Least squares DOA estimation with an informed phase unwrapping and full bandwidth robustness

The weighted least-squares (WLS) direction-of-arrival estimator that minimizes an error based on interchannel phase differences is both computationally simple and flexible. However, the approach has several limitations, including an inability to cope with spatial aliasing and a sensitivity to phase wrapping. The recently proposed phase wrapping robust (PWR)-WLS estimator addresses the latter of these issues, but requires solving a nonconvex optimization problem. In this contribution, we focus on both of the described shortcomings. First, a conceptually simpler alternative to PWR is presented that performs comparably given a good initial estimate. This newly proposed method relies on an unwrapping of the phase differences vector. Secondly, it is demonstrated that all microphone pairs can be utilized at all frequencies with both estimators. When incorporating information from other frequency bins, this permits a localization above the spatial aliasing frequency of the array. Experimental results show that a considerable performance improvement is possible, particularly for arrays with a large microphone spacing

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

Nonlinear theory of resonant slow waves in anisotropic and dispersive plasmas

The solar corona is a typical example of a plasma with strongly anisotropic transport processes. The main dissipative mechanisms in the solar corona acting on slow magnetoacoustic waves are the anisotropic thermal conductivity and viscosity [Ballai et al., Phys. Plasmas 5, 252 (1998)] developed the nonlinear theory of driven slow resonant waves in such a regime. In the present paper the nonlinear behavior of driven magnetohydrodynamic waves in the slow dissipative layer in plasmas with strongly anisotropic viscosity and thermal conductivity is expanded by considering dispersive effects due to Hall currents. The nonlinear governing equation describing the dynamics of nonlinear resonant slow waves is supplemented by a term which describes nonlinear dispersion and is of the same order of magnitude as nonlinearity and dissipation. The connection formulas are found to be similar to their nondispersive counterparts

Axisymmetric Scattering of p Modes by Thin Magnetic Tubes

We examine the scattering of acoustic p-mode waves from a thin magnetic fibril embedded in a gravitationally stratified atmosphere. The scattering is mediated through the excitation of slow sausage waves on the magnetic tube, and only the scattering of the monopole component of the wavefield is considered. Since such tube waves are not confined by the acoustic cavity and may freely propagate along the field lines removing energy from the acoustic wavefield, the excitation of fibril oscillations is a source of acoustic wave absorption as well as scattering. We compute the mode mixing that is achieved and the absorption coefficients and phase shifts. We find that for thin tubes the mode mixing is weak and the absorption coefficient is small and is a smooth function of frequency over the physically relevant band of observed frequencies. The prominent absorption resonances seen in previous studies of unstratified tubes are absent. Despite the relatively small absorption, the phase shift induced can be surprisingly large, reaching values as high as 15 degree for f modes. Further, the phase shift can be positive or negative depending on the incident mode order and the frequency.Comment: 39 pages, 6 figure

Resonant Absorption of Axisymmetric Modes in Twisted Magnetic Flux Tubes

It has been shown recently that magnetic twist and axisymmetric MHD modes are ubiquitous in the solar atmosphere, and therefore the study of resonant absorption for these modes has become a pressing issue because it can have important consequences for heating magnetic flux tubes in the solar atmosphere and the observed damping. In this investigation, for the first time, we calculate the damping rate for axisymmetric MHD waves in weakly twisted magnetic flux tubes. Our aim is to investigate the impact of resonant damping of these modes for solar atmospheric conditions. This analytical study is based on an idealized configuration of a straight magnetic flux tube with a weak magnetic twist inside as well as outside the tube. By implementing the conservation laws derived by Sakurai et al. and the analytic solutions for weakly twisted flux tubes obtained recently by Giagkiozis et al. we derive a dispersion relation for resonantly damped axisymmetric modes in the spectrum of the Alfvén continuum. We also obtain an insightful analytical expression for the damping rate in the long wavelength limit. Furthermore, it is shown that both the longitudinal magnetic field and the density, which are allowed to vary continuously in the inhomogeneous layer, have a significant impact on the damping time. Given the conditions in the solar atmosphere, resonantly damped axisymmetric modes are highly likely to be ubiquitous and play an important role in energy dissipation. We also suggest that, given the character of these waves, it is likely that they have already been observed in the guise of Alfvén waves

ASTRONOMY AND ASTROPHYSICS Random driven fast waves in coronal loops I. Without coupling to Alfvén waves

Abstract. In this paper we study the time evolution of fast MHD waves in a coronal loop driven by footpoint motions in linear ideal MHD. We restrict the analysis to footpoint motions polarized normal to the magnetic flux surfaces such that the fast waves are driven directly. By supposing the azimuthal wave number ky to be zero, the fast waves are decoupled from the Alfvén waves. As a first step to real stochastic driving, we consider the loop to be driven by a train of identical pulses with random time intervals in between. The solution is written as a superposition of eigenmodes whose excitation is determined by the time dependence of the footpoint motion through a convolution and by the spatial dependence of the footpoint motion through a scalar product. An important result from the simulations is that the amount of kinetic energy associated with the body modes is much larger than the amount corresponding to the leaky modes. This means that most of the input energy is stored within the loop. For ky /= 0, body modes can resonantly couple to Alfvén waves at certain magnetic surfaces and hence the energy of the body modes can then be dissipated around the resonant magnetic surfaces. Using a gamma distribution for the time intervals between the successive pulses, we analytically derive a relation between the mean value of the kinetic energy contribution of each eigenmode, the eigenfrequency, the number of pulses and the width of the pulses. The larger the variance of the distribution, the less the power spectrum reveals fine structure, peaks around certain preferred frequencies. The analytical results confirm the output from the numerical simulations