Oblique injection of EC ordinary waves in a Tokamak plasma

Summary A detailed analysis of the propagation and damping of ordinary waves in the electron cyclotron frequency range in a Tokamak-like stratified plasma is given. The waves are supposed to be launched from the low-magnetic-field side of the machine in the meridian plane, with an angle, with respect to the perpendicular at the launching point, to the toroidal magnetic field. In this first part of the paper the emphasis, is on the WKB analysis of the process,i.e. on the study of the local-dispersion relation, first in the cold case and then taking full account of finite-Larmor-radius effects. A thorough study of the intricacies presented by both cold and hot dispersions around the Preinhaelter, and Kopecky critical angle of injection is made. This complicated behaviour has not been analysed in previous works on the subject.

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Riassunto Si presenta un’analisi molto dettagliata della propagazione e dell’assorbimento di onde ordinarie con frequenza vicina alla frequenza ciclotronica degli elettroni in un plasma stratificato che simula la geometria, del Tokamak. Si suppone che l’onda venga lanciata dalla parte esterna della macchina, nel piano meridiano, ma obliquamente rispetto alla normale alle linee di forza del campo toroidale nella posizione di lancio. In questa prima parte del lavoro si pone l’accento sull’analisi locale, di tipo WKB, del fenomeno, vale a dire sulle caratteristiche delle dispersioni e si studia prima di tutto la dispersione fredda e poi quella piú completa basata sull’equazione di Vlasov. Si studia in grande dettaglio il comportamento intricato di entrambe le dispersioni nell’intorno del valore critico di Preinhaelter e Kopecky dell’angolo d’iniezione. Questo andamento complicato della dispersione non era stato studiato nei lavori esistenti sull’argomento.

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Резюме Проводится подробный анализ распространения и затухания обыкновенных волн в области электронной циклотронной частоты в стратифицированной плазме Токамака. Прелполагается, что волны запускаются со стороны слабого магнитного поля машины в меридианной плоскости под углом к перпендикуляру в точке запуска к тороидаляному магнитному полю. В первой части статьи проводится ВКБ анализ процесса,. т.е. исследуется локальное дисперсионное соотношение, сначала в холодном случае, а затем, учитывая эффекты, связанные с конечным ларморовским радиусом. Особое внимание уделяется трудностям, связанным с холодной и горячей дисперсиями вокруг критического угла инжектирования Преннхалтера и Копецкого. Это сложное поведение не было проанализировано в предыдущих работах на эту тему.

     

Thermal effects on parallel resonance energy of whistler mode wave

In this short communication, we have evaluated the effect of thermal velocity of the plasma particles on the energy of resonantly interacting energetic electrons with the propagating whistler mode waves as a function of wave frequency and L-value for the normal and disturbed magnetospheric conditions. During the disturbed conditions when the magnetosphere is depleted in electron density, the resonance energy of the electron enhances by an order of magnitude at higher latitudes, whereas the effect is small at low latitudes. An attempt is made to explain the enhanced wave activity observed during magnetic storm periods.     

Test particle simulations of resonant interactions between energetic electrons and discrete,multi-frequency artificial whistler waves in the plasmasphere

Modulated high frequency(HF) heating of the ionosphere provides a feasible means of artificially generating extremely low frequency(ELF)/very low frequency(VLF) whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high energy electrons. Combining the ray tracing method and test particle simulations, we evaluate the effects of energetic electron resonant scattering driven by the discrete, multi-frequency artificially generated ELF/VLF waves. The simulation results indicate a stochastic behavior of electrons and a linear profile of pitch angle and kinetic energy variations averaged over all test electrons. These features are similar to those associated with single-frequency waves. The computed local diffusion coefficients show that, although the momentum diffusion of relativistic electrons due to artificial ELF/VLF whistlers with a nominal amplitude of ～ 1 pT is minor, the pitch angle scattering can be notably efficient at low pitch angles near the loss cone, which supports the feasibility of artificial triggering of multi-frequency ELF/VLF whistler waves for the removal of high energy electrons from the magnetosphere. We also investigate the dependences of diffusion coefficients on the frequency interval(△f) of the discrete, multi-frequency waves.We find that there is a threshold value of △f for which the net diffusion coefficient of multi-frequency whistlers is inversely proportional to △f(proportional to the frequency components Nw) when △f is below the threshold value but it remains unchanged with increasing △f when △f is larger than the threshold value. This is explained as being due to the fact that the resonant scattering effect of broadband waves is the sum of the effects of each frequency in the ‘effective frequency band’. Our results suggest that the modulation frequency of HF heating of the ionosphere can be appropriately selected with reasonable frequency intervals so that better performance of controlled precipitation of high energy electrons in the plasmasphere by artificial ELF/VLF whistler waves can be achieved.     

