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.     

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.     

Stationary Propagation of Coupled Nonlinear High Frequency Waves and Ion-Acoustic Waves in a Plasma

Stationary solutions of the coupled equations for high frequency transverse waves in a plasma and for the low frequency ion motion (T_e?T_i) are investigated numerically. The use of the nonlinear hydrodynamic equations instead of the linear wave equation for ion acoustic waves allows to look for solutions without restrictions of the Mach number M = V/c_s (V group velocity, c_s ion acoustic velocity) and the ratio ω/ω_pe (ω frequency of the HF-field, ω_pe electron plasma frequency at the undisturbed region). In particular, supersonic soliton-like solutions with n/n_o > 1 were found. Dispersion effects due to charge separation are not included.     

Trivelpiece-Gould-Modes in an Axial Inhomogeneous Plasma

Experiments on the propagation of TG-modes in a weakly inhomogeneous plasma are reported. The modes travel from the high density part (ω < ω_pe) to that of lower density (ω > ω_pe). The wavelength decreases as expected but an increase of the longitudinal fieldstrength predicted by collisionless theory could not be observed. Two nonlinear effects appear one after another with increasing wave amplitude. These are the sideband instability and a decay into the drift frequency range occuring in the whole plasma column. Neither the region ω ≈ ω_pe nor the very vicinity of the exciter antenna are distinguished. The second instability is accompanied by effective electron heating.     

Experimental Evidence of Parametric Instabilities in an Unmagnetized Plasma Subjected to a Strong H.F. Electric Field

Experimental evidence of parametric excitation, by an intense external H.F. field, of an electron surface mode and an ion wave is presented. The pumping electromagnetic energy density is equal to or slightly larger than the thermal energy density of the electrons. The value of f_pc/f₀ (electron plasma frequency/external field frequency) is that for an electron surface wave. Depending on the pressure and field intensity, this decay instability can lead to three types of low frequency oscillations, with frequencies close to the ion plasma frequency. Two of these are described by Aliev and Silin's intense field theory: one is the volume ion plasma oscillation and the other a surface ion plasma oscillation. The third corresponds to no known ion eigenmode. Several other features of the theory by Aliev and co-workers are also confirmed experimentally, such as the harmonic excitation of the instability (nf₀ ≈ f_pe/√2, where n is an integer), the instability amplitude as a function of f_pe/f₀ (above threshold conditions), the value of the mismatch parameter as a function of field strength and ion mass, and the existence of a fine structure corresponding to the symmetric and antisymmetric electron surface oscillations. Even at high pump field strengths, the decay products are nearly monochromatic i.e. the plasma does not become turbulent.     

Analytical and numerical calculations of optimum design frequency for focused ultrasound therapy and acoustic radiation force

Focused ultrasound therapy relies on acoustic power absorption by tissue. The stronger the absorption the higher the temperature increase is. However, strong acoustic absorption also means faster attenuation and limited penetration depth. Hence, there is a trade-off between heat generation efficacy and penetration depth. In this paper, we formulated the acoustic power absorption as a function of frequency and attenuation coefficient, and defined two figures of merit to measure the power absorption: spatial peak of the acoustic power absorption density, and the acoustic power absorbed within the focal area. Then, we derived “rule of thumb” expressions for the optimum frequencies that maximized these figures of merit given the target depth and homogeneous tissue type. We also formulated a method to calculate the optimum frequency for inhomogeneous tissue given the tissue composition for situations where the tissue structure can be assumed to be made of parallel layers of homogeneous tissue. We checked the validity of the rules using linear acoustic field simulations. For a one-dimensional array of 4 cm acoustic aperture, and for a two-dimensional array of 4 × 4 cm² acoustic aperture, we found that the power absorbed within the focal area is maximized at 0.86 MHz, and 0.79 MHz, respectively, when the target depth is 4 cm in muscle tissue. The rules on the other hand predicted the optimum frequencies for acoustic power absorption as 0.9 MHz and 0.86 MHz, respectively for the 1D and 2D array case, which are within 6% and 9% of the field simulation results. Because radiation force generated by an acoustic wave in a lossy propagation medium is approximately proportional to the acoustic power absorption, these rules can be used to maximize acoustic radiation force generated in tissue as well.     

Low frequency electrostatic nonlinear structures in an inhomogeneous magnetized non-Maxwellian electron–positron–ion plasma

The properties of low frequency (coupled acoustic and drift wave) nonlinear structures including solitary waves and double layers in an inhomogeneous magnetized electron–positron–ion (EPI) nonthermal plasma with density and temperature inhomogeneities are studied in a simplified way. The nonlinear differential equation derived here for the study of double layers in the inhomogeneous EPI plasma resembles with the modified KdV equation in the stationary frame. But the method used for the derivation of nonlinear differential equation is simple and consistent to give both the stationary solitary waves and double layers. Further, the illustrations show that superthermality κ, drift velocity and temperature inhomogeneity have significant effects on the amplitude, width, and existence range of the structures.     

