scholarly journals Exact nonlinear solutions for three-dimensional Alfvén-wave packets in relativistic magnetohydrodynamics

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Alfred Mallet ◽  
Benjamin D.G. Chandran
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Rest Frame ◽  
Three Dimensional ◽  
Alfven Wave ◽  
Magnetohydrodynamic Equations ◽  
Astrophysical Objects ◽  
Analytic Expressions ◽  
Relativistic Magnetohydrodynamics ◽  
Nonlinear Solutions

We show that large-amplitude, non-planar, Alfvén-wave (AW) packets are exact nonlinear solutions of the relativistic magnetohydrodynamic equations when the total magnetic-field strength in the local fluid rest frame ( $b$ ) is a constant. We derive analytic expressions relating the components of the fluctuating velocity and magnetic field. We also show that these constant- $b$ AWs propagate without distortion at the relativistic Alfvén velocity and never steepen into shocks. These findings and the observed abundance of large-amplitude, constant- $b$ AWs in the solar wind suggest that such waves may be present in relativistic outflows around compact astrophysical objects.

scholarly journals On heating of solar wind protons by the parametric decay of large-amplitude Alfvén waves

2018 ◽  
Vol 36 (6) ◽  
pp. 1647-1655 ◽  
Author(s):  
Horia Comişel ◽  
Yasuhiro Nariyuki ◽  
Yasuhito Narita ◽  
Uwe Motschmann
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Alfven Wave ◽  
Sound Waves ◽  
Parametric Decay ◽  
Left Handed ◽  
Propagating Waves ◽  
The Mean

Abstract. By three-dimensional hybrid simulations, proton heating is investigated starting from a monochromatic large-amplitude Alfvén wave with left-handed circular polarization launched along the mean magnetic field in a low-beta plasma. We find that the perpendicular scattering is efficient in three dimensions and the protons are heated by the obliquely propagating waves. The thermal core proton population is heated in three dimensions as well in the longitudinal and parallel directions by the field-aligned and obliquely propagating sound waves out of the parametric decay. The astrophysical context is discussed.

scholarly journals Multi-channel coupling of decay instability in three-dimensional low-beta plasma

2019 ◽  
Author(s):  
Horia Comişel ◽  
Yasuhito Narita ◽  
Uwe Motschmann
Keyword(s):  
Magnetic Field ◽  
Solar Corona ◽  
Large Amplitude ◽  
Three Dimensional ◽  
Decay Process ◽  
Alfven Wave ◽  
Upstream Region ◽  
Channel Coupling ◽  
Dispersion State ◽  
The Mean

Abstract. Three-dimensional hybrid simulations have been carried out to verify the hypothesis of simultaneous multi-channel decay of a large-amplitude Alfvén wave in a low-beta plasma, e.g., in the shock-upstream region or the solar corona. Obliquely-propagating daughter modes are excited along the perpendicular direction to the mean magnetic field at the same parallel wavenumbers and frequencies with the daughter modes driven by the field-aligned decay. We find that the transversal spectrum of waves is controlled by the multi-channel coupling of the decay process in low-beta plasmas and originates in the dispersion state of the shear Alfvén wave.

scholarly journals Multi-channel coupling of decay instability in three-dimensional low-beta plasma

2019 ◽  
Vol 37 (5) ◽  
pp. 835-842 ◽  
Author(s):  
Horia Comişel ◽  
Yasuhito Narita ◽  
Uwe Motschmann
Keyword(s):  
Magnetic Field ◽  
Solar Corona ◽  
Large Amplitude ◽  
Three Dimensional ◽  
Decay Process ◽  
Alfven Wave ◽  
Upstream Region ◽  
Channel Coupling ◽  
Dispersion State ◽  
The Mean

Abstract. Three-dimensional hybrid simulations have been carried out to verify the hypothesis of simultaneous multi-channel decay of a large-amplitude Alfvén wave in a low-beta plasma, e.g., in the shock-upstream region or the solar corona. Obliquely propagating daughter modes are excited along the perpendicular direction to the mean magnetic field at the same parallel wavenumbers and frequencies as the daughter modes driven by the field-aligned decay. We find that the transversal spectrum of waves is controlled by the multi-channel coupling of the decay process in low-beta plasmas and originates in the dispersion state of the shear Alfvén wave.

