共查询到20条相似文献，搜索用时 31 毫秒
1.
The propagation of magnetohydrodynamic (MHD) waves is an area that has been thoroughly studied for idealised static and steady state magnetised plasma systems applied to numerous solar structures. By applying the generalisation of a temporally varying background density to an open magnetic flux tube, mimicking the observed slow evolution of such waveguides in the solar atmosphere, further investigations into the propagation of both fast and slow MHD waves can take place. The assumption of a zero-beta plasma (no gas pressure) was applied in Williamson and Erdélyi (Solar Phys. 2013, doi: 10.1007/s11207-013-0366-9 , Paper I) is now relaxed for further analysis here. Firstly, the introduction of a finite thermal pressure to the magnetic flux tube equilibrium modifies the existence of fast MHD waves which are directly comparable to their counterparts found in Paper I. Further, as a direct consequence of the non-zero kinetic plasma pressure, a slow MHD wave now exists, and is investigated. Analysis of the slow wave shows that, similar to the fast MHD wave, wave amplitude amplification takes place in time and height. The evolution of the wave amplitude is determined here analytically. We conclude that for a temporally slowly decreasing background density both propagating magnetosonic wave modes are amplified for over-dense magnetic flux tubes. This information can be very practical and useful for future solar magneto-seismology applications in the study of the amplitude and frequency properties of MHD waveguides, e.g. for diagnostic purposes, present in the solar atmosphere. 相似文献
2.
We investigate the propagation of MHD waves in a magnetised plasma in a weakly stratified atmosphere, representative of hot
coronal loops. In most earlier studies, a time-independent equilibrium was considered. Here we abandon this restriction and
allow the equilibrium to develop as a function of time. In particular, the background plasma is assumed to be cooling due
to thermal conduction. The cooling is assumed to occur on a time scale greater than the characteristic travel times of the
perturbations. We investigate the influence of cooling of the background plasma on the properties of magneto–acoustic waves.
The MHD equations are reduced to a 1D system modelling magneto–acoustic modes propagating along a dynamically cooling coronal
loop. A time-dependent dispersion relation that describes the propagation of the magneto–acoustic waves is derived using the
WKB theory. An analytic solution for the time-dependent amplitude of waves is obtained, and the method of characteristics
is used to find an approximate analytical solution. Numerical calculations of the analytically derived solutions are obtained
to give further insight into the behaviour of the MHD waves in a system with a variable, time-dependent background. The results
show that there is a strong damping of MHD waves and the damping also appears to be independent of the position along the
loop. Studies of MHD wave behaviour in a time-dependent backgrounds seem to be a fundamental and very important next step
in the development of MHD wave theory that is applicable to a wide range of situations in solar physics. 相似文献
3.
4.
The present paper discusses the implementation of the SGHR method (Sakurai, Goossens, and Hollweg, 1991; Goossens, Ruderman, and Hollweg, 1995) in a numerical scheme for determining resonantly driven Alfvén waves in nonuniform magnetic flux tubes. This method is based on jump conditions over the dissipative layer which are obtained from an asymptotic analysis of analytical solutions to simplified versions of the linear non-ideal MHD equations in this dissipative layer. The emphasis is on the computational simplicity and the accuracy of the method. The method derives its computational simplicity from the fact that it circumvents the numerical integration of the non-ideal MHD equations. The implementation only requires the numerical integration of the ideal MHD equations away from the resonant position. There is no need for a special integration scheme and a PC suffices as a hardware tool.The accuracy of the method is verified by means of test computations. These test computations deal with the loss of power of acoustic waves in sunspots by resonant absorption of Alfvén waves. Results for the absorption coefficients obtained with the SGHR method are compared with known results in the literature obtained by integration of the full set of the linearized non-ideal MHD equations. The agreement is excellent and identifies the SGHR method as a powerful and extremely easy to use tool for studying resonant Alfvén waves. 相似文献
5.
