ity a nonlocal potential which could fit neutron elastic scattering data in the energy range from 0.4 to 24 MeV and where the optical-model parameters were energy independent. This is, of course, a remarkable result since we know that the absorption, for instance, is changing quite dramatically by going from 0.4 to 24 MeV incident projectile energy. We believe that these findings of Perey and Buck strongly support our result that there exists a nonlocal potential, which is not explicitly energy-dependent, which describes elastic nucleon scattering in a wide energy range. The theory presented in this paper may serve as a convenient tool in deriving such a potential. Actual calculation of an energy-independent optical-model potential as outlined in this paper is in progress.We are grateful to Professor A. Faessler, Professor A. Weiguny, Professor M. stingl, and Professor G. Vagradov for many helpful discussions.A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, p, ~, :8, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables.PACS numbers: 47.10.+g, 03.40.0c, 47.65.+a, 52.30.+r Several advantages may be gained from expres-Hamiltonian systems are most elegant when exsing a set of equations in Hamiltonian form. In pressed in canonical coordinates. Hydrodynamaddition to their formal elegance, Hamiltonian ics is most usefully expressed in Eulerian varisystems possess Poincare invariants that influ-abIes. These two desiderata conflict. In pracence the dispersion of an ensemble of systems tice, the penalty paid for adopting noncanonical with clustered initial conditions. A manifestly coordinates is not severe, so that branch of the Hamiltonian formulation of a given problem makes dichotomy is pursued here. it easier to find those approximations that pre-Previously, the equations of hydrodynamics 1 serve the Hamiltonian character. Here we pre-and magnetohydrodynamics,2 in both Eulerian and sent such a formulation of hydrodynamics and Lagrangian form, have been shown to arise from magnetohydrodynamics. a suitable Hamilton's principle. Such a Lagrang-790

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We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

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A generalization of reduced magnetohydrodynamics is constructed from moments of the Fokker–Planck equation. The new model uses familiar aspect-ratio approximations but allows for (i) evolution as slow as the diamagnetic drift frequency, thereby including certain finite Larmor radius effects, (ii) pressure gradient terms in a generalized Ohm’s law, thus making accessible the adiabatic electron limit, and (iii) plasma compressibility, including the divergence of both parallel and perpendicular flows. The system is isothermal and surprisingly simple, involving only one additional field variable, i.e., four independent fields replace the three fields of reduced magnetohydrodynamics. It possesses a conserved energy. The model’s equilibrium limit is shown to reproduce not only the large-aspect-ratio Grad–Shafranov equation, but also such finite Larmor radius effects as the equilibrium ion parallel flow. Its linearized version reproduces, among other things, crucial physics of the long mean-free-path electron response. Nonlinearly, the four-field model is shown to describe diffusion in stochastic magnetic fields with good qualitative accuracy.

Transport and mixing properties of Rossby waves in shear flow are studied using tools from Hamiltonian chaos theory. The destruction of barriers to transport is studied analytically, by using the resonance overlap criterion and the concept of separatrix reconnection, and numerically by using PoincarC sections. Attention is restricted to the case of symmetric velocity profiles with a single maximum; the Bickley jet with velocity profile sech' is considered in detail. Motivated by linear stability analysis and experimental results, a simple Hamiltonian model is proposed to study transport by waves in these shear flows. Chaotic transport, both for the general case and for the sech* profile, is investigated. The resonance overlap criterion and the concept of separatrix reconnection are used to obtain an estimate for the destruction of barriers to transport and the notion of banded chaos is introduced to characterize the transport that typically occurs in symmetric shear flows. Comparison between the analytical estimates for barrier destruction and the numerical results is given. The role of potential vorticity conservation in chaotic transport is discussed. An area preserving map, termed standard nontwist map, is obtained from the Hamiltonian model. It is shown that the map reproduces the transport properties and the separatrix reconnection observed in the Hamiltonian model. The conclusions reached are used to explain experimental results on transport and mixing by Rossby waves in rotating fluids.

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