## Self-sustaining sound in collisionless, high-beta plasma

JOURNAL OF PLASMA PHYSICS **86** (2020) ARTN 905860603

## Elasticity of tangled magnetic fields

Journal of Plasma Physics Cambridge University Press **86** (2020) 905860511

The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. Furthermore, a tangled field should support the propagation of ‘magnetoelastic waves’, the isotropic analogue of Alfvén waves on a straight magnetic field. Here, we study magnetoelasticity in the idealised context of an equilibrium tangled field configuration. In contrast to previous treatments, we explicitly account for intermittency of the Maxwell stress, and show that this intermittency necessarily decreases the frequency of magnetoelastic waves in a stable field configuration. We develop a mean-field formalism to describe magnetoelastic behaviour, retaining leading-order corrections due to the coupling of large- and small-scale motions, and solve the initial-value problem for viscous fluids subjected to a large-scale shear, showing that the development of small-scale motions results in anomalous viscous damping of large-scale waves. Finally, we test these analytic predictions using numerical simulations of standing waves on tangled, linear force-free magnetic-field equilibria.

## Fluctuation dynamo in a weakly collisional plasma

JOURNAL OF PLASMA PHYSICS **86** (2020) ARTN 905860503

## Transport of high-energy charged particles through spatially-intermittent turbulent magnetic fields

Astrophysical Journal American Astronomical Society **892** (2020) 114

Identifying the sources of the highest energy cosmic rays requires understanding how they are deflected by the stochastic, spatially intermittent intergalactic magnetic field. Here we report measurements of energetic charged-particle propagation through a laser-produced magnetized plasma with these properties. We characterize the diffusive transport of the particles experimentally. The results show that the transport is diffusive and that, for the regime of interest for the highest-energy cosmic rays, the diffusion coefficient is unaffected by the spatial intermittency of the magnetic field.

## Supersonic plasma turbulence in the laboratory

Nature Communications Nature Research **10** (2019) 1758

## Overview of new MAST physics in anticipation of first results from MAST Upgrade

Nuclear Fusion IOP Science **59** (2019) 112011

The mega amp spherical tokamak (MAST) was a low aspect ratio device (R/a = 0.85/0.65 ~ 1.3) with similar poloidal cross-section to other medium-size tokamaks. The physics programme concentrates on addressing key physics issues for the operation of ITER, design of DEMO and future spherical tokamaks by utilising high resolution diagnostic measurements closely coupled with theory and modelling to significantly advance our understanding. An empirical scaling of the energy confinement time that favours higher power, lower collisionality devices is consistent with gyrokinetic modelling of electron scale turbulence. Measurements of ion scale turbulence with beam emission spectroscopy and gyrokinetic modelling in up-down symmetric plasmas find that the symmetry of the turbulence is broken by flow shear. Near the non-linear stability threshold, flow shear tilts the density fluctuation correlation function and skews the fluctuation amplitude distribution. Results from fast particle physics studies include the observation that sawteeth are found to redistribute passing and trapped fast particles injected from neutral beam injectors in equal measure, suggesting that resonances between the m = 1 perturbation and the fast ion orbits may be playing a dominant role in the fast ion transport. Measured D–D fusion products from a neutron camera and a charged fusion product detector are 40% lower than predictions from TRANSP/NUBEAM, highlighting possible deficiencies in the guiding centre approximation. Modelling of fast ion losses in the presence of resonant magnetic perturbations (RMPs) can reproduce trends observed in experiments when the plasma response and charge-exchange losses are accounted for. Measurements with a neutral particle analyser during merging-compression start-up indicate the acceleration of ions and electrons. Transport at the plasma edge has been improved through reciprocating probe measurements that have characterised a geodesic acoustic mode at the edge of an ohmic L-mode plasma and particle-in-cell modelling has improved the interpretation of plasma potential estimates from ball-pen probes. The application of RMPs leads to a reduction in particle confinement in L-mode and H-mode and an increase in the core ionization source. The ejection of secondary filaments following type-I ELMs correlates with interactions with surfaces near the X-point. Simulations of the interaction between pairs of filaments in the scrape-off layer suggest this results in modest changes to their velocity, and in most cases can be treated as moving independently. A stochastic model of scrape-off layer profile formation based on the superposition of non-interacting filaments is in good agreement with measured time-average profiles. Transport in the divertor has been improved through fast camera imaging, indicating the presence of a quiescent region devoid of filament near the X-point, extending from the separatrix to ψ n ~ 1.02. Simulations of turbulent transport in the divertor show that the angle between the divertor leg on the curvature vector strongly influences transport into the private flux region via the interchange mechanism. Coherence imaging measurements show counter-streaming flows of impurities due to gas puffing increasing the pressure on field lines where the gas is ionised. MAST Upgrade is based on the original MAST device, with substantially improved capabilities to operate with a Super-X divertor to test extended divertor leg concepts. SOLPS-ITER modelling predicts the detachment threshold will be reduced by more than a factor of 2, in terms of upstream density, in the Super-X compared with a conventional configuration and that the radiation front movement is passively stabilised before it reaches the X-point. 1D fluid modelling reveals the key role of momentum and power loss mechanisms in governing detachment onset and evolution. Analytic modelling indicates that long legs placed at large major radius, or equivalently low at the target compared with the X-point are more amenable to external control. With MAST Upgrade experiments expected in 2019, a thorough characterisation of the sources of the intrinsic error field has been carried out and a mitigation strategy developed.

