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

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

On the precession of the isolated pulsar PSR B1828-11

Analysis of both pulse timing and pulse shape variations of the isolated pulsar PSR B1828-11 shows highly correlated and strong Fourier power at periods \~ 1000, 500, and 250 d (Stairs et al. 2000). The only description based on a free precession of star's rigid crust coupled to the magnetic dipole torque, explains the 500-component, as the fundamental Fourier frequency, with its harmonic 250-component (Link & Epstein 2001). In this paper, we show that if the dipole moment vector varies with time with a period nearly equal to the longest (probably fundamental) observed period (~ 1000 d), the dipole torque may produce the all other harmonics. We also find the second and fourth harmonics at periods ~ 500 and 250 d are dominant for small wobble angle ~ 3^o and large field's inclination angle 89^o.Comment: 11 pages, discussion is change

Propagation of solitons of the Derivative Nonlinear Schrodinger equation in a plasma with fluctuating density

The propagation of quasi-parallel nonlinear small-amplitude magnetohydrodynamic waves in a cold Hall plasma with fluctuating density is studied. The density is assumed to be a homogeneous random function of one spatial variable. The modified Derivative Nonlinear Schrodinger equation (DNLS) is derived with the use of the mean waveform method developed by Gurevich, Jeffrey, and Pelinovsky [Wave Motion 17, 287 (1993)], which is the generalization of the reductive perturbation method for nonlinear waves propagating in random media. This equation differs from the standard DNLS equation by one additional term describing the interaction of nonlinear waves with random density fluctuations. As an example of the use of the modified DNLS equation, the quasi-adiabatic evolution of a one-parametric DNLS soliton propagating through a plasma with fluctuating density is studied

Freak waves in laboratory and space plasmas

Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed. Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show the possibility of generation of freak ion-acoustic waves due to the modulational instability. The second wave mode is the Alfv,n wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation using the linearized DNLS equation shows that the generation of freak Alfv,n waves is possible due to linear dispersive focusing. The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfv,n waves

Impulse-Based Hybrid Motion Control

The impulse-based discrete feedback control has been proposed in previous work for the second-order motion systems with damping uncertainties. The sate-dependent discrete impulse action takes place at zero crossing of one of both states, either relative position or velocity. In this paper, the proposed control method is extended to a general hybrid motion control form. We are using the paradigm of hybrid system modeling while explicitly specifying the state trajectories each time the continuous system state hits the guards that triggers impulsive control actions. The conditions for a stable convergence to zero equilibrium are derived in relation to the control parameters, while requiring only the upper bound of damping uncertainties to be known. Numerical examples are shown for an underdamped closed-loop dynamics with oscillating transients, an upper bounded time-varying positive system damping, and system with an additional Coulomb friction damping.Comment: 6 pages, 4 figures, IEEE conferenc