离子对电磁波传播特性的影响

对等离子体中电磁波传播的平板几何模型进行了修正, 讨论了离子对电磁波在大气压均匀非磁化弱电离等离子体中的反射、吸收和透射等传播特性的影响。数值分析的结果表明: 大气条件下, 离子对电磁波在均匀非磁化弱电离等离子体中传播特性的影响是显著的, 同时给出等离子体对电磁波的最大吸收值和吸收宽带。     

Propagation of waves in a multicomponent plasma having charged dust particles

Propagation of both low and high frequency waves in a plasma consisting of electrons, ions, positrons and charged dust particles have been theoretically studied. The characteristics of dust acoustic wave propagating through the plasma has been analysed and the dispersion relation deduced is a generalization of that obtained by previous authors. It is found that nonlinear localization of high frequency electromagnetic field in such a plasma generates magnetic field. This magnetic field is seen to depend on the temperatures of electrons and positrons and also on their equilibrium density ratio. It is suggested that the present model would be applicable to find the magnetic field generation in space plasma.     

Kinetic study of instability growth rate in a helicon plasma discharge source

In this work, a kinetic model is developed to study the effects of the radio frequency antenna wavenumber, helicon plasma electron density, as well as their drift velocity and temperature on the instability increment rate of the helicon wave in both longitudinal and transverse directions. The ion acoustic (IA) wave frequencies and wavenumbers of the helicon waves are obtained when the maximum wave energy is deposited on the plasma ions. Moreover, it is shown that, at the IA wavenumber and frequencies, while the longitudinal instability increment rates for both the helicon and IA waves are ignorable, the transverse instability increment rate for both the helicon and IA wave increases. Besides, the longitudinal instability increment rate for the helicon or IA wave has non‐zero resonant frequencies. On the other hand, the transverse instability increment rate of helicon or IA wave can be neglected. Furthermore, it is observed that, while both the imaginary part of longitudinal permittivity and longitudinal instability increment rate are not influenced by the electron temperature, their transverse component increases linearly with the electron temperature. In addition, the imaginary part of transverse permittivity increases almost linearly with the drift velocity of the plasma electrons.     

Ionization self-channeling of whistler waves in a collisional magnetized plasma

An investigation is made of the self-interaction of whistler waves (whistlers) involving the formation of waveguide channels in a collisional magnetoactive plasma as a result of its additional ionization by the field of the propagating wave. Simplified equations are derived to describe the behavior of the whistler field in a channel of enhanced plasma density in the presence of electron collisions. Self-consistent distributions of the field and the plasma corresponding to steady-state ionization self-channeling of whistlers are obtained by numerically solving the equations for the field together with balance equations for the electron density and energy. Our estimates indicate that this effect can be observed under laboratory conditions. Zh. éksp. Teor. Fiz. 112, 1285–1298 (October 1997)     

Modulation of the non-linear ion acoustic waves in a plasma consisting of warm ions and isothermal electrons

Summary Modulation of one-dimensional ion acoustic waves in a plasma consisting of a mixture of warm ions and isothermal electrons has been studied using the derivative expansion method. A non-linear Schr?dinger-type equation governing the complex amplitude of the perturbed ion density is obtained. The small-wave-number limit has been considered to compare it with the oscillatory solution of the Korteweg-de Vries equation obtained by Tagare and Lai using the reductive perturbation method. A good agreement has been found.     

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.     

