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 International Journal of Mathematics and Mathematical Sciences , 1997, DOI: 10.1155/s0161171297000227 Abstract: A new approach for the determination of exact solutions of steady plane infinitely conducting MHD aligned flows is presented. In this approach, the ( , )- or the ( ·, )- coordinates is used to obtain exact solutions of these flows where =(x,y) is the streamfunction and w= (x,y)+i ·(x,y) is an analytic function of z=x+iy.
 Physics , 2013, DOI: 10.1093/mnras/stt275 Abstract: We obtain the general forms for the current density and the vorticity from the integrability conditions of the basic equations which govern the stationary states of axisymmetric magnetized self-gravitating barotropic objects with meridional flows under the ideal magnetohydrodynamics (MHD) approximation. As seen from the stationary condition equations for such bodies, the presence of the meridional flows and that of the poloidal magnetic fields act oppositely on the internal structures. The different actions of these two physical quantities, the meridional flows and the poloidal magnetic fields, could be clearly seen through stationary structures of the toroidal gaseous configurations around central point masses in the framework of Newtonian gravity because the effects of the two physical quantities can be seen in an amplified way for toroidal systems compared to those for spheroidal stars. The meridional flows make the structures more compact, i.e. the widths of toroids thinner, while the poloidal magnetic fields are apt to elongate the density contours in a certain direction depending on the situation. Therefore, the simultaneous presence of the internal flows and the magnetic fields would work as if there were no such different actions within and around the stationary gaseous objects such as axisymmetric magnetized toroids with internal motions around central compact objects under the ideal MHD approximation, although these two quantities might exist in real systems.
 Physics , 2012, DOI: 10.1051/0004-6361:20053062 Abstract: A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as a super-Alfvenic tail flow. An example is our own heliosphere and its heliotail. We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few parameters, like the inner Alfven Mach number and the outer Alfven Mach number, the magnetic field strength within and outside the stellar wind cavity, and the distribution of singular points of the magnetic field within these flows. Within the framework of a one-fluid approximation, it is possible to obtain solutions of the MHD equations for stationary flows from corresponding static MHD equilibria, by using noncanonical mappings of the canonical variables. The canonical variables are the Euler potentials of the magnetic field of magnetohydrostatic equilibria. Thus we start from static equilibria determined by the distribution of magnetic neutral points, and assume that the Alfven Mach number for the corresponding stationary equilibria is finite. The topological structure determines the geometrical structure of the interstellar gas - stellar wind interface. Additional boundary conditions like the outer magnetic field and the jump of the magnetic field across the astropause allow determination of the noncanonical transformations. This delivers the strength of the magnetic field at every point in the astrotail region beyond the reverse shock. The mathematical technique for describing such a scenario is applied to astrospheres in general, but is also relevant for the heliosphere. It shows the restrictions of the outer and the inner magnetic field strength in comparison with the corresponding Alfven Mach numbers in the case of subalfvenic flows.
 International Journal of Mathematics and Mathematical Sciences , 1990, DOI: 10.1155/s0161171290000138 Abstract: A study is made of non-Newtonian HHD aligned steady plane fluid flows to find exact solutions for various flow configurations. The equations of motion have been transformed to the hodograph plane. A Legendre-transform function is used to recast the equations in the hodograph plane in terms of this transform function. Solutions for various flow configurations are obtained. Applications are investigated for the fluids of finite and infinite electrical conductivity bringing out the similarities and contrasts in the solutions of these types of fluids.
 Physics , 2010, DOI: 10.1088/0004-637X/737/2/62 Abstract: The large-scale dynamics of plasmas is well described within the framework of magnetohydrodynamics (MHD). However, whenever the ion density of the plasma becomes sufficiently low, the Hall effect is likely to become important. The role of the Hall effect has been studied in several astrophysical plasma processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence or MHD instabilities. In particular, the development of small-scale instabilities is essential to understand the transport properties in a number of astrophysical plasmas. The magneto-rotational instability, which takes place in differentially rotating accretion disks embedded in relatively weak magnetic fields, is just one example. The influence of the large-scale velocity flows on small-scale instabilities is often approximated by a linear shear flow. In this paper we quantitatively study the role of the Hall effect on plasmas embedded in large-scale shear flows. More precisely, we show that a new instability develops as long as the Hall effect is present, which we therefore term as the Hall magneto-shear instability. As a particular case, we recover the so-called magneto-rotational instability and quantitatively assess the role of the Hall effect on its development and evolution.
