Electromagnetic waves in plasmas

Abstract

This thesis embodies the investigations on the electromagnetic waves in plasmas. The investigations fall under two general headings, namely, wave propagation in plasmas in the presence of the Coriolis force (Part I) and crossover frequencies in plasmas (Part II). In Part I, the wave propagation in plasmas in the presence of the Coriolis force is analyzed and is based on the following papers: (i) Wave propagation in cold plasma in the presence of the Coriolis force, Plasma Phys., 12, 661, 1970. (ii) Wave propagation in cold plasma with negative ions in the presence of the Coriolis force, (to be published). Based on several investigations on the effect of Coriolis force on the problems of hydrodynamic and hydromagnetic instability, Chandrasekhar (1953) proposed that the Coriolis force, however small in magnitude, may have a dominant role in cosmic phenomena. He also pointed out that the superposition of the Coriolis force and magnetic force will not give rise to just the superposed results but the interaction of these two forces will lead to various new phenomena. Further, the numerical estimates made by Lehnert (1954) and Hide (1966) of the ratio of the Coriolis force to the magnetic force for the plasmas in the interior of the Sun and for conducting fluid in the Earth's core respectively, showed that for waves with very long wavelengths, the Coriolis force can play a dominant role especially in the presence of low magnetic fields. These basic studies led to the interest in the study of wave propagation in space plasmas in the presence of the Coriolis force. On the other hand, in laboratory plasmas the effect of rotation on wave propagation becomes important from the point of view of understanding certain basic properties of the rotating plasmas. The effects of Coriolis force on the Alfvén waves have been studied in detail by using the MHD model of description for plasmas. However, this model restricts the range of frequency much below ion cyclotron frequency i.e. ? « ?_ci. Also this model does not allow the study of ion-gyration effects which are very important for rotating plasmas, since the Coriolis force introduces an overall rotation of plasma in the same sense as positively charged species and opposite to that of negatively charged species. The interaction of these two rotational effects can give rise to new phenomena, especially in the case of negative ion plasmas. Thus, to study the effect of rotation on all kinds of waves in the ELF and ULF range for which 0 < ? < 2?, 2? < ? < (2?, 0 < ? ? ?_ci, ?_ci < ?, the inclusion of ion-cyclotron waves in the MHD waves is necessary. For this a two or multicomponent fluid model plasma has to be taken into account. Moreover, the collision effects can be very important especially when collision frequencies are of the same order as rotational frequency. Thus, our aim in Chapter 2 has been to give a detailed analysis of the wave propagation in a two-component plasma rotating with uniform angular velocity around the magnetic field lines. The collisional effects are also taken into account. The main emphasis has been to study the effects of rotational frequency on resonant and cut-off frequencies of the waves. Due to the introduction of the Coriolis force, the cut-offs and resonances show a characteristic variation with rotation affecting the widths of the stop and pass-bands. The change of relative location of resonances and cut-offs for the extraordinary wave gives rise to a new and interesting feature of phase reversal. The above investigation is extended in Chapter 3 for the plasma with one species of negative ions. The interaction of the Coriolis and magnetic forces in the presence of negative ions gives rise to interesting new phenomena which are not present in the positive ion plasmas. The most interesting result of two-ion hybrid resonant frequency together with its application in a rotating plasma is discussed. Though the model chosen is an ideal one, since solid body rotation is not a possibility for real plasmas, the various interesting results regarding the effect of the Coriolis force on the cut-offs, resonances, absorption coefficient, and refractive indices of waves justify this model. Some of the results which do need a further investigation with real models, as they can be of application in space or laboratory plasmas, have been mentioned and discussed. Part II deals with the discussions of the existence and behavior of the crossover frequencies in plasmas and is based on the following papers: (i) Crossover frequencies in multicomponent plasmas with negative ions, J. Geophys. Res., 77, 5597, 1972. (ii) Crossover frequencies in multicomponent plasmas. (To be published). (iii) Crossover frequencies in plasma with two species in the presence of the Coriolis force. Plasma Phys., 201, 1972. (iv) Crossover frequencies in plasmas with negative ions in the presence of the Coriolis force. (To be published). The study of low-frequency electromagnetic waves in plasmas in the vicinity of the crossover frequencies, the frequencies at which the refractive indices of two modes are equal, has received much attention because of the manifestation of the phenomena of intermode coupling and the reversal of polarization of the waves. These studies have led to an understanding of proton-whistlers in the ionospheric plasmas and the crossover frequency measurements have been used to determine the composition of the local ionospheric plasma. Most of the work on the understanding of the crossover phenomena has been confined to multicomponent plasmas consisting of positive ions only. Apart from the fact that the ionospheric plasmas can be composed of negative ions and the applications of negative ion-whistlers can be of great importance in measurement of negative ion concentration and mass ratio in plasmas (Shawhan, 1966), the study of the crossover frequencies in plasmas with negative ions encounters several difficulties, which are not present for the positive ion plasmas, thus creating an intrinsic interest in the problem. The aim of investigations made in Chapter 2 and 3 has been to point out these difficulties and then give an elegant and general mathematical treatment which gives a great deal of qualitative information regarding the crossover. Frequencies for any given plasma model without recourse to the cumbersome numerical study. We have also tried to discuss the applications of the measurement of crossover frequencies of negative ion-whistlers to estimate the concentrations and masses of negative ions. While dealing with waves in rotating plasmas in Part I, we came across an interesting phenomenon that crossover frequency, which is due to the presence of an additional ion species in the plasma, can exist in a plasma with one ionic species in the presence of the Coriolis force. Further investigation in Chapter 4 showed that the Coriolis force introduces a crossover frequency in the two-component plasma and is approximately equal to ?_gi. The numerical value of the crossover frequency for the Earth's rotation, ? ? 10?? rad/s and for the gyro frequency, ?_ci ? 10? c/s, is ? 0.45 × 10 c/s. This result can provide a diagnostic tool in the measurement of the magnetic field strength in the plasmas. The investigation is directly generalized for a multicomponent plasma with only positive ions and is shown that, in addition to the crossover frequencies due to positive ions, there is always a crossover frequency deriving from the Coriolis force. The above results, however, cannot be generalized for the plasma with negative ions in the same way as those for the plasmas with only positive ions. Hence, in Chapter 5, we have taken up the study of crossover frequencies in negative ion plasma.