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BASIC PLASMA EXPERIMENTS 145 development of compact, subpicosecond terawatt lasers with beams that can be focused to intensities greater than 1018 W/cm2. At these intensities, an electron is accelerated to relativistic energies in one period of the laser light. This permits the study of highly nonlinear, fast, relativistic processes in laser-plasma interactions. If the laser is focused on an overdense plasma target, dc magnetic fields of the order of 109 G are predicted to occur. It will be important to determine whether the nonlinear ponderomotive forces and relativistic effects can reduce the diffraction of these ultrahigh-intensity laser beams, so that the light can be focused to beam sizes smaller than a few Rayleigh lengths, the limit expected at lower values of light intensity and in a linear medium. Chaos, Turbulence, and Localized Structures Nonlinear Particle Dynamics and Chaos. Modern concepts of nonlinear dynamics have created a renaissance in classical physics, bringing new techniques to bear on long-standing problems. One crucial issue in plasma physics is the onset of chaotic particle motion in response to coherent or turbulent wave fields. Of particular interest are a self- consistent description of the system under such circumstances and the evolution of the system from regular particle motion to chaos. It is now possible to conduct precisely controlled experiments in the laboratory to address these important problems, which are of interest in a wide variety of contexts, ranging from fluid dynamics to advanced particle accelerators. Nonlinear Wave Phenomena. With the exception of AlfvÃ©n waves, most of the other linear branches of the plasma dispersion relation have been explored. In addition, many nonlinear, three-wave coupling processes have been observed. However, the transition from linear to turbulent wave behavior is not understood. This includes the nonlinear behavior associated with almost every branch of the plasma dispersion relation. Turbulence. Very generally, plasmas are electrodynamic, many-body systems far from equilibrium that are dominated by nonlinear effects. Consequently, plasmas are typically highly turbulent, exhibiting large fluctuations in such quantities as the local density, temperature, and magnetic field, which can vary rapidly in time and space. Important examples of plasmas whose behavior is influenced profoundly by turbulence include essentially all magnetically confined fusion plasmas and many astrophysical and space plasmas. We have no first-principles understanding of turbulence in any plasma, and understanding such turbulent behavior is perhaps the key unsolved problem in plasma physics. This problem presents an important synergism with fluid dynamics, in that plasmas can often be modeled as fluids and understanding turbulence is central to a complete description of fluid systems.