Nonresonant Wave Research Articles

On the wave excitation and the formation of recirculation eddies in an axisymmetric flow of uniformly rotating fluids

The inertial waves excited in a uniformly rotating fluid passing through a long circular tube are studied numerically. The waves are excited either by a local deformation of the tube wall or by an obstacle located on the tube axis. When the flow is subcritical, i.e. when the phase and group velocity of the fastest wave mode in their long-wave limit are larger than the incoming axial flow velocity, the excited waves propagate upstream of the excited position. The non-resonant waves have many linear aspects, including the upstream-advancing speed of the wave and the coexisting lee wavelength. When the flow is critical (resonant), i.e. when the long-wave velocity is nearly equal to the axial flow velocity, the large-amplitude waves are resonantly excited. The time development of these waves is described well by the equation derived by Grimshaw & Yi (1993). The integro-differential equation, which describes the strongly nonlinear waves until the axial flow reversal occurs, can predict the onset time and position of the recirculation eddies observed in the solutions of the Navier-Stokes equations. The numerical results and the theory both show that the flow reversal most probably occurs on the tube axis and also when the waves are excited by a contraction of the tube wall. The structure of the recirculation eddies obtained in the solutions of the Navier-Stokes equations at Re = 105 is similar to the axisymmetric or ‘bubble-type’ breakdown observed in the experiments of the vortex-breakdown which used a different non-uniform (Burgers-type) rotation. In uniformly rotating fluids the formation of the recirculation eddies has not been observed in the previous numerical studies of vortex breakdown where a straight tube was used and thus the inertial waves were not excited. This shows that the generation of the recirculation eddies in this study is genuinely explained by the topographically excited large-amplitude inertial ‘waves’ and not by other ‘instability’ mechanisms. Since the wave cannot be excited in a straight tube even in the non-uniformly rotating flows, the generation mechanism of the recirculation eddies in this study is different from the previous numerical studies for the vortex breakdown. The occurrence of the recirculation eddies depends not only on the Froude number and the strength of the excitation source but also on the Reynolds number since the wave amplitude generally decreases by the viscous effects. Some relations to the experiments of vortex breakdown, which have been exclusively done for non-uniformly rotating fluids but done in a ‘non-uniform tube’, are discussed. The flow states, which are classified as supercritical, subcritical or critical in hydraulic terminology, changes along the flow when the upstream flow is near resonant conditions and a non-uniform tube is used.

Investigation of Langmuir turbulence excited by a relativistic electron beam in a magnetic field

The Thomson scattering technique has been employed for the observation of turbulent waves excited by a relativistic electron beam. The frequency and k-spectra of the Langmuir waves are measured both in the excited and damped regions. The waves interact directly with the beam electrons inside a narrow section of k-sppace amid the region occupied by the non-resonant waves, which concentrate near k ∼ ω pe/ c. Both resonant and non-resonant waves hold equal (to within an order of magnitude) amounts of energy. Incoherent scattering of the second harmonic of a Nd : glass laser is used to measure the time history of the electron distribution function including the super thermal tails. The typical beam and plasma parameters are as follows: ( ne ∼ 10 15 cm −3, n b/ n e ∼ 10 −4, B = 1–4 T, t b = 100–200 ns). The peculiarity of these experiments is the presence of a strong magnetic field ( ω Be c/ ω pe V Te ⪢ 1, but cope ⪢ ω Be) which, together with plasma non-isothermality ( T e ⪢ T i), sets conditions typical for laboratory and space plasmas. At present, the processes under these conditions have not been adequately investigated, either experimentally or theoretically, especially for our case of developed Langmuir turbulence, when the spatial and temporal scales far exceed those for a single caviton. This work is centred on the study of developed Langmuir turbulence in a magnetized plasma.

Energy and number of quanta of nonresonant waves in nonstationary closed systems

Expressions for the energy density and number of quanta of nonresonant waves in nonstationary media are obtained. The system is supposed to be closed, and the nonstationarity is due to internal processes in it only. The general theorem connecting the characteristic scale of the slow change in time of the dielectric permittivity and the (nonlinear) dissipation rate in such kind of systems is proved. All calculations use the macroscopic approach based on general principles of the electrodynamics of continious media.

