Pump Wave Amplitude Research Articles

Energy mode distribution: An analysis of the ratio of anti-Stokes to Stokes amplitudes generated by a pair of counterpropagating Langmuir waves

Results from plasma wave experiments in spacecrafts give support to nonlinear interactions involving Langmuir, electromagnetic, and ion-acoustic waves in association with type III solar radio bursts. Starting from a general form of Zakharov equation (Zakharov, V.E., 1985. Collapse and self-focusing of Langmuir waves. Hand-book of Plasma Physics Cap.2, 81–121) the equations for electric fields and density fluctuations (density gratings) induced by a pair of counterpropagating Langmuir waves are obtained. We consider the coupling of four triplets. Each two triplets have in common the Langmuir pump wave (forward or backward wave) and a pair of independent density gratings. We numerically solve the dispersion relation for the system, extending the work of (Alves, M.V., Chian, A.C.L., Moraes, M.A.E., Abalde, J.R., Rizzato, F.B., 2002. A theory of the fundamental plasma emission of type- III solar radio bursts. Astronomy and Astrophysics 390, 351–357). The ratio of anti-Stokes ( AS ) ( ω 0 + ω ) to Stokes ( S ) ( ω 0 - ω * ) electromagnetic mode amplitudes is obtained as a function of the pump wave frequency, wave number, and energy. We notice that the simultaneous excitation of AS and S distinguishable modes, i.e., with Re { ω } = ω r ≠ 0 , only occurs when the ratio between the pump wave amplitudes, r is ≠ 1 and the pump wave vector k 0 is < ( 1 3 ) W 0 1 / 2 , W 0 being the forward pump wave energy. We also observe that the S mode always receives more energy.

Effect of a large‐amplitude circularly polarized wave on linear beam‐plasma electromagnetic instabilities

In a previous paper, sufficiently large‐amplitude and left‐handed “pump waves” propagating parallel to the background magnetic field were shown to stabilize a moderately dense beam in a proton plasma against the generation of waves drawing their energy from the differential streaming motion of the beam [Gomberoff, 2003]. We now examine the general case of both left‐hand and right‐hand pump waves and their effects on beam instability as a function of pump wave amplitude and frequency, beam speed, and plasma component temperatures. We find that the left‐hand pump wave always gives beam stability above a threshold amplitude. Larger threshold trend with increasing beam speed and lower ones with increasing temperature. It is also shown that they can stabilize left‐hand polarized instabilities in the case of large drift velocities. The right‐hand pump similarly suppresses beam instabilities when its pump frequency is below the linearly unstable range of frequencies. However, when its pump frequency is within the range of instability, that part of the range below the pump frequency is stabilized beyond a threshold amplitude, but the part above becomes even more unstable in the presence of a right‐hand pump.

Self-induced hysteresis for nonlinear acoustic waves in cracked material.

A new phenomenon of self-induced hysteresis has been observed in the interaction of bulk acoustic waves with a cracked solid. It consists in a hysteretic behavior of material nonlinearity as a function of the incident pump wave amplitude. Hysteresis manifests itself in the self-action of the monochromatic pump wave and in the excitation of its superharmonics and of its subharmonics. The proposed theoretical models attribute the phenomenon to hysteresis in transition of the acoustically forced oscillation of cracks from a nonclapping regime to a regime of clapping contacts.

Physics of Plasma Radiation

We present a theory of the fundamental plasma emission of type-III solar radio bursts. Starting from the generalized Zakharov equations, considering the pump wave as a pair of oppositely propagating Langmuir waves with different amplitudes, and the excitation of electromagnetic and induced Langmuir waves, we obtain a general dispersion relation for the coupled waves. We numerically solve the general dispersion relation using the pump wave amplitude and plasma parameters observed in the interplanetary medium.