S. Parhi B.P. Pandey M. Goossens G.S. Lakhina P. De Bruyne 《Astrophysics and Space Science》1997,250(1):147-162
The solar corona, modelled by a low β, resistive plasma slab sustains MHD wave propagations due to footpoint motions in the
photosphere. The density, magnetic profile and driver are considered to be neither very smooth nor very steep. The numerical
simulation presents the evolution of MHD waves and the formation of current sheet. Steep gradients in slow wave at the slab
edges which are signature of resonance layer where dissipation takes place are observed. Singularity is removed by the inclusion
of finite resistivity. Dissipation takes place around the resonance layer where the perturbation develops large gradients.
The width of the resonance layer is calculated. The thickness of the Alfvén resonance layer is more than that of the slow
wave resonance layer. Attempt is made to distinguish between slow and Alfvén wave resonance layers. Fast waves develop into
kink modes. As plasma evolves the current sheets which provide the heating at the edges gets distorted and fragment into two
current sheets at each edge which in turn come closer when the twist is enhanced.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
The resonant absorption of small amplitude surface Alfvén waves is studied in nonlinear incompressible MHD for a viscous and resistive plasma. The reductive perturbation method is used to obtain the equation that governs the spatial and temporal behaviour of small amplitude nonlinear surface Alfvén waves. Numerical solutions to this equation are obtained under the initial condition that att = 0 the spatial variation is purely sinusoidal. The numerical results show that nonlinearity accelerates the wave damping due to resonant absorption. Resonant absorption is a more efficient wave damping mechanism than can be anticipated on the basis of linear theory. 相似文献
7.
8.
Interaction of Alfvén waves with plasma inhomogeneities generates phase mixing which can lead to dissipate Alfvén waves and to heat the solar plasma. Here we study the dissipation of Alfvén waves by phase mixing due to viscosity and resistivity variations with height. We also consider nonlinear magnetohydrodynamic (MHD) equations in our theoretical model. Non-linear terms of MHD equations include perturbed velocity, magnetic field, and density. To investigate the damping of Alfvén waves in a stratified atmosphere of solar spicules, we solve the non-linear MHD equations in the x–z plane. Our simulations show that the damping is enhanced due to viscosity and resistivity gradients. Moreover, energy variations is influenced due to nonlinear terms in MHD equations. 相似文献
9.
Nonlinear theory of driven magnetohydrodynamic (MHD) waves in the slow dissipative layer in isotropic steady plasmas developed by Ballai and Erdélyi (Solar Phys. 180 (1998)) is used to study the nonlinear interaction of sound waves with one-dimensional isotropic steady plasmas. An inhomogeneous magnetic slab with field-aligned plasma flow is sandwiched by a homogeneous static magnetic-free plasma and by a homogeneous steady magnetic plasma. Sound waves launched from the magnetic-free plasma propagate into the inhomogeneous region interacting with the localised slow dissipative layer and are partially reflected, dissipated or transmitted by this region. The nonlinearity parameter, introduced by Ballai and Erdélyi, is assumed to be small and a regular perturbation method is used to obtain analytical wave solutions. Analytical studies of resonant absorption of sound waves show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We also find that a steady equilibrium shear flow can significantly influence the nonlinear resonant absorption in the limits of thin inhomogeneous layer and weak nonlinearity. The presence of an equilibrium flow may therefore be important for the nonlinear resonant MHD wave phenomena. A parametric analysis also shows that the nonlinear part of resonant absorption can be strongly enhanced by the equilibrium flow. 相似文献
10.
A fast-wave pulse in a simple, cold, inhomogeneous MHD model plasma is constructed by Fourier superposition over frequency
of harmonic waves that are singular at their respective Alfvén resonances. The pulse partially reflects before reaching the
resonance layer, but also partially tunnels through to it to convert to an Alfvén wave. The exact absorption/conversion coefficient
for the pulse is shown to be given precisely by a function of transverse wavenumber tabulated in Paper I of this sequence,
and to be independent of frequency and pulse width. 相似文献
11.