Excitation of wake-field waves in plasma by a microtron beam

The experimental study of excitation of wake-field waves in plasma by a sequence of electron bunches of a microtron beam has been carried out. Results of measurement of the spectrum of electrons after their passage through plasma confirm the effect of adding of waves from a sequence of about 100 bunches which leads to the increase in the amplitude from 1 V/cm up to 100 V/cm.     

Scattering of electromagnetic waves by static wormholes

Scattering of electromagnetic waves by static and traversable wormholes is discussed. Based on the fact that these spacetimes have no horizon, and regarding their non-trivial topology, we have developed the perturbation theory of scattering and the Born approximation for obtaining the differential scattering cross section. Some of the zeros of the scattering pattern at long wavelengths are determined which can be used for estimating the radius of the throat. The known result that in scattering by static spacetimes the linear polarization remains unchanged is verified here.     

Dust ion acoustic waves in non-thermal Cairns bi-Maxwellian plasma

Using kinetic theory approach, the dispersion relation ω_r and Landau damping rate γ for dust ion acoustic waves are investigated numerically and analytically in an unmagnetized collisionless dusty plasma considering Cairns distribution for electrons and ions in stationary dust particles background. The phase velocity and Landau damping rate are calculated in the limits v_td∥ < v_ti∥ << ω/k << v_te∥ . The electrons and ions non-thermality effects are incorporated via the non-thermality parameter (0 ≤ α < 1) . The real frequency ω_r and Landau damping rate γ of the mode in Cairns bi-Maxwellian distributed plasma are graphically shown to depend on plasma parameters namely non-thermality index α , ion to electron temperature ratio T_i∥/T_e∥ and the dust concentration parameter δ (=1 − ηZ_d) .     

Nonlinear propagation of relativistically intense electromagnetic waves in a collisionless plasma

We discuss the nonlinear propagation of relativistically intense electromagnetic waves into collisionless plasmas with special emphasis on one dimensional plane wave solutions of the propagating, standing and modulated types. These solutions exhibit a rich variety of phenomena associated with relativistic electron mass variation and coupling between transverse electromagnetic and longitudinal fields. They have important applications to problems of laser propagation, self-focusing in overdense plasmas, particle and photon acceleration and to electromagnetic radiation around pulsars.     

Ion cyclotron electrostatic waves in a low-temeprature low-density magnetized plasma

Summary The electrostatic dispersion relation for a low-temperature, low-density magnetized plasma has been studied in the range of the ion cyclotron frequency and its first harmonics. The presence of a forward wave and of an infinite number of backward waves has been shown. The characteristics of propagation of these modes and the possibility of conversion are analysed.

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Riassunto Viene studiata la relazione di dispersione elettrostatica relativa ad un plasma magnetizzato di bassa densità e di bassa temperatura nel campo della frequenza ciclotronica ionica e delle sue prime armoniche. Si mostra la presenza di un unico modo forward e di un insieme infinito di modi backward. Si analizzano le caratteristiche di propagazione di queste onde e la possibilità di conversioni tra di esse.

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Резюме Исследуется электростатическое дисперсионное соотношение для намагниченной плазмы с низкой температурой и низкой плотностью в области ионной циклотронной частоты и ее первой гармоники. Показывается наличие единственной моды в направлении вперед и бесконечного числа волн в обратном направлении. Анализируются характеристики распространения этих мод и возможность конверсии.

     

Dressed ion acoustic solitary waves in quantum plasmas with two polarity ions and relativistic electron beams

A theory for dressed quantum ion acoustic waves (QIAWs), which includes higher-order corrections when QIAWs are investigated by the reductive perturbation method, is presented for unmagnetized plasmas containing positive and negative ions and weakly relativistic electron beams. The properties of the QIAWs are investigated using a quantum hydrodynamic model, from which a Korteweg–de Vries equation is derived using the reductive perturbation method. An equation including higher-order dispersion and nonlinearity corrections is also derived, and the physical parameter space is discussed for the importance of these corrections.     