Parametric decay instabilities in the HELIX helicon plasma source

Parametric decay of the electromagnetic helicon pump wave into two electrostatic waves, thought to be a lower hybrid wave and an ion acoustic wave, is observed. The parametric excitation of the electrostatic waves is strongest near the axis of the helicon source. The parametrically excited wave amplitudes can be as large as 8% of the pump wave amplitude. Thus, efficient coupling between the parametrically excited waves and plasma particles (ions and electrons) can lead to enhanced plasma densities, electron temperatures, and ion temperatures. A correlation between the lower hybrid wave and electron temperatures and a correlation between the ion acoustic wave and ion temperatures near the antenna are observed.

Frequency up-conversion and frequency down-conversion of acoustic waves in damaged materials

Experimental results have been obtained on thermally damaged thick glass plates. A study of nonlinear phenomena with different amounts of damages from the virgin (undamaged) case to a strongly cracked configuration has been performed. The cascade process of harmonic excitation, interaction of a high-frequency wave with a low-frequency one (nonlinear parametric receiving antenna) and demodulation of the amplitude modulated high-frequency wave (nonlinear parametric emitting antenna) have been implemented. One observes a dramatic increase in generation of the second harmonic as well as the demodulation signals versus the pump wave amplitude. A clear correlation exists between these nonlinear signatures and the amount of damages. Preliminary determinations of the coefficient of quadratic nonlinearity have been achieved. The results in the configuration of parametric emitting antenna are believed to be the very first on cracked materials.

A theory of the fundamental plasma emission of type-III solar radio bursts

Results from plasma wave experiments in spacecraft give support to nonlinear interactions involving Langmuir waves, electromagnetic waves and ion-acoustic waves in association with type III solar radio bursts. In this paper we present a theory of the fundamental plasma emission of type-III solar radio bursts. Starting from the generalized Zakharov equations, considering the pump wave as a pair of oppositely propagating Langmuir waves with different amplitudes, and the excitation of electromagnetic and induced Langmuir waves, we obtain a general dispersion relation for the coupled waves. We numerically solve the general dispersion relation using the pump wave amplitude and plasma parameters as observed in the interplanetary medium. We compare our results with previous models. We find that the stability properties depend on the pump wave numbers and on the ratio of wave amplitude between the forward and backward pump wave. The inclusion of a second pump wave allows the simultaneous generation of up and down converted electromagnetic waves. The presence of a second pump with different amplitude from the first one brings a region of convective instability not present when amplitudes are the same.

Parametric instabilities and wave coupling in Alfvén simple waves

A wave coupling formalism for magnetohydrodynamic (MHD) waves in a non-uniform background flow is used to study parametric instabilities of the large-amplitude, circularly polarized, simple plane Alfvén wave in one Cartesian space dimension. The large-amplitude Alfvén wave (the pump wave) is regarded as the background flow, and the seven small-amplitude MHD waves (the backward and forward fast and slow magnetoacoustic waves, the backward and forward Alfvén waves, and the entropy wave) interact with the pump wave via wave coupling coefficients that depend on the gradients and time dependence of the background flow. The dispersion equation for the waves D(k,ω) = 0 obtained from the wave coupling equations reduces to that obtained by previous authors. The general solution of the initial value problem for the waves is obtained by Fourier and Laplace transforms. The dispersion function D(k,ω) is a fifth-order polynomial in both the wavenumber k and the frequency ω. The regions of instability and the neutral stability curves are determined. Instabilities that arise from solving the dispersion equation D(k,ω) = 0, both in the form ω = ω(k), where k is real, and in the form k = k(ω), where ω is real, are investigated. The instabilities depend parametrically on the pump wave amplitude and on the plasma beta. The wave interaction equations are also studied from the perspective of a single master wave equation, with multiple wave modes, and with a source term due to the entropy wave. The wave hierarchies for short- and long-wavelength waves of the master wave equation are used to discuss wave stability. Expanding the dispersion equation for the different long-wavelength eigenmodes about k = 0 yields either the linearized Korteweg–deVries equation or the Schrödinger equation as the generic wave equation at long-wavelengths. The corresponding short-wavelength wave equations are also obtained. Initial value problems for the wave interaction equations are investigated. An inspection of the double-root solutions of the dispersion equation for k, satisfying the equations D(k,ω) = 0 and ∂D(k,ω) = ∂k = 0 and pinch point analysis shows that the solutions of the wave interaction equations for hump or pulse-like initial data develop an absolute instability. Fourier solutions and asymptotic analysis are used to study the absolute instability.

