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Weakly nonlinear surface waves are examined in the context of the beam model for jetlike radio sources. By introducing a finite scale length, viz. the beam radius, geometrical dispersion can act to balance nonlinear wave growth and thereby produce solitons, localized wave packets of stable waveform. A method for obtaining a soliton equation from the MHD equations is presented and then applied to radio knots in jets.
The interaction of the Crab pulsar with its surrounding nebula is modeled as a steady state, spherically symmetric relativistic wind which is confined by the outer layers of the supernova remnant. The pulsar wind is assumed to contain only positrons and electrons, and is terminated by a strong shock at a distance of 10 arcseconds from the pulsar, at the outer edge of the underluminous region. Down-stream of the shock, the flow decelerates and increases its pressure in order to match the boundary conditions imposed by outer nebula. Consistent flow solutions can be found if the magnetic luminosity of the pulsar wind is about 0.3 percent of its particle luminosity. The immediate postshock plasma is modeled as a power law distribution whose density and pressure moments satisfy the strong shock Rankine-Hugoniot relations. Using the downstream flow solution, the synchrotron continuum is calculated. The parameters of the pulsar wind and assumed power law spectral index are adjusted until the calculated total synchrotron power and the spectral distribution of the nebular continuum from optical to gamma-rays, are in reasonable accord with observations.
The unstable transition behavior of a bounded current-carrying two-dimensional magnetofluid is explored, using the hydrodynamic theory developed for parallel shear flows as a guide. Nonlinear excitation of the higher wavenumbers results in the development of electric current sheets of finite extent, as well as the formation of 'attraction currents' centered at the magnetic O-points. A secondary instability mechanism, the dynamic tearing of the electric current sheet, is also observed. This dynamic tearing leads to sawtoothlike temporal oscillations in certain global quantities. The long-time state of the system resembles a nonlinearly saturated state with significant excitation of many wavenumbers. Some features of this state can be understood by means of a Landau nonlinear stability theory based on certain assumptions about the perturbation energy balance.
It is shown how the phenomenon of MHD surface wave resonance absorption can be described in simple terms, both physically and mathematically, by applying the 'thin flux tube equations' to the finite-thickness transition layer which supports the surface wave. The thin flux tubes support incompressible slow-mode waves that are driven by fluctuations in the total pressure which exist due to the presence of the surface wave. It is shown that the equations for the slow-mode waves can be reduced to a simple equation, equivalent to a driven harmonic oscillator. Certain field lines within the transition layer are equivalent to a harmonic oscillator driven at resonance, and neighboring field lines are effectively driven at resonance as long as a given condition is satisfied. Thus, a layer which secularly extracts energy from the surface wave develops. The analysis indicates that nonlinear effects may destroy the resonance which is crucial to the whole effect.
Approximate analytic solutions are sought for the dispersion relation for the MHD stability of magnetized medium in current-driven filamentation modes such as those observed in the solar atmosphere. The magnetic field is assumed to have a self-consistent sheared equilibrium structure. The analysis is carried out in the small wavenumber regime, where shear length is similar to the mode wavelength. Instability is found to depend on the ratio between the thermal and magnetic diffusivities, i.e., the Prandtl number, which identifies the unstable transverse wavenumbers. The instability conditions are expressed in an algebraic equation amenable to numerical solution. Results are provided from use of the model to determine the maximum growth rate and typical scale lengths of instabilities in a precoronal atmosphere and the lower transition region.
A computational code for solving two-dimensional, time-dependent MHD equations by the method of characteristics is presented. Its capabilities are demonstrated by solving two very different problems for which analytical solutions exist: linearized, standing MHD wave motions in a magnetized cylindrical plasma, and nonlinear self-similar expansion of a magnetized plasma ball. The nonlinear development of standing MHD wave solutions in a cylindrical plasma is also studied. The method can be naturally embedded in the computational architecture of massively parallel processors.
The generation of MHD waves by turbulent motions in a stratified medium with an embedded uniform magnetic field, a topic which is relevant to the study of the solar atmosphere, is considered. Both compressible and incompressible MHD waves are treated in a one-dimensional approach; however, the direction of the background magnetic field is permitted to vary in an arbitrary direction. Theoretical expressions for MHD energy fluxes are obtained as a function of wave frequency and multipole coefficients. It is shown that monopole, dipole, and quadrupole emissions are responsible for the generation of the compressible components of the fast and slow modes. However, the incompressible components and the Alfven modes can be generated by the dipole emission only. Specific results obtained for special magnetic field geometries are discussed for the fast and slow modes.
The nonlinear properties of MHD surface waves in the solar atmosphere are investigated analytically, assuming that the fluid is incompressible and that the waves are confined to a single surface, with semiinfinite regions on both sides. The governing equations are derived in detail, and qualitative results are presented in a graph. For propagating waves, second-order terms in the wave amplitude are found to lead to wave steepening at leading or trailing edges, the steepening rate becoming very large as the threshold for the linear Kelvin-Helmholtz instability is approached. Second-order effects on standing waves include crest and trough sharpening (increasing with time), a current independent of distance on the surface but decreasing exponentially with distance from the surface, and pressure-field fluctuations of infinite extent. It is suggested that these effects could account for a large fraction of solar-atmosphere heating.
Nonlinear solitary wave propagation in a compressible magnetic beam model of an extragalactic radio jet is examined and shown to lead to solitons of the Benjamin-Ono type. A number of similarities between such magnetic beam models of jets and models of solar photospheric flux tubes are pointed out and exploited. A single soliton has the appearance of a symmetric bulge on the jet which propagates faster than the jet's flow.
