Nonlinear waves propagating transverse to the magnetic field

2001 ◽  
Vol 65 (3) ◽  
pp. 213-233 ◽  
Author(s):  
J. F. McKENZIE ◽  
E. DUBININ ◽  
K. SAUER
Keyword(s):  
Magnetic Field ◽  
Mach Number ◽  
Soliton Solutions ◽  
Momentum Conservation ◽  
Plasma Pressure ◽  
Mirror Image ◽  
Stationary Flows ◽  
Classical Work ◽  
Mach Numbers ◽  
The Magnetic Field

We generalize the classical work of Adlam and Allen [Phil. Mag.3, 448 (1958)] on solitons in a cold plasma propagating perpendicular to the magnetic field to include the effects of plasma pressure. This is done by making extensive use of the properties of total momentum conservation (denoted by the term ‘momentum hodograph’, since it yields a locus in the plane of the electron and proton speeds in the direction of the wave) and the energy integral of the system as a whole. These relations elucidate the phase and integral curves of stationary flows, from which soliton solutions may be constructed. In general, only compressive solitons are permitted, and we have found an analytical expression for the critical fast Mach number as a function of the proton acoustic Mach number, which shows that it varies from its classical value of 2 (at large proton acoustic Mach numbers) to unity, where the incoming flow is proton-sonic. At the critical fast Mach number, two possible soliton-like solutions can be constructed. One is the classical compression, in which the magnetic field develops a cusp in the centre of the wave. The other is a compression in the magnetic field followed by a deep depression in the centre of the wave, which is completed by the mirror image of this signature of compression–rarefaction. This structure involves a smooth supersonic–subsonic transition in the proton flow. For Mach numbers in excess of the critical one, this kind of structure can also be constructed, but now the magnetic field is cusp-like at the points of maximum compression.

scholarly journals Nonlinear waves and solitons propagating perpendicular to the magnetic field in bi-ion plasma with finite plasma pressure

2002 ◽  
Vol 9 (2) ◽  
pp. 87-99 ◽  
Author(s):  
E. M. Dubinin ◽  
K. Sauer ◽  
J. F. McKenzie ◽  
G. Chanteur
Keyword(s):  
Magnetic Field ◽  
Nonlinear Waves ◽  
Plasma Pressure ◽  
Compound System ◽  
Sonic Point ◽  
Flow Parameters ◽  
Ion Plasma ◽  
Wide Range ◽  
Mach Numbers ◽  
The Magnetic Field

Abstract. We investigate the nature of nonlinear waves propagating transverse to the magnetic field in a bi-ion plasma including plasma pressure. By using the conservation laws derived from the multi-ion fluid equations the system may be described by a single order differential equation whose properties control the structure of the flow and the magnetic field. Compressive solitons exist in specific ranges of the characteristic Mach numbers. Various features of solitons differ in different existence "windows". For example, there are solitons that contain a strong proton rarefaction core embedded in the main compressional structure. Compressive solitons are found in a wide range of flow parameters. Finite ion pressure introduces critical Mach numbers. In contrast to a plasma consisting only of protons and electrons these singular points are reached where a specific combination of ion and electron speeds lies on particular locii, in multi-parameter space, which corresponds to the generalized "sonic point" of the compound system.

scholarly journals ANALYTICAL MODEL OF THE PLANETARY BOW SHOCK FOR VARIOUS MAGNETIC FIELD DIRECTIONS BASED ON MHD CALCULATIONS

2020 ◽  
Vol 6 (4) ◽  
pp. 51-58
Author(s):  
Galina Kotova ◽  
Mikhail Verigin ◽  
Tamash Gomboshi ◽  
Konstantin Kabin
Keyword(s):  
Magnetic Field ◽  
Computer Time ◽  
Bow Shock ◽  
Radius Of Curvature ◽  
Dynamic Flow ◽  
Physical Processes ◽  
Downstream Slope ◽  
Mach Numbers ◽  
Semi Empirical ◽  
The Magnetic Field