Ion acoustic damping effects on parametric decays of Alfvén waves: Right‐hand polarization

We study ion acoustic damping effects on parametric decays of right‐hand‐polarized electromagnetic waves. We do this because ion beams have been observed in a variety of space environments, and consequently, these waves can exist in those places. Damping effects are incorporated into the model by adding to the longitudinal component of the equation of motion a collision‐like term. Like for left‐hand‐polarized waves, the effect of damping is twofold. On the one hand, damping decreases the maximum growth rate of the existing instabilities while increasing the instability range, and on the other hand, it destabilizes regions that are stable in the absence of damping. Thus, for low‐frequency pump waves, ω0 ≪ ωci, and for low β = vt/vA (ωci is the ion gyrofrequency, and vt and vA are the thermal and the Alfvén velocities, respectively), where the only parametric instability is a decay instability, damping destabilizes the frequency range between ω = 0 and the threshold of the decay instability. As β increases, two new parametric instabilities develop: One of them is a modulational instability, and above some threshold value of the pump wave amplitude, there is also a beat wave instability. The decay instability is also possible for pump wave amplitude above some threshold. For even larger β the decay instability is no longer possible. In all cases, damping effects reduce the growth rate of the existing instabilities and destabilize regions which are stable in the absence of damping. These results are in agreement with those obtained by Vasquez [1995]. It is also shown that for large‐frequency pump waves, electron/ion whistler waves, the decay instability reappears even for large β and has very large growth rates.

Acousto-Optic Solitons in Fibers

It is shown that the deceleration of light pulses down to the velocity of a sound value can be realized in a case of unidirectional parametric interaction of two electromagnetic waves with an acoustic one in the regime of forming three wave acousto-optic solitons. This nonlinear acousto-optic interaction can be realized in long distance systems like fibers. As the result of such an interaction, two types of acousto-optic envelope solitons can propagate in fibers. Modulation of the amplitude of the electromagnetic pump wave can control the soliton velocity.

Ion acoustic damping effects on parametric decays of Alfvén waves

It is well known that in plasmas with β = (υs/υA)2 &lt; 1 (υs is the ion acoustic velocity and υA is the Alfvén velocity), Alfvén waves propagating along an external magnetic field can have three kinds of parametric instabilities: ordinary decay instability, beat wave instability, and modulational instability. However, when β ≥ 1, there is only a beat wave instability, although decay and modulational instabilities are also possible from the point of view of the resonance conditions. When β ≤ 1, there is, in general, a beat wave instability, but a modulational and a decay instability can also occur for some values of the pump wave amplitude. It is shown here that damping effects can destabilize regions that are stable under nondissipative fluid theory. This is done by using only fluid theory. Landau damping effects on the ion acoustic modes are simulated by a collisional‐like term in the longitudinal component of the fluid equations. It is shown that when there is only a beat wave instability, damping effects can destabilize modulational‐ and decay‐type instabilities. When there is a beat wave and a modulational instability, damping effects destabilize the region where one could expect a decay instability. The modulational‐like instability is shown to trigger a forward propagating Alfvén wave. On the other hand, the decay‐like instability generates backward propagating Alfvén waves. These results are in agreement with hybrid kinetic‐fluid approaches and hybrid simulation codes.