Coronal bright points are known to be magnetic in nature. A two-dimensional MHD code was devleoped to investigate the rsponse of a stratified atmosphere to a localized magnetic structure. If a bright point occurs at a region where flux tubes of opposite polarity have encountered by chance it is found that, in the presence of stratification, a net upward mass flux results. Upflow velocities of up to one half of the Alfven speed are produced. The implications of the results for mass outflows from bright points in coronal holes are discussed.
Solar flare energy buildup at the photospheric level and energy release and transport into heliospheric space are examined using a composite MHD model. A four phase composite MHD model is described. An example demonstrating the applicability of the model is presented; the model was applied to the active region AR 2372. The limitations of this composite MHD model approach to analyzing solar flare energy buildup are discussed.
The effects of viscosity on the resonance absorption of incompressible MHD surface waves, which occurs when the waves are supported by a thin 'transition layer' rather than by a discontinuous surface, are considered. The behavior of the plasma and fields inside the transition layer is considered, allowing for classical viscosity. An inhomogeneous Airy equation for the velocity component along the propagative direction is obtained in the vicinity of the resonant field line. The viscous stress tensor for a magnetized plasma is considered, and a simple algebraic steady state equation is obtained for the velocity component along the background magnetic field. The net heating rate is evaluated and found to be independent of the viscosity coefficient, and to correspond to the surface wave 'decay rate' obtained from ideal MHD equations.
The time-dependent behavior of a shocked spherically symmetric relativistic fluid with tangential magnetic field is investigated, considering the case where the boundaries of the shocked fluid move at constant velocity so that self-similar solutions exist. The behavior of the fluid in the ultrarelativistic regime is compared to that in the nonrelativistic regime; there is a smooth transition between these limits. If a magnetic field is present, the magnetic pressure becomes increasingly important with distance from the shock wave; the gas pressure vanishes at the contact discontinuity that bounds the flow. Analytic expressions are given which describe the flow. The solutions can be applied to the evolution of shocked relativistic pulsar winds, which are probably observed as Crab-like supernova remnants. A model for the Crab Nebula, based on the steady-state model of Kennel and Coroniti (1984), indicates that sigma = 0.0016, where sigma is twice the ratio of magnetic to particle energy in the wind as measured in the fluid frame. This is about half the value suggested by Kennel and Coroniti and is much smaller than the value that might be expected for a pulsar wind.
The magnetic field and plasma data acquired by Voyager between 1 and 11 AU are used to investigate the properties of interplanetary MHD fluctuations and to attempt to answer several related questions regarding the Alfvenicity of solar wind fluctuations. These questions are: (1) the extent to which the interplanetary fluctuations are Alfvenic; (2) whether there is any evolution in propagation direction of the Alfvenic fluctuations; (3) whether the degree and evolution of Alfvenicity are correlated with structure; and (4) the importance and evolution of compressive contributions to the fluctuations. The conclusions on these points are summarized, and the results are related to theoretical work.
This paper considers two-dimensional nonlinear MHD waves of large horizontal spatial scales for a thin magnetofluid layer on the surface of a rotating sphere. The 'shallow fluid' hydrodynamic equations are generalized to include the effects of magnetic fields, and it is shown that the resulting MHD equations can be reduced to a single scalar equation for a stream function involving several free functions. For special choices of these free functions, two kinds of finite-amplitude MHD waves are obtained, propagating in the azimuthal direction relative to the uniformly rotating background atmosphere in the presence of a background zonal magnetic field and a steady differential zonal flow. These two kinds of MHD waves are fundamentally due to the joint effects of the uniform rotation of the background atmosphere and background magnetic field; the first is an inertial wave of the Rossby (1939) and Haurwitz (1940) type, modified by the presence of the background zonal magnetic field, while the second is a magnetic Alfven-like wave which is modified by the uniform rotation of the background atmosphere.
The radiative damping of acoustic and MHD waves that propagate through white dwarf photospheric layers is studied, and other damping processes that may be important for the propagation of the MHD waves are calculated. The amount of energy remaining after the damping processes have occurred in different types of waves is estimated. The results show that lower acoustic fluxes should be expected in layered DA and homogeneous DB white dwarfs than had previously been estimated. Acoustic emission manifests itself in an enhancement of the quadrupole term, but this term may become comparable to or even lower than the dipole term for cool white dwarfs. Energy carried by the acoustic waves is significantly dissipated in deep photospheric layers, mainly because of radiative damping. Acoustically heated corona cannot exist around DA and DB white dwarfs in a range T(eff) = 10,000-30,000 K and for log g = 7 and 8. However, relatively hot and massive white dwarfs could be exceptions.
Stationary point analysis is used to compute generalized critical Mach numbers for finite-amplitude fast and slow shocks in classical MHD fluids. Particular attention is paid to the case where the resistive and thermal conduction dissipation scale lengths are comparable and much larger than the viscous scale lengths. With both resistivity and thermal conduction, the critical Mach number at which viscosity must be invoked is determined by the condition that the downstream flow speed equals the isothermal sound speed. It is also shown that resistivity and thermal conduction can provide convergent stationary point solutions for nearly all slow shocks, except perhaps switch-off-shocks.
A spectral-method numerical code is used to compute mass-density fluctuation spectra in turbulent magnetofluids. The computations are used to test and extend the analytical theory of density variations in slightly compressible magnetofluids given by Montgomery, et al. (1987) and used to infer inertial-range density-fluctuation spectra for the nearby interstellar medium and solar wind. A local equation of state is assumed, relating density to pressure. Constant, scalar resistivities and viscosities are used. In the limit of low Mach numbers and high mechanical-to-magnetic pressure ratios, the fit of the computations to the analytical theory is seen to be close.