Browsing by Author "Govender, Jagathesan."

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The crossfield current-driven ion acoustic instability in a two-ion plasma.
(1987) Govender, Jagathesan.; Bharuthram, Ramesh.
The behaviour of the crossfield current-driven ion acoustic instability in a plasma containing two ion species is theoretically examined. In our model the electrons are assumed to be hot and the ions cold, i.e. Tₑ »Tᵢ (~ 0), where both ion species are given the same temperature. The length and time scales are such that the electrons are magnetized and the ions unmagnetized. The linearised Vlasov equation is used to set up a dispersion relation for electrostatic waves for Maxwellian equilibrium velocity distributions of the electrons and ions. For the ion acoustic wave, a study is made of the dependence of the critical electron drift velocity (Vͨₒ) required to excite an instability on several parameters. The parameters include light ion fraction, heavy to light ion mass ratio, magnetic field strength and the propagation angle. In general the maximum value of Vͨₒ is found to be smaller than that for an unmagnetized plasma. Approximate analytic solutions of the dispersion relation are used to make comparisons with solutions from the full dispersion relation. The effect of drifts due to inhomogeneities in external magnetic field, perpendicular electron temperature and electron density on the growth rate of the ion acoustic instability are investigated in the ion rest frame. Finally, in a reference frame in which the electrons are stationary, both ion species are given external drifts. The effects of the ion drift velocities (both equal and unequal), electron to ion temperature ratio, light ion fraction, and heavy to light ion mass ratio on the growth rate of the ion acoustic instability are then studied.
Spherically symmetric cosmological solutions.
(1996) Govender, Jagathesan.; Maharaj, Sunil Dutt.
This thesis examines the role of shear in inhomogeneous spherically symmetric spacetimes in the field of general relativity. The Einstein field equations are derived for a perfect fluid source in comoving coordinates. By assuming a barotropic equation of state, two classes of nonaccelerating solutions are obtained for the Einstein field equations. The first class has equation of state p = ⅓µ and the second class, with equation of state p = µ, generalises the models of Van den Bergh and Wils (1985). For a particular choice of a metric potential a new class of solutions is found which is expressible in terms of elliptic functions of the first and third kind in general. A class of nonexpanding cosmological models is briefly studied. The method of Lie symmetries of differential equations generates a self-similar variable which reduces the field and conservation equations to a system of ordinary differential equations. The behaviour of the gravitational field in this case is governed by a Riccati equation which is solved in general. Another class of solutions is obtained by making an ad hoc choice for one of the gravitational potentials. It is demonstrated that for a stiff fluid a particular case of the generalised Emden-Fowler equation arises.