Study of physical processes in plasma near planets often requires knowledge of the position and shape of the planetary bow shock. Empirical models are usually used since theoretical MHD and kinetic models consume too much computer time and cannot be used to track fast processes. M.I. Verigin proposed a semi-empirical approach based on the use of exact theoretical expressions with a small number of parameters, which have a clear physical meaning. These parameters are estimated by fitting experimental data or detailed MHD calculations. A model of the bow shock near an arbitrary-shaped obstacle has previously been developed for a gas-dynamic flow. This model can be applied to any sonic Mach numbers and large values of the Alfven Mach number. In addition, the asymptotic Mach cone — the angle of inclination of the shock wave at an infinite distance from the planet — has been calculated analytically in the MHD approximation. In this paper, we propose a model of the bow shock for any direction of the magnetic field with respect to the upcoming flow and for any Mach numbers. Parameters of the model are the distance of the nose point from the obstacle, radius of curvature and bluntness of the bow shock at the nose point, a parameter related to the transition to the asymptotic downstream slope of the shock, and a skewing angle appearing when the interplanetary magnetic field is directed at an angle to the solar wind velocity.

Infinite solitons in ferromagnetic materials with an internal magnetic field

2021 ◽  
pp. 2150413
Author(s):  
Hamdy I. Abdel-Gawad
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
External Field ◽  
Model Equation ◽  
Graphical Representation ◽  
Magnetic Moments ◽  
Soliton Solutions ◽  
Internal Magnetic Field ◽  
Multiple Soliton Solutions ◽  
The Magnetic Field

The ferromagnetism induced by an external magnetic field (EMF), in (3+1) dimensions, is governed by Kraenkel–Manna–Merle system (KMMS). A (1+1) dimension model equation was derived in the literature. The magnetic moments are parallel to the magnetic field in ferromagnetism as they are aligning in the same direction of the external field. Here, it is shown that the KMMS supports the presence of internal magnetic field. This may be argued to medium characteristics. The objective of this work is to mind multiple soliton solutions, which are obtained via the generalized together with extended unified methods. Graphical representation of the results are carried. They describe infinite soliton shapes, which arise from the multiple variation of the arbitrary functions in the solutions. It is, also, shown that internal magnetic field decays, asymptotically, to zero with time.

scholarly journals Filaments and striations: anisotropies in observed, supersonic, highly magnetized turbulent clouds

2019 ◽  
Vol 492 (1) ◽  
pp. 668-685 ◽  
Author(s):  
James R Beattie ◽  
Christoph Federrath
Keyword(s):  
Magnetic Field ◽  
Column Density ◽  
Three Dimensional ◽  
High Density ◽  
Systematic Analysis ◽  
Guide Field ◽  
Degree Of Anisotropy ◽  
Mach Numbers ◽  
Magnetohydrodynamic Simulations ◽  
The Magnetic Field

ABSTRACT Stars form in highly magnetized, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields and magnetosonic striations introduce anisotropies into the cloud. In this study, we use the two-dimensional power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers ($\operatorname{\mathcal {M}_{\text{A}}}=0.1{\!-\!10}$) and turbulent Mach numbers ($\operatorname{\mathcal {M}}=2{\!-\!20}$), with 20 high-resolution, three-dimensional turbulent magnetohydrodynamic simulations. We find that for cases with a strong magnetic guide field, corresponding to $\operatorname{\mathcal {M}_{\text{A}}}\lt 1$, and $\operatorname{\mathcal {M}}\lesssim 4$, the anisotropy in the column density is dominated by thin striations aligned with the magnetic field, while for $\operatorname{\mathcal {M}}\gtrsim 4$ the anisotropy is significantly changed by high-density filaments that form perpendicular to the magnetic guide field. Indeed, the strength of the magnetic field controls the degree of anisotropy and whether or not any anisotropy is present, but it is the turbulent motions controlled by $\operatorname{\mathcal {M}}$ that determine which kind of anisotropy dominates the morphology of a cloud.

