Relativistic electron cyclotron theory,revisited

Summary The stages of the relativistic theory leading from the Maxwell-Vlasov system to the absorption and emission coefficients for electromagnetic electron cyclotron waves in a thermonuclear magnetoactive plasma are critically followed, with a particular attention to the approximations involved. Simple and general forms are obtained, holding to arbitrary order in the electron Larmor radius expansion. The applicability limits of the lowest order in this expansion are analysed.     

The fully relativistic dielectric tensor for electron cyclotron interaction in a Maxwellian plasma

Summary A thorough analytical and numerical study of the fully relativistic dielectric tensor relevant to the electron cyclotron propagation and absorption in a Maxwellian plasma is presented for arbitrary values of the wave refractive index parallel to the equilibrium magnetic field. Both the Hermitian and the anti-Hermitian part are calculated relativistically and, in particular, as for the anti-Hermitian part, the finite Larmor radius effects are accounted for to any order. Limiting forms are obtained along with a detailed numerical comparison with the nonrelativistic form.

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Riassunto Si calcola, sia analiticamente che numericamente, il tensore dielettrico completamente relativistico di rilevanza nella propagazione e nell'assorbilnento ciclotronico elettronico in un plasma maxwelliano, per valori arbitrari dell'indice di rifrazione parallelo al campo magnetico di equilibrio. Si tien conto degli effetti relativistici sia nella parte Hermitiana che nella parte anti-Hermitiana, in questa ultima pure gli effetti di raggio di Larmor finito sono inclusi a tutti gli ordini. Si ottengono e si discutono limiti significativi e si presenta un dettagliato confronto numerico con la forma non relativistica del tensore dielettrico.

     

Instability of plasma waves in an electromagnetic field

Summary In the presence of a weak laser field the plasma scattering by electrons is discussed.

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Riassunto In presenza di un campo laser debole, si discute la diffusione del plasma mediante elettroni.

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Резюме В присутствии слабого лазерного поля обсуждается рассеяние плазмы на электронах.

     

Effect of self-generated magnetic field on the two-plasmon decay instability in a laser-produced plasma

Summary In this paper we have made a theoretical investigation on the two-plasmon decay instability of laser radiation in the presence of the selfgenerated magnetic field at the quarter-critical density region in a laserproduced plasma. The Vlasov equation in terms of guiding centre coordinates has been employed to obtain the nonlinear response of electrons in the plasma. The threshold power density of the incident laser radiation for the two-plasmon decay instability is always exceeded in currently employed power densities in laser-target experiments and above the threshold the growth rate of the instability is quite large. It is also noticed that the selfgenerated magnetic field enhances the threshold to a large extent, thus drastically reducing the growth rate of the instability. To speed up publication, the author of this paper has agreed to not receive the proofs for correction     

On a kinetic approach to the modulational stability of envelope solitons in a relativistic plasma in an external electric field

Summary The formation of envelope solitons is discussed in a relativistic plasma under the influence of a fluctuating electric field. We use the kinetic-theory approach for our analysis. Due to the larger inertia, only the electrons are considered to be relativistic and the ions to be nonrelativistic. A NLS equation is derived describing the motion of the solitary wave. This NLS equation actually comes from an approximation of a pair of equations which can be considered to be a relativistic generalisation of the Zakharov equation. We next discuss the exact form of the envelope solitary-wave solution of the NLS equation and the modulation stability of such a wave. When the density, momentum and energy of such wave packets are fixeda priori, conditions are derived for the parameters of the problem from such stability consideration.     

Ultrarelativistic excitation of beat waves in a hot magnetized plasma

Summary A theoretical investigation is made on the nonlinear relativistic excitation of an electrostatic electron plasma wave at the beat frequency of two high-power colinear laser beams in a hot, homogeneous and magnetized plasma. The relativistic Vlasov equation expressed in gyrokinetic variables has been employed to find the nonlinear response of the magnetized plasma electrons. It is noted that the power density associated with the excited beat wave is much higher for the relativistic consideration than that for the nonrelativistic consideration. The authors of this paper have agreed to not receive the proofs for correction.     

Decay and modulation instabilities of beat waves in a plasma

Summary A large-amplitude beat wave excited at the beat frequency of two copropagating laser beams is extremely unstable and suffers strong three- and fourwave parametric instabilities with large growth rates. The relativistic effects are seen to be negligible on both the decay and modulation instabilities. However, the growth rates of these instabilities are sensitive functions of the plasma parameters. The authors of this paper have agreed to not receive the proofs for correction.     

Theory of weak modified electron acoustic double layers

Summary We have obtained the double-layer solutions for the small-amplitude modified electron acoustic waves propagating in a plasma having one ion and two electron components. No DLs solutions are found to exist when the temperature of the free and trapped particles is considered to be the same for all the species. However, when the effects of the reflected hot electrons are considered, DL solutions are found to exist.

