Inhomogeneous Beam Research Articles

Physical Interpretation of the WKB or Eikonal Approximation for Waves and Vibrations in Inhomogeneous Beams and Plates

The WKB or eikonal approximation is derived for flexural waves of constant frequency in inhomogeneous Euler-Bernoulli beams and plates and for waves in inhomogeneous Timoshenko beams. The derivation is based on the assumption of negligible partial reflection of waves and holds when the relative variation of parameters characterizing the medium is small over distances comparable to one wavelength. The approximate relations governing the variation of wave amplitude from point to point are derived from the requirement that no energy be lost from the wave. The extension of this technique to include evanescent waves as well as propagating waves is also discussed. As an application of the method, some simple results are given for the modal frequencies and normal modes of a cantilevered inhomogeneous Euler-Bernoulli beam. A general development of the eikonal method applicable to a wide class of mechanical systems is also given, which establishes the consistency of the energy-conservation technique with the results obtained by taking the eikonal approximation as the zeroth-order approximation to a series.

Excitation of waves in magnetoactive plasma by a strongly “spread” inhomogeneous electron beam

The stability of beam-plasma systems is studied assuming that the distribution of beam-electrons in the velocity space corresponds to the first period of the quasilinear relaxation. The necessary condition is derived for the usual quasilinear equations to be applicable within the whole period of quasilinear relaxation.

Stability of inhomogeneous relativistic electron beams

The authors investigate the stability of a space-bounded relativistic beam of electrons accelerated by a nonuniform electric field under conditions where the transverse dimension of the beam is significantly greater than the Debye radius and a collective approach is necessary for describing small oscillations. For currents exceeding some critical value, there may develop in such a system an instability analogous to the ‘slipping’ instability of non-relativistic electron beams with a nonuniform velocity profile. The instability conditions are established and the instability growth rates calculated both in the absence and in the presence of a strong longitudinal magnetic field. The energy spread of the electrons has a stabilizing effect on the beam instability in question. In the Annex it is shown that the slipping instability is characteristic of any non-uniform plasma flow. In particular, it may develop in an isotropic plasma if the flow velocities exceed the thermal velocity of the ions.

Interaction of inhomogeneous beam with surface waves in magnetoactive plasma

The present work investigates the excitation of potential surface oscillations on the plane boundary of the magnetoactive plasma by an inhomogeneous hot beam of charged particles. Expressions for the growth rates have been obtained.

Stability of an inhomogeneous electron beam

Stability of an inhomogeneous electron beam

Nonlinear effects and the transformation of wave energy in an inhomogeneous plasma

This paper discusses the problem: under what conditions does the quasilinear transformation of waves in plasma with an inhomogeneous beam remain a dominant effect if the nonlinear interaction of waves is respected. It is shown that in the region of densitiesω p 2 ω B 2 the nonlinear interaction between the high-frequency and the newly excited waves can already affect the initial stage of the process and can result in the establishment of the Rayleigh-Jeans distribution for the two groups of waves. If, on the other hand, the low-frequency waves grow first with a quasilinear increment, the nonlinear transformation of energy inside a group of low-frequency waves is again apt to affect substantially their final amplitude and thus also the total amount of energy that can be transformed into those waves. The conditions under which a particular nonlinear effect predominates are derived for various characteristic values of the density of a cold plasma.

Trapping of electrons in a spatially inhomogeneous laser beam

Measurements are reported of the energy of electrons ejected by multiphoton ionization of N2 and Ar. Electrons with energy > 160 eV were found and the angular distribution using plane polarized light was anisotropic, at least for low electron energies. The data is interpreted in terms of multiphoton ionization followed by acceleration of free electrons by an EM field gradient force.

On two stream instability of radial inhomogeneous electron beams

On two stream instability of radial inhomogeneous electron beams

Bending Vibrations of Inhomogeneous Beams and Systems of Beams

This paper is concerned mainly with the vibrations of point-driven beams that have sudden discontinuities in material, cross section, etc. In such structures, an initially excited wave, such as a bending wave, will be partially reflected; but, there may also be a transformation into other wave types, such as longitudinal or torsional waves. It is shown how the impedance, the average transmitted power, and the propagation constant of a beam with one or more discontinuities can be calculated; the results are compared with experimental data. It is possible to extend the results to systems of beams such as grillages.