Parametric Excitation of Plasma instabilities by two Monochromatic Pump waves

The dispersion characteristics of a plasma in a pump field ??(t) = ?? sub ω₀t + ??₁ sin ω₁t are considered. Firstly we assume, that the second wave is weak (|??₁| ? |??₀|) and the frequency ω₁ is near sω₀(ω₁ = sω₀ + Ω,Ω ? ω₀). We obtain the dispersion equation, describing the parametric coupling of the waves driven by the strong field ??₀ sin ω₀t under the resonance condition ω₀ ≈ ω_Le/P and derive the expressions for the growth rates (ω_Le is the electron LANGMUIR frequency; s, p are integers). In the second part it is shown, that a strong field ??₁ with a frequency ω₁ much larger than ω _Le(ω _Le ≈ pω₀) stabilizes the plasma; the growth rates are reduced and the frequency region of the parametric instability is contracted.     

Parametrische Anregung von elektrostatischen Oberflächenwellen in einer inhomogenen Plasmaschicht durch ein amplituden-moduliertes UHF-Pumpfeld

Parametric resonance phenomena are investigated in a plasma layer with thickness d and thin inhomogeneous boundary regions. The modulated UHF electric field is parallel to the plasma layer. We consider both strong and low modulation of the field amplitude and suppose, that the carrier frequency ω₀ of the pump wave is much larger than the Langmuir frequency ω_Le. We find the region for the modulation frequency ω, in which the parametric growing of the asymmetric and symmetric surface waves occurs. The maximum growth rates of these waves, the direction of their propagation and the threshold value of the modulation depth α of the UHF pump field are calculation.     

Dynamic phenomena connected with magnetic and antiferroelectric interactions in trirutiles

Dynamic effects caused by the magnetoelectric and antiferroelectric interactions in tetragonal antiferromagnets are studied. The analysis is based on the example of trirutiles that are a series of antiferromagnets with different exchange structures and orientation states. We are mainly dealing with the excitation by an alternating electric field E(t) of spin waves typical of these magnets (antiferroelectric resonance) and the nuclear magnetoelectric resonance connected with these interactions. In the first case, special emphasis is placed on specific magnons (antimagnons), where only the antiferromagnetism vectors L take part in oscillations, whereas the total ferromagnetism vector M remains unchanged. The nuclear magnetoelectric resonance can be generated by oscillations of both L and M caused by field E(t). In this way, the field contributes to the hyperfine field, which acts on the nuclear spins. It is shown that the magnetic and antiferroelectric interactions in the dynamics can manifest themselves both at high (usually, exchange) frequencies ωw_E (antiferroelectric resonance) and at rather low nuclear frequencies of ω_n?ω_E. Particular cases of magnetic structures (phases) are considered where field E(t) can excite not only antimagnons, but also quasiantiferromagnons that have lower eigenfrequencies than those of quasimagnons (relativistic and semirelativistic).     

Parametric dispersion and amplification in semiconductor plasmas: Effects of carrier heating

Using the hydrodynamic model of a semiconductor plasma, the influence of carrier heating on the parametric dispersion and amplification has been analytically investigated in a doped III-V semiconductor, viz. n-InSb. The origin of the phenomena lies in the effective second-order optical susceptibility (χ_e⁽²⁾) arising due to the induced nonlinear current density of the medium. Using the coupled-mode theory, the threshold value of pump electric field (|E_0T|_para) and parametric gain coefficient (α_para) are obtained via χ_e⁽²⁾. The relevant experiment has not been performed. Proper selection of the doping level not only lowers |E_0T|_para required for the onset of parametric excitation but also enhances α_para. The carrier heating induced by the intense pump modifies the electron collision frequency and hence the nonlinearity of the medium, which in turn further lowers |E_0T|_para and enhances α_para by a factor of ∼10³ and ∼2×10², respectively. The results strongly suggest that the incorporation of carrier heating by the pump in the analysis leads to a better understanding of parametric processes in solids and gaseous plasmas, which can be of great use in the generation of squeezed states.     

[Russian Text Ignored]

The stability of the electromagnetic plasma confinement by powerful external s-polarized pump waves is considered. The parametric excitation of standing electromagnetic waves along the plasma boundary with frequencies close to the frequency of the pump wave leads to a periodic density modulation of the plasma boundary. The density disturbances along the direction of the external wave field are connected to the excitation of transverse p-polarized surface waves while the modulation in the direction perpendicular to the pump field are created by the parametric interaction between the external wave and s-polarized trapped leaking oscillations. Only when the leaking waves are excited the scale length of the modulation is larger than half the free space wave length of the incident radiation.     

