MHD surface waves in high- and low-beta plasmas. Part 1. Normal-mode solutions

1989 ◽  
Vol 42 (1) ◽  
pp. 75-89 ◽  
Author(s):  
Z. E. Musielak ◽  
S. T. Suess
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Normal Mode ◽  
General Structure ◽  
Normal Modes ◽  
Resonant Absorption ◽  
Normal Surface ◽  
Phase Mixing ◽  
Cold Plasmas ◽  
The Waves

Since the first paper by Barston (1964) on electrostatic oscillations in inhomogeneous cold plasmas, it has been commonly accepted that all finite layers with a continuous profile in pressure, density and magnetic field cannot support normal surface waves but instead the waves always decay through phase mixing (also called resonant absorption). Here we reanalyse the problem by studying a compressible current sheet of a general structure with rotation of the magnetic field included. We find that all inhomogeneous layers considered in the high-β plasma limit do not support normal modes. However, in the limit of a low-β plasma there are some cases when normal-mode solutions are recovered. The latter means that the process of resonant absorption is not common for all inhomogeneous layers.

Resistive Alfvén normal modes in a non-uniform plasma

1985 ◽  
Vol 34 (2) ◽  
pp. 259-270 ◽  
Author(s):  
G. Einaudi ◽  
Y. Mok
Keyword(s):  
Magnetic Field ◽  
Normal Mode ◽  
Uniform Magnetic Field ◽  
Normal Modes ◽  
Mhd Equations ◽  
Damping Rate ◽  
Uniform Plasma

Resistive normal-mode solutions of the MHD equations are found numerically in a smooth, non-uniform, magnetic field. The (α, S) boundary within which normal-mode solutions exist is explicitly computed, where α is the normalized wavenumber and Sthe Lundquist number. As an extension of our previous analytic results (Mok & Einaudi 1985), the damping rate of these modes is computed to a higher accuracy, and is found to have an a + bS−1/3 dependence, where a and b are independent of S.

scholarly journals Normal-mode-based theory of collisionless plasma waves

2019 ◽  
Vol 85 (4) ◽  
Author(s):  
J. J. Ramos
Keyword(s):  
Magnetic Field ◽  
Normal Mode ◽  
Initial Conditions ◽  
Hermitian Operator ◽  
Collisionless Plasma ◽  
Normal Modes ◽  
Propagation Direction ◽  
Linear Wave ◽  
Temperature Plasma ◽  
Direction Parallel

The Van Kampen normal-mode method is applied in a comprehensive study of the linear wave perturbations of a homogeneous, magnetized and finite-temperature plasma, described by the collisionless Vlasov–Maxwell system in its non-relativistic version. The analysis considers a stable, Maxwellian background, but is otherwise completely general in that it allows for arbitrary wave propagation direction relative to the equilibrium magnetic field, multiple plasma species and general polarization states of the perturbed electromagnetic fields. A convenient formulation is introduced whereby the generator of the time advance is a Hermitian operator, analogous to the Hamiltonian in the Schrödinger equation of quantum mechanics. This guarantees a real frequency spectrum and complete bases of normal modes. Expansions in these normal-mode bases yield immediately the solutions of initial-value problems for general initial conditions. With standard initial conditions and propagation direction parallel to the equilibrium magnetic field, all the familiar results obtained following Landau’s Laplace transform approach are recovered. Considering such parallel propagation, the present work shows also explicitly and provides an example of how to construct special initial conditions that result in different, damped but otherwise arbitrarily prescribed time variations of the macroscopic variables. The known dispersion relations for perpendicular propagation are also recovered.