Quantization of plasma density irregularities under the action of a powerful electromagnetic wave: The spectrum of upper hybrid oscillations self-consistently trapped in density cavities

We present a theoretical model of the self-localization of the upper hybrid (UH) oscillations in plasma density depletions due to thermal nonlinearities driven by a homogeneous and monochromatic pump electric field. The Bohr-Sommerfeld condition for the trapped UH oscillations demands that the parameters of the density cavity be quantized. The depth and square of the depletion width across the magnetic field is proportional to an integer. The depth of the parabolically shaped cavity is proportional to the square of its width. The characteristic relative value of the density minimum is a few percent and the width is of the order of one meter for the pump wave amplitudes used in the ionospheric F-region experiments. We consider also the parametric decay of primary, localized UH oscillations trapped in the quantized plasma density depletions into secondary UH oscillations and lower-hybrid waves. We calculated the spectrum of the non-linear stabilized secondary UH oscillations which are also self-consistently trapped in the same density cavity. The spectrum of the UH oscillations is consistent with the observed spectrum of the downshifted (DM) and upshifted (UM) maximum in the stimulated electromagnetic emissions (SEE).

Suitability of drift nonlinearity in Si, GaAs, and InP for high-power frequency converters with a 1 THz radiation output

We investigate the nonlinear drift response of electrons in Si, GaAs, and InP crystals to high-power electromagnetic waves by means of a Monte Carlo technique, with the aim of developing an efficient frequency converter for 1 THz output radiation. Drift velocity amplitudes and phases determining the conversion efficiency are calculated for the first, third, and fifth harmonics in the pumping wave amplitude range of 10&amp;lt;E1&amp;lt;100 kV/cm, for frequencies between 30 and 500 GHz, and at the lattice temperatures of 80, 300, and 400 K. It is found that the efficiency is a maximum at the pumping wave amplitude of the order of 10 kV/cm depending on the intervalley electron scattering parameters and the lattice temperature. Cooling the nonlinear crystal down to the liquid-nitrogen temperature enhances the efficiency several times in Si and by orders of magnitude in GaAs and InP. This is promising for obtaining a 10% conversion efficiency.

Three‐dimensional kinetic simulation of the nonlinear evolution of lower hybrid pump waves

Nonlinear evolution of lower hybrid (LH) waves is studied by means of a fully three‐dimensional parallel particle‐in‐cell (PPIC) code. The plasma is driven by a monochromatic LH pump wave, which drives secondary LH and low‐frequency waves having a broad frequency spectrum from , to ω∼ωo &gt;ωlh, where Ωi, ωo and ωlh are the ion cyclotron, pump and LH resonance frequencies, respectively. The temporal variations in the electric field components show both amplitude and phase modulations. In a plasma with equal electron and ion temperatures the dominant amplitude modulation occurs at the ion cyclotron timescale τci. The pondermotive force associated with the vector nonlinearity arising from theE ×B drift of electrons is seen to generate both density depletions and enhancements depending on the time‐varying phase difference between the orthogonal electric field componentsEx andEy transverse to the ambient magnetic fieldBo in thez direction. Despite the use of quite strong pump wave amplitude, wave collapse in density cavities alone is not seen; instead, equally strong density cavities (cavitons) and enhancements (pilons) occur quasi‐periodically both in time and space. The phase difference betweenEx andEy and its evolution yield a rotating transverse electric field vector with hodograms ofEx andEy changing with time. The temporal evolution of the parallel acceleration of electrons and transverse heating of ions are discussed. For relatively slow pumps the electron acceleration is predominantly unidirectional parallel to the pump phase velocityVp‖o. On the other hand, for sufficiently large pump phase velocities the acceleration becomes bidirectional. The parallel electron acceleration up toV‖max ∼ 2Vp‖o is common, and the transverse ion acceleration occurs up toV⊥max ≅(m/M)1/2Vp‖o ≅Vp⊥o, wherem andM are the electron and ion mass, respectively. The relevance of the above results to the observations on LH waves and their role in electron and ion accelerations is discussed.