基于试验粒子模拟的电离层人工调制激发的极低频和甚低频波对磁层高能电子的散射效应

电离层调制加热能够有效激发极低频和甚低频(ELF/VLF)波,其中向上传播进入磁层的ELF/VLF波能够与高能电子发生共振相互作用,具有人工沉降高能电子、消除辐射带等潜在实际用途.本文综合运用射线追踪和试验粒子方法模拟电离层人工激发的单频ELF/VLF波在电离层和磁层的传播,以及在外辐射带层与高能电子的共振相互作用过程,通过投掷角和能量散射系数评估人工ELF/VLF波对磁层高能电子的共振散射效应.研究表明,电离层人工ELF/VLF波传播到磁层后呈现高倾斜性,传播所能跨域的空间范围主要取决于加热的纬度位置和调制频率.在内辐射带,与～100 keV到几个MeV高能电子发生一阶共振相互作用的为10 kHz的VLF波段;在外辐射带,为几百Hz到1 kHz的ELF波段.对于L=4.5的外辐射带,试验粒子模拟结果显示,单个粒子在人工ELF波作用下投掷角和能量(α,E)的改变具有随机性,而所有试验粒子平均化的?α2和?E2随时间呈现出近似线性的增大,说明波粒共振散射过程体现出整体性.基于试验粒子模拟得到的共振散射系数表明,幅度为10 pT的人工ELF波可在外辐射带的磁赤道局地对1 MeV电子产生较强的投掷角散射效应,进而影响高能电子的损失、沉降等动力学过程.当人工ELF/VLF波在传播过程中变得高度倾斜,不仅最基本的一阶共振十分重要,高阶共振散射也具有较大效应.这些定量分析结果表明,通过电离层加热激发人工ELF/VLF哨声波来沉降、消除辐射带高能电子具有可行性.     

Parametric generation of whistler waves due to the interaction of high-frequency wave beams with a magnetoplasma

The parametric generation of low-frequency whistler waves by a pump wave beam formed by high-frequency whistler waves with close frequencies is studied experimentally. The electromagnetic fields excited by the beats of two co- or counterpropagating high-frequency waves, or by an amplitude-modulated pump are studied. It is shown that the nonlinear currents at the beat (modulation) frequency are generated by a transverse ponderomotive force arising due to the finite width of the high-frequency beam. In this case, the nonlinear azimuthal drift currents enclose the pump beam and can radiate low-frequency whistler waves to the surrounding plasma.     

Radiation of whistler waves in a magnetized plasma medium in the presence of density ducts

We investigate the influence of density ducts on the radiation of given sources in a magnetoplasma. We obtain the full-wave solution for the problem of radiation from annular electric and magnetic currents in the presence of a plasma column (density duct) oriented along an external magnetic field and surrounded by a uniform background magnetoplasma. Both the discrete part of the spatial spectrum of excited waves and the continuous part of the spectrum are considered. We calculate the total radiated power and partial powers radiated in separate eigenmodes guided by the column. It is established that in the whistler frequency range the presence of a channel with enhanced plasma density can cause a considerable increase in the radiation power of annular sources. We give concrete estimations for the ionospheric conditions and compare these results with the results obtained previously for the case of a uniform magnetoplasma without density ducts.Nizhnii Novgorod University. Tranlated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 7, pp. 887–908, July, 1994.     

Low-frequency variable charge solitary waves in a collisionless dusty plasma with a Cairns-Gurevich ion velocity distribution

In this paper, the problem of large amplitude dust acoustic (DA) solitons has been addressed in a charge varying dusty plasma with ions following a Cairns-Gurevich distribution. Based on the orbit motion limited approach, the correct Cairns-Gurevich ion charging current is presented for the first time. The expression relating the variable dust charge to the plasma potential is given in terms of the Lambert function and we take advantage of this transcendental function to, carefully, analyse DA solitons in a charge varying dusty plasma with trapped nonthermal ions. Our results show that the spatial patterns of the variable charge solitary wave are significantly changed due to the presence of ion population modelled by the Cairns-Gurevich distribution. An addition of a small concentration of trapped nonthermal ions makes the solitary structure less spiky, grows the net negative charge residing on the dust grain surface, and contributes to the electron depletion. Finally, our investigation is extended to highlight the effect of the grain dust charge variation. We have shown that under certain conditions, the impact of dust charge fluctuation may furnish an alternate physical mechanism rasing anomalous dissipation, which becomes more strong and may predominate over the dispersion as the nonthermal character of ions following the Cairns-Gurevich distribution increases.