Chaotic magnetic fields in Vlasov-Maxwell equilibria

Ghosh, Abhijit; Janaki, M. S.; Dasgupta, B.; Bandyopadhyay, Alak

doi:10.1063/1.4865253

Cited by 9 publications

(6 citation statements)

References 34 publications

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“…Previous studies, such as Ghosh et al. (2014), have reported similar behaviour of magnetic fields in Vlasov–Maxwell equilibria. However, our analysis is more general than that of Ghosh et al.…”

Section: Introductionsupporting

confidence: 60%

“…Furthermore, chaotic behaviour is not unexpected in the context of kinetic equilibria. Previous studies, such as Ghosh et al (2014), have reported similar behaviour of magnetic fields in Vlasov-Maxwell equilibria. However, our analysis is more general than that of Ghosh et al (2014) because we prove the Hamiltonian nature of the equilibrium system for a wider class of distribution functions.…”

Section: Introductionsupporting

confidence: 55%

“…However, our analysis is more general than that of Ghosh et al. (2014) because we prove the Hamiltonian nature of the equilibrium system for a wider class of distribution functions. Also, our analysis is concerned with the hybrid Vlasov–Maxwell model that treats the electrons as a massless fluid.…”

Section: Introductionmentioning

confidence: 81%

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Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

2023

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The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov–Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behaviour for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behaviour of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus, the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

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Section: Introductionsupporting

confidence: 60%

Section: Introductionsupporting

confidence: 55%

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Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

2023

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“…Research comprising dynamics of nonlinear magnetic fields in different systems including plasmas is an interesting field that has attracted numerous scientists in recent years. In this context, the phenomenon of occurrence of chaos in dynamical investigations of nonlinear magnetic fields in certain systems can be frequently encountered; this fact leads to chaotic magnetic fields in such systems with a predominance in plasmas [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. This is because plasmas consist of different types of charged particles which generate electric and magnetic fields intrinsically and externally applied magnetic fields are required for their confinement.…”

Section: Introductionmentioning

confidence: 99%

“…Similarly, occurrences of chaotic magnetic fields in tokamak plasma systems have been explored in [4,7,9] due to magnetic limiters. The phenomenon of charged particle energization in presence of regular as well as chaotic magnetic fields has been investigated by Samanta et al whereas occurrence of chaotic magnetic fields in Vlasov-Maxwell equilibria is discussed in [10]. Occurrence of chaotic magnetic fields in atmospheres has been discussed in [12] in context of reflections of various radiations.…”

Section: Introductionmentioning

confidence: 99%

Effects of electron-to-ion mass ratio in driving magnetic oscillations of magnetohydrodynamic plasmas and self-organized criticality

Acharya,

Shaw,

Jha

et al. 2024

Phys. Scr.

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Evolutions of nonlinear magnetic fields have been shown to be governed by a set of coupled nonlinear equations of second order in magnetohydrodynamic (MHD) plasmas by Lee and Parks [Geophys. Res. Lett. 19, 7, 637-640 (1992)]. We have considered the same set of coupled nonlinear equations for further analysis in this work by neglecting the presence of external forcing term in it. Different modes of oscillations of magnetic field have been found to exist in special limiting cases of this set of undriven second order coupled nonlinear equations having frequencies that are multiples of lower hybrid frequency. Numerical solutions of these coupled equationshave been analysed revealing a quasi-periodic route to chaotic oscillations of the nonlinear magnetic fields as electron-to-ion mass ratio signifying presence of linear coupling effects is increased. Some signatures of the phenomenon of self-organized criticality (SOC) in typical quasi-periodic oscillations of magnetic field have also been noticed using Fourier analysis. The presence of long range correlations has been witnessed in quasi-periodic oscillations whereas both long range correlations and anticorrelationsare found in chaotic oscillations using rescaled range analysis. Concluding remarks are provided in addition to various results and discussions.

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Introduction

Allanson¹

2018

Theory of One-Dimensional Vlasov-Maxwell Equilibria

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Chaotic magnetic fields in Vlasov-Maxwell equilibria

Cited by 9 publications

References 34 publications

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

Effects of electron-to-ion mass ratio in driving magnetic oscillations of magnetohydrodynamic plasmas and self-organized criticality

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