G. Lampis

Global wave treatment of mode conversion and wave damping for perpendicular propagation across the electron cyclotron and upper-hybrid resonances

The processes of propagation and absorption of electron cyclotron extraordinary modes in a Tokamak type plasma slab are studied by means of a wave-dynamical system of differential equations in which temperature effects are taken into account. Also the mode conversion of the incoming wave into Bernstein waves is described by the propagation equations and is analysed in the parameter space together with its effects on the global absorption. Similarities and discrepancies between the results of the numerical integration of the full-wave system and those provided by the WKB approximation are discussed as a function of the electron density and temperature.

Oblique extraordinary and Bernstein electron cyclotron waves in a wave dynamical approach

The properties of the propagation and of the absorption of electron cyclotron extraordinary waves injected obliquely with respect to the external magnetic field in the meridian plane of a Tokamak-like plasma slab are studied by means of a system of wave-dynamical, hot and weakly relativistic propagation equations. The boundary value problem associated to this system is solved in a global way, thereby permitting the analysis of mode conversion between the incident extraordinary wave and the electron Bernstein wave. The results of rather wide scanning in density, electron temperature and injection angle are presented. In the low density regime the total absorption increases with the obliquity of the launch, according to the WKB theory. In the high density regime, well above the cold high-density cut-off, an unexpected absorption is found for small values of the angle of injection, respect to the direction of the magnetic field. This absorption is appreciable even for moderately high values of the electron temperature.

Wave-dynamical treatment of the ordinary electron cyclotron mode propagating perpendicularly to the magnetic field across the resonance region

A wave-dynamical analysis of the interaction of the ordinary wave propagating perpendicularly to the magnetic field across the electron cyclotron resonance is performed. A sufficient condition for the validity of a WKB approach is obtained, but it is shown that as far as the calculation of wave absorption is concerned, WKB results remain a good approximation, even if this condition is violated.

Role of the Bernstein modes in the electron cyclotron second-harmonic wave absorption

The propagation and absorption of perpendicular second‐harmonic electron cyclotron waves in a plasma slab are studied by means of propagation equations directly deduced from the Vlasov–Maxwell system. An electromagnetic wave injected from the vacuum into the plasma can be transformed into a quasielectrostatic forward mode, which, in turn, is converted into a Bernstein backward wave. The occurrence of this double‐conversion process and the global absorption and reflection are analyzed and the dependence of the phenomena on the plasma parameters and wave characteristics is investigated.

Absorption of electron cyclotron extraordinary waves in large size, high density plasmas

The absorption of oblique extraordinary waves in the electron cyclotron frequency range is analysed by means of a wave-dynamical scheme in hot high density plasmas. Strong wave damping is found for densities that largely exceed the nominal value of the cold high-density cut-off. The dependence of this phenomenon on the parameters of the plasma is studied and commented upon.

Oblique injection of EC ordinary waves in a Tokamak plasma

SummaryA 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.RiassuntoSi 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.РезюмеПроводится 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.

Model for description of transient behaviour of a Tokamak discharge

SummaryThe transient behaviour of a Tokamak discharge is analysed through a, simple electrodynamical model. From this model indications are obtained on the macroscopic parameters, controlled by the experimentalists, defining the range of existence and gross stability of the discharge. The findings of the analysis are compared with the experimental results of the Tokamak Thor.RiassuntoIl coniportamento di transitorio di una scarica Tokamak è analizzato attraverso un seniplice modello elettrodinamico. Da questo modello si ottengono indicazioni sui parametri macroscopiei, controllati sperimentalmente, i quali definiscono la regione di esistenza e di stability macroscopica della scarica. I risultati dell’analisi sono paragonati con i risultati sperimentali del Tokamak Thor.

Energy extraction from intense electron beams in hot plasmas by electron cyclotron waves

A hot weakly relativistic plasma in a magnetic field is considered in the slab description with an electron distribution which is the sum of an isotropic Maxwellian function plus a second shifted Maxwellian function describing an electron population drifting along the external magnetic field. The interaction of such a beam–plasma system with ordinary and extraordinary electron cyclotron waves propagating in a direction perpendicular to the external magnetic field and to the beam is studied. The physical system is analyzed in the geometrical optics limit and also by means of a wave‐dynamical treatment. A resonance layer due to the beam appears where the condition ωce=γω is verified, where γ=(1−v02/c2)−1/2 and v0 is the beam drift velocity. If the electron beam has a sufficiently high density, an ordinary wave coming from the high‐field side can be converted into an extraordinary mode precisely at ωce=γω, propagating then up to the upper‐hybrid layer where electron Bernstein waves are generated. When the be...

Wave‐dynamical analysis of conversion and absorption of oblique extraordinary and Bernstein modes near the second electron‐cyclotron harmonic

The propagation and absorption of oblique second‐harmonic electron‐cyclotron waves in a plasma slab are studied by means of propagation equations directly deduced from the Vlasov–Maxwell system. An electromagnetic wave injected from the vacuum into the plasma can be transformed into a quasielectrostatic forward mode, which, in turn, is converted into a Bernstein backward wave. The occurrence of this double conversion process and the global absorption and reflection are analyzed, and the dependence of these phenomena on the plasma parameters and on the wave characteristics is investigated.

Local power deposition for the perpendicular propagation of an ordinary wave across the electron cyclotron resonance layer

It is shown how the concept of local power deposition can be identified with the time rate of increase of the particle kinetic energy density at second order in the linearization procedure. The secular behaviour of the second order part of the distribution function is also explicitly pointed out.