arXiv subjects

Amitava Bhattacharjee

Publications and source records attributed to Amitava Bhattacharjee.

At least 37 records · Page 2Linked to original sources

arXiv2025

Whistler Chorus Amplification in the Magnetosphere: The Nonlinear Free-Electron Laser Model and the Ginzburg-Landau Equation

We present a novel nonlinear model for whistler-mode chorus amplification based on the free-electron laser (FEL) mechanism. First, we derive the nonlinear collective variable equations for the whistler-electron interaction. Consistent with in situ satellite observations, these equations predict that a small seed wave can undergo exponential growth, reaching a peak of a few hundred picoteslas after a few milliseconds, followed by millisecond timescale amplitude modulations. Next, we show that when one accounts for multiple wave frequencies and wave spatial variations, the amplitude and phase of the whistler wave can be described by the Ginzburg-Landau equation (GLE), providing a framework for the investigation of solitary wave behavior of chorus modes. These findings enhance our understanding of wave-particle interactions and space weather in the Van Allen radiation belts, deepen the connection between whistler-electron dynamics and FELs, and reveal a novel connection between whistler-mode chorus and the GLE.

physics.space-ph↗

arXiv2025

A class of high-beta, large-aspect-ratio quasiaxisymmetric Palumbo-like configurations

The space of high-beta, approximately quasiaxisymmetric, large-aspect-ratio stellarator configurations is explored using an inverse coordinate approach and a quadratic polynomial ansatz for the flux function, following the method of Palumbo, extended by Hernandes and Clemente. This approach yields a system of nonlinear ODEs that, when solved, give equilibria exhibiting positive or negative triangularity, cusps, and (in an extreme limit) current singularities. It is shown that a cubic ansatz may also be used, but that polynomials of degree four or higher will lead to overdetermination.

physics.plasm-ph↗

arXiv2025

Universal power-law distribution functions in an electromagnetic kinetic plasma: implications for the inverted temperature profile in the solar corona

We develop a self-consistent quasilinear theory for the relaxation of electromagnetic kinetic plasmas, and demonstrate that the mean distribution functions of both electrons and ions tend to relax to a universal $v^{-5}$ tail. Large-scale electromagnetic (EM) fields efficiently accelerate the unscreened, fast particles but not the screened, slow ones. This non-thermal tail may arise in the solar corona from EM turbulence despite collisions, allowing suprathermal particles to escape the sun's gravity (velocity filtration) and inverting the temperature $(T)$ profile with $T$ rising to $10^6$ K.

astro-ph.SR↗

arXiv2025

Taking control of compressible modes: bulk viscosity and the turbulent dynamo

Many polyatomic astrophysical plasmas are compressible and out of chemical and thermal equilibrium, introducing a bulk viscosity into the plasma via the internal degrees of freedom of the molecular composition, directly impacting the decay of compressible modes, $\mathbf{v}_{\parallel}(\mathbf{k})$. This is especially important for small-scale, turbulent dynamo processes in the interstellar medium, which are known to be sensitive to the effects of compression. To control the viscous properties of $\mathbf{v}_{\parallel}(\mathbf{k})$, we perform trans-sonic, visco-resistive dynamo simulations with additional bulk viscosity $ν_{\rm bulk}$, deriving a new $ν_{\rm bulk}$ Reynolds number $\rm{Re}_{\rm bulk}$, and viscous Prandtl number $\rm{P}ν\equiv \rm{Re}_{\rm bulk} / \rm{Re}_{\rm shear}$, where $\rm{Re}_{\rm shear}$ is the shear viscosity Reynolds number. We derive a framework for decomposing $E_{\rm mag}$ growth rates into incompressible and compressible terms via orthogonal tensor decompositions of $\nabla\otimes\mathbf{v}$, where $\mathbf{v}$ is the fluid velocity. We find that $\mathbf{v}_{\parallel}(\mathbf{k})$ play a dual role, growing and decaying $E_{\rm mag}$, and that field-line stretching is the main driver of growth, even in compressible dynamos. In the absence of $ν_{\rm bulk}$ ($\rm{P}ν\to \infty$), $\mathbf{v}_{\parallel}(\mathbf{k})$ pile up on small-scales, creating a spectral bottleneck, which disappears for $\rm{P}ν\approx 1$. (abridged). We emphasize the importance of further understanding the role of $ν_{\rm bulk}$ in compressible astrophysical plasmas, which we estimate could be as strong as the shear viscosity in the cold ISM, and highlight that compressible direct numerical simulations without bulk viscosity have unresolved compressible mode dissipation scales.