Exact nonlinear wave solutions of the incompressible magnetohydrodynamic equations in a sheared magnetic field

1990 ◽  
Vol 44 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Hiromitsu Hamabata
Keyword(s):  
Magnetic Field ◽  
Incompressible Fluid ◽  
Large Amplitude ◽  
Uniform Magnetic Field ◽  
Magnetohydrodynamic Equations ◽  
Wave Solutions ◽  
Field Lines ◽  
Incompressible Magnetohydrodynamic Equations ◽  
Physical Quantities ◽  
Nonlinear Wave Solutions

Exact wave solutions of the nonlinear jnagnetohydrodynamic equations for a highly conducting incompressible fluid are obtained for the cases where the physical quantities are independent of one Cartesian co-ordina.te and for where they vary three-dimensionally but both the streamlines and magnetic field lines lie in parallel planes. It is shown that there is a class of exact wave solutions with large amplitude propagating in a straight but non-uniform magnetic field with constant or non-uniform velocity.

scholarly journals Exact Solutions of the Heisenberg Equations and Zitterbewegung of the Electron in a Constant Uniform Magnetic Field

1982 ◽  
Vol 35 (4) ◽  
pp. 353 ◽  
Author(s):  
AO Barut ◽  
AJ Bracken
Keyword(s):  
Magnetic Field ◽  
Rest Frame ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Internal Motion ◽  
Mass Motion ◽  
Internal Dynamics ◽  
Classical Motion ◽  
Dirac Electron ◽  
Heisenberg Equations

For a free Dirac electron, the Heisenberg equations define an internal dynamical system in the rest frame, isomorphic to a finite three-dimensional oscillator with a compact SO(5) phase space, such that the spin of the electron is the orbital angular momentum of the internal dynamics (Barut and Bracken 1980, 1981a). In the present work, the change in this internal dynamics due to an external magnetic field is studied. In order that the internal motion can be distinguished from the centre of mass motion, the solutions of the corresponding Hamilton and Heisenberg equations for the relativistic classical motion and the relativistic quantum mechanical spinless motion are also presented. The solutions for the electron exhibit the effect of the spin terms both in the internal motion and external motion, and we are able to identify the properties of the Zitterbewegung in the external field.

scholarly journals 2D and 3D turbulent magnetic reconnection

2009 ◽  
Vol 5 (H15) ◽  
pp. 434-435
Author(s):  
A. Lazarian ◽  
G. Kowal ◽  
E. Vishniac ◽  
K. Kulpa-Dubel ◽  
K. Otmianowska-Mazur
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Large Scale ◽  
Gamma Ray ◽  
Three Dimensional ◽  
Turnover Time ◽  
Turbulent Fluid ◽  
Astrophysical Objects ◽  
Field Lines ◽  
The Magnetic Field

AbstractA magnetic field embedded in a perfectly conducting fluid preserves its topology for all times. Although ionized astrophysical objects, like stars and galactic disks, are almost perfectly conducting, they show indications of changes in topology, magnetic reconnection, on dynamical time scales. Reconnection can be observed directly in the solar corona, but can also be inferred from the existence of large scale dynamo activity inside stellar interiors. Solar flares and gamma ray busts are usually associated with magnetic reconnection. Previous work has concentrated on showing how reconnection can be rapid in plasmas with very small collision rates. Here we present numerical evidence, based on three dimensional simulations, that reconnection in a turbulent fluid occurs at a speed comparable to the rms velocity of the turbulence, regardless of the value of the resistivity. In particular, this is true for turbulent pressures much weaker than the magnetic field pressure so that the magnetic field lines are only slightly bent by the turbulence. These results are consistent with the proposal by Lazarian & Vishniac (1999) that reconnection is controlled by the stochastic diffusion of magnetic field lines, which produces a broad outflow of plasma from the reconnection zone. This work implies that reconnection in a turbulent fluid typically takes place in approximately a single eddy turnover time, with broad implications for dynamo activity and particle acceleration throughout the universe. In contrast, the reconnection in 2D configurations in the presence of turbulence depends on resistivity, i.e. is slow.

