The effects of an axial magnetic field on the convective amplification and the threshold intensity of Raman backscattering instability in an underdense, inhomogeneous plasma is investigated. Two cases of incident pump wave were considered. For the R-circularly polarization case it is shown that the amplification factor increases with the magnetic field, it also increases with the plasma density while the threshold intensity decreases. For the L-circularly polarization case, it is shown that the amplification factor decreases as the magnetic field and the plasma density increase, while the threshold intensity increases as the magnetic field increases but it decreases as the plasma density increases.

A recent analytic test of the instanton method performed by comparing the exact spectrum of the Lamé potential (derived from representations of a finite dimensional matrix expressed in terms of su(2) generators) with the results of the tight-binding and instanton approximations as well as the standard WKB approximation is commented upon. It is pointed out that in the case of the Lamé potential as well as others the WKB-related method of matched asymptotic expansions yields the exact instanton result as a result of boundary conditions imposed on wave functions which are matched in domains of overlap.

Recently, a growing research on the electromagnetic properties of biological tissues has been observed, particularly at microwave frequencies. The frequency variation of the dielectric properties of tissues at microwave frequencies may be described by the Cole-Cole relaxation model. This model is frequently used by researchers to extrapolate the measured permittivity data to higher frequencies based on polynomial frequency fits. Robust theoretical model that takes into consideration the geometry and distribution of tissue materials is much demanded. The aim of this paper is to develop a structured model to predict the dielectric properties of human cartilage tissues based on their microstructure. The presented approach is multi-scale which begins from the microscopic scale and derives the macroscopic properties after several scale-steps. The predicted model agrees reasonably with the estimated values of Cole-Cole relaxation model. Such a model would be useful in developing microwave imaging and patient treatment planning. Moreover, this model is expected to find application in non-invasive medical sensing where it can relate dielectric response to pathological structural changes in the tissue.