Simulation studies of processes associated with stimulated electromagnetic emission (SEE) in the ionosphere

Results of numerical simulation studies of processes associated with Stimulated Electromagnetic Emission (SEE) produced during ionospheric heating experiments are presented. A one-dimensional magnetized electrostatic Particle-In-Cell (PIC) simulation model with uniform plasma density is used to investigate electrostatic wave generation in the region where the pump frequency ω 0 approximately equals the upper hybrid frequency ω uh . In particular, the simulation plasma is driven with a uniform oscillating electric field to represent the long wavelength pump wave and power spectra of the electrostatic waves produced are taken. The pump wave frequency and amplitude are varied to consider the effects on the simulation power spectrum. The upper hybrid frequency in the model is varied through harmonics of the electron cyclotron frequency Ω ce to consider the effects of stepping the pump frequency through cyclotron harmonics. The power spectrum from the simulation plasma is richly structured. The resulting power spectra show sidebands upshifted and downshifted from the pump frequency by multiples of the lower hybrid frequency ω lh . The structure of the spectrum is highly sensitive to the proximity of the upper hybrid frequency to the cyclotron harmonic frequencies.

Parametric decays of a linearly polarized electromagnetic wave in an electron-positron plasma

We study the parametric decays of a large amplitude, linearly polarized electromagnetic wave in an electron-positron plasma. We include harmonic generation, the ponderomotive force, and weakly relativistic effects. It is shown that when ${v}_{s}/cl{c/v}_{p}$ (${v}_{s}$ is the electroacoustic velocity, $c$ is the speed of light, and ${v}_{p}$ is the phase velocity of the electromagnetic wave), there are two instabilities. One is an ordinary decay instability, in which the pump wave decays into a sideband wave, propagating backward relative to the pump wave, and an electroacoustic mode propagating forward. The other is an essentially electromagnetic nonresonant modulational instability (which is due to higher order effects of the pump wave amplitude), in which the pump wave decays into two sideband waves. When ${v}_{s}/cg~{c/v}_{p},$ there is a modulational nonresonant instability, and an ordinary modulational instability, in which the pump wave decays into a sideband wave and a forward propagating electroacoustic mode.

Parametric interaction of surface waves guided by a plasma layer

We study the linear stage of the parametric instability of high-frequency surface waves guided by a homogeneous plasma layer on a metallic substrate when a TM-polarized plane electromagnetic wave is incident on the layer. The instability growth rate and the threshold value of the pumping wave amplitude are determined. It is shown that the instability can be thresholdless in a certain range of permittivities and thicknesses of the layer.

Negative dynamic mobility of electrons in silicon in the far-infrared range

We performed Monte Carlo simulation of electron response to a strong pumping wave (443 GHz) and weak signal harmonic waves (886 and 1329 GHz) in silicon. A negative dynamic conductivity is found to arise for 1329 GHz above a threshold value of the pumping wave amplitude and below a maximum value of the signal wave amplitude in a limited range of phase difference between the waves.

Parametric Instability of Surface Waves on the Second Harmonic of Electron Cyclotron Frequency in a Plasma Layer

AbstractThe parametric instability of surface waves on the second harmonic of electron cyclotron frequency (SWCF) in a plasma filled dielectric wave guide is examined in a kinetic approximation. The studied surface waves are extraordinary polarized modes and propagate across the external steady magnetic field. The amplitude of the electrical pump wave is assumed to be small. Simple expressions for increments of the parametric instability of the SWCF are calculated. The otained results can be used in controlled fusion researches in order to avoid undesirable regimes of plasma periphery heating in that fusion devices which use the resonance electron cyclotron heating method.

Some possible parametric instabilities in unmagnetized plasma: kinetic theory

Some possible parametric instabilities, viz, modulation, filamentation, and stimulated Raman scattering instabilities in uniform and unmagnetized plasma have been investigated by using kinetic theory. The fully relativistic Vlasov equation has been employed to find the nonlinear response of electrons for these parametric processes. The analytical and numerical calculations of the growth rates of these instabilities are made and the nonlinear variation of the growth rates of each of these instabilities with the power of the incident laser beam are observed. For low powers, the growth rate is proportional to the pump wave amplitude, but at high powers the relativistic mass increase of the electrons produces a decrease in growth rate with amplitude. The dependence of these growth rates on some plasma parameters, such as plasma density, is also investigated.