astro-ph.GA↗

arXiv2025

Computation of Magnetohydrodynamic Equilibria with Voigt Regularization

This work presents the first numerical investigation of using Voigt regularization as a method for obtaining magnetohydrodynamic (MHD) equilibria without the assumption of nested magnetic flux surfaces. Voigt regularization modifies the MHD dynamics by introducing additional terms that vanish in the infinite-time limit, allowing for magnetic reconnection and the formation of magnetic islands, which can overlap and produce field-line chaos. The utility of this approach is demonstrated through numerical solutions of two-dimensional ideal and resistive test problems. Our results show that Voigt regularization can significantly accelerate the convergence to solutions in resistive MHD problems, while also highlighting challenges in applying the method to ideal MHD systems. This research opens up new possibilities for developing more efficient and robust MHD equilibrium solvers, which could contribute to the design and optimization of future fusion devices.

physics.plasm-ph↗

arXiv2025

Global Stellarator Coil Optimization with Quadratic Constraints and Objectives

Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and forces exist at the equilibrium stage. Rapid initial state finding for both stages is a topic of active research. Most present convex coil optimization codes use the least square winding surface method by Merkel (NESCOIL), with recent improvement in conditioning, regularization , sparsity and physics objectives. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a fast, global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics objectives unavailable in NESCOIL and REGCOIL, including the Lorentz force, magnetic energy, curvature, field-current alignment, and the maximum density of a dipole array. QUADCOIL requires no initial guess and runs nearly $10^2\times$ faster than filament optimization. Integrating it in the equilibrium optimization stage can potentially exclude equilibria with difficult-to-design coils, without significantly increasing the computation time per iteration. QUADCOIL finds the exact, global minimum in a large parameter space when possible, and otherwise finds a well-performing approximate global minimum. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate QUADCOIL's effectiveness in coil topology control, minimizing non-convex penalties, and predicting filament coil complexity with three numerical examples.

physics.plasm-ph↗

arXiv2025

A self-consistent quasilinear theory for collisionless relaxation to universal quasi-steady state attractors in cold dark matter halos

Collisionless self-gravitating systems, e.g., cold dark matter halos, harbor universal density profiles despite the intricate non-linear physics of hierarchical structure formation, the origin of which has been a persistent mystery. To solve this problem, we develop a self-consistent quasilinear theory (QLT) in action-angle space for the collisionless relaxation of driven, inhomogeneous, self-gravitating systems by perturbing the governing Vlasov-Poisson equations. We obtain a quasilinear diffusion equation (QLDE) for the secular evolution of the mean distribution function $f_0$ of a halo due to linear fluctuations (induced by random perturbations in the force field) that are collectively dressed by self-gravity, a phenomenon described by the response matrix. Unlike previous studies, we treat collective dressing up to all orders. Well-known halo density profiles $ρ(r)$ commonly observed in $N$-body simulations, including the $r^{-1}$ NFW cusp, an Einasto central core, and the $r^{-1.5}$ prompt cusp, emerge as quasi-steady state attractor solutions of the QLDE. The $r^{-1}$ cusp is a constant flux steady-state solution for a constantly accreting massive halo perturbed by small-scale white noise fluctuations induced by substructure. It is an outcome of the universal nature of collisionless relaxation: lower energy particles attract more particles, gain higher effective mass and get less accelerated by the fluctuating force field. The zero-flux steady state solution for an isolated halo is an $f_0$ that is flat in energy, and the corresponding $ρ(r)$ can either be cored or an $r^{-1.5}$ cusp depending on the inner boundary condition. The latter forms around a central dense object, e.g., a compact subhalo or a black hole. We demonstrate for the first time that these halo profiles emerge as quasi-steady state attractors of collisionless relaxation described by a self-consistent QLT.

astro-ph.GA↗

arXiv2025

Numerical asymptotics of near-axis expansions of quasisymmetric magnetohydrostatic equilibria with anisotropic pressure