Kinetic Alfvén solitons in a low-beta plasma

1997 ◽  
Vol 57 (2) ◽  
pp. 235-245 ◽  
Author(s):  
B. C. KALITA ◽  
R. P. BHATTA
Keyword(s):  
Magnetic Field ◽  
Mach Number ◽  
Solitary Waves ◽  
Magnetic Pressure ◽  
Hot Electrons ◽  
Mass Ratio ◽  
Ion Motion ◽  
Electron Inertia ◽  
Theoretical Investigations ◽  
The Magnetic Field

Kinetic Alfvén solitons with hot electrons and finite electron inertia in a low-beta (β=8πn0T/B2G, the ratio of the kinetic to the magnetic pressure) plasma is studied analytically, with the ion motion being considered dominant through the polarization drift. Both compressive and rarefactive kinetic Alfvén solitons are found to exist within a definite range of kz (the direction of propagation of the kinetic Alfvén solitary waves with respect to the direction of the magnetic field) for each pair of assigned values of β and M (Mach number). Unlike in previous theoretical investigations, β appears as an explicit parameter for the kinetic Alfvén solitons in this case. In addition, consideration of the electron pressure gradient is found to suppress the speed of both the Alfvén solitons considerably for A (=2QM2/βk2z, with Q the electron-to-ion mass ratio) less than unity.

Magnetohydrodynamic Equilibria

2020 ◽  
Author(s):  
Thomas Wiegelmann
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Lorentz Force ◽  
Plasma Flow ◽  
Plasma Pressure ◽  
Mhd Equations ◽  
The Sun ◽  
Planetary Magnetospheres ◽  
Mhd Equilibria ◽  
The Magnetic Field

Magnetohydrodynamic equilibria are time-independent solutions of the full magnetohydrodynamic (MHD) equations. An important class are static equilibria without plasma flow. They are described by the magnetohydrostatic equations j×B=∇p+ρ∇Ψ,∇×B=μ0j,∇·B=0. B is the magnetic field, j the electric current density, p the plasma pressure, ρ the mass density, Ψ the gravitational potential, and µ0 the permeability of free space. Under equilibrium conditions, the Lorentz force j×B is compensated by the plasma pressure gradient force and the gravity force. Despite the apparent simplicity of these equations, it is extremely difficult to find exact solutions due to their intrinsic nonlinearity. The problem is greatly simplified for effectively two-dimensional configurations with a translational or axial symmetry. The magnetohydrostatic (MHS) equations can then be transformed into a single nonlinear partial differential equation, the Grad–Shafranov equation. This approach is popular as a first approximation to model, for example, planetary magnetospheres, solar and stellar coronae, and astrophysical and fusion plasmas. For systems without symmetry, one has to solve the full equations in three dimensions, which requires numerically expensive computer programs. Boundary conditions for these systems can often be deduced from measurements. In several astrophysical plasmas (e.g., the solar corona), the magnetic pressure is orders of magnitudes higher than the plasma pressure, which allows a neglect of the plasma pressure in lowest order. If gravity is also negligible, Equation 1 then implies a force-free equilibrium in which the Lorentz force vanishes. Generalizations of MHS equilibria are stationary equilibria including a stationary plasma flow (e.g., stellar winds in astrophysics). It is also possible to compute MHD equilibria in rotating systems (e.g., rotating magnetospheres, rotating stellar coronae) by incorporating the centrifugal force. MHD equilibrium theory is useful for studying physical systems that slowly evolve in time. In this case, while one has an equilibrium at each time step, the configuration changes, often in response to temporal changes of the measured boundary conditions (e.g., the magnetic field of the Sun for modeling the corona) or of external sources (e.g., mass loading in planetary magnetospheres). Finally, MHD equilibria can be used as initial conditions for time-dependent MHD simulations. This article reviews the various analytical solutions and numerical techniques to compute MHD equilibria, as well as applications to the Sun, planetary magnetospheres, space, and laboratory plasmas.

scholarly journals Nonlinear equilibrium structure of thin currents sheets: influence of electron pressure anisotropy

