Showing papers on "Nonlinear resonance published in 1977"

Nonlinear plasma waves excited near resonance

Abstract: The nonlinear resonant response of a uniform plasma to an external plane‐wave field is formulated in terms of the mismatch Δnl between the driving frequency and the time‐dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δnl and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations.

The Passage of Weakly Coupled Nonlinear Oscillators through Internal Resonance

Abstract: An asymptotic procedure for deriving equations governing the passage of a weakly coupled nonlinear system of oscillators is discussed The procedure avoids an inner-outer-matching technique and is valid when the small coupling and detuning parameters are arbitrary Resonance is permitted to occur at one or several instances of time or to last for a finite length of time Numerical results are discussed

Nonlinear Resonances in the Attitude Motion of Dual-Spin Spacecraft

Abstract: The attitude motion of a class of dual-spin spacecraft which exhibit nonlinear resonances during the despin process is studied. The model adopted consists of a rigid slightly asymmetric rotor and a rigid symmetric platform that is dynamically unbalanced with respect to the rotor's axis of maximum moment of inertia. No external torques are considered. Attitude equations are derived in an unconventional form that allows easy incorporation of the integral of angular momentum. The presence of a nonlinear resonance is shown to depend on the coexistence of rotor asymmetry and platform dynamic unbalance. An approximate solution for the attitude motion near resonance is obtained for the case of zero despin-motor torque by using the generalized method of averaging. The salient characteristics of the near-resonant motion are obtained from integrals of the averaged equations.

A model explaining type IV continuum bursts by coherent nonlinear interaction of Bernstein waves

Abstract: The investigated model supposes Bernstein waves emerging from Harris instabilities at a definite coronal level. The nonlinear process is considered for a higher region, where the quasimonochromatic waves forming the primary spectrum are reflected. Spatial dispersion takes place corresponding to the decreasing magnetic field. Thus each quasimonochromatic wave can be treated separately. According to the nonlinear resonance condition there result electromagnetic waves of twice the primary frequency, the power density of which is calculated. Assuming a coherence time of 480 periods and an oscillation velocity of the electrons of 10-3 times the thermal velocity the effective radiation temperature 1011 K of a type IVmA-burst is obtained at about 180 MHz, if the range of the nonlinear interaction is about 3.9 km long. In the discussion the interpretation of occurring zebra patterns is treated.

On the Internal Resonance in a Nonlinear Two-Degree-of-Freedom System : Forced Vibrations near the Higher Resonance Point When the Natural Frequencies Are in the Ratio 1:2

Abstract: A two-degree-of-freedom vibrating system tuned to internal resonance with the higher natural frequency twice the lower natural frequency, having nonlinear characteristic of second and third order polynomials of the displacements, subjected to harmonic excitation, is taken up. Steady forced vibrations are investigated in the vicinity of the higher resonance point of the system. Through the theoretical analysis it is found that the system has two types of resonances depending on the excitation frequency, namely one in which only harmonic occurs, and the other in which sub-harmonic with the frequency half the excitation frequency occurs strongly in addition to harmonic. Also found is the phenomenon that almost periodic motions occur in a certain range of the excitation frequencies. It is shown that the results of the theoretical analysis agree with those of an analog computer.

Numerical Investigation of Nonlinear Wave Interaction in a Two-Dimensional Boundary Layer.

Abstract: : A spectral method is used to solve for the unsteady, two-dimensional flow over a flat plate in the Reynolds number range of transition. The physical problem considered is the propagation of large amplitude (nonlinear) Tollmien-Schlichting waves in a boundary layer. The solutions are generally in qualitative agreement with nonlinear stability theories in that: (1) nonlinear effects can be destabilizing, (2) the growth/decay behavior of the primary mode is changed only slightly by nonlinear effects, and (3) the second temporal harmonic is usually a second spatial harmonic. There are, however, regions in the flow in which both (1) and (3) are not true. Details of the solution in such a region are given to illustrate the complex nonlinear wave interactions possible in a boundary layer. (Author)

Slowly varying nonlinear waves in a cold plasma stream

Abstract: This paper is concerned with the propagation of one-dimensional nonlinear waves in the relatively simple physical situation of a cold, collisionless, field-free, slightly non-uniform plasma comprising a stream of oscillating electrons and a stream of ions whose oscillatory motion is neglected The waves are considered as a small perturbation from the corresponding uniform periodic solution The equations which govern the slow variation of certain gross quantities associated with the waves are obtained by applying the ‘two-timing’ technique to the basic plasma equations The properties of the resulting modulation equations are discussed and an exact solution of an initial value problem for them is given

High-resolution polarization spectroscopy in the 10 μ region

Abstract: A report is given of the experimental results obtained using a CO2-laser saturation spectrometer with an external absorption cell, mounted between two polarizers, the saturating and probing beams having different polarizations. The molecules SF6, NH3, CF2Cl2, and BCl3 were investigated and the nonlinear resonance corresponding to transitions with Δ J=0,±1 was observed.

Nonlinear wave‐wave interactions without resonance conditions

Abstract: Third-order nonlinear wave-wave interactions are possible without any resonance conditions which link frequencies and wave-vectors of the interacting waves. Usually, but not always, interactions without resonances result in a mere frequency shift. Some models, however, involve changes in the amplitudes as well. This is illustrated on several examples of the self-modulation of one wave, firstly in general terms, then for a model equation in a dissipative medium, and finally for an electrostatic wave in a medium with various nonlinear conductivities. Depending upon the medium, three cases are possible: either the wave amplitude does not change, or the wave dissipates its energy into the medium, or the medium feeds an explosive instability.

Problem of reproducibility of the output frequency of a CO2/OsO4 laser

Abstract: Two frequency-stabilized CO2/OsO4 lasers were used in an investigation of the behavior of the peak of a narrow nonlinear resonance in the spectrum of the 192OsO4 molecule. The investigation was carried out in a wide range of laser radiation intensities and OsO4 pressures in an external absorption cell. There were no power or collisional shifts of the molecular transition frequency to within ~2×10–11.

Nonlinear effects in generation of optical and acoustic phonons by infrared resonance radiation

Abstract: An analysis is made of the possibility of observation of nonlinear optical resonance effects in the lattice absorption range of crystals. Results are derived from the theory of nonlinear interaction of strong resonance radiation with dipole-active lattice vibrations, resulting in the appearance of nonequilibrium optical and acoustic phonons. Steady-state saturation of the lattice absorption and generation of acoustic phonons, occurring at infrared resonance field intensities of the order of 103 W/cm2, are considered. It is shown that these effects can conveniently be detected experimentally by active spectroscopy of light scattering.