Applications of Lie-Transform Methods in Plasma Physics

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Brizard The investigator develops and analyzes low-frequency plasmakinetic and fluid models for studying the long-time-scaletransport processes and global magnetohydrodynamic behavior ofstrongly magnetized imhomogeneous plasmas. He uses Lie transformmethods to formulate the models. This provides certain technicaladvantages, both analytically and computationally, in exposingimportant features of global nonlinear plasma dynamics. Astrophysical plasmas, space plasmas, and "laboratory"plasmas seen in magnetic and inertial confinement plasma systemsshare certain fundamental properties that are not wellunderstood. In part this is because a plasma consists of a greatmany charged particles in motion, and the plasma's collectivebehavior is the result of interactions between all theseparticles. These interactions take place on very small lengthscales and time scales, and show themselves on larger scales. Theinvestigator develops formal methods to produce effectivedescriptions of the behavior of plasmas across multiple scales.This leads to a better understanding of fundamental properties ofplasmas.