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Self-organization of an ordered structure occurs in a plasma under rather restrictive conditions. A new framework for a variational principle invokes a coercive form that results in a criterion for self-organizing relaxation of a two-fluid plasma. The constraints (constants of motion of the ideal model) are adjusted, through a weakly dissipative process, so that the relaxed state, under well-defined conditions, is a stable equilibrium independent of the direct effects of dissipation.

Abstract. The extended magnetohydrodynamics (MHD) system, including the Hall effect and the electron inertia effect, has a Hamiltonian structure embodied by a noncanonical Poisson algebra on an infinitedimensional phase space. A nontrivial part of the formulation is the proof of Jacobi's identity for the Poisson bracket. We unearth a basic Lie algebra that generates the Poisson bracket. A class of similar Poisson algebra may be generated by the same Lie algebra, which encompasses the Hall MHD system and inertial MHD system.

The Clebsch parameterization (u=∇φ+α∇β) has advantages in elucidating structural properties of vector fields; for example, it helps formulating the Hamiltonian form of ideal fluid mechanics, representing topological constraints (Casimir invariants), integrating the Cauchy characteristics of vortex fields, etc. Because of its “nonlinear” formulation, however, there are some difficulties which must be carefully overcome. (1) It is not complete, i.e., for an arbitrary vector field u, we may fail to find three scalar fields (Clebsch parameters) φ, α, and β that satisfy u=∇φ+α∇β globally in space. (2) It is not uniquely determined, i.e., the map (u1,u2,u3)↦(φ,α,β) is not injective. A generalized form such that u=∇φ+∑j=1ναj∇βj is complete if ν=n−1 (n is the space dimension). However, when we need to control the boundary values of φ, αj, and βj (for example, to determine them uniquely), we have to set ν=n.

A magnetospheric configuration gives rise to various peculiar plasma phenomena that pose conundrums to astrophysical studies; at the same time, innovative technologies may draw on the rich physics of magnetospheric plasmas. We have created a "laboratory magnetosphere" with a levitating superconducting ring magnet. Here we show that charged particles (electrons) self-organize a stable vortex, in which particles diffuse inward to steepen the density gradient. The rotating electron cloud is sustained for more than 300 s. Because of its simple geometry and self-organization, this system will have wide applications in confining single- and multispecies charged particles.

Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic reconnection. By contrast, in the Taylor relaxation model for formation of macroscopically self-organized plasma equilibrium states, all these constraints are relaxed save for the global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, relaxed magnetohydrodynamics (RxMHD), such that all static solutions are Taylor states but also allows state with flow. By postulating that some long-lived macroscopic current sheets can act as barriers to relaxation, separating the plasma into multiple relaxation regions, a further generalization, multi-region relaxed magnetohydrodynamics (MRxMHD) is developed.

By modelling the coronal structures by "slowly" evolving Double-Beltrami two-fluid equilibria (created by the interaction of the magnetic and velocity fields), the conditions for catastrophic transformations of the original state are derived. It is shown that, at the transition, much of the magnetic energy of the original state is converted to the the flow kinetic energy.