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Riassunto Si sono ottenute soluzioni del doppio strato per onde acustiche modificate dall’elettrone di piccola ampiezza, che si propagano in un plasma avente una componente ionica e 2 componenti elettroniche. Si trova che non esistono soluzioni DL quando la temperatura delle particelle libere e intrappolate si considera stessa per tutte le specie. Tuttavia si trova che le soluzioni DL esistono quando si considerano gli effetti degli elettroni caldi riflessi.

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Резюме Мы получили решения для двойных слоев в случае акустических волн с малой амплитудой, распространяющихся в плазме, имеющей одну ионную и две электронные компоненты. Показано, что не существуют решения для двойных слоев, когда температура свободных и захваченных частиц является одинаковой для всех компонент. Однако, когда учитывается влияние отраженных горячих электронов, решения для двойных слоев существуют.

     

Hydromagnetic surface waves in a moving compressible plasma column

Summary The dispersive characteristic of hydromagnetic surface waves along a plasma-plasma interface when one of the fluids has a relative motion has been studied as a function of the compressibility factors ₁/V ₁, wheres ₁ andV ₁ are the acoustic and Alfvén wave speed in one of the media. Both slow and fast magnetosonic surface waves for each symmetric and asymmetric modes can exist. The nature and existence of these modes depend on the values ofs ₁/V ₁ and ϑ, the angle of wave propagation. The phase velocity of the slow wave increases whereas for the fast wave it decreases with increase in the angle ϑ. The authors of this paper have agreed to not receive the proofs for correction.     

On the modulation of ion-acoustic solitary waves in a cylindrical warm plasma near critical density

Summary We have derived a modified cylindrical K-dV (MCK-dV) equation for an ion-acoustic wave in a warm plasma with two-temperature electrons, in a cylindrical geometry, near the critical density where the nonlinearity of the usual CK-dV vanishes. The solitary-wave solution of MCK-dV is then discussed analytically using the concept of adiabatic invariants and the basic theorem due to Lax, instead of any numerical evaluation. This modulated form of the solitary wave is then discussed graphically as regards its variation with respect to the change in concentration of law- and high-temperature electrons.     

Comments on heuristic models for electron turbulence

Summary The difficulties imposed by the largely nonlinear character of the differential equations governing turbulence resulted in many proposals for empirical models. We shall prove that some often used models are incorrect as they are clearly not properly normalized.

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Riassunto Le difficoltà imposte dal carattere largamente non lineare delle equazioni differenziali che regolano la turbolenza hanno dato come risultato molte proposte per modelli empirici. Si prova che alcuni modelli spesso usati non sono corretti poiché non possono essere normalizzati appositamente.

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Резюме Трудности, накладываемые нелинейным характером дифференциальных уравнений, описывающих турбулентность, приводят к большому числу эмпирических моделей. Мы доказываем, что некоторые часто используемые модели не являются корректными, так как они не нормированы надлежащим образом.

     

Cylindrical blast wave with radiation heat flux in self-gravitating gas

Summary A similarity solution of cylindrical shock waves propagating in a uniform atmosphere through self-gravitating gas including the influence of radiation heat flux has been investigated. This problem has also been studied in isothermal conditions. The total energy of the line explosion is assumed to be constant. The solutions of the problem are compared with the results obtained in adiabatic conditions through figures.     

On the envelope soliton near critical density in a plasma with cold ions and two-temperature electrons

Summary We have analysed the formation of envelope soliton near critical density in a plasma consisting of two-temperature electrons and cold ions. The non-linear Schr?dinger-like equation obtained isiφ _t +pφ _xx +q|φ|⁴φ=0 which we call the modified non-linear Schr?dinger equation. It is also observed that this approach leads to a physical situation where a linear combination of both the modified and usual NLS equations holds, in the formiφ _t +pφ _xx +q ₁|φ|²φ +q ₂|φ|⁴φ=0. It is demonstrated through graphical analysis thatq ₁,q ₂, thought of as a function of β(=T _el/T _eh), behave in opposite way. That is, whenq ₁ grows,q ₂ decays, or vice versa. Lastly we demonstrate that this equation can sustain a type of solution other than the usual solitary profile. The form of such a wave is also depicted graphically.     

Similarity solutions of isothermal flows behind a MGD blast wave in an inhomogeneous medium

Summary Self-similar solutions of isothermal flows behind a cylindrical magnetogasdynamic blast wave have been obtained. A strong cylindrical shock wave generated by a sudden line source explosion in an inhomogeneous medium of electrically conducting gas has been studied. Numerical and analytical treatments have been presented and a uniformly valid distribution of pressure, density and velocity profiles has been determined and the magnetic-field effects on the flow distributions have been investigated. The shock propagation law is determined by extending Whitham’s rule for a MGD flow with infinite electrical conductivity.