Berechnung der Amplitudenfluktuation eines mit Laserlicht gepumpten optischen parametrischen Oszillators

The intensity fluctuations of the radiation of an optical parametric oscillator have been calculated by taking into account the corresponding fluctuations of the pump light. The latter are shown to have a strong influence on the fluctuations of signal and idler waves. In contrary to the laser case, they are essentially reproduced in the signal and idler radiation; more quantitatively, the correlation function 〈?(t₁) ?(t₂)〉 where ? denotes the deviation of the amplitude of the signal (or idler) wave from its mean value is, for t₁ = t₂, equal to the corresponding quantity for the pump wave apart from a reduction factor, whose value depends on the resonator losses and the relative excitation of both the pumping laser and the optical parametric oscillator and is found to be of the order of one for the normal case. It is interesting to note that for sufficiently strong pumping, the correlation function 〈?(t₁) ?(t₂)〉 approaches the value zero for |t₁ – t₂| → ∞ not monotonically but in form of damped oscillations.     

Linear and Nonlinear Wavetransformation and Absorption in the Inhomogeneous Plasma Capacitor

The parametric decay process in inhomogeneous layers existing near the plasma boundaries or in front of antennas and probes in a plasma has been investigated. The linear enhancement of the pump field near ω = ω_p, the threshold fieldstrength, the wavenumber selection rules and the influence of spontaneous low frequency fluctuations are discussed in detail using a one-dimensional model of the inhomogeneous plasma capacitor. According to this model the instabilities appear in the layers with maximum linear transformation and (linear) absorption. In addition, a strong nonlinear part of absorption in the presence of the instability has been observed. The level of the spontaneous low frequency fluctuations influences strongly the spectrum of the parametrically excited ion waves. The experiments show a redistribution of the transferred ion acoustic wave energy over the whole wave continuum up to ω_pi, if a sufficient strong spontaneous fluctuation level exists in the plasma. It is impossible, however, to excite ion acoustic turbulence by the decay of the high frequency pump field under the present conditions. The conditions for the linear field enhancement are disturbed by the action of the ponderomotive forces changing the density profile near the critical point before reaching the strong pump amplitude being necessary for the excitation of a cascade of decay processes.     

Non-adiabatic transitions for random processes in a two-level system

Non-adiabatic transitions in two-level systems are investigated theoretically for a random time dependence of ?ω, the energy difference, between the levels. We assumed that ω = ω(x) and the coordinate x = x(t) is a random function of time. Diffusion and Poisson processes (both homogeneous and with a source) for x(t) were assumed. The cases of linear crossing terms (ω = γx) and non-linear terms (ω = ω _e exp (- αx) + ω₀) were considered. Values of the non-adiabatic transition probability per unit time were obtained by perturbation theory for ω₁τ _c ? 1 where τ _c is the correlation time and ω₁ is the off-diagonal matrix element.     

CHAOTIC AND NON-LINEAR DYNAMIC ANALYSIS OF A TWO-AXIS RATE GYRO WITH FEEDBACK CONTROL MOUNTED ON A SPACE VEHICLE

An analysis is presented in this paper for a two-axis rate gyro subjected to linear feedback control mounted on a space vehicle, which is spinning with uncertain angular velocity ω_z(t) about its spin of the gyro. For the autonomous case in which ω_z(t) is steady, the stability analysis of the system is studied by Routh-Hurwitz theory. For the non-autonomous case in which ω_z(t) is sinusoidal function, this system is a strongly non-linear damped system subjected to parametric excitation. By varying the amplitude of sinusoidal motion, periodic and chaotic responses of this parametrically excited non-linear system are investigated using the numerical simulation. Some observations on symmetry-breaking bifurcations, period-doubling bifurcations, and chaotic behavior of the system are investigated by various numerical techniques such as phase portraits, Poincaré maps, average power spectra, and Lyapunov exponents. In addition, some discussions about chaotic motions of this system can be suppressed and changed into regular motions by a suitable constant motor torque are included.     

Zur nichtlinearen Theorie der Strahl-Plasma-Wechselwirkung I

Beam-plasma-interaction is theoretically investigated on the basis of the non-linear Vlasov equation. The case of amplifying longitudinal waves is described by a non-linear approximation including “quasilinear” and mode-coupling terms. By evaluating the electric field vector E(x, t) and the distribution functions f_a(x, v, t) for the beam and plasma electrons in Fourier series and approximating the non-oscillating parts of the f_a by the first terms in an expansion using Hermite polynomials in velocity space a system of ordinary differential equations for the complex wave number k, the mean and thermal velocities and the quasimoments b_as is obtained, which can be solved numerically, if terms with E for which m + n > 3 are neglected. The numerical results will be given in a further part of the paper.     