## Suppressed effective viscosity in the bulk intergalactic plasma

Nature Astronomy Nature Research **3** (2019) 832-837

<p>Transport properties, such as viscosity and thermal conduction, of the hot intergalactic plasma in clusters of galaxies are largely unknown. Whereas for laboratory plasmas these characteristics are derived from the gas density and temperature<sup>1</sup>, such recipes can be fundamentally different for the intergalactic plasma<sup>2</sup> owing to a low rate of particle collisions and a weak magnetic field<sup>3</sup>. In numerical simulations, these unknowns can often be avoided by modelling these plasmas as hydrodynamic fluids<sup>4,5,6</sup>, even though local, non-hydrodynamic features observed in clusters contradict this assumption<sup>7,8,9</sup>. Using deep Chandra observations of the Coma Cluster<sup>10,11</sup>, we probe gas fluctuations in intergalactic medium down to spatial scales where the transport processes should prominently manifest themselves—provided that hydrodynamic models<sup>12</sup> with pure Coulomb collision rates are indeed adequate. We do not find evidence of such transport processes, implying that the effective isotropic viscosity is orders of magnitude smaller than naively expected. This indicates either an enhanced collision rate in the plasma due to particle scattering off microfluctuations caused by plasma instabilities<sup>2,13,14</sup> or that the transport processes are anisotropic with respect to the local magnetic field<sup>15</sup>. This also means that numerical models with high Reynolds number appear more consistent with observations. Our results demonstrate that observations of turbulence in clusters<sup>16,17</sup> are giving rise to a branch of astrophysics that can sharpen theoretical views on galactic plasmas.</p>

## Field reconstruction from proton radiography of intense laser driven magnetic reconnection

Physics of Plasmas AIP Publishing **26** (2019)

Magnetic reconnection is a process that contributes significantly to plasma dynamics and energy transfer in a wide range of plasma and magnetic field regimes, including inertial confinement fusion experiments, stellar coronae, and compact, highly magnetized objects like neutron stars. Laboratory experiments in different regimes can help refine, expand, and test the applicability of theoretical models to describe reconnection. Laser-plasma experiments exploring magnetic reconnection at a moderate intensity (IL ∼1014 W cm-2) have been performed previously, where the Biermann battery effect self-generates magnetic fields and the field dynamics studied using proton radiography. At high laser intensities (ILλL2>1018 Wcm-2μm2), relativistic surface currents and the time-varying electric sheath fields generate the azimuthal magnetic fields. Numerical modeling of these intensities has shown the conditions that within the magnetic field region can reach the threshold where the magnetic energy can exceed the rest mass energy such that σcold = B2/(μ0nemec2) > 1 [A. E. Raymond et al., Phys. Rev. E 98, 043207 (2018)]. Presented here is the analysis of the proton radiography of a high-intensity (∼1018 W cm-2) laser driven magnetic reconnection geometry. The path integrated magnetic fields are recovered using a "field-reconstruction algorithm" to quantify the field strengths, geometry, and evolution.

## Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma

Nature Communications Springer Nature **9** (2018) 591

Magnetic fields are ubiquitous in the Universe. Diffuse radiosynchrotron emission observations and Faraday rotation measurements have revealed magnetic field strengths ranging from a few nG and tens of µG in extragalactic disks, halos and clusters [1], up to hundreds of TG in magnetars, as inferred from their spin-down [2]. The energy density of these fields is typically comparable to the energy density of the fluid motions of the plasma in which they are embedded, making magnetic fields essential players in the dynamics of the luminous matter. The standard theoretical model for the origin of these strong magnetic fields is through the amplification of tiny seed fields via turbulent dynamo to the level consistent with current observations [3–7]. Here we demonstrate, using laser-produced colliding plasma flows, that turbulence is indeed capable of rapidly amplifying seed fields to near equipartition with the turbulent fluid motions. These results support the notion that turbulent dynamo is a viable mechanism responsible for the observed present-day magnetization.

## Generation of Internal Waves by Buoyant Bubbles in Galaxy Clusters and Heating of Intracluster Medium

Monthly Notices of the Royal Astronomical Society Blackwell Publishing Inc. (2018)

Buoyant bubbles of relativistic plasma in cluster cores plausibly play a key role in conveying the energy from a supermassive black hole to the intracluster medium (ICM) - the process known as radio-mode AGN feedback. Energy conservation guarantees that a bubble loses most of its energy to the ICM after crossing several pressure scale heights. However, actual processes responsible for transferring the energy to the ICM are still being debated. One attractive possibility is the excitation of internal waves, which are trapped in the cluster's core and eventually dissipate. Here we show that a sufficient condition for efficient excitation of these waves in stratified cluster atmospheres is flattening of the bubbles in the radial direction. In our numerical simulations, we model the bubbles phenomenologically as rigid bodies buoyantly rising in the stratified cluster atmosphere. We find that the terminal velocities of the flattened bubbles are small enough so that the Froude number ${\rm Fr}\lesssim 1$. The effects of stratification make the dominant contribution to the total drag force balancing the buoyancy force. In particular, clear signs of internal waves are seen in the simulations. These waves propagate horizontally and downwards from the rising bubble, spreading their energy over large volumes of the ICM. If our findings are scaled to the conditions of the Perseus cluster, the expected terminal velocity is $\sim100-200{\,\rm km\,s^{-1}}$ near the cluster cores, which is in broad agreement with direct measurements by the Hitomi satellite.

## Self-inhibiting thermal conduction in a high-β, whistler-unstable plasma

Journal of Plasma Physics Cambridge University Press **84** (2018) 905840305

A heat flux in a high-β plasma with low collisionality triggers the whistler instability. Quasilinear theory predicts saturation of the instability in a marginal state characterized by a heat flux that is fully controlled by electron scattering off magnetic perturbations. This marginal heat flux does not depend on the temperature gradient and scales as 1/β. We confirm this theoretical prediction by performing numerical particle-in-cell simulations of the instability. We further calculate the saturation level of magnetic perturbations and the electron scattering rate as functions of β and the temperature gradient to identify the saturation mechanism as quasilinear. Suppression of the heat flux is caused by oblique whistlers with magnetic-energy density distributed over a wide range of propagation angles. This result can be applied to high-β astrophysical plasmas, such as the intracluster medium, where thermal conduction at sharp temperature gradients along magnetic-field lines can be significantly suppressed. We provide a convenient expression for the amount of suppression of the heat flux relative to the classical Spitzer value as a function of the temperature gradient and β. For a turbulent plasma, the additional independent suppression by the mirror instability is capable of producing large total suppression factors (several tens in galaxy clusters) in regions with strong temperature gradients.