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Riassunto Si sono ottenute soluzioni autosimili di flussi isotermici dietro un’onda espansiva, magnetogasdinamica, cilindrica. è stata studiata un’onda d’urto forte cilindrica generata da un’improvvisa esplosione a sorgente lineare in un mezzo non omogeneo di un gas elettricamente conduttore. Si presentano trattamenti numerici e analitici e si è determinata una distribuzione uniformemente valida dei profili di pressione, densità e velocità e si sono studiati gli effetti del campo magnetico sulle distribuzioni del flusso. La legge di propagazione dell’urto si determina estendendo la regola di Whitham per un flusso MGD con conduttività elettrica infinita.

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Резюме Получются самоподобные решения для изотермических потоков за цилиндрической магнитогазодимамической ударной. Исследется сильная цилиндческая ударная волна, которая обрзуетсяв резуль↦ате внеапного взрыва линейного истоника в неоднородной среде электрически проводящего газа. Проводятся численное и аналитическое рассмотрение. Определяжтся распредение давления, профили плотности и скорости. йсследуется влияние магнитного поля на распредение потока. Определется закон распространения ударной волны, обобшая правило Витама для магнитогазодинамического потока с бесконечной электрической проводимостью.

     

Relativistic and nonrelativistic modulational instability of a laser radiation in an unmagnetized laser-produced plasma: Kinetic theory

Summary This paper presents a rigorous theoretical investigation of the relativistic and nonrelativistic modulational instability of a high-power laser radiation propagating in a collisionless and unmagnetized laser-produced plasma. The kinetic equationviz. the relativistic Vlasov equation has been employed to find the nonlinear response of electrons for this four-wave parametric process in the plasma. The actual motivation behind this theoretical investigation is to find the relativistic effect on this four-wave paremetric processviz. the modulational instability. Here, it can be noted that the modulational instability of the laser radiation under our situation has not a large but considerable relativistic effect and for the same set of plasma parameters the growth rate of the instability in ultrarelativistic consideration is approximately three times higher than that in the nonrelativistic consideration. The authors of this paper have agreed to not rective the proofs for correction.     

Analysis of electron cyclotron emission by lower-hybrid current drive plasmas

Summary Electron cyclotron emission may be used for diagnosing non-thermal electron distribution functions generated by radio-frequency current drive. Our attention is concentrated in theX-mode-downshifted second-harmonic range of frequencies, by inspecting at the radiation collected in the horizontal low-magnetic-field side of a tokamak. The cut-off presence eliminates the thermal first-harmonic emission and the non-thermal one may be observed without other inference. The electron distribution function is modelled by a suitable sum of drifting Maxwellians for reproducing the flat tails usually obtained in the presence of lower-hybrid power injection. This model is time saving as far as the computer simulations are concerned and permits a lot of runs in order to accomplish a wide parameters exploitation. A sensitivity analysis of ECE intensity is performed with respect to the main moments of the suprathermal electrons distribution function. The analysis shown that the radiation spectra are very sensitive to the perpendicular energy and to the number of fast electrons, while only a weak dependence on the parallel energy is found.     

Drift dissipative instabilities in hybrid frequency range

Summary The instabilities of electron convection mode in a collisional plasma including electromagnetic effects are investigated. It is found that all the three solutions of the linear-dispersion relation are unstable. It is shown that the ion temperature fluctuations can play a stabilizing role. An application to a typical low-temperature plasma is discussed. The authors of this paper have agreed to not receive the proofs for correction.     

MHD cylindrical shock wave in self-gravitating gas

Summary Similarity solutions of the propagation of cylindrical blast waves through a self-gravitating polytropic gas caused by an instantaneous release of finite energy are investigated theoretically including the influence of transverse magnetic field. A comparative study of the distributions of velocity, density, mass, pressure, temperature and magnetic field has been illustrated through figures. The authors of this paper have agreed to not receive the proofs for correction.     

Ion acoustic soliton propagation in a magnetized relativistic plasma

Summary The Korteweg-de Vries equation for ion acoustic waves in the presence of weakly relativistic ion streaming velocity is derived in a magnetic plasma. It is found that relativistic effects are important in the solitary wave propagation for both fast and slow modes. Earlier results are reconfirmed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Propagation of electron cyclotron waves in a weakly relativistic plasma with steep density and temperature profiles

Summary A detailed analysis is made of the deduction of systems of differential equations describing the propagation of both ordinary and extraordinary waves in the electron cyclotron frequency range in a stratified plasma, perpendicularly to the magnetic field and across the electroncyclotron fundamental resonance layer. The equations are derived under conditions of not too large electron temperature (the so-called weakly relativistic condition) and of very weak nonuniformities of the confining magnetic field. The effects of the nonhomogeneities of the equilibrium plasma density and temperature are carefully examined. It is shown that the propagation equations derived previously in the literature can be extended with only a moderately larger effort in computations to take account also of very strong density and temperature gradients.