Nonstationary driven oscillations of a magnetic cavity

The problem of transition to the steady state of driven oscillations in a magnetic cavity in a cold resistive plasma is addressed. The foot point driving polarized in the inhomogeneous direction is considered, and it is assumed that the cavity length in the direction of the equilibrium magnetic field is much larger than the cavity width in the inhomogeneous direction. The latter assumption enables one to neglect the variation of the magnetic pressure in the inhomogeneous direction, which strongly simplifies the analysis. The explicit solution describing the nonstationary behavior of the magnetic pressure and the velocity is obtained. This solution is used to study the properties of the transition to the steady state of oscillation. The main conclusion is that, in general, there are two different characteristic transitional times. The first time is inversely proportional to the decrement of the global mode. It characterizes the transition to the steady state of the global motion, which is the coherent oscillation of the cavity in the inhomogeneous direction. The second time is the largest of the two times, the first transitional time and the phase-mixing time, which is proportional to the magnetic Reynolds number in 1/3 power. It characterizes the transition to the steady state of the local motion, which is oscillations at the local Alfvén frequencies, and the saturation of the energy damping rate. An example from solar physics shows that, in applications, the second transitional time can be much larger than the first one

Non-axisymmetric oscillations of stratified coronal magnetic loops with elliptical cross-sections

We study non-axisymmetric oscillations of a straight magnetic tube with an elliptic cross-section and density varying along the tube. The governing equations for kink and fluting modes in the thin tube approximation are derived. We found that there are two kink modes, polarised along the large and small axes of the elliptic cross-section. We have shown that the ratio of frequencies of the first overtone and fundamental harmonic is the same for both kink modes and independent of the ratio of the ellipse axes. On the basis of this result we concluded that the estimates of the atmospheric scale height obtained using simultaneous observations of the fundamental harmonic and first overtone of the coronal loop kink oscillations are independent of the ellipticity of the loop cross-section

On the vertical and horizontal transverse oscillations of curved coronal loops

Kink oscillations of curved coronal loops with the density varying along the loop are studied in the thin tube approximation. The equilibrium magnetic field is assumed to be potential, and the field potential and flux function are used as curvilinear coordinates. It is also assumed that the loop expansion is weak, and the solution to the problem is looked for in the form of power series with respect to the tube expansion parameter lambda << 1. The main result of the study is that the eigenfrequencies of the vertical and horizontal tube oscillations are, in general, different, their difference being proportional to lambda. As an example a simple equilibrium with the magnetic field magnitude exponentially decaying with the height is considered. The implication of the obtained results for the interpretation of observational data is discussed

On the validity of nonlinear Alfvén resonance in space plasmas

Aims. In the approximation of linear dissipative magnetohydrodynamics (MHD), it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfvén (or slow) frequency of a magnetic surface. This behaviour is confined to a thin region, known as the dissipative layer, which embraces the resonant magnetic surface. Although driven MHD waves have small dimensionless amplitude far away from the resonant surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. Our aim is to study the nonlinear effects in Alfvén dissipative layer Methods. In the present paper, the method of simplified matched asymptotic expansions developed for nonlinear slow resonant waves is used to describe nonlinear effects inside the Alfvén dissipative layer. Results. The nonlinear corrections to resonant waves in the Alfvén dissipative layer are derived, and it is proved that at the Alfvén resonance (with isotropic/anisotropic dissipation) wave dynamics can be described by the linear theory with great accuracy

Resonantly damped oscillations of longitudinally stratified coronal loops

Soon after coronal loop oscillations were observed by TRACE spacecraft for the first time in 1999, various theoretical models have been put forward to explain the rapid damping of the oscillations of these intriguing objects. Coronal loop oscillations are often interpreted as fast kink modes of a straight cylindrical magnetic flux tube with immovable edges modelling dense photospheric plasma at the ends of the loop. Taking this model as a basis we use cold plasma approximation and consider the tube to be thin to simplify the problem and be able to deal with it analytically. In its equilibrium state the tube is permeated by a homogeneous magnetic field directed along the tube axis. We include the effect of stratification in our model supposing that plasma density varies along the tube. There is also density inhomogeneity in the radial direction confined in a layer with thickness much smaller than the radius of the tube. Considering the system of linearized MHD equations we study the dependence of the spectrum of tube oscillations and its damping due to resonant absorption on the parameters of the unperturbed state. The implication of the obtained results on coronal seismology is discussed

Torsional Alfvén waves: magneto-seismology in static and dynamic coronal plasmas

Aims: We study the properties of torsional Alfvén waves in coronal loops so that they may be exploited for coronal seismological applications. Methods: The governing equation is obtained for standing torsional Alfvén waves of a dynamic, gravitationally stratified plasma. The footpoints are assumed to obey line-tying conditions necessary for standing oscillations. Solutions are found in a number of different but typical scenarios to demonstrate the possibilities for both temporal and spatial magneto-seismology exploitation of waveguides with the standing torsional Alfvén oscillations. Results: It is found that the frequency of the standing Alfvén oscillation increases as the stratification of the plasma increases. The ratio of the periods of the fundamental modeand the first overtone is also found to change as the stratification of the plasma increases. Further, the eigenfunctions of the higher overtones of the standing oscillations are found to experience a shift of their anti-nodes. The influence of a dynamic plasma on the amplitudes of the mode is also investigated. The amplitude of the torsional Alfvén mode is found to increase as the plasma within the coronal loop experiences cooling

Soft x ray properties of the Geminga pulsar

The ROSAT soft x ray spectrum and pulse profile of the Geminga pulsar are analyzed and interpreted in terms of thermal emission from the surface of the neutron star. The x ray spectrum appears to consist of two blackbody components with T(sub 1) = (5.2 +/- 1.0) x 10 (exp 5) K and T(sub 2) approximately 3 x 10(exp 6) K, respectively. The inferred ratio of surface areas, A(sub 2)/A(sub 1), is approximately 3 x 10(exp -5). Both components are highly modulated at the pulsar rotation period, but the harder x ray pulse is narrower, and leads the main (soft) x ray pulse by about 105 deg of phase. The soft x ray component is interpreted as photospheric cooling of much of the neutron star's surface area, while the small, hot region could be part of the much smaller polar cap heated by energetic particles flowing inward from the magnetospheric accelerator which is responsible for the production of Geminga's gamma rays. Geminga's gamma ray emission is consistent with outer-magnetosphere accelerator models for highly inclined dipoles. These predict the beaming of energetic gamma rays close enough to the star to give copious e(+/-) production in the stellar magnetic field and a large circumstellar pair density from pair inflow toward the surface. These pairs may quench radio emission, and also reflect most of the hard polar cap x rays back to the stellar surface by cyclotron resonance scattering. They are then reemitted from that much larger area at the lower temperature T(sub 1). The single-peaked nature of the x ray pulse and its energy-dependent phase suggest an off-center dipole geometry for the surface magnetic field. Under the assumption that the soft x ray emission comes from the full surface of a neutron star of radius R = 10 km, a distance estimate of (150-400) pc is derived. This range is consistent with the fit interstellar column density of (1.5 +/- 0.5) x 10(exp 20) cm(exp -2). Distances less than 150 pc are probably ruled out both by the lower limit on the column density, and also by the requirement that the Rayleigh-Jeans extrapolation of the soft x ray spectrum not exceed the observed blue flux of the faint optical counterpart. This distance estimate implies that Geminga's efficiency for converting spindown power into gamma-rays is near unity, and that there may be significant beaming of the gamma rays as well. These results tend to bolster the prospect that most of the unidentified high-energy gamma ray sources in the Galactic plane are pulsars, some of which may be radio quiet