## Polarization of Sunyaev-Zeldovich signal due to electron pressure anisotropy in galaxy clusters

Monthly Notices of the Royal Astronomical Society Oxford University Press **474** (2017) 2389-2400

We describe polarization of the Sunyaev-Zel’dovich (SZ) effect associated with electron pressure anisotropy likely present in the intracluster medium (ICM). The ICM is an astrophysical example of a weakly collisional plasma where the Larmor frequencies of charged particles greatly exceed their collision frequencies. This permits formation of pressure anisotropies, driven by evolving magnetic fields via adiabatic invariance, or by heat fluxes. SZ polarization arises in the process of Compton scattering of the cosmic microwave background (CMB) photons off the thermal ICM electrons due to the difference in the characteristic thermal velocities of the electrons along two mutually orthogonal directions in the sky plane. The signal scales linearly with the optical depth of the region containing large-scale correlated anisotropy, and with the degree of anisotropy itself. It has the same spectral dependence as the polarization induced by cluster motion with respect to the CMB frame (kinematic SZ effect polarization), but can be distinguished by its spatial pattern. For the illustrative case of a galaxy cluster with a cold front, where electron transport is mediated by Coulomb collisions, we estimate the CMB polarization degree at the level of 10−8 (∼10 nK). An increase of the effective electron collisionality due to plasma instabilities will reduce the effect. Such polarization, therefore, may be an independent probe of the electron collisionality in the ICM, which is one of the key properties of a high-β weakly collisional plasma from the point of view of both astrophysics and plasma theory.

## Proton imaging of stochastic magnetic fields

Journal of Plasma Physics Cambridge University Press **83** (2017) 905830614

Recent laser-plasma experiments [1, 2, 3, 4] report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a proton imaging diagnostic can be used to determine a range of relevant magnetic field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. This ‘Kugland image-flux relation’ was previously derived [5] under simplifying assumptions typically valid in actual proton-imaging set-ups. We conclude that, as in the case of regular electromagnetic fields, features of the beam’s final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter – the contrast parameter µ ≡ ds/MlB – which quantifies the relative size of the correlation length lB of the stochastic field, proton displacements ds due to magnetic deflections, and the image magnification M. For stochastic magnetic fields, we establish the existence of four contrast regimes – linear, nonlinear injective, caustic and diffusive – under which proton-flux images relate to their parent fields in a qualitatively distinct manner. As a consequence, it is demonstrated that in the linear or nonlinear injective regimes, the path-integrated magnetic field experienced by the beam can be extracted uniquely, as can the magnetic-energy spectrum under a further statistical assumption of isotropy. This is no longer the case in the caustic or diffusive regimes. We also discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one’s ability to extract magnetic field statistics. The results presented in this paper are of consequence in providing a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of individual proton-flux images, or for optimising implementation of proton-imaging diagnostics on future laser-plasma experiments.

## Disruption of Alfvenic turbulence by magnetic reconnection in a collisionless plasma

Journal of Plasma Physics Cambridge University Press **83** (2017) 905830609

We calculate the disruption scale λD at which sheet-like structures in dynamically aligned Alfvénic turbulence are destroyed by the onset of magnetic reconnection in a low-β collisionless plasma. The scaling of λD depends on the order of the statistics being considered, with more intense structures being disrupted at larger scales. The disruption scale for the structures that dominate the energy spectrum is λD ∼ L 1/9 ⊥ (deρs) 4/9 , where de is the electron inertial scale, ρs is the ion sound scale and L⊥ is the outer scale of the turbulence. When βe and ρs/L⊥ are sufficiently small, the scale λD is larger than ρs and there is a break in the energy spectrum at λD, rather than at ρs . We propose that the fluctuations produced by the disruption are circularised flux ropes, which may have already been observed in the solar wind. We predict the relationship between the amplitude and radius of these structures and quantify the importance of the disruption process to the cascade in terms of the filling fraction of undisrupted structures and the fractional reduction of the energy contained in them at the ion sound scale ρs . Both of these fractions depend strongly on βe , with the disrupted structures becoming more important at lower βe . Finally, we predict that the energy spectrum between λD and ρs is steeper than k −3 ⊥ , when this range exists. Such a steep ‘transition range’ is sometimes observed in short intervals of solar-wind turbulence. The onset of collisionless magnetic reconnection may therefore significantly affect the nature of plasma turbulence around the ion gyroscale.

