arXiv subjects

Amitava Bhattacharjee

Publications and source records attributed to Amitava Bhattacharjee.

At least 73 records · Page 4Linked to original sources

arXiv2021

Adjoint methods for quasisymmetry of vacuum fields on a surface

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared to finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasisymmetry and a rotational transform value on a surface. To measure quasisymmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations.

physics.plasm-ph↗

arXiv2021

Small-Scale Dynamo in Stably Stratified Turbulence

We present numerical investigations into three principal properties of the small-scale dynamo in stably stratified turbulence: the onset criterion, the growth rate, and the nature of the magnetic field anisotropy in the kinematic regime. The results suggest that all three dynamo properties are controlled by the scale separation between the Ozmidov scale and the viscous or resistive scale. In addition to the critical magnetic Reynolds number, this allows for the definition of critical buoyancy and magnetic buoyancy Reynolds numbers for stratified small-scale dynamo onset in the high and low magnetic Prandtl number regimes, respectively. The presence of a small-scale dynamo in stellar radiative zones could affect dynamics through resulting Maxwell stresses and/or influence large-scale dynamo mechanisms in regions of differential rotation. Taking the solar radiative zone as a representative example and applying the onset criterion, we find that the stratification is strong enough to make the small-scale dynamo marginally active in the stably stratified turbulence of the solar tachocline.

physics.flu-dyn↗

arXiv2020

Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1: Solutions near an axisymmetric surface

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer 1991a,b; Plunk & Helander 2018), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic PDE for a function $η$ such the field strength satisfies $B = B(η)$. Closed-form solutions are obtained in cylindrical, slab, and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasi-helical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side.

physics.plasm-ph↗

arXiv2020

Compressional Alfvén eigenmodes excited by runaway electrons

Compressional Alfvén eigenmodes (CAE) driven by energetic ions have been observed in magnetic fusion experiments. In this paper, we show that the modes can also be driven by runaway electrons formed in post-disruption plasma, which may explain kinetic instabilities observed in DIII-D disruption experiments with massive gas injection. The mode-structure is calculated, as are the frequencies which are in agreement with experimental observations. Using a runaway electron distribution function obtained from a kinetic simulation, the mode growth rates are calculated and found to exceed the collisional damping rate when the runaway electron density exceeds a threshold value. The excitation of CAE poses a new possible approach to mitigate seed runaway electrons during the current quench and surpassing the avalanche.

physics.plasm-ph↗

arXiv2020

Structure and overstability of resistive modes with runaway electrons

We investigate the effects of runaway electron current on the dispersion relation of resistive magnetohydrodynamic modes in tokamaks. We present a new theoretical model to derive the dispersion relation, which is based on the asymptotic analysis of the resistive layer structure of the modes. It is found that in addition to the conventional resistive layer, a new runaway current layer can emerge whose properties depend on the ratio of the Alfvén velocity to the runaway electron convection speed. Due to the contribution from this layer, both the tearing mode and kink mode will have a real frequency in addition to a growth rate. The derived dispersion relation has been compared with numerical results using both a simplified eigenvalue calculation and a M3D-C1 linear simulation, and good agreement is found in both cases.

physics.plasm-ph↗

arXiv2020

Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions. II. Circular axis stellarators

We apply the near-axis expansion method for quasisymmetric magnetic fields with anisotropic pressure (developed in the companion paper, Part I [E. Rodriguez, A. Bhattacharjee, arXiv:2008.04715 (2020)]) to construct numerical solutions to circular axis stellarators. The solutions are found to second order in the distance from the axis, not possible in the standard Garren-Boozer construction [D. A. Garren and A. H. Boozer, Physics of Fluids B: Plasma Physics, 2822 (1991)], which assumes magnetostatic equilibria with isotropic pressure. In the limit of zero anisotropy, it is shown that a subset of coefficients can be chosen to avoid the overdetermination problem.

physics.plasm-ph↗

arXiv2020

Solving the problem of overdetermination of quasisymmetric equilbrium solutions by near-axis expansions: I. Generalised force balance

It is well known that the process of construction of quasisymmetric magnetic fields in magnetostatic equilibrium with isotropic pressure suffers from the problem of overdetermination. This has led to the widespread belief that global quasisymmetric solutions are likely not to exist. We develop a general near-axis expansion procedure that does not rely on the assumption of magnetostatic equilibria with isotropic pressure. We then demonstrate that in equilibria with anisotropic pressure, it is possible to circumvent the problem of overdetermination and carry out the power-series solutions to higher order. This suggests, contrary to current belief, that the existence of globally quasisymmetric fields is likely if one relaxes the assumption of magnetostatic equilibria with isotropic pressure.