Quasisymmetry (QS) is a property of special magnetic configurations, where the magnetic field strength, but not necessarily the full vector field, has a direction of symmetry. QS leads to reduced neoclassical transport and thus can be a desirable property in stellarator design. The Garren-Boozer (GB) conundrum has been interpreted to mean that globally quasisymmetric magnetohydrostatic (MHS) equilibria, other than axisymmetric solutions, with isotropic pressure do not exist. When expanded as power series of an effective minor radius, the governing equations become overdetermined at the 3rd order. Despite this, recent optimization efforts have found numerical isotropic-pressure equilibria with nearly exact global QS. To reconcile these two perspectives, Rodriguez and Bhattacharjee (RB) showed that by introducing pressure anisotropy into the problem, one can overcome the GB conundrum. This formally enables the study of equilibria with exact, global QS. Building on RB's work, we present pyAQSC, the first code for solving the near-axis expansion (NAE) of anisotropic-pressure quasisymmetric equilibria to any order. As a demonstration, we present a 6th order, QA near-axis equilibrium with anisotropic pressure, and a convergence analysis. PyAQSC opens the door to the study of higher-order properties of equilibria with exact global QS. Like existing isotropic-pressure NAE codes, PyAQSC can accelerate stellarator optimization as an initial state tool. However, by optimizing for low pressure anisotropy in a space that allows anisotropy, pyAQSC may discover practical QS stellarator designs previously hard to access. We give results comparing the RB method with DESC equilibria with anisotropic pressure.

physics.plasm-ph↗

arXiv2025

The spectrum of magnetized turbulence in the interstellar medium

The interstellar medium (ISM) of our Galaxy is magnetized, compressible and turbulent, influencing many key ISM properties, like star formation, cosmic ray transport, and metal and phase mixing. Yet, basic statistics describing compressible, magnetized turbulence remain uncertain. Utilizing grid resolutions up to $10,080^3$ cells, we simulate highly-compressible, magnetized ISM-style turbulence with a magnetic field maintained by a small-scale dynamo. We measure two coexisting kinetic energy cascades, $\mathcal{E}_{\rm kin}(k) \propto k^{-n}$, in the turbulence, separating the plasma into scales that are non-locally interacting, supersonic and weakly magnetized $(n=2.01\pm 0.03\approx 2)$ and locally interacting, subsonic and highly magnetized $(n=1.465\pm 0.002\approx 3/2)$, where $k$ is the wavenumber. We show that the $3/2$ spectrum can be explained with scale-dependent kinetic energy fluxes and velocity-magnetic field alignment. On the highly magnetized modes, the magnetic energy spectrum forms a local cascade $(n=1.798\pm 0.001\approx 9/5)$, deviating from any known \textit{ab initio} theory. With a new generation of radio telescopes coming online, these results provide a means to directly test if the ISM in our Galaxy is maintained by the compressible turbulent motions from within it.

astro-ph.GA↗

arXiv2025

A Grad-Shafranov model for compact quasisymmetric stellarators

A Grad-Shafranov equation (GSE) valid for compact quasisymmetric stellarators is derived by an asymptotic expansion around a vacuum field carried to first order. We obtain an equation for the existence of flux surfaces leading up to the GSE. The flux surface label must simultaneously satisfy the existence equation and the GSE, which generally leads to an overdetermined problem. We show how the overdetermined problem can be resolved within our model for a class of hybrid devices similar to that studied by Henneberg and Plunk (S. Henneberg and G. Plunk, PRR 2024). We are also able to solve the existence equation for flux surfaces analytically in the most general case by introducing a special coordinate system. This will enable us to carry out an optimization seeking to minimize the error in our GSE while obeying the flux surface existence equation, which will allow us to find solutions outside the class of hybrid devices. This will allow for a coarse-grained approximate search in the space of quasisymmetric equilibria that should be faster than a conventional stellarator optimization. Nevertheless, it would still be necessary to fine-tune the approximate solutions using conventional tools to obtain a more precise optimized equilibrium.

physics.plasm-ph↗

arXiv2025

Density fluctuation-Mach number scaling in compressible, high plasma beta turbulence: in-situ space observations and high-Reynolds number simulations

Understanding the nature of compressible fluctuations in a broad range of turbulent plasmas, from the intracluster medium to the solar wind, has been an active field of research in the past decades. Theoretical frameworks for weakly compressible MHD turbulence in an inhomogeneous background magnetic field predict a linear scaling of the normalized mass density fluctuation ($δρ/ ρ_0$), as a function of the turbulent Mach number ($\mathcal{M}_t$), $δρ/ ρ_0 \propto \mathcal{M}_t$. However, so far the scaling relation has been tested only using moderate to low plasma beta ($β\lesssim 1$) solar wind observational data where the compressibility is weak $δρ/ ρ_0 \sim 0.1$. Here, we combine NASA's Magnetospheric Multiscale Mission data in Earth's magnetosheath, where $β\sim 10$ is high, and $β\sim 1$ highly-compressible magnetohydrodynamic turbulence simulations at unprecedented resolutions. Both show that $δρ/ ρ_0 \propto \mathcal{M}_t$ holds across a broad range of $δρ/ ρ_0$, $\mathcal{M}_t$ and $β$, demonstrating that $δρ/ ρ_0 \propto \mathcal{M}_t$ is a robust compressible turbulence relation, going beyond the asymptotics of the weakly compressible theory. We discuss the findings in the context of understanding the nature of strongly compressible turbulent fluctuations and the driving parameter in astrophysical and space plasmas.