2004 ◽  
Vol 11 (5/6) ◽  
pp. 579-587 ◽  
Author(s):  
L. M. Zelenyi ◽  
H. V. Malova ◽  
V. Yu. Popov ◽  
D. Delcourt ◽  
A. S. Sharma
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Magnetic Energy ◽  
Plasma Pressure ◽  
Quasi Equilibrium ◽  
Electrostatic Effects ◽  
Current Sheets ◽  
Thin Current Sheet ◽  
Field Lines ◽  
The Magnetic Field

Abstract. Thin current sheets represent important and puzzling sites of magnetic energy storage and subsequent fast release. Such structures are observed in planetary magnetospheres, solar atmosphere and are expected to be widespread in nature. The thin current sheet structure resembles a collapsing MHD solution with a plane singularity. Being potential sites of effective energy accumulation, these structures have received a good deal of attention during the last decade, especially after the launch of the multiprobe CLUSTER mission which is capable of resolving their 3D features. Many theoretical models of thin current sheet dynamics, including the well-known current sheet bifurcation, have been developed recently. A self-consistent 1D analytical model of thin current sheets in which the tension of the magnetic field lines is balanced by the ion inertia rather than by the plasma pressure gradients was developed earlier. The influence of the anisotropic electron population and of the corresponding electrostatic field that acts to restore quasi-neutrality of the plasma is taken into account. It is assumed that the electron motion is fluid-like in the direction perpendicular to the magnetic field and fast enough to support quasi-equilibrium Boltzmann distribution along the field lines. Electrostatic effects lead to an interesting feature of the current density profile inside the current sheet, i.e. a narrow sharp peak of electron current in the very center of the sheet due to fast curvature drift of the particles in this region. The corresponding magnetic field profile becomes much steeper near the neutral plane although the total cross-tail current is in all cases dominated by the ion contribution. The dependence of electrostatic effects on the ion to electron temperature ratio, the curvature of the magnetic field lines, and the average electron magnetic moment is also analyzed. The implications of these effects on the fine structure of thin current sheets and their potential impact on substorm dynamics are presented.

scholarly journals Asymmetries in the Earth's dayside magnetosheath: results from global hybrid-Vlasov simulations

2020 ◽  
Author(s):  
Lucile Turc ◽  
Vertti Tarvus ◽  
Andrew Dimmock ◽  
Markus Battarbee ◽  
Urs Ganse ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Mach Number ◽  
Bow Shock ◽  
Strong Impact ◽  
Parker Spiral ◽  
Wide Range ◽  
The Magnetic Field ◽  
Single Set ◽  
Shock Configuration

Abstract. Bounded by the bow shock and the magnetopause, the magnetosheath forms the interface between solar wind and magnetospheric plasmas and regulates solar wind-magnetosphere coupling. Previous works have revealed pronounced dawn-dusk asymmetries in the magnetosheath properties. The dependence of these asymmetries on the upstream parameters remains however largely unknown. One of the main sources of these asymmetries is the bow shock configuration, which is typically quasi-parallel on the dawn side and quasi-perpendicular on the dusk side of the terrestrial magnetosheath because of the Parker spiral orientation of the interplanetary magnetic field (IMF) at Earth. Most of these previous studies rely on collections of spacecraft measurements associated with a wide range of upstream conditions which are processed in order to obtain average values of the magnetosheath parameters. In this work, we use a different approach and quantify the magnetosheath asymmetries in global hybrid-Vlasov simulations performed with the Vlasiator model. We concentrate on three parameters: the magnetic field strength, the plasma density and the flow velocity. We find that the Vlasiator model reproduces accurately the polarity of the asymmetries, but that their level tends to be higher than in spacecraft measurements, probably because the magnetosheath parameters are obtained from a single set of upstream conditions in the simulation, making the asymmetries more prominent. We investigate how the asymmetries change when the angle between the IMF and the Sun-Earth line is reduced and when the Alfven Mach number decreases. We find that a more radial IMF results in a stronger magnetic field asymmetry and a larger variability of the magnetosheath density. In contrast, a lower Alfven Mach number leads to a reduced magnetic field asymmetry and a decrease in the variability of the magnetosheath density and velocity, the latter likely due to weaker foreshock processes. Our results highlight the strong impact of the foreshock on global magnetosheath properties, in particular on the magnetosheath density, which is extremely sensitive to transient foreshock processes.