physics.plasm-ph↗

arXiv2020

Necessary and Sufficient Conditions for Quasisymmetry

A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma, conditions for quasisymmetry are constructed starting from the single-particle Lagrangian to leading order. The conditions presented in the paper are less restrictive than the set recently obtained by Burby et al. [arXiv:1912.06468], and could facilitate ongoing efforts towards investigating the existence of global quasisymmetric MHD equilibria. It is also shown that quasisymmetry implies the existence of flux surfaces, regardless of whether the field corresponds to an MHD equilibrium.

physics.plasm-ph↗

arXiv2019

Weibel instability drives large magnetic field generation in laser-driven single plume ablation

First-principles kinetic simulations are used to investigate magnetic field generation processes in expanding ablated plasmas relevant to laser-driven foils and hohlraums. In addition to Biermann-battery-generated magnetic fields, strong filamentary magnetic filaments are found to grow in the corona of single expanding plasma plumes; such filaments are observed to dominate Biermann fields at sufficiently large focal radius, reaching saturation values of $\sim$ 100 T at National Ignition Facility-like drive conditions. The filamentary fields result from the ion Weibel instability driven by relative counterstreaming between the ablated ions and a sparse background population, which could be the result of a gas prefill in a hohlraum or laser pre-pulse. The ion-Weibel instability is robust with the inclusion of collisions and grows on a timescale of 100 ps, with a wavelength on the scale of 100-250 $μ$m, over a wide range of background population densities; the instability also gives rise to coherent density oscillations. These results are of particular interest to inertial confinement fusion experiments, where such field and density perturbations can modify heat-transport as well as laser propagation and absorption.

physics.plasm-ph↗

arXiv2019

Global Ten-Moment Multifluid Simulations of the Solar Wind Interaction with Mercury: From the Planetary Conducting Core to the Dynamic Magnetosphere

For the first time, we explore the tightly coupled interior-magnetosphere system of Mercury by employing a three-dimensional ten-moment multifluid model. This novel fluid model incorporates the non-ideal effects including the Hall effect, inertia, and tensorial pressures that are critical for collisionless magnetic reconnection; therefore, it is particularly well suited for investigating $collisionless$ magnetic reconnection in Mercury's magnetotail and at the planet's magnetopause. The model is able to reproduce the observed magnetic field vectors, field-aligned currents, and cross-tail current sheet asymmetry (beyond the MHD approach) and the simulation results are in good agreement with spacecraft observations. We also study the magnetospheric response of Mercury to a hypothetical extreme event with an enhanced solar wind dynamic pressure, which demonstrates the significance of induction effects resulting from the electromagnetically-coupled interior. More interestingly, plasmoids (or flux ropes) are formed in Mercury's magnetotail during the event, indicating the highly dynamic nature of Mercury's magnetosphere.

physics.space-ph↗

arXiv2019

Scalings Pertaining to Current Sheet Disruption Mediated by the Plasmoid Instability

Analytic scaling relations are derived for a phenomenological model of the plasmoid instability in an evolving current sheet, including the effects of reconnection outflow. Two scenarios are considered, where the plasmoid instability can be triggered either by an injected initial perturbation or by the natural noise of the system (here referred to as the system noise). The two scenarios lead to different scaling relations because the initial noise decays when the linear growth of the plasmoid instability is not sufficiently fast to overcome the advection loss caused by the reconnection outflow, whereas the system noise represents the lowest level of fluctuations in the system. The leading order approximation for the current sheet width at disruption takes the form of a power-law multiplied by a logarithmic factor, and from that, the scaling relations for the wavenumber and the linear growth rate of the dominant mode are obtained. When the effects of the outflow are neglected, the scaling relations agree, up to the leading order approximation, with previously derived scaling relations based on a principle of least time. The analytic scaling relations are validated with numerical solutions of the model.

physics.plasm-ph↗

arXiv2019

A model of solar equilibrium: the hydrodynamic limit

Helioseismology has revealed the internal density and rotation profiles of the Sun. Yet, knowledge of its magnetic fields and meridional circulation is confined much closer to the surface, and latitudinal entropy gradients are below detectable limits. While numerical simulations can offer insight into the interior dynamics and help identify which ingredients are necessary to reproduce particular observations, some features of the Sun can be understood analytically from an equilibrium perspective. Examples of such features include: the 1D density profile arising from steady-state energy transport from the core to the surface, and the tilting of isorotation contours in the convection zone (CZ) due to baroclinic forcing. To help identify which features can be explained by equilibrium, we propose analyzing stationary axisymmetric ideal magnetohydrodynamic flows in the solar regime. By prescribing an appropriate entropy profile at the surface, we recover a rotation profile that reasonably matches observations in the bulk of the CZ. Additionally, by including the effects of poloidal flow, we reproduce a feature that is reminiscent of the near surface shear layer. However, no tachocline-like feature is seen in hydrodynamic equilibrium, suggesting the importance of either dynamics or magnetic fields in its description.

