Stability Studies For Fast Electron Beams In Dense Plasmas

Fast ignition (FI) inertial fusion is a varied concept to the standard inertial confinement fusion (ICF) approach, -one which offers the relaxed symmetry conditions, reduced energy requirements and high energy gains. It involves the separation of the fuel compression and ignition phases, where the fuel compressed by using the conventional long pulse lasers is ignited by using the separate short pulse laser beams. In the later, laser beam energy is converted to the fast electrons at the critical density surface which then carry it to the ignition spot in the compressed fuel. To carry the minimum required energy to the ignition spot, stable propagation of the fast electron beam through the dense plasma fuel, ahead of the critical density surface, is a crucial step for FI concept. Furthermore, similar situations, where motion of relativistic electron beams through plasmas is involved, are also encountered in many high energy astrophysical phenomena. Therefore, in the last ten to fifteen years, various theoretical and numerical studies have been carried out to investigate the propagation properties of such relativistic electron beams through dense plasmas. However, due to the fact that such beams carry large amount of electric currents, their self-generated electromagnetic fields are very strong and that beam-plasma system involves various kinds of instabilities, their propagation through plasmas is a complex process that is still far from being well understood.In this dissertation, applying two-electron fluid model approximations, we study the propagation stability of the fast electron beams through the dense plasmas. Under macroscopic relativistic flow conditions, those related to the large beam velocities (i.e. u_b-c, where u_b is the beam flow velocity and c the speed of light), but non-relativisticthermal (microscopic) motions (with T_b<<(γ_b-1)m_ec²,where T_b is the beam temperature in KeV andγ_b the mass relativistic factor), our two-fluid analysis not only confirms theexisting notions about beam stability but also reveals for the first time the onset of quasi-electrostatic (QES) modes as well as an improved understanding of the beam hollowing structures. In chapter 1, a brief introduction about fast electron beams and their applications, the basics of nuclear fusion as well as the concept of FI inertial fusion energy, is provided.In chapter 2, axisymmetric radial modes of the fast electron beams in dense plasmas are investigated by employing an initial value approach under two-electron fluid approximations. The non-relativistic temperatures as well as collisional drag effects on the excited radial modes are studied by varying beam-plasma configurations,α=r₀/R₀,(where r₀ and R₀are the radial size of the beam and plasma respectively). It has been found that various radial modes are excited over the entire range of axial wavelengths, with long-wavelength regime dominated by hollowing-like modes characterized by azimuthal number of m=0 and radial numbers of n=2 and n=3, while short-wavelength regime dominated by higher radial mode numbers electromagnetic beam-plasma instabilities. Under asymmetric beam-plasma density conditions, finite temperatures and collisional effects are found to reduce the growth rate of the instabilities.In chapter 3, the nonlinear mode evolution for relativistic electron beams in dense plasmas is investigated with the help of power spectrum analysis in a three-dimensional (3D) space. It is found that various modes are excited over the entire 3D space. While, linear stage analysis confirms the onset and hierarchy of the known excited modes, with oblique modes dominating the two-stream and filamentation ones, as shown in the previous particle-in-cell (PIC) studies, the power spectrum analysis of the early nonlinear stage reveals excitation and development of the higher wavenumber modes. The electrostatic pinching like characteristics of such newly explored modes are further studied in chapter 4.In chapter 4, effect of various beam distribution profiles, those including uniform, Gaussian and flat-front cylindrical type profiles, is studied on hollowing or ring like evolution of the beam. It is found that the hollow or ring like structures occur only for that profile which has steep gradients. The hollow formation mechanism is explained with the help of net current (beam plus plasma) and density evolution. Investigations based on power spectrum analysis reveal the nonlinear development of the high wavenumber modes, which further help to understand the mechanism of beam hollowing and filamentation. Chapter 5 contains a two-fluid model, with fully relativistic fluid equations for the hot electron beam, a plan for ongoing research, for studying the microscopic dynamics of the relativistic hot electron beams in dense plasmas. The analysis based on such a model is currently in progress.Finally, a brief summary ends the dissertation.