## Magneto-optic probe measurements in low density-supersonic jets

Journal of Instrumentation IOP Publishing **12** (2017) P12001

A magneto-optic probe was used to make time-resolved measurements of the magnetic field in both a single supersonic jet and in a collision between two supersonic turbulent jets, with an electron density ⇡ 1018 cm3 and electron temperature ⇡ 4 eV. The magneto-optic data indicated the magnetic field reaches B ⇡ 200 G. The measured values are compared against those obtained with a magnetic induction probe. Good agreement of the time-dependent magnetic field measured using the two techniques is found.

## Ion-scale turbulence in MAST: anomalous transport, subcritical transitions, and comparison to BES measurements

Plasma Physics and Controlled Fusion Institute of Physics **59** (2017) 114003-

We investigate the effect of varying the ion temperature gradient (ITG) and toroidal equilibrium scale sheared flow on ion-scale turbulence in the outer core of MAST by means of local gyrokinetic simulations. We show that nonlinear simulations reproduce the experimental ion heat flux and that the experimentally measured values of the ITG and the flow shear lie close to the turbulence threshold. We demonstrate that the system is subcritical in the presence of flow shear, i.e., the system is formally stable to small perturbations, but transitions to a turbulent state given a large enough initial perturbation. We propose that the transition to subcritical turbulence occurs via an intermediate state dominated by low number of coherent long-lived structures, close to threshold, which increase in number as the system is taken away from the threshold into the more strongly turbulent regime, until they fill the domain and a more conventional turbulence emerges. We show that the properties of turbulence are effectively functions of the distance to threshold, as quantified by the ion heat flux. We make quantitative comparisons of correlation lengths, times, and amplitudes between our simulations and experimental measurements using the MAST BES diagnostic. We find reasonable agreement of the correlation properties, most notably of the correlation time, for which significant discrepancies were found in previous numerical studies of MAST turbulence.

## Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High-β Plasma.

Physical review letters **119** (2017) 155101-155101

Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear "interruption" of standing and traveling shear-Alfvén waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfvénic perturbation, and occurs for wave amplitudes δB_{⊥}/B_{0}≳β^{-1/2} (where β is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-scale magnetic field of the wave decays rapidly. The dynamics are strongly affected by the excitation of oblique firehose modes, which transition into long-lived parallel fluctuations at the ion gyroscale and cause significant particle scattering. Traveling waves are damped more slowly, but are also influenced by small-scale parallel fluctuations created by the decay of firehose modes. Our results demonstrate that collisionless plasmas cannot support linearly polarized Alfvén waves above δB_{⊥}/B_{0}∼β^{-1/2}. They also provide a vivid illustration of two key aspects of low-collisionality plasma dynamics: (i) the importance of velocity-space instabilities in regulating plasma dynamics at high β, and (ii) how nonlinear collisionless processes can transfer mechanical energy directly from the largest scales into thermal energy and microscale fluctuations, without the need for a scale-by-scale turbulent cascade.

## Overview of recent physics results from MAST

Nuclear Fusion **57** (2017)

© 2017 Culham Centre for Fusion Energy. New results from MAST are presented that focus on validating models in order to extrapolate to future devices. Measurements during start-up experiments have shown how the bulk ion temperature rise scales with the square of the reconnecting field. During the current ramp-up, models are not able to correctly predict the current diffusion. Experiments have been performed looking at edge and core turbulence. At the edge, detailed studies have revealed how filament characteristics are responsible for determining the near and far scrape off layer density profiles. In the core the intrinsic rotation and electron scale turbulence have been measured. The role that the fast ion gradient has on redistributing fast ions through fishbone modes has led to a redesign of the neutral beam injector on MAST Upgrade. In H-mode the turbulence at the pedestal top has been shown to be consistent with being due to electron temperature gradient modes. A reconnection process appears to occur during edge localized modes (ELMs) and the number of filaments released determines the power profile at the divertor. Resonant magnetic perturbations can mitigate ELMs provided the edge peeling response is maximised and the core kink response minimised. The mitigation of intrinsic error fields with toroidal mode number n > 1 has been shown to be important for plasma performance.

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

New Journal of Physics Institute of Physics **19** (2017) 055005-

This work, which extends Squire et al (Astrophys. J. Lett. 2016 830 L25), 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.

## Numerical modeling of laser-driven experiments aiming to demonstrate magnetic field amplification via turbulent dynamo

PHYSICS OF PLASMAS **24** (2017) ARTN 041404