astro-ph.SR↗

arXiv2024

Universal non-thermal power-law distribution functions from the self-consistent evolution of collisionless electrostatic plasmas

Distribution functions of collisionless systems are known to show non-thermal power law tails. Interestingly, collisionless plasmas in various physical scenarios, (e.g., the ion population of the solar wind) feature a $v^{-5}$ tail in the velocity ($v$) distribution, whose origin has been a long-standing mystery. We show this power law tail to be a natural outcome of the self-consistent collisionless relaxation of driven electrostatic plasmas. We perform a quasilinear analysis of the perturbed Vlasov-Poisson equations to show that the coarse-grained mean distribution function (DF), $f_0$, follows a quasilinear diffusion equation with a diffusion coefficient $D(v)$ that depends on $v$ through the plasma dielectric constant. If the plasma is isotropically forced on scales much larger than the Debye length with a white noise-like electric field, then $D(v)\sim v^4$ for $σ<v<ω_{\mathrm{P}}/k$, with $σ$ the thermal velocity, $ω_{\mathrm{P}}$ the plasma frequency and $k$ the maximum wavenumber of the perturbation; the corresponding $f_0$, in the quasi-steady state, develops a $v^{-\left(d+2\right)}$ tail in $d$ dimensions ($v^{-5}$ tail in 3D), while the energy ($E$) distribution develops an $E^{-2}$ tail irrespective of the dimensionality of space. Any redness of the noise only alters the scaling in the high $v$ end. Non-resonant particles moving slower than the phase-velocity of the plasma waves ($ω_{\mathrm{P}}/k$) experience a Debye-screened electric field, and significantly less (power law suppressed) acceleration than the near-resonant particles. Thus, a Maxwellian DF develops a power law tail. The Maxwellian core ($v<σ$) eventually also heats up, but over a much longer timescale than that over which the tail forms. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the development of the universal $v^{-5}$ tail.

astro-ph.SR↗

arXiv2024

Relaxation of weakly collisional plasma: continuous spectra, discrete eigenmodes, and the decay of echoes

The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory and astrophysical plasmas, can be described by the Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a perturbative analysis of these equations, and obtain exact analytic solutions that resolve long-standing controversies regarding the impact of weak collisions on the continuous spectra, discrete Landau eigenmodes, and the decay of plasma echoes. We retain both damping and diffusion terms in the collision operator. We find that the linear response is a temporal convolution of a continuum that depends on the continuous velocities of particles (crucial for the plasma echo) and discrete modes that describe coherent oscillations of the entire system. The discrete modes are exponentially damped over time due to collective effects or wave-particle interactions (Landau damping) as well as collisional dissipation. The continuum is also damped by collisions, but somewhat differently. Up to a collision time, the inverse of the collision frequency $ν_{\mathrm{c}}$, the continuum decay is driven by the diffusion of particle velocities and occurs cubic exponentially over a timescale $\sim ν^{-1/3}_{\mathrm{c}}$. After a collision time, however, the continuum decay is driven by the damping of velocities and diffusion of positions, and occurs exponentially over a timescale $\sim ν_{\mathrm{c}}$. This slow exponential decay damps perturbations the most on scales $λ$ comparable to the mean free path $λ_{\mathrm{c}}$, but very slowly on larger scales. This establishes local thermal equilibrium, the essence of the fluid limit, and enhances the detectability of the plasma echo. The long-term decay is driven by the discrete modes for $λ<λ_{\mathrm{c}}$, but, by the slowly decaying continuum and the least damped mode for $λ>λ_{\mathrm{c}}$.

physics.plasm-ph↗

arXiv2024

Three-dimensional plasmoid-mediated reconnection and turbulence in Hall magnetohydrodynamics

