Phase Space Hydrodynamics of Equivalent Nonlinear Systems: Experimental and Computational Observations

The one-dimensional Vlasov equation describes the behavior of an incompressible self-interacting classical fluid which moves in the (q, p) phase plane. This type of phase fluid occurs in many physical problems and its hydrodynamic properties can be examined from a general point of view. A characteristic feature with initially unstable spatially homogeneous configurations is the development of stable nonlinear phase structures. Such examples occur as the result of the gravitational Jeans instability, or the two-stream and negative-mass instabilities of charged-particle beams. These structures can be related to one another by extending a duality principle due to Dory. The stable cavities in phase space which have been observed in numerical calculations on the two-stream instability are compared with stable proton clusters which develop from the negative-mass instability in the mirror experiment DCX-1.