Beam-plasma instability excited by non-thermal electrons with arbitrary distribution function and comparison with electron-cyclotron master instability

An equation is derived for the growth rates of the beam-plasma instability excited by non-thermal electrons with arbitrary distribution function, and it is shown that the reactive instability does not depend on the assumption of a monoenergetic distribution. Hence the properties of electromagnetic waves are calculated for the hollow beam and loss-cone distribution. Hence the properties of electromagnetic waves are calculated for the hollow beam and loss-cone distribution functions. The general characteristics and structures of the growth rates are similar to the results for the monoenergetic distribution, but there are still some differences in the relation between the growth rates and the relevant parameters, such as the ambient parameter ωpe/Ωe, the angle of propagation θ and the pitch angle a. The main purpose of this paper is to compare the properties of the beam-plasma instability (reactive) and the electron-cyclotron maser instability (kinetic) under similar ambient conditions. The calculations show that both kinds of instabilities are easily excited at larger angles of propagation with respect to the ambient magnetic field, which means that both depend mainly on the free energy of the non-thermal electrons perpendicular to the magnetic field. The magnitudes of the growth rates of the two kinds of instabilities are comparable under the same ambient conditions. However, because the non-resonant wave—particle interaction is taken into consideration for the beam-plasma instability, which makes the resonant peaks broaden and connect with each other, the spectra of the beam-plasma instability are also more complicated than that of the maser instability, and the range of the angle of propagation of the growing waves in the non-resonant case is also larger than that in the resonant case.

Fractional photon model of three-photon mixing in the non-linear interaction process

In this paper, a fractional photon model is proposed by considering the photon-exchange interaction in the reverse process of the non-linear three-photon mixing interaction. The phase matching condition for various types of uniaxial crystals can be simplified and classified by this model with the consideration of the unequal fractional photon-exchange of the two generated waves in the reverse manner. This also leads to the explanation of observing the phase mismatch and output bandwidth of the resonant and non-resonant waves in a cavity. Finally, a quantitative approach to this model, with experimental results, is also demonstrated.

Spontaneous emission effects in nonlinear interactions of nonresonant waves with resonant plasma fluctuations

Spontaneous emission effects on propagation of nonresonant waves in plasmas in the presence of resonant fluctuations are studied. It is demonstrated that in closed plasma systems the number of nonresonant quanta is conserved as an adiabatic invariant. The conservation is due to the vanishing polarizational contribution that resulted from the symmetry of the system as well as to the balance of the direct nonlinear coupling and reverse absorption by particle collisions. Energy of the nonresonant waves as well as their amplitudes may vary with time even when the resonant field fluctuations are at the thermal level.

Energy and momentum conservation in closed plasma systems with resonant and nonresonant wave turbulence

Total energy and momentum balance is demonstrated for the resonant and nonresonant waves in closed plasma systems which can evolve due to the resonant interaction of particles and the resonant waves. The complete expression for the turbulent collision integral which takes into account all nonlinear (in the considered approximation) effects as well as effects due to the system’s nonstationarity is derived. Additional contribution to the correlation function of the wave fields in the nonstationary system is calculated. Change of the energy of the nonresonant waves in the time-dependent background medium is discussed.

Damping of the resonant mode in a plasma-maser

The damping rate of resonant waves is evaluated considering their interaction with nonresonant waves and plasma particles due to the plasma-maser effect. It is found that the polarization coupling terms gives the dominant contribution to the damping rate. On the other hand, the growth rate of the nonresonant waves consists only of the direct coupling term contribution. The significance of our result is discussed.

The evolution of the resonant mode in plasma-maser interaction

We study the evolution of the resonant waves considering its interaction with the nonresonant waves and the plasma particles due to plasma-maser effect. The nonlinear dielectric function of the resonant wave is calculated and is found to consist of two parts: the direct and the polarization coupling terms. On the other hand, the nonlinear dielectric function of the nonresonant wave consists only of the direct coupling term. The significance of our results is discussed.

Wave stochasticity and nonlinear plasma–maser effect

Influence of wave stochasticity on the interaction of resonant and nonresonant plasma waves is considered. As the correlations of the resonant waves grow, the plasma-maser interaction becomes more effective. It is demonstrated with an example of resonant Langmuir waves that a rapid decrease of the wave stochasticity due to modulational instability leads to enhanced interaction of nonresonant electromagnetic waves with plasma particles via transition processes.

Continuous-wave singly resonant pump-enhanced type II LiB_3O_5 optical parametric oscillator

We report what is to our knowledge the first demonstration of a pump-enhanced singly resonant continuous-wave optical parametric oscillator. The nonlinear material used was lithium triborate cut for noncritical phase matching along the z axis, and the device was pumped by a single-frequency argon-ion laser. The oscillation threshold was ~1.0 W at 514.5 nm. For 3.4 W of pump power, we obtained single-frequency output powers of 500 mW in the nonresonant wave, which we temperature tuned over 14 nm.

Transition effects and interactions of nonresonant waves with plasma particles

Transition processes and their influence on the evolution of nonresonant waves in the presence of a resonant field in unmagnetized plasmas are considered. The difference between the cases of regular and random resonant waves is connected with the stronger transition interaction of plasma particles with the nonresonant wave on density inhomogeneities which appear as a result of the resonant interaction of the particles and regular resonant waves.