astro-ph.SR↗

arXiv2018

Role of the Plasmoid Instability in Magnetohydrodynamic Turbulence

The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic (MHD) turbulence by means of high-resolution direct numerical simulations. At sufficiently large magnetic Reynolds number ($R_m=10^6$), the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets. The disruption of current sheet structures facilitates the energy cascade towards small scales, leading to the breaking and steepening of the energy spectrum. In the plasmoid-mediated regime, the energy spectrum displays a scaling that is close to the spectral index $-2.2$ as proposed by recent analytic theories. We also demonstrate that the scale-dependent dynamic alignment exists in 2D MHD turbulence and the corresponding slope of the alignment angle is close to 0.25.

physics.plasm-ph↗

arXiv2018

Using the maximum entropy distribution to describe electrons in reconnecting current sheets

Particle distributions in weakly collisional environments such as the magnetosphere have been observed to show deviations from the Maxwellian distribution. These can often be reproduced in kinetic simulations, but fluid models, which are used in global simulations of the magnetosphere, do not necessarily capture any of this. We apply the maximum entropy fluid closure of Levermore, which leads to well posed moment equations, to reconstruct particle distributions from a kinetic simulation in a reconnection region. Our results show that without information other than the moments, the model can reproduce the general structure of the distributions but not all of the finer details. The advantages of the closure over the traditional Grad closure are also discussed.

physics.space-ph↗

arXiv2018

A tight-coupling scheme sharing minimum information across a spatial interface between gyrokinetic turbulence codes

A new scheme that tightly couples kinetic turbulence codes across a spatial interface is introduced. This scheme evolves from considerations of competing strategies and down-selection. It is found that the use of a composite kinetic distribution function and fields with global boundary conditions as if the coupled code were one, makes the coupling problem tractable. In contrast, coupling the two solutions from each code across the overlap region is found to be more difficult due to numerical dephasing of the turbulent solutions between two solvers. Another advantage of the new scheme is that the data movement can be limited to the 3D fluid quantities, instead of higher dimensional kinetic information, which is computationally more efficient for large scale simulations on leadership class computers.

physics.plasm-ph↗

arXiv2018

Energy spectrum of tearing mode turbulence in sheared background field

The energy spectrum of tearing mode turbulence in a sheared background magnetic field is studied in this work. We consider the scenario where the nonlinear interaction of overlapping large-scale modes stirs up a broad spectrum of small-scale modes, generating tearing mode turbulence. The spectrum of such turbulence is of interest since it is relevant to the small-scale back-reaction to the large-scale field. The turbulence we discuss here differs from traditional MHD turbulence mainly in two aspects, one being the existence of many linearly stable small-scale modes which cause an effective damping during energy cascade; the other being the scale independent anisotropy induced by the large scale modes tilting the sheared background field, as opposed to the scale dependent anisotropy frequently encountered in traditional weak turbulence or critically balanced turbulence theory. These two differences result in the deviation of energy spectrum from a simple power law behavior, taking the form of a power law multiplied by an exponential falloff. Numerical simulation is carried out using viscous resistive MHD equations to verify our theoretical prediction, and reasonable agreement is found between numerical result and our model.

physics.plasm-ph↗

arXiv2018

Biermann battery-mediated magnetic reconnection in 3-D colliding plasmas

Recent experiments have demonstrated magnetic reconnection between colliding plasma plumes, where the reconnecting magnetic fields were self-generated in the plasma by the Biermann battery effect. Using fully kinetic 3-D simulations, we show the full evolution of the magnetic fields and plasma in these experiments including self-consistent magnetic field generation about the expanding plume. The collision of the two plasmas drives the formation of a current sheet, where reconnection occurs in a strongly time-and space-dependent manner, demonstrating a new 3-D reconnection mechanism. Specifically, we observe fast, vertically-localized Biermann-mediated reconnection, an inherently 3-D process where the temperature profile in the current sheet coupled with the out-of-plane ablation density profile conspires to break inflowing field lines, reconnecting the field downstream. Fast reconnection is sustained by both the Biermann effect and the traceless electron pressure tensor, where the development of plasmoids appears to modulate the contribution of the latter. We present a simple and general formulation to consider the relevance of Biermann-mediated reconnection in general astrophysical scenarios.

physics.plasm-ph↗

arXiv2018

Algebraic motion of vertically displacing plasmas

The vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear "sinking" behaviour shown to be algebraic and decelerating. The acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma and the wall or from the thermal quench dynamics precipitating loss of plasma current.

physics.plasm-ph↗