scholarly journals Magnetohydrostatic modeling of AR11768 based on a SUNRISE/IMaX vector magnetogram

2020 ◽  
Vol 640 ◽  
pp. A103 ◽  
Author(s):  
X. Zhu ◽  
T. Wiegelmann ◽  
S K. Solanki
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Field Measurements ◽  
Plasma Pressure ◽  
Photospheric Magnetic Field ◽  
Solar Photosphere ◽  
Free Layer ◽  
Lower Boundary Condition ◽  
Magnetic Field Measurements ◽  
The Magnetic Field

Context. High-resolution magnetic field measurements are routinely only done in the solar photosphere. Higher layers, such as the chromosphere and corona, can be modeled by extrapolating these photospheric magnetic field vectors upward. In the solar corona, plasma forces can be neglected and the Lorentz force vanishes. This is not the case in the upper photosphere and chromosphere where magnetic and nonmagnetic forces are equally important. One way to deal with this problem is to compute the plasma and magnetic field self-consistently, in lowest order with a magnetohydrostatic (MHS) model. The non-force-free layer is rather thin and MHS models require high-resolution photospheric magnetic field measurements as the lower boundary condition. Aims. We aim to derive the magnetic field, plasma pressure, and density of AR11768 by applying the newly developed extrapolation technique to the SUNRISE/IMaX data embedded in SDO/HMI magnetogram. Methods. We used an optimization method for the MHS modeling. The initial conditions consist of a nonlinear force-free field (NLFFF) and a gravity-stratified atmosphere. During the optimization procedure, the magnetic field, plasma pressure, and density are computed self-consistently. Results. In the non-force-free layer, which is spatially resolved by the new code, Lorentz forces are effectively balanced by the gas pressure gradient force and gravity force. The pressure and density are depleted in strong field regions, which is consistent with observations. Denser plasma, however, is also observed at some parts of the active region edges. In the chromosphere, the fibril-like plasma structures trace the magnetic field nicely. Bright points in SUNRISE/SuFI 3000 Å images are often accompanied by the plasma pressure and electric current concentrations. In addition, the average of angle between MHS field lines and the selected chromospheric fibrils is 11.8°, which is smaller than those computed from the NLFFF model (15.7°) and linear MHS model (20.9°). This indicates that the MHS solution provides a better representation of the magnetic field in the chromosphere.

scholarly journals The relative orientation between the magnetic field and gradients of surface brightness within thin velocity slices of 12CO and 13CO emission from the Taurus molecular cloud

2020 ◽  
Vol 496 (4) ◽  
pp. 4546-4564
Author(s):  
M Heyer ◽  
J D Soler ◽  
B Burkhart
Keyword(s):  
Magnetic Field ◽  
Mach Number ◽  
Turbulent Flows ◽  
Molecular Cloud ◽  
Random Errors ◽  
Spatial Gradients ◽  
Low Levels ◽  
The Magnetic Field ◽  
Taurus Molecular Cloud

ABSTRACT We examine the role of the interstellar magnetic field to modulate the orientation of turbulent flows within the Taurus molecular cloud using spatial gradients of thin velocity slices of 12CO and 13CO antenna temperatures. Our analysis accounts for the random errors of the gradients that arise from the thermal noise of the spectra. The orientations of the vectors normal to the antenna temperature gradient vectors are compared to the magnetic field orientations that are calculated from Planck 353 GHz polarization data. These relative orientations are parameterized with the projected Rayleigh statistic and mean resultant vector. For 12CO,   strongly parallel and strongly perpendicular relative orientations are found in 28 percent and 39 percent of the cloud area respectively. For the lower opacity 13CO emission, strongly parallel and strongly perpendicular orientations are found in 7 per cent and 43 per cent of the cloud area, respectively. For both isotopologues, strongly parallel or perpendicular alignments are restricted to localized regions with low levels of turbulence. If the relative orientations serve as an observational proxy to the Alfvénic Mach number then our results imply local variations of the Alfvénic Mach number throughout the cloud.

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