 Physics , 2001, DOI: 10.1080/03091920108203409 Abstract: It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov, Catto, and Hazeltine [Phys. Rev. Lett. {\bf 82}, 2689 (1999)] are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime $\beta_0\approx \gamma_0\approx \delta_0 \approx\epsilon_0\ll 1$, where $\beta_0$, $\gamma_0$, $\delta_0$, and $\epsilon_0$ are related to the thermal, poloidal-current, flow and gravitating energies normalized to the poloidal-magnetic-field energy, respectively, and (b) in the high-energy regime $\beta_0\approx \gamma_0\approx \delta_0 \approx\epsilon_0\gg 1$. It turns out that in the high-energy regime all four forces, pressure-gradient, toroidal-magnetic-field, inertial, and gravitating contribute equally to the formation of magnetic surfaces very extended and localized about the symmetry plane such that the resulting equilibria resemble the accretion disks in astrophysics.
 Nonlinear Processes in Geophysics (NPG) , 2004, Abstract: There is abundant observational evidence that the energization of plasma particles in space is correlated with an enhanced activity of large-scale MHD waves. Since these waves cannot interact with particles, we need to find ways for these MHD waves to transport energy in the dissipation range formed by small-scale or high-frequency waves, which are able to interact with particles. In this paper we consider the dissipation range formed by the kinetic Alfvén waves (KAWs) which are very short- wavelengths across the magnetic field irrespectively of their frequency. We study a nonlocal nonlinear mechanism for the excitation of KAWs by MHD waves via resonant decay AW(FW)→KAW1+KAW2, where the MHD wave can be either an Alfvén wave (AW), or a fast magneto-acoustic wave (FW). The resonant decay thus provides a non-local energy transport from large scales directly in the dissipation range. The decay is efficient at low amplitudes of the magnetic field in the MHD waves, B/B0~10-2. In turn, KAWs are very efficient in the energy exchange with plasma particles, providing plasma heating and acceleration in a variety of space plasmas. An anisotropic energy deposition in the field-aligned degree of freedom for the electrons, and in the cross-field degrees of freedom for the ions, is typical for KAWs. A few relevant examples are discussed concerning nonlinear excitation of KAWs by the MHD wave flux and consequent plasma energization in the solar corona and terrestrial magnetosphere.
 Patrick Hennebelle Physics , 2013, DOI: 10.1051/0004-6361/201321292 Abstract: {Filaments are ubiquitous in the interstellar medium as recently emphasized by Herschel, yet their physical origin remains elusive} {It is therefore important to understand the physics of molecular clouds to investigate how filaments form and what is the role played by various processes such as turbulence and magnetic field.} {We use ideal MHD simulations to study the formation of clumps in various conditions including different magnetization and Mach numbers as well as two completely different setup. We then perform several analysis to compute the shape of the clumps and their link to velocities and forces using various approaches.} {We find that on average, clumps in MHD simulations are more filamentary that clumps in hydrodynamical simulations. Detailed analyses reveal that the filaments are in general preferentially aligned with the strain which means that these structures simply result from the strech induced by turbulence. Moreover filaments tend to be confined by the Lorentz force which therefore lead them to survive longer in magnetized flows. We show that they have in all simulations a typical thickness equal to a few grid cells suggesting that they are primarily associated to the energy dissipation within the flow. We estimate the order of magnitude of the dissipation length associated to the ion-neutral friction and conclude that in well UV shielded regions it is of the order of 0.1 pc and therefore could possibly set the typical size of non self-gravitating filaments.} {Filaments are ubiquitous because they are the results of the very generic turbulent strain and because magnetic field help to keep them coherent. We suggest that energy dissipation is playing a determinant role in their formation.}
 Astrophysics and Space Sciences Transactions (ASTRA) , 2011, DOI: 10.5194/astra-7-21-2011 Abstract: Magnetohydrodynamical simulations of turbulent plasmas have been performed to study the transport of energetic test particles. Several parameters of the underlying MHD simulation have been varied to gain insight into the main processes governing transport. Here also the distinct effects of wave-particle resonance and field line wandering shall be studied.
 Physics , 2000, DOI: 10.1046/j.1365-8711.2001.04290.x Abstract: Magnetohydrodynamic (MHD) and two-fluid quasi-neutral equilibria with azimuthal symmetry, gravity and arbitrary ratios of (nonrelativistic) flow speed to acoustic and Alfven speeds are investigated. In the two-fluid case, the mass ratio of the two species is arbitrary, and the analysis is therefore applicable to electron-positron plasmas. The methods of derivation can be extended in an obvious manner to several charged species. Generalized Grad-Shafranov equations, describing the equilibrium magnetic field, are derived. Flux function equations and Bernoulli relations for each species, together with Poisson's equation for the gravitational potential, complete the set of equations required to determine the equilibrium. These are straightforward to solve numerically. The two-fluid system, unlike the MHD system, is shown to be free of singularities. It is demonstrated analytically that there exists a class of incompressible MHD equilibria with magnetic field-aligned flow. A special sub--class first identified by S. Chandrasekhar, in which the flow speed is everywhere equal to the local Alfven speed, is compatible with virtually any azimuthally symmetric magnetic configuration. Potential applications of this analysis include extragalactic and stellar jets, and accretion disks.
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