3/9/2009 Colloquium - Jack Dorning

Jack Dorning Univeristy of Virginia

Event Info

Title:  The Metamorphosis of Nonlinear Plasma Waves: Periodic Waves to Solitary Waves to Shock Waves to Solitary Waves

Date: Mar 9, 2009
Location: 3105 Etcheverry Hall
Time: 4-5pm

Abstract

Many plasmas that arise in laboratory experiments and space physics environments are, to a very good approximation, collisionless on the time scales of interest, and are therefore very well describe by the Vlasov-Maxwell equations of plasma kinetic theory. It is well known that this nonlinear system of equations has an infinite number of spatially uniform equilibria—so-called Vlasov equilibria—and the question of the stability of these equilibria has been a longstanding one. Motivated by this question, we have studied this problem using the techniques of bifurcation theory and nonlinear dynamical systems analysis, and we have obtained exact analytical small-amplitude nonlinear wave solutions to the Vlasov-Poisson-Ampere equations. Since these waves are arbitrarily close to the manifold of Vlasov equilibria, they naturally have implications about the stability of the equilibria they are nearby. The waves are of three general types—periodic waves, solitary waves, and collisionless shock waves (also called cusps or traveling double-layers). We also have continued these small-amplitude wave solutions to large amplitude via numerical solutions to the related nonlinear equation for the electrostatic potential. The transitions, or metamorphoses, among these three types of waves were also studied, and will be described and explained. Since the solutions were obtained using bifurcation theory and nonlinear dynamical systems analysis, the basic ideas of these methods of nonlinear analysis will be reviewed before their application to the equations of plasma kinetic theory are described

Speaker Biography

Jack Dorning received his BS in Marine Engineering from the US Merchant Marine Academy at Kings Point, after which he served in the US Navy and then went to sea as a ship’s engineer in the US Merchant Marine. Subsequently, he pursued graduate studies at Columbia University where he earned his MS and PhD in Nuclear Science and Engineering. He began his career in science and engineering at Brookhaven National Laboratory (BNL), first as Assistant Physicist then as Associate Physicist and Group Leader. After three years, he moved from BNL to the University of Illinois, where he served as Associate Professor and Professor of Nuclear Engineering for fourteen years. Then he left for his current position as Whitney Stone Professor of Nuclear Science and Engineering, of Engineering Physics, and of Applied Mathematics at the University of Virginia. He is the recipient of several awards, including the Department of Energy’s E. O. Lawrence Memorial Award for research, and the American Nuclear Society’s A. H. Compton Award for education and E. P. Wigner Award for research; and he is a member of the National Academy of Engineering. His main research activities have been in the areas of reactor physics, neutron transport theory, computational methods development, and the kinetic theory of plasmas; he also has worked on nonlinear dynamical systems and deterministic chaos, and computational fluid mechanics.