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THEORETICAL AND COMPUTATIONAL PLASMA PHYSICS 165 Kinetic Theory In the past, much theoretical work has been done employing fluid theories in circumstances where they are strictly not valid, because fluid descriptions are more tractable than kinetic ones. Such treatments are commonplace in astrophysics, space plasma physics, and long mean-free-path fusion physics. Advances driven by novel analytical approaches coupled with advances in computation are highly likely. The systematic exploitation of dimensionless small parameters to obtain reduced kinetic descriptions is one promising approach. Stochastic Effects in Evolving Plasmas In plasma physics, the conceptual advances of nonlinear dynamics and stochasticity theory have been applied to abstracted, simplified problems, capable of formulation in terms of Hamiltonian dynamics. Examples include criteria for stochastic magnetic field line "orbits" in tokamak and stellarator devices, nonlinear wave-particle interactions, and particle orbits near magnetic field nulls in the magnetosphere. During the next decade a key challenge for theoreticians will be to incorporate stochasticity self-consistently into evolving plasma systems. Magnetospheric magnetic reconnection serves as a useful example. How will stochastic orbits alter the evolution of magnetic fields and field nulls when the extent of the stochastic regions must be self-consistently determined in terms of the evolving field? Diagnostic and data processing advances that can identify stochasticity in plasma systems must be developed concurrently. Alpha-Particle Effects in Magnetically Confined Plasmas The level of sophistication of theoretical models and instrumentation techniques, and the high quality of plasma conditions achieved in laboratory experiments have progressed to the point that the deuterium-tritium experiments planned on the Tokamak Fusion Test Reactor (TFTR) and the Joint European Torus (JET) are expected to elucidate important physics issues regarding the influence of alpha particles on plasma stability and transport processes. There are two major phenomena associated with the appearance of significant densities of alpha particles in fusion devices. First, coherent plasma oscillations can be excited by resonant interaction with the alpha particles, either at low frequencies, corresponding to the toroidal precession rate, or at high frequencies, corresponding to the direct interaction of alpha particles with shear AlfvÃ©n waves. Such collective oscillations are driven unstable by the alpha- particle pressure gradient and result in the rapid expulsion of a significant number of high-energy particles. Several such modes have already been predicted theoretically and identified on existing devices, where they are excited by high-energy particles produced by injected beams or ion cyclotron heating. Second, high-energy particle orbits are