| dc.description.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. | |