Parametrische Phononen-Turbulenz im Feld zweier zirkular polarisierter UHF-Wellen

The interaction of two strong circulary polarized u.h.f. pump waves with a fully ionized homogeneous plasma is considered. If the difference Ω of their frequencies is near or smaller than twice the ion plasma frequency phonons can be parametrically excited. The threshold value (E₀E₁)_s for this decay-process depends on Ω and the dissipative effects in the plasma. After exceeding the thermal level the phonons are stabilized due to the scattering by the ions. The evolution of the parametrically excited phonon turbulence and the transition into a stationary state are described by a nonlinear integro-differential equation for the spectral energy density of the phonons. This equation is solved analytically as well as numerically and it is shown, that the phonon turbulence is strongly influence by the propagation directions of the pump waves and the ratio of electron- to ion-temperature.     

Resonances,Absorption and Linear Excitation of Cyclotron Harmonic Waves in a Discharge Plasma

Standing cyclotron harmonic waves below the second harmonic are observed using the noise radiation of a mercury discharge tube at 1465 MHz. From the positions of the Buchsbaum-Hasegawa resonances the density profile and the electron temperature are derived, these parameters agree quite well with the behaviour of the collision-free, magnetized plasma column. A onedimensional model applicable to our waveguide geometry is developed taking into account linear excitation of cyclotron harmonic waves by a quasistationary external field in a bounded plasma. Absorption and excitation are controlled by the scale length L₁ at the hybrid point and a coupling length l_c, introduced by Eq. (20); the electron gyration radius r_c, scale length L₁, coupling length l_c, and slab thickness 2a obeying the relation r_c?l_c?L₁?2a. The main absorption is caused by enhanced collisional damping at the upper hybrid region and only a small fraction being dissipated in the wave mode, though its field strength is large compared with that at the plasma boundary (E_W/E(a) ≈ 6). An estimation of the mean field strength within the coupling region shows, that such a low power as 1 mW/cm² absorbed in the hybrid region may produce fieldstrength exceeding the typical threshold values for non-linear excitation mechanism.     

Compression of whistler waves in a plasma with a nonstationary magnetic field

We present the results of our experiments in which the propagation of whistler waves in a plasma with a nonstationary magnetic-field perturbation (B=B₀+δB(t), δB/B₀ ≤ 5%) was investigated. The parametric and dispersive phenomena in a variable magnetic field were studied on the unique Krot plasma bench (the plasma column was 4 m in length and 1.5 m in diameter). A periodic field perturbation is shown to lead to an amplitude-frequency modulation of the whistler wave and to fragmentation of the signal into separate frequency-modulated wavepackets followed by their compression. The formation and compression of pulses is attributable to strong whistler group-velocity dispersion near the electron cyclotron frequency (ω ≤ ω_H). The results can be used to interpret the spectral shapes of the signals received from the Earth’s magnetosphere and ionosphere in the electron and ion whistler frequency ranges.     

Parametric instability in a two-hole species semiconductor-plasma

The parametric excitation of a low frequency wave has been investigated analytically in a two-hole species semiconductor-plasma in the region of kl ? 1 using the hydrodynamic model of the plasmas in the presence of a high frequency oscillatory electric field (E₀ cos ω₀t applied along the X-axis) and a d.c. magnetic field B₀ normal to the electric field (along the Z-axis), the low frequency wave propagating in the X–Z plane making a very small angle θ with the X-axis. The system supports a purely growing unstable mode. The variation of the growth rate of the unstable mode has been studied over a wide range of system parameters for the specific case of an intrinsic GaAs crystal at 300 K. The oscillatory electric field can be obtained by irradiating the crystal with a 119μm H₂O laser.     

Propagation of electromagnetic waves generated by moving sources in dispersive media

The propagation of electromagnetic waves issued by modulated moving sources of the form j( t,x ) = a( t )e ^{- iw₀ t} [(x)\dot]₀ ( t )d( x - x₀ ( t ) )j\left( {t,x} \right) = a\left( t \right)e^{ - i\omega _0 t} \dot x_0 \left( t \right)\delta \left( {x - x_0 \left( t \right)} \right) is considered, where j(t, x) stands for the current density vector, x = (x ₁, x ₂, x ₃) ∈ ℝ³ for the space variables, t ∈ ℝ for time, t → x ₀(t) ∈ ℝ³ for the vector function defining the motion of the source, ω ₀ for the eigenfrequency of the source, a(t) for a narrow-band amplitude, and δ for the standard δ function. Suppose that the media under consideration are dispersive. This means that the electric and magnetic permittivity ɛ(ω), μ(ω) depends on the frequency ω. We obtain a representation of electromagnetic fields in the form of time-frequency oscillating integrals whose phase contains a large parameter λ > 0 characterizing the slowness of the change of the amplitude a(t) and the velocity [(x)\dot]₀ ( t )\dot x_0 \left( t \right) and a large distance between positions of the source and the receiver. Applying the two-dimensional stationary phase method to the integrals, we obtain explicit formulas for the electromagnetic field and for the Doppler effects. As an application of our approach, we consider the propagation of electromagnetic waves produced by moving source in a cold nonmagnetized plasma and the Cherenkov radiation in dispersive media.     