Observation of the decay instability of a beam plasma wave

The spontaneous decay of a beam plasma wave into an ion acoustic and an electron plasma wave has been observed during the interaction of a monoenergetic electron beam with a helium and a neon plasma.     

Hydrodynamics of Plasma Interaction with an Intense Laser Field

A set of moment relations, which can describe the charged fluids response to an intense pump laser, and a linearization substitution relation, which is more appropriate as compared with the past treatment, are given by theoretical analyses. The relevant equations of state (adiabatic and isothermal), momentum and energy equations are derived self-consistently.The dispersion relations of the electron plasma wave and the ion acoustic wave driven by an intense pump laser field are-obtained. The results show that the frequencies of both the excited electron plasma wave and the excited ion acoustic wave have a great modification in the case of strong pump. The former bears out the theoretical result obtained from Vlasov equation and the later is consistent with experimental observations. It is proved that the zero-frequency component of the laser light wave contribution to the plasma pressure tensor is un-neglected,which implies a greatly change to the wave excitation properties, particularly in the direction of parallel or approximately parallel to the laser field vector.     

Electrostatic instability in magnetically confined inhomogeneous plasma driven by nonlinear force

A theoretical investigation on amplification of electrostatic ion acoustic wave in magnetically confined plasma has been presented in this paper. This investigation considers nonlinear wave–particle interaction process, called plasma maser effect, in presence of drift wave turbulence supported by magnetically confined inhomogeneous plasma. The role of associated nonlinear dissipative force in this effect in a confined plasma has been analyzed. The nonlinear force, which arises as a result of resonant interaction between electrons and modulated fields, is shown to drive the instability. Using the ion fluid equation and the ion equation of continuity, the nonlinear dispersion relation of a test ion acoustic wave has been derived, and the growth rate of ion acoustic wave in presence of low frequency drift wave turbulence has been estimated using Helimak data.     

Empirical power law for magnetic turbulence spectra of an anisotropic plasma

Three-dimensional dynamic distributions of oscillations of the magnetic field over wave vectors k have been obtained from the plasma and magnetic measurements on four satellites in the Cluster experiment in a turbulent plasma in the outer Earth’s cusp and near it. The resulting k spectra exhibit strong inhomogeneous anisotropy. The dependences of the energy of magnetic oscillations on the wavenumber have been analyzed for 288 three-dimensional spectra in the wavelength interval covering the magnetohydrodynamic and ion scales. It has been shown that the energy density of magnetic fluctuations per unit volume in the wave vector space that is averaged over the total solid angle decreases in the wavelength interval from ～2000 to ～10 km with an increase in according to a power law with an exponent of α = -5.0 ± 0.3 for any magnitude and character of anisotropy.     

受激布里渊散射的非线性增强和饱和

针对典型激光聚变等离子体参数条件,利用弗拉索夫程序研究非均匀流等离子体中受激布里渊散射的非线性行为。在动理学效应占主导的参数区域,观察到受激布里渊散射激发的离子声波由于非线性动理学频移和非均匀流空间失谐相互补偿引起的离子声波自共振增长,这会导致受激布里渊水平量级的增强;提出用光束时间去相干抑制这种绝对增长。在流体非线性占主导的参数区域,观察到由于离子声波谐波导致的孤立波产生、离子加热以及受激布里渊散射饱和现象。     

Resonant decay of a Langmuir wave in the presence of dust grains in a cylindrical plasma

The resonant parametric decay of a Langmuir wave into a backward propagating Langmuir wave and an ion acoustic (IA) wave is studied in a cylindrical dusty plasma. The analysis shows that the frequency of the IA mode decreases with the parameter δ_c (where δ_c is the ratio of the ion density to the electron density) for negatively charged dust grains. The growth rate of the resonance decay instability (RDI) and the threshold required for its onset also decrease with δ_c and are strongly dependent on the electron to ion temperature ratio for both positively and negatively charged dust grains. The results obtained also illustrate the dependence of the threshold of the resonance decay instability (μ_th) on the plasma cylinder radius.     

