Finite Frequency Effects Research Articles

Multipath propagation in a deep ocean including modified rays near grazing incidence at the bottom

A ray description of acoustic propagation between communicators submerged in a deep ocean may include rays that almost graze the interface between water and sea‐floor sediment. For example, this can occur in range‐independent environments where the squared refractive indices in water and in sediment decrease linearly with depth. Four pairs of such rays connect communicators near the surface and separated in range by at most 4(H/γ)1/2, where H is the ocean depth and γ is the gradient of square refractive index in water. One ray in each pair is entirely waterborne; the other intercepts the sediment and grazes a caustic. We present a uniform asymptotic analysis of these ray pairs that incorporates diffractive finite frequency effects as in the modified ray theory of Murphy and Davis. These effects include the appearance of a frequency‐dependent caustic and a modification of the usual π/2 phase shift experienced by the classical ray that intercepts the sediment. Comparison of these results with normal mode calculations is excellent. Vector diagrams (after Bartberger) also identify mode groups corresponding to the modified rays.

Finite frequency effects on magnetosonic wave mode conversion

The theory of the damping of the magnetosonic wave due to resonance mode conversion is extended to include finite omega / Omega i effects. Mode conversion is limited by the evanescence of the magnetosonic wave between its turning point and the Alfven resonance. The finite frequency effects change the damping by modifying the wave fields at resonance and their rate of evanescence between the magnetosonic wave turning point and the Alfven resonance.

Diamagnetic drift frequency effects on Tokamak ballooning stability

The stabilizing effect of finite ion diamagnetic drift frequency on ballooning modes in realistic Tokamak geometry is investigated. The inclusion of temperature gradient effects can significantly enhance the stability of a Tokamak with broad mass density profiles.

Dynamic correlations in Fermi fluids

We consider dynamic correlations in normal liquid $^{3}\mathrm{He}$ following the kinetic theory approach introduced in earlier work. The connection between the kinetic theory formalism and the Landau and polarization potential theories is discussed in detail and the approximations implicit in the latter approach are pointed out. We present a phenomenological approach to the dynamic memory function which incorporates finite frequency and wave-vector effects. This form of the dynamic kernel is used to evaluate the shear viscosity, including contributions from nonlocal effects. Estimates of these contributions indicate that they are non-negligible. The consequences of our method and its future application to the evaluation of collisional broadening of collective modes observed in neutron scattering experiments are discussed.

Alfvén Resonance Effects on Magnetosonic Modes in Large Tokamaks

The theory of Alfv\'en resonance effects on the wave modes of a tokamak is extended beyond the incompressible magnetohydrodynamic model to include finite-($\frac{\ensuremath{\omega}}{{\ensuremath{\Omega}}_{i}}$) effects and compressibility. The discrete spectrum of compressional Alfv\'en waves consists of a sequence of frequencies with finite damping decrements resulting from the Alfv\'en resonance. The finite-frequency effects can cause the damping to almost vanish. This permits Alfv\'en resonance heating via high-$Q$ eigenmodes in large tokamaks.

Differential equations for long-period gravity waves on fluid of rapidly varying depth

The conventional long-wave equations for waves propagating over fluid of variable depth depend for their formal derivation on a Taylor series expansion of the velocity potential about the bottom. The expansion, however, is not possible if the depth is not an analytic function of the horizontal co-ordinates and it is a necessary condition for its rapid convergence that the depth is also slowly varying. We show that if in the case of two-dimensional motions the undisturbed fluid is first mapped conformally onto a uniform strip, before the Taylor expansion is made, the analytic condition is removed and the approximations implied in the lowest-order equations are much improved.In the limit of infinitesimal waves of very long period, consideration of the form of the error suggests that by modifying the coefficients of the reformulated equation we may find an equation exact for arbitrary depth profiles. We are thus able to calculate the reflexion coefficients for long-period waves incident on a step change in depth and a half-depth barrier. The forms of the coefficients of the exact equation are not simple; however, for these particular cases, comparison with the coefficients of the reformulated long-wave equation suggests that in most cases the latter may be adequate. This opens up the possibility of beginning to study finite amplitude and frequency effects on regions of rapidly varying depth.

Large-amplitude hydromagnetic waves

Several aspects of the theory of large-amplitude hydromagnetic waves and their behavior in the interplanetary medium are examined. The characteristic modes of the full (i.e., nonlinearized) MHD equations and their modification by collisionless and finite-frequency effects are considered. Special attention is paid to the transverse Alfven mode, which is undamped and characterized by strictly constant pressure, density, and B; this seems to be the predominant propagating fluctuation at 1 AU. It is shown that its propagation in the small-wavelength (WKB) approximation is essentially identical to that of the small-amplitude Alfven wave of linearized theory. It is also suggested that its presence at 1 AU may provide a natural explanation of the observed power anisotropy of the fluctuations. A second-order analysis is used to study fluctuations that are not characteristic modes. It is found that for a small range of propagation directions, and subject to third-order effects, a finite-amplitude wave can exist that is linearly polarized with delta B perpendicular to both B sub zero and k; such a wave can damp nonlinearly.

Propagation of Alfvén waves in ion-sound turbulent plasma

The propagation of low-frequency, large-scale (compared to the ion Larmor frequency Ωi and radius Ri), oblique Alfvén waves in a turbulent plasma is investigated in the framework of kinetic theory. The turbulent field is the statistical average of one-dimensional ion-sound waves of very high frequency and short wavelength (ω ≫ ΩiRe≫ λ). In the absence of resonant particle effects, and to first order in a finite Larmor radius expansion, it is shown that the turbulence can lead either to spatial diffusion (damping) or anti-diffusion (growth), with Bohm scaling, of the low frequency wave. Finite Larmor radius and frequency effects in the propagation of oblique Alfvén waves are simultaneously obtained for arbitrary β plasma; the results can easily be generalized, merely by deforming certain integration contours, to obtain the corresponding Landau decrement.

Faradaic reactions not governed by electrode collision frequencies

Summary It is shown theoretically that at least one class of faradaic reactions exists for which formal exchange currents are characterizable and for which no obvious necessity of rate governed by collision frequency with the electrode is obvious. This implies that upper limits to the rate constants for faradaic processes proposed by previous workers need not generally exist. It is suggested that the effect of finite collision frequency should manifest itself in the mass transfer impedance rather than the charge transfer impedance of the faradaic process.

Hydromagnetic Waves in a Plasma with Finite Larmor Radius

The effect of finite Larmor radius and Larmor frequency on hydromagnetic waves in a plasma is investigated. It is concluded that the finite Larmor radius has considerable influence. A uniform rotation is also included in view of its astrophysical importance.