Second-harmonic generation taking into account dispersion of nonlinear susceptibility

Second-harmonic generation in the field of an ultrashort pulse and the propagation of extremely short pulses in a medium with quadratic nonlinearity are analyzed. Second-harmonic generation is analyzed taking into account the effect of second-and third-order group velocity dispersion and dispersion of nonlinear susceptibility up to the second order. Corrections, whose order of smallness is determined by the parameter (ω_L t _p)^?1, where t _p is the pulse duration and ω_L is the carrier frequency of the pump wave, are obtained. For a large phase mismatch, two new solutions are found that describe the stationary evolution of solitary pump and second-harmonic waves in the regions of both anomalous and normal group velocity dispersions.     

Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

Phonons,Diffusons, and the Boson Peak in Two-Dimensional Lattices with Random Bonds

Within the model of stable random matrices possessing translational invariance, a two-dimensional (on a square lattice) disordered oscillatory system with random strongly fluctuating bonds is considered. By a numerical analysis of the dynamic structure factor S(q, ω), it is shown that vibrations with frequencies below the Ioffe-Regel frequency ω_IR are ordinary phonons with a linear dispersion law ω(q) ∝ q and a reciprocal lifetime б ~ q³. Vibrations with frequencies above ω_IR, although being delocalized, cannot be described by plane waves with a definite dispersion law ω(q). They are characterized by a diffusion structure factor with a reciprocal lifetime б ~ q², which is typical of a diffusion process. In the literature, they are often referred to as diffusons. It is shown that, as in the three-dimensional model, the boson peak at the frequency ωb in the reduced density of vibrational states g(ω)/ω is on the order of the frequency ω_IR. It is located in the transition region between phonons and diffusons and is proportional to the Young’s modulus of the lattice, ω _b ≃E.

     

Transient optically detected ESR in the excited state of ruby

The dynamics of the(² E) state of Cr³⁺ in Al₂O₃ have been investigated. After excitation by a short laser pulse (<10ns) the relative intensity of the optically detected ESR signal (ODMR) as a function of the delay timet _d after the excitation is measured. A remarkable increase was found upon lengtheningt _d, while the line width remained constant. This increasing population difference of the Zeeman levels of(² E) can be explained by different resonant-reabsorption induced effective lifetimes. The experimental data could be reproduced by use of a phenomenological model.     

Computation and analysis of the dynamic structure factor S(k, ω) for small wave vectors

Molecular dynamics (MD) calculations have been performed for the Lennard-Jones (12-6) potential function using 2048 particles. Using conventional parameters the results may be compared with those for liquid argon.

The dynamic structure factor S(k, ω) has been determined both by Fourier inversion of the intermediate scattering function F(k, t) and from the longitudinal current-current correlation function C _∥(k, t). Particular attention was paid to the recurrence time of the system. The results for S(k, ω) by the two methods agree within 5 per cent for the whole region of small k-vectors considered. Double Fourier inversion of the van Hove function G(r, t) led to insufficiently accurate results for these small k-values. In view of the present data, the MD-results of Levesque et al. [1] for S(k, ω) have only a qualitative character. These latter data appear to contain truncation errors due to incomplete Fourier transformations.

Using a hydrodynamic assumption for F(k, t) we were able to extract the transport coefficients, the velocity of sound and the ratio of the specific heats in the limit of large wave lengths or small k. The velocity of sound was obtained by exploiting the MD generated anomalous dispersion curve of sound waves. Anomalous dispersion was found to set in for kσ ～ 0·25. A sound speed of 880 ms^-1 has been determined which is in excellent agreement with experimental values for liquid argon. The total error for the MD value amounts to about 5 per cent. In contrast, the ratio of the specific heats γ and the transport coefficients D _T and Γ (thermal diffusivity and sound attenuation) were determinable only with an accuracy of 15 per cent due to the need for larger extrapolations. Nevertheless, we found D _T, Γ and γ in agreement with experimental values within 5-10 per cent.