Propagation in slowly varying waveguides

1968 ◽  
Vol 302 (1471) ◽  
pp. 555-576 ◽  
Keyword(s):  
Variational Principle ◽  
Order Approximation ◽  
General Structure ◽  
Normal Modes ◽  
General System ◽  
Higher Order ◽  
Necessary Condition ◽  
Linear Partial Differential Equations ◽  
Lateral Boundary Conditions ◽  
The Waves

The W. K. B. approximation is applied to a general system of linear partial differential equations which may be derived from a variational principle of a certain type. The theory describes slowly varying wavetrains, with the oscillation locally in one of the normal modes of a waveguide of quite general structure. The governing equations need not be hyperbolic; the wavelike character of the solution may be imparted by the lateral boundary conditions in the waveguide (e. g. surface waves on water). Variations in amplitude of the waves along rays are governed by conservation of an adiabatic invariant, as suggested by Whitham’s averaged variational principle. Higher order approximations may be constructed and the equations integrated b y quadrature. The averaged variational principle is also derived directly, in a manner applicable also to general nonlinear systems. It is shown to be a necessary condition governing the lowest order approximation for an asymptotic expansion of the same type as that for linear systems, provided such an expansion exists. However, it is not clear from this second approach how to construct higher order approximations.

Transverse surface waves in magneto-elasticity

1966 ◽  
Vol 62 (3) ◽  
pp. 541-545 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Waves ◽  
Elastic Medium ◽  
Uniform Magnetic Field ◽  
Shear Waves ◽  
Plane Shear ◽  
Electrically Conducting ◽  
Velocity Of Propagation

AbstractIt has been shown that uncoupled surface waves of SH type can be propagated without any dispersion in an electrically conducting semi-infinite elastic medium provided a uniform magnetic field acts non-aligned to the direction of wave propagation. In general, the velocity of propagation will be slightly greater than that of plane shear waves in the medium.

Acoustic Green's Function Approximations

1998 ◽  
Vol 06 (04) ◽  
pp. 435-452 ◽  
Author(s):  
Robert P. Gilbert ◽  
Zhongyan Lin ◽  
Klaus Hackl
Keyword(s):  
Inverse Problem ◽  
Normal Mode ◽  
Eigenvalue Problems ◽  
Normal Modes ◽  
Modal Parameters ◽  
Mindlin Plate ◽  
Ocean Bottom ◽  
Hankel Transformation ◽  
Poroelastic Materials ◽  
Function Approximations

Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.

Parametric excitation of magnetoacoustic waves by a pump magnetic field in a high-β plasma

1977 ◽  
Vol 17 (1) ◽  
pp. 93-103 ◽  
Author(s):  
N. F. Cramer
Keyword(s):  
Magnetic Field ◽  
Parametric Excitation ◽  
Acoustic Waves ◽  
Magnetic Pressure ◽  
Gas Pressure ◽  
Alfven Wave ◽  
Fast Wave ◽  
Magnetoacoustic Waves ◽  
Background Magnetic Field ◽  
The Waves

The parametric excitation of slow, intermediate (Alfvén) and fast magneto-acoustic waves by a modulated spatially non-uniform magnetic field in a plasma with a finite ratio of gas pressure to magnetic pressure is considered. The waves are excited in pairs, either pairs of the same mode, or a pair of different modes. The growth rates of the instabilities are calculated and compared with the known result for the Alfvén wave in a zero gas pressure plasma. The only waves that are found not to be excited are the slow plus fast wave pair, and the intermediate plus slow or fast wave pair (unless the waves have a component of propagation direction perpendicular to both the background magnetic field and the direction of non-uniformity of the field).

Effect of magnetic field on parametrically driven surface waves

2006 ◽  
Vol 463 (2079) ◽  
pp. 711-722 ◽  
Author(s):  
Supriyo Paul ◽  
Krishna Kumar
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Liquid Metals ◽  
Tricritical Point ◽  
Thin Layers ◽  
Vertical Magnetic Field ◽  
Harmonic Solution ◽  
Chandrasekhar Number ◽  
The Magnetic Field ◽  
Primary Instability

Stability analysis of parametrically driven surface waves in liquid metals in the presence of a uniform vertical magnetic field is presented. Floquet analysis gives various subharmonic and harmonic instability zones. The magnetic field stabilizes the onset of parametrically excited surface waves. The minima of all the instability zones are raised by a different amount as the Chandrasekhar number is raised. The increase in the magnetic field leads to a series of bicritical points at a primary instability in thin layers of a liquid metal. The bicritical points involve one subharmonic and another harmonic solution of different wavenumbers. A tricritical point may also be triggered as a primary instability by tuning the magnetic field.

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

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