Parametric instabilities of circularly polarized large-amplitude dispersive Alfvén waves: excitation of parallel-propagating electromagnetic daughter waves

1991 ◽  
Vol 46 (1) ◽  
pp. 107-127 ◽  
Author(s):  
Adolfo F. Viñas ◽  
Melvyn L. Goldstein
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Large Amplitude ◽  
Wave Amplitude ◽  
Pump Wave ◽  
Modulational Instability ◽  
Alfven Wave ◽  
Circularly Polarized ◽  
Background Magnetic Field ◽  
Electromagnetic Instability

We investigate the parametric decay and modulational instabilities of a large-amplitude circularly polarized dispersive Alfvén wave. Our treatment is more general than that of previous derivations based on the two-fluid equations in that we allow for propagation of the unstable daughter waves at arbitrary angles to the background magnetic field, although our main concern in this paper is the exploration of new aspects of propagation parallel to the DC magnetic field. In addition to the well-known coupling of pump waves to electrostatic daughter waves, we find a new parametric channel where the pump wave couples directly to electromagnetic daughter waves. Excitation of the electromagnetic instability occurs only for modulation (k/k0 ≤ 1) and not for decay (k/k0 < 1). In contrast with the modulational instability excited by the electrostatic coupling, the electromagnetic modulational instability exists for both left-hand (K > 0) and right-hand (K < 0) polarization. For large k/k0, the electromagnetic channel dominates, while at lower values the electrostatic channel has a larger growth rate for modest values of dispersion, pump-wave amplitude and plasma β. Unlike the electrostatic modulational instability, the growth rate of the electromagnetic instability increases monotonically with increasing pump wave amplitude. This analysis confirms that, for decay, the dominant process is coupling to electrostatic daughter waves, at least for parallel propagation. For modulation, the coupling to electromagnetic daughter waves usually dominates, suggesting that the parametric modulational instability is really an electromagnetic phenomenon.

On the existence of transverse MHD oscillations in an inhomogeneous magnetoplasma

1990 ◽  
Vol 43 (1) ◽  
pp. 83-99 ◽  
Author(s):  
Andrew N. Wright
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Background Field ◽  
Alfven Wave ◽  
Field Perturbation ◽  
Independent Field ◽  
Background Magnetic Field ◽  
Field Geometry ◽  
Divergence Free ◽  
Field Lines

In a cold plasma with no compressional field perturbation the equations governing the two perpendicular components of magnetic-field perturbation decouple. These two equations depend only upon spatial derivatives along the background magnetic field, and give the impression of independent field-line motion in the two transverse directions. However, the perturbation magnetic field b must be divergence-free. It is not meaningful to ask if the field perturbation on an individual background line of force satisfies ∇. b = 0. To decide whether b is divergence-free, we need to know about its spatial variation, i.e. what the state of the neighbouring field lines is. In this paper we investigate two classes of solutions: first we allow the perturbation magnetic flux to satisfy ∇. b = 0 by threading across the background lines of force; the second solution closes b by allowing the perturbation flux to encircle the background field lines (torsional Alfvén waves). For both of these solutions we study the relationship between neighbouring field lines, and are able to derive a set of criteria that the background medium must satisfy. For both classes we find restrictions upon the background magnetic-field geometry - the first class also has a constraint upon the plasma density. The introduction of perfectly conducting massive boundaries is also considered, and a relation given that they must satisfy if the field perturbation is to remain transverse. The criteria are presented in such a manner that it is easy to test if a given medium will be able to support the solutions described above. For example, a three-dimensional dipolo geometry is able to carry oscillatory toroidal fields; but not purely poloidal ones or a torsional Alfvén wave.

Nonlinear solutions of modified plane Couette flow in the presence of a transverse magnetic field

1996 ◽  
Vol 307 ◽  
pp. 231-243 ◽  
Author(s):  
M. Nagata
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Transverse Magnetic ◽  
Finite Amplitude ◽  
Parallel Plates ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Nonlinear Solutions

A nonlinear analysis is performed numerically for the motion of an electrically conducting fluid between parallel plates in relative motion when a transverse magnetic field is applied. It is found that steady three-dimensional finite-amplitude solutions exist even when the linear analysis predicts an infinite critical Reynolds number.

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