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"plasma instabilities"
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Investigation of the collisionless plasmoid instability based on gyrofluid and gyrokinetic integrated approach
In this work, the development of two-dimensional current sheets with respect to tearing modes, in collisionless plasmas with a strong guide field, is analysed. During their nonlinear evolution, these thin current sheets can become unstable to the formation of plasmoids, which allows the magnetic reconnection process to reach high reconnection rates. We carry out a detailed study of the effect of a finite $\\beta _e$, which also implies finite electron Larmor radius effects, on the collisionless plasmoid instability. This study is conducted through a comparison of gyrofluid and gyrokinetic simulations. The comparison shows in general a good capability of the gyrofluid models in predicting the plasmoid instability observed with gyrokinetic simulations. We show that the effects of $\\beta _e$ promotes the plasmoid growth. The effect of the closure applied during the derivation of the gyrofluid model is also studied through the comparison among the variations of the different contributions to the total energy.
Journal Article
Equatorial Plasma Bubbles: A Review
The equatorial plasma bubble (EPB) phenomenon is an important component of space weather as the ionospheric irregularities that develop within EPBs can have major detrimental effects on the operation of satellite-based communication and navigation systems. Although the name suggests that EPBs occur in the equatorial ionosphere, the nature of the plasma instability that gives rise to EPBs is such that the bubbles may extend over a large part of the global ionosphere between geomagnetic latitudes of approximately ±15°. The scientific challenge continues to be to understand the day-to-day variability in the occurrence and characteristics of EPBs, such as their latitudinal extent and the development of irregularities within EPBs. In this paper, basic theoretical aspects of the plasma processes involved in the generation of EPBs, associated ionospheric irregularities, and observations of their characteristics using different techniques will be reviewed. Special focus will be given to observations of scintillations produced by the scattering of VHF and higher frequency radio waves while they propagate through ionospheric irregularities associated with EPBs, as these observations have revealed new information about the non-linear development of Rayleigh–Taylor instability in equatorial ionospheric plasma, which is the genesis of EPBs.
Journal Article
Predicting disruptive instabilities in controlled fusion plasmas through deep learning
Nuclear fusion power delivered by magnetic-confinement tokamak reactors holds the promise of sustainable and clean energy
1
. The avoidance of large-scale plasma instabilities called disruptions within these reactors
2
,
3
is one of the most pressing challenges
4
,
5
, because disruptions can halt power production and damage key components. Disruptions are particularly harmful for large burning-plasma systems such as the multibillion-dollar International Thermonuclear Experimental Reactor (ITER) project
6
currently under construction, which aims to be the first reactor that produces more power from fusion than is injected to heat the plasma. Here we present a method based on deep learning for forecasting disruptions. Our method extends considerably the capabilities of previous strategies such as first-principles-based
5
and classical machine-learning
7
–
11
approaches. In particular, it delivers reliable predictions for machines other than the one on which it was trained—a crucial requirement for future large reactors that cannot afford training disruptions. Our approach takes advantage of high-dimensional training data to boost predictive performance while also engaging supercomputing resources at the largest scale to improve accuracy and speed. Trained on experimental data from the largest tokamaks in the United States (DIII-D
12
) and the world (Joint European Torus, JET
13
), our method can also be applied to specific tasks such as prediction with long warning times: this opens up the possibility of moving from passive disruption prediction to active reactor control and optimization. These initial results illustrate the potential for deep learning to accelerate progress in fusion-energy science and, more generally, in the understanding and prediction of complex physical systems.
Using data from plasma-based tokamak nuclear reactors in the US and Europe, a machine-learning approach based on deep neural networks is taught to forecast disruptions, even those in machines on which the algorithm was not trained.
Journal Article
Magnetohydrodynamics of protoplanetary discs
Protoplanetary discs are made of gas and dust orbiting a young star. They are also the birth place of planetary systems, which motivates a large amount of observational and theoretical research. In these lecture notes, I present a review of the magnetic mechanisms applied to the outer regions ($R\\gtrsim 1\\ \\mathrm {AU}$) of these discs, which are the planet-formation regions. In contrast to usual astrophysical plasmas, the gas in these regions is noticeably cold ($T < 300\\ \\mathrm {K}$) and dense, which implies a very low ionisation fraction close to the disc midplane. In these notes, I deliberately ignore the innermost$(R\\sim 0.1\\ \\mathrm {AU})$region, which is influenced by the star–disc interaction and various radiative effects. I start by presenting a short overview of the observational evidence for the dynamics of these objects. I then introduce the methods and approximations used to model these plasmas, including non-ideal magnetohydrodynamics, and the uncertainties associated with this approach. In this framework, I explain how the global dynamics of these discs is modelled, and I present a stability analysis of this plasma in the local approximation, introducing the non-ideal magneto-rotational instability. Following this mostly analytical part, I discuss numerical models that have been used to describe the saturation mechanisms of this instability, and the formation of large-scale structures by various saturation mechanisms. Finally, I show that local numerical models are insufficient because magnetised winds are also emitted from the surface of these objects. After a short introduction on wind physics, I present global models of protoplanetary discs, including both a large-scale wind and the non-ideal dynamics of the disc.