Plasmoid instability accelerates reconnection in collisional plasmas by transforming a laminar reconnection layer into numerous plasmoids connected by secondary current sheets in two dimensions (2D) and by fostering self-generated turbulent reconnection in three dimensions (3D). In large-scale astrophysical and space systems, plasmoid instability likely initiates in the collisional regime but may transition into the collisionless regime as the fragmentation of the current sheet progresses toward kinetic scales. Hall MHD models are widely regarded as a simplified yet effective representation of the transition from collisional to collisionless reconnection. However, plasmoid instability in 2D Hall MHD simulations often leads to a single-X-line reconnection configuration, which significantly differs from fully kinetic particle-in-cell simulation results. This study shows that single-X-line reconnection is less likely to occur in 3D compared to 2D. Moreover, depending on the Lundquist number and the ratio between the system size and the kinetic scale, Hall MHD can also realize 3D self-generated turbulent reconnection. We analyze the features of the self-generated turbulent state, including the energy power spectra and the scale dependence of turbulent eddy anisotropy.

physics.plasm-ph↗

arXiv2024

An asymptotic Grad-Shafranov equation for quasisymmetric stellarators

A first-order model is derived for quasisymmetric stellarators where the vacuum field due to coils is dominant, but plasma-current-induced terms are not negligible and can contribute to magnetic differential equations, with $β$ of the order of the ratio of induced to vacuum fields. Under these assumptions, it is proven that the aspect ratio must be large and a simple expression can be obtained for the lowest-order vacuum field. The first-order correction, which involves both vacuum and current-driven fields, is governed by a Grad-Shafranov equation and the requirement that flux surfaces exist. These two equations are not always consistent, and so this model is generally overconstrained, but special solutions exist that satisfy both equations simultaneously. One family of such solutions are the first-order near-axis solutions. Thus, the first-order near-axis model is a subset of the model presented here. Several other solutions outside the scope of the near-axis model are also found. A case study comparing one such solution to a VMEC-generated solution shows good agreement.

physics.plasm-ph↗

arXiv2024

Magnetized compressible turbulence with a fluctuation dynamo and Reynolds numbers over a million

Supersonic magnetohydrodynamic (MHD) turbulence is a ubiquitous state for many astrophysical plasmas. However, even the basic statistics for this type of turbulence remains uncertain. We present results from supersonic MHD turbulence simulations at unparalleled resolutions, with plasma Reynolds numbers of over a million. In the kinetic energy spectrum we find a break between the scales that are dominated by kinetic energy, with spectral index $-2$, and those that become strongly magnetized, with spectral index $-3/2$. By analyzing the Helmholtz decomposed kinetic energy spectrum, we find that the compressible modes are not passively mixed through the cascade of the incompressible modes. At high magnetic Reynolds number, above $10^5$, we find a power law in the magnetic energy spectrum with spectral index $-9/5$. On the strongly magnetized, subsonic scales the plasma tends to self-organize into locally relaxed regions, where there is strong alignment between the current density, magnetic field, velocity field and vorticity field, depleting both the nonlinearities and magnetic terms in the MHD equations, which we attribute to plasma relaxation on scales where the magnetic fluctuations evolve on shorter timescales than the velocity fluctuations. This process constrains the cascade to inhomogenous, volume-poor, fractal surfaces between relaxed regions, which has significant repercussions for understanding the nature of magnetized turbulence in astrophysical plasmas and the saturation of the fluctuation dynamo.

astro-ph.GA↗

arXiv2024

Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared to unoptimised configurations. Though stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratio and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation, and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared to solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface; three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

physics.plasm-ph↗

arXiv2024

Structure of pressure-gradient-driven current singularity in ideal magnetohydrodynamic equilibrium

Singular currents typically appear on rational surfaces in non-axisymmetric ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces and a continuous rotational transform. These currents have two components: a surface current (Dirac $δ$-function in flux surface labeling) that prevents the formation of magnetic islands and an algebraically divergent Pfirsch--Schlüter current density when a pressure gradient is present across the rational surface. At flux surfaces adjacent to the rational surface, the traditional treatment gives the Pfirsch--Schlüter current density scaling as $J\sim1/Δι$, where $Δι$ is the difference of the rotational transform relative to the rational surface. If the distance $s$ between flux surfaces is proportional to $Δι$, the scaling relation $J\sim1/Δι\sim1/s$ will lead to a paradox that the Pfirsch--Schlüter current is not integrable. In this work, we investigate this issue by considering the pressure-gradient-driven singular current in the Hahm\textendash Kulsrud\textendash Taylor problem, which is a prototype for singular currents arising from resonant magnetic perturbations. We show that not only the Pfirsch--Schlüter current density but also the diamagnetic current density are divergent as $\sim1/Δι$. However, due to the formation of a Dirac $δ$-function current sheet at the rational surface, the neighboring flux surfaces are strongly packed with $s\sim(Δι)^{2}$. Consequently, the singular current density $J\sim1/\sqrt{s}$, making the total current finite, thus resolving the paradox.

physics.plasm-ph↗