Study of Collective Interactions in Low Beta Dense Plasmas

Abstract

The low-beta plasmas reflect the strong magnetic pressure in the comparison of thermal statistical pressure which affects the plasma characteristics and the wave propagation. The collective interactions in low beta plasmas, for the reason of its micro and nano scale applications in the latest technological era, is studied in this research thesis. The electrostatic and electromagnetic modes, their instabilities and growth rates to study new horizon of frequency spectrum is focused in this dissertation. Whenever two charged particles mutually interact, it is done through Coulomb interaction. Though the separation distance among two particles becomes greater than the mean separation distance of particles and as a result the particles immediately interact with many other charged particles in its surroundings and causes collective interactions in plasma. In dense plasmas the charged particles act as a Fermi gas, so the quantum mechanical effects due to significant associated de Broglie length become important while studying the dynamics of charge carriers. The quantum hydrodynamic (QHD) model is helpful for the study of collective interactions in dense plasmas that works well for low beta. The QHD is comparatively simple and captures many of the essential properties of plasma dynamics. This thesis contains three papers. The first paper discussion reveals novel aspects of dusty plasmas as the dust particles can coagulate and grow in size ranging from tens of nanometers to about hundreds of microns size. A semi classical Quantum Hydrodynamic Model (QHD) is employed which includes the quantum effects for plasma electrons in the terms of statistical degenerate pressure, Landau quantization, exchange-correlation potential, and tunneling potential. The low beta plasma characteristics provides the opportunity for the usage of two potential theory in order to derive a complex equation of dispersion of the shear Alfvén wave in quantum dusty magneto plasmas. Analytical simplification of dispersion equation provides the damping rate of the shear Alfvén wave which is verified graphically for a typical set of parameters. It is noticed that the damping rate depends upon the quantum properties of Landau quantization, exchange-correlation, and tunneling potential in addition to the dust radius which modifies the floating potential of the dust particles. Secondly, a system of single wall carbon nano-tubes is considered to study dispersive properties of plasma waves in the presence of uniform axial magnetic field. The impact of quantum characteristics of plasma electrons on the growth rate in the carbon nanotubes are studied. It is noticed that wave-guide configuration of the plasma system plays a significant role in the growth rate. The graphical analysis depicts the significant role of axial magnetic field in the Landau quantization. Thirdly, an electrostatic wave in a bounded geometry is studied for e-p-i quantum plasmas. The quantum hydrodynamic model is employed to find the dispersion relation xi

of waveguide mode. The complex frequency leads to the growth rate and the phase speed in the cylindrical geometry.