Journal Article
Laguerre–Hermite pseudo-spectral velocity formulation of gyrokinetics
First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a pseudo-spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower resolution three-dimensional (3-D) gyrofluid representation and the conventional but more expensive 5-D gyrokinetic representation. Our formulation is a projection of the nonlinear gyrokinetic equation onto a Laguerre–Hermite velocity-space basis. We discuss issues related to collisions, closures and entropy. While any collision operator can be used in the formulation, we highlight a model operator that has a particularly sparse Laguerre–Hermite representation, while satisfying conservation laws and the H theorem. Free streaming, magnetic drifts and nonlinear phase mixing each give rise to closure problems, which we discuss in relation to the instabilities of interest and to free energy conservation. We show that the model is capable of reproducing gyrokinetic results for linear instabilities and zonal flow dynamics. Thus the final model is appropriate for the study of instabilities, turbulence and transport in a wide range of geometries, including tokamaks and stellarators.
Journal Article
Kinetic Turbulence in Collisionless High- β Plasmas
We present results from three-dimensional hybrid-kinetic simulations of Alfvénic turbulence in a high-β, collisionless plasma. The key feature of such turbulence is the interplay between local wave-wave interactions between the fluctuations in the cascade and the nonlocal wave-particle interactions associated with kinetic microinstabilities driven by anisotropy in the thermal pressure (namely, firehose, mirror, and ion cyclotron). We present theoretical estimates for, and calculate directly from the simulations, the effective collisionality and plasma viscosity in pressure-anisotropic high-βturbulence, demonstrating that, for strong Alfvénic turbulence, the effective parallel-viscous scale is comparable to the driving scale of the cascade. Below this scale, the kinetic-energy spectrum indicates an Alfvénic cascade with a slope steeper than−5/3due to the anisotropic viscous stress. The magnetic-energy spectrum is shallower than−5/3near the ion-Larmor scale due to fluctuations produced by the firehose instability. Most of the cascade energy (≈80%–90%) is dissipated as ion heating through a combination of Landau damping and anisotropic viscous heating. Our results have implications for models of particle heating in low-luminosity accretion onto supermassive black holes, the effective viscosity of the intracluster medium, and the interpretation of near-Earth solar-wind observations.
Journal Article
MHD stability and disruptions in the SPARC tokamak
SPARC is being designed to operate with a normalized beta of $\\beta _N=1.0$, a normalized density of $n_G=0.37$ and a safety factor of $q_{95}\\approx 3.4$, providing a comfortable margin to their respective disruption limits. Further, a low beta poloidal $\\beta _p=0.19$ at the safety factor $q=2$ surface reduces the drive for neoclassical tearing modes, which together with a frozen-in classically stable current profile might allow access to a robustly tearing-free operating space. Although the inherent stability is expected to reduce the frequency of disruptions, the disruption loading is comparable to and in some cases higher than that of ITER. The machine is being designed to withstand the predicted unmitigated axisymmetric halo current forces up to 50 MN and similarly large loads from eddy currents forced to flow poloidally in the vacuum vessel. Runaway electron (RE) simulations using GO+CODE show high flattop-to-RE current conversions in the absence of seed losses, although NIMROD modelling predicts losses of ${\\sim }80$ %; self-consistent modelling is ongoing. A passive RE mitigation coil designed to drive stochastic RE losses is being considered and COMSOL modelling predicts peak normalized fields at the plasma of order $10^{-2}$ that rises linearly with a change in the plasma current. Massive material injection is planned to reduce the disruption loading. A data-driven approach to predict an oncoming disruption and trigger mitigation is discussed.
Journal Article
Simulation study of the formation of a non-relativistic pair shock
We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed
$c/5$
, where
$c$
is the speed of light in vacuum, and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.
Journal Article
Fluctuation dynamo in a weakly collisional plasma
The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number (${Pm}\\gtrsim {1}$) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.
Journal Article