Kinetics and Optical Properties of the Strongly Driven Gas Medium of Interacting Atoms

This paper investigates stimulated emission and absorption near resonance for a driven system of interacting two-level atoms. Microscopic kinetic equations for the density matrix elements of N-atom states including atomic motion are built, taking into account atom-field and atom-atom interactions. Analytical solutions are given for the resulting macroscopic equations in different limits, for a system composed of a strong coherent “pump” field and a weak counter-propagating “probe” field. It was shown that the existence of a dipole-dipole (long-range) interaction between atoms separated by distance less than the pump wave-length can cause the formation of periodic polarization and population structures (gratings in time and space) in the pumped medium without a probe field. The magnitude of pump induced population grating can have a strong dependence on the relation between the pump field detuning and the polarization decay rate. The “interaction” between pump and probe induced polarization/population gratings through a dipole-dipole interaction mechanism causes the absorption line shape asymmetry. Under certain conditions, this asymmetry is revealed in increasing probe gain for the “red”-shifted (relative to pump) probe and suppressing the gain for the “blue”-shifted probe field when pump is “red”-shifted relative to the ensemble averaged resonant frequency. The theoretical results are consistent with experimental data for the probe gain or absorption as the function of frequency and the dependance of the gain on atomic density for sodium vapor when the pump laser is tuned near the D ₂ line. Here the dependance of gain on particle density was explained in the terms of the long-range interaction between the atoms.     

Free carrier absorption in quantizing magnetic fields: Nonpolar optical phonon scattering

A quantum theory of free carrier absorption in nondegenerate semiconductors and in strong magnetic fields which was previously developed to treat the case when acoustic phonon scattering dominates the free carrier absorption process [1] is extended to treat the case when nonpolar optical scattering is important. When the electromagnetic radiation field is polarized parallel to the direction of the applied magnetic field, results are obtained which are similar to those when acoustic phonon scattering is dominant. The free carrier absorption is an oscillatory function of the magnetic field which on the average increases in magnitude with the magnetic field. However, more structure in the free carrier absorption occurs when nonpolar optical phonon scattering dominates. This is due to the fact that there are two periods in the oscillatory magnetic field dependence associated with the emission or the absorption of optical phonons during the intraband transitions. When the cyclotron frequency exceeds the sum of the photon and optical phonon frequencies, i.e. ω_c > θ + ω_o, the free carrier absorption is predicted to increase linearly with magnetic field when ?ω_c? k_BT. The magnetic field dependence of the free carrier absorption can be explained in terms of phonon-assisted transitions between the various Landau levels in a band involving the emission and absorption of optical phonons.     

Excitation of short-wave oscillations in the ionospheric plasma by the field of a high-power radio wave with extraordinary polarization due to induced scattering by ions

We analyze excitation of electron-cyclotron or upper hybrid oscillations of the ionospheric plasma at a frequency that is close to the pump frequency as a result of induced scattering of a high-power radio wave with extraordinary polarization by ions. The excited oscillations have a small wavelength of the order of the Larmor electron radius, which allows them to propagate near and below the reflection level of an extraordinary radio wave. We found the instability increment and threshold field, which results from collisional absorption of plasma waves. It is shown that the threshold field is minimal near the reflection level of an extraordinary radio wave when the radio wave frequency f₀ is between electron harmonics nf_Be with n≥2. In an ionospheric F layer it is of the order of 1 W/m. Such fields are easily obtained in ionospheric heating experiments allowing for radio-wave field swelling in the reflection region. In the vicinity of electron harmonics f_o≅nf_Be, the threshold field is increasing. For f_o<nf_Be with f_o≅nf_Be the instability does not develop because of the absence of plasma oscillations with a frequency that is close to the pump frequency (the latter also refers to the case f_o<2f_Be). The expressions obtained are generalized to the case in which the instability under consideration is excited by the field of an ordinary radio wave in the region of its quasilongitudinal propagation. We discuss the possibility of using the emergence of very short-wave plasma oscillations for explaining the experimentally observed phenomena. Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow Region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 5, pp. 541–560, May, 1997.     

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 Mechanism of Anomalous Microwave Power Absorption in Experiments on Electron Cyclotron Heating in Toroidal Magnetic Traps

The nonlinear stage of the parametric decay instability of an extraordinary wave is analyzed in the presence of a nonmonotonic density profile. The decay excites an electron Bernstein wave, which is localized in the vicinity of a local density maximum, and an ion Bernstein wave, which leaves a nonlinear interaction region and is absorbed by ions in the vicinity of the harmonics of the ion cyclotron frequency. The main mechanism of instability saturation is considered to be a cascade of decays of a primary daughter electron Bernstein wave, which leads to the excitation of localized secondary electron Bernstein waves and ion cyclotron (Bernstein) waves. The localization of electron Bernstein waves causes a significant decrease in the secondary- decay excitation threshold, which is thought to provide saturation of the primary instability at the lowest level. The saturation of the primary parametric decay instability of a pump wave and the anomalous absorption of the pump power are analytically estimated. A numerical simulation is performed using the parameters that are typical of the experiments on the electron cyclotron resonance heating of plasma at the second resonance harmonic in TCV tokamak.     

Parametric excitation of circularly polarized and ion waves in a magnetized plasma

Threshold intensities and growth rates are calculated for the parametric decay instability in which a circularly polarized pump wave excites a low frequency electrostatic ion wave and an electromagnetic circularly polarized wave in a magnetized plasma.