This paper considers driven resonant nonlinear slow magnetohydrodynamic (MHD) waves in dissipative steady plasmas. A theory developed by Ruderman, Hollweg, and Goossens (1997) is used and extended to study the effect of steady flows on the nonlinear resonant behaviour of slow MHD waves in slow dissipative layers. The method of matched asymptotic expansions is used to describe the behaviour of the wave variables in the slow dissipative layer. The nonlinear analogue of the connection formulae for slow MHD waves obtained previously by Goossens, Hollweg, and Sakurai (1992) and Erdélyi (1997) in linear MHD, are derived. The effect of an equilibrium flow results partly in a Doppler shift of the available frequency for slow resonance and partly in the modification of the width of the dissipative layer. 相似文献
12.
The excitation of Alfvénic waves in solar spicules by localized Alfvénic pulses is investigated. A set of incompressible MHD equations in the two-dimensional x–z plane with steady flows and sheared magnetic fields is solved. Stratification due to gravity and transition region between chromosphere and corona is taken into account. An initially localized Alfvénic pulse launched below the transition region can penetrate from transition region into the corona. We show that the period of the transversal oscillations is in agreement with those observed in spicules. Moreover, it is found that the excited Alfvénic waves spread during propagation along the spicule length, and suffer efficient damping of the oscillations amplitude. The damping time of the transverse oscillations increased with decreasing k b values. 相似文献
13.
The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfvén waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfvén waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for
r
, andP across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for
r
, andP in terms of double integrals of Hankel functions of complex argument of order
with compact analytical solutions that allow a straightforward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpendicular to the magnetic field lines which enables us to determine the dominant dynamics of resonant Alfvén waves in dissipative MHD. 相似文献
14.
The resonances that appear in the linear compressible MHD formulation of waves are studied for equilibrium states with flow. The conservation laws and the jump conditions across the resonance point are determined for 1D cylindrical plasmas. For equilibrium states with straight magnetic field lines and flow along the field lines the conserved quantity is the Eulerian perturbation of total pressure. Curvature of the magnetic field lines and/or velocity field lines leads to more complicated conservation laws. Rewritten in terms of the displacement components in the magnetic surfaces parallel and perpendicular to the magnetic field lines, the conservation laws simply state that the waves are dominated by the parallel motions for the modified slow resonance and by the perpendicular motions for the modified Alfvén resonance.The conservation laws and the jump conditions are then used for studying surface waves in cylindrical plasmas. These waves are characterized by resonances and have complex eigenfrequencies when the classic true discontinuity is replaced by a nonuniform layer. A thin non-uniform layer is considered here in an attempt to obtain analytical results. An important result related to earlier work by Hollweg et al. (1990) for incompressible planar plasmas is found for equilibrium states with straight magnetic field lines and straight velocity field lines. For these equilibrium states the incompressible and compressible surface waves have the same frequencies at least in the long wavelength limit and there is an exact correspondence with the planar case. As a consequence, the conclusions formulated by Hollweg et al. still hold for the straight cylindrical case. The effects of curvature are subsequently considered. 相似文献
15.
《Planetary and Space Science》2007,55(6):694-700
Stochastic fluctuations of the magnetospheric plasma and background magnetic field, especially intense during geomagnetically active periods, can provide an additional mechanism of damping of Alfvén field line oscillations. To quantify this hypothesis, we consider a driven Alfvén field line resonator with stochastic fluctuations of the Alfvén resonant frequency. This problem is first considered analytically for a low level of fluctuations, then a more general numerical approach is introduced. The results of analytical calculations and numerical modeling both indicate the deterioration of resonant properties of the resonator owing to stochastic background fluctuations. 相似文献
16.
We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvénic wave in the entire loop. 相似文献
17.