Thermal-wave-modulated superconducting quantum interference device susceptometry for thin magnetic layers

Thermal waves are excited by a chopped nonresonant light wave in a 3.2 μm EuTe layer on a crystalline BaF2 substrate. The glass fiber optic sample holder is at rest within the pickup coil of a superconducting quantum interference device susceptometer. The thermal wave amplitude (simulated by a two-dimensional heat conduction model) is a function of temperature and chop rate of illumination and modulates only the magnetic properties of the epitaxial layer. Therefore, the novel method has an enhanced dynamic range and sensitivity (resolution of magnetic moment ≤2×10−9 emu) and resolves the antiferromagnetic phase transition of the EuTe layers at TN=9.8 K even for small magnetic fields of 10 G.

On the physics of the plasma maser

We consider the plasma-maser interactions of electrostatic waves for both magnetized and unmagnetized plasmas. The difference between these two cases is clarified. A correct transition to the zero magnetic field is presented. The accuracy of the conservation of the adiabatic invariant (the number of quanta of the nonresonant waves) is calculated.

Quantum electrodynamic effects in semiconductor microcavities - Microlasers and coherent exciton-polariton emission

We discuss the spontaneous emission of quantum well excitons in a monolithic microcavity. When the quantum well is excited by a nonresonant pump wave at high above the bandgap, the incoherent spontaneous emission is concentrated on the single resonant mode and the laser threshold is reduced by many orders of magnitude. When the quantum well exciton is excited by a resonant pump wave, the coherent spontaneous emission based on a «microcavity exciton-polariton» is observed. The spectral linewidth and the polarization of the pump wave are preserved and the coupling efficiency into the single resonant mode approaches 100%. The microcavity-induced normal mode splitting is observed in the frequency domain by photoexcitation spectrum measurements and in the time domain by pump-probe measurements

Simulations of wave–particle interactions in stimulated Raman forward scattering in a magnetized plasma

Stimulated Raman forward scattering in a high-temperature, magnetized plasma is investigated with relativistic Vlasov–Maxwell simulations and with envelope and test particle calculations. The parameters correspond to Raman current drive by free-electron lasers in reactor grade tokamak plasmas. The phase velocity of the Raman excited plasma wave is large, and therefore the Landau damping is initially weak. The electron plasma wave grows to a large amplitude and accelerates electrons to high energies. Simultaneous pump depletion weakens the driving ponderomotive force, which leads to a collapse of the plasma wave if the number of the interacting electrons is large enough. Spatially the wave–particle interaction takes place in a distance of a few wavelengths of the plasma wave. The electron energies can largely exceed the kinetic energy at the phase velocity of the electron plasma wave. Short-wavelength amplitude modulations of the plasma wave appear at high amplitudes. Efficient generation of the nonresonant anti-Stokes wave and of the second Stokes wave are also observed. Analytical growth rates and envelope calculations explain well the early evolution of the Raman process. Later on, nonlinear wave–particle interactions and relativistic effects start to dominate, and the system is not satisfactorily described by simple envelope equations.

Resonant and nonresonant wave excitation in a double beam free electron laser

Resonant and nonresonant parametric instabilities of longitudinal and transverse waves are studied for a double-beam free electron laser system. Enhanced excitation of waves is obtained with possible consequences of increased gain for operation of the system. The enhancement is considerably increased when the resonant condition for the excited electromagnetic wave and the beam electrons is fulfilled. A comparison with ordinary FEL operation using one electron beam is made for resonant as well as nonresonant cases. It demonstrates some interesting features of the dynamics for the double-beam system.

Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 2. Stationary solution and evolution of initial distributions

The evolution of the distribution function due to the simultaneous nonlinear interaction of plasma particles with resonant and non-resonant waves is studied. A stationary particle distribution resulting from a balance of the quasi-linear interaction and the nonlinear one is found. The temporal evolution of an initial δ-function-shaped distribution (like a ‘beam’) is examined in the one-dimensional case. General formulae are obtained for stochastic particle acceleration (taking account of the nonlinear interaction studied here).

Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1. Collision integral

An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a ‘direct’ nonlinear interaction of particles and waves, and the influence of the non-stationarity of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one.

Adiabatic amplification of optical solitons.

We study the adiabatic evolution of the fundamental nonlinear Schr\"odinger soliton under a general integro-differential perturbation. This perturbation is shown to model a saturable bandwidth-limited amplification of an optical soliton with a nonresonant carrier wave. We use the soliton perturbation theory to calculate the evolution of the amplitude, frequency, group velocity, and phase of the pulse. The perturbative analytical steady-state solution is obtained and its stability is studied using the phase-plane formalism.