P. C. W. Fung

Theory of radiation in an anisotropic plasma

We follow up the work of Fung and Young (1982) to derive explicit expressions for the power emitted and the power observed per unit solid angle along the direction of the group velocity in an anisotropic plasma. We have deduced the ratio of the time interval during which the energy is emitted and the corresponding time interval during which the energy is received in this anisotropic case. Our result obtained is consistent to the basic well-known concept of group-ray propagation in a plasma.

The radiation of energy by a current in a plasma

The derivation of the differential power emitted in any given direction by a current J in a linear, homogeneous and non-absorbing plasma is reviewed in detail. The conventional derivation is shown to give the poweremitted; a formalism for the powerreceived is established by evaluating the Poynting vector in terms of the far field. It is pointed out that the two power expressions differ because the same energy dE is emitted in a time dte but received over a different time dtr. Moreover, a careful scrutiny of both the formalism for the power emission and for the power reception exposes implicit assumptions which do not hold if the plasma is anisotropic. The necessary steps for establishing a valid formalism for anisotropic media are briefly sketched.

Special features of cyclotron radiation in anisotropic plasmas

We analyze the special features of cyclotron radiation in four different modes radiated by a mildly relativistic electron current in an anisotropic plasma, taking into consideration that the radiation is transmitted along the group velocity, rather than the wave normal direction. A systematic series of numerical analysis is carried out, to demonstrate the characteristics of the focussing effect and Doppler effect of the radiation, arising from anisotropy. The parameters used pertain to plasmas and radiators of the types encountered in the terrestrial upper atmosphere and the solar corona.

The equation of polarization transfer in an inhomogeneous magnetized plasma

Recently we have derived the equation of polarization transfer in an inhomogeneous magnetized plasma in the case where absorption is so weak that the characteristic modes can be considered to be orthogonal. We extend this investigation to the study of polarization transfer in a plasma where the characteristic polarizations need not be orthogonal. We obtain explicit expressions for the Faraday rotation tensor, the absorption tensor, the mode-coupling tensor and the tensor describing the explicit spatial variation of characteristic polarizations due to plasma inhomogeneity.

Viscous Fluid Cosmological Models in a Bianchi Type I Universe

Exact solutions of the gravitational field equations for a Bianchi type I anisotropic space-time, filled with a viscous cosmological fluid obeying an equation of state of the form p = γ ρ, 0 ≤ γ ≤ 1, are obtained. We investigate both the viscous Zeldovich (γ = 1) and γ < 1 fluid cases, with constant and time varying (proportional to the mean Hubble factor) shear and bulk viscosity coefficients. It is shown that independently of the matter content, the equation of state and the time dependence of the shear and bulk viscosity coefficients, a viscous Bianchi type I universe experiences a transition to an inflationary era. Due to dissipative processes, the mean anisotropy and the shear of the Bianchi type I universe tend very rapidly to zero.

Exact two-soliton solutions to the Einstein gravitational field equations

Following our previous work on the existence of 1-soliton solution to the Einstein gravitational field equations in the presence of a spherically-symmetric static background field, we have found six sets of analytical 2-soliton solutions to the Einstein field equations under a certain ansatz in the absence of the stated background field. Numerical analysis shows that if the two solitons of the transverse nature are injected at space variable z→±∞, the longitudinal field componentg33 will acquire non-zero values for a bounded spatial region at later time. The nature of the solitons becomes rather complex when they interact. The amplitudegμν of each soliton may change its magnitude resulting from the interaction. We have found that we might interpret the evolution of one field component as the gravitational instanton in our solutions. We must remark also that the total energy of the interacting solitons remains constant, as expected, at all time. These solutions correspond to the situation where the Riemann tensor is in general non-zero and are truly non-trivial solutions.

Spectral analysis of cyclotron radiation in anisotropic plasmas

Following up our previous analysis of cyclotron radiation in anisotropic plasmas, we derived expression for the power received at a far field point per unit frequency range along the group velocity direction dP(ξ, α)/dξ. We then carry out a series of numerical analysis presenting the spectral features rather than directional features of cyclotron radiation. In particular, we analyse the power received per unit solid angle per unit frequency range d2P(ξ, α)/(dΦ dξ). It is expected the analysis result presented here can be compared directly with observation for parameters pertaining to astrophysical plasmas in stellar and terrestrial atmospheres.

Čerenkov radiation in anisotropic plasmas

Following our series of works on anisotropic radiation, we analyze the Čerenkov condition in magnetized plasmas in this paper. We have discovered that the usual Čerenkov condition cos θ=1/nβ‖ isnot satisfied at a far field point in anisotropic media, implying that when a charge is moving in a magnetized plasma, a linear shock wave front does not form. Thus we can calculate the power received at a far field per unit time in such a medium — this quantity could not be evaluated according to previous theory. Numerical examples are presented to show various relevant characteristics of Čerenkov radiation in model plasmas.

Soliton solutions to the Einstein gravitational field equations in the presence of a spherically-symmetric static background field

Using a differential geometry approach, we have found two sets of new solutions to Einsteins equation of gravity in the presence of a spherically-symmetrical gravitational background, like the Earth. The transverse and longitudinal components of the metric tensor representing the gravity waves are all soliton solutions, propagating towards the origin of the Earth. If we consider the situation where the static background field is absent, the solutions still remain soliton-like in nature. The difference between our result and Einsteins is attributed to the two approximations taken previously — weak field and ‘harmonic condition’.

COMPARISON OF SPIN-FLIP AND NORMAL SYNCHROTRON RADIATIONS FROM A CHARGE ROTATING IN A MAGNETIZED PLASMA

We have deduced the intensity spectral function for the spin-flip synchrotron radiation in the presence of a plasma. Using parameters appropriate to astrophysical conditions, we have attempted to compare the characteristics of the spin-flip synchrotron radiation and the normal synchrotron radiation in a magnetized plasma arising from an electron or positron rotating around the magnetic field. A rotating charge gives the maximum possible synchrotron radiative power as compared to a charge of the same energy but moving in a helical path. Since the spin-flip radiational does not depend on the form of the orbital path, whether circular or helical or along a straight line, the analysis presented here gives the lower limit of the relative importance of the spin-flip radiation to the normal synchrotron radiation emitted by the same radiator.