The influence of a constant coronal magnetic field on solar global oscillations is investigated for a simple planar equilibrium model. The model consists of an atmosphere with a constant horizontal magnetic field and a constant sound speed, on top of an adiabatic interior having a linear temperature profile. The focus is on the possible resonant coupling of global solar oscillation modes to local slow continuum modes of the atmosphere and the consequent damping of the global oscillations. In order to avoid Alfvén resonances, the analysis is restricted to propagation parallel to the coronal magnetic field. Parallel propagating oscillation modes in this equilibrium model have already been studied by Evans and Roberts (1990). However, they avoided the resonant coupling to slow continuum modes by a special choice of the temperature profile. The physical process of resonant absorption of the acoustic modes with frequency in the cusp continuum is mathematically completely described by the ideal MHD differential equations which for this particular equilibrium model reduce to the hypergeometric differential equation. The resonant layer is correctly dealt with in ideal MHD by a proper treatment of the logarithmical branch cut of the hypergeometric function. The result of the resonant coupling with cusp waves is twofold. The eigenfrequencies become complex and the real part of the frequency is shifted. The shift of the real part of the frequency is not negligible and within the limit of observational accuracy. This indicates that resonant interactions should definitely be taken into account when calculating the frequencies of the global solar oscillations. 相似文献
18.
The present paper considers resonant slow waves in 1D non-uniform magnetic flux tubes in dissipative MHD. Analytical solutions are obtained for the Lagrangian displacement and the Eulerian perturbation of the total pressure for both static and stationary equilibrium states. From these analytical solutions we obtain the fundamental conservation law and the jump conditions for resonant slow waves in dissipative MHD. The validity of the ideal conservation law and jump conditions obtained by Sakurai, Goossens, and Hollweg (1991) for static equilibria and Goossens, Hollweg, and Sakurai (1992) for stationary equilibria is justified in dissipative MHD. 相似文献
19.
Where spatial gradients in the amplitude of an Alfvén wave are non-zero, a nonlinear magnetic-pressure gradient acts upon the medium (commonly referred to as the ponderomotive force). We investigate the nature of such a force in inhomogeneous 2.5D MHD plasmas by analysing source terms in the nonlinear wave equations for the general case of inhomogeneous B and ρ, and consider supporting nonlinear numerical simulations. Our equations indicate that there are two distinct classes of ponderomotive effect induced by Alfvén waves in general 2.5D MHD, each with both a longitudinal and transverse manifestation. i) Geometric effects: Gradients in the pulse geometry relative to the background magnetic field cause the wave to sustain cospatial disturbances, the longitudinal and transverse daughter disturbances – where we report on the transverse disturbance for the first time. ii) ?(c A) effects: Where a pulse propagates through an inhomogeneous region (where the gradients in the Alfvén-speed profile c A are non-zero), the nonlinear magnetic-pressure gradient acts to accelerate the plasma. Transverse gradients (phase mixing regions) excite independently propagating fast magnetoacoustic waves (generalising the result of Nakariakov, Roberts, and Murawski (Solar Phys. 175, 93, 1997)) and longitudinal gradients (longitudinally dispersive regions) perturb along the field (thus creating static disturbances in β=0, and slow waves in β≠0). We additionally demonstrate that mode conversion due the nonlinear Lorentz force is a one-way process, and does not act as a mechanism to nonlinearly generate Alfvén waves due to propagating magnetoacoustic waves. We conclude that these ponderomotive effects are induced by an Alfvén wave propagating in any MHD medium, and have the potential to have significant consequences on the dynamics of energy transport and aspects of dissipation provided the system is sufficiently nonlinear and inhomogeneous. 相似文献
20.
K. H. Tsui 《Solar physics》1996,168(1):171-182
The generation of bright solar radio spikes by the beam-driven cyclotron resonance maser mechanism (the resonant interaction of an electron beam with a circularly polarized wave in a background plasma under the action of a guide magnetic field) is studied. Nonlinear effects such as radiation damping and gyrophase bunching on electron energy and momentum are responsible for the enhanced direct energy conversion between the beam and the coherent wave. Factors such as beam energy spread and pitch angle distribution are analyzed. The intense maser radiation is carried at the source by the circularly polarized wave propagating along the magnetic field. Due to the magnetic field curvature, the outgoing maser radiation converts into extraordinary and ordinary modes. The extraordinary mode suffers from plasma absorption at the second harmonic layer, whereas the ordinary mode is likely to get through. 相似文献