arXiv subjects

Zensho Yoshida

Publications and source records attributed to Zensho Yoshida.

32 records · Page 2Linked to original sources

arXiv2015

Observation of particle acceleration in laboratory magnetosphere

The self-organization of magnetospheric plasma is brought about by inward diffusion of magnetized particles. Not only creating a density gradient toward the center of a dipole magnetic field, the inward diffusion also accelerates particles and provides a planetary radiation belt with high energy particles. Here, we report the first experimental observation of a 'laboratory radiation belt' created in the Ring Trap 1 (RT-1) device. By spectroscopic measurement, we found an appreciable anisotropy in the ion temperature, proving the betatron acceleration mechanism which heats particles in the perpendicular direction with respect to the magnetic field when particles move inward. The energy balance model including the heating mechanism explains the observed ion temperature profile.

physics.plasm-ph↗

arXiv2015

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

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 global magnetic fluxes and helicity. A Lagrangian variational principle is presented that leads to a new, fully dynamical, \emph{relaxed magnetohydrodynamics} (RxMHD), such that all static solutions are Taylor states but also allows 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, \emph{multi-region relaxed magnetohydrodynamics} (MRxMHD) is developed.

physics.plasm-ph↗

arXiv2015

Nonlinear Alfvén waves in extended magnetohydrodynamics

Large-amplitude Alfvén waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfvén wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfvén waves by an extended MHD model that includes both the Hall and electron inertia effects. Interestingly, these \small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat different from that of solitons.

physics.plasm-ph↗

arXiv2015

Gauge Symmetries and Noether Charges in Clebsch-Parameterized Magnetohydrodynamics

It is shown that the Clebsch parameterization, upon canonizing the Hamiltonian system of ideal fluid or plasma dynamics, converts the Casimir invariants (mass and helicities) in the original noncanonical formulation into the Noether charges pertinent to the gauge symmetries of the parameterization. The problem is addressed in the context of magnetohydrodynamics. The concrete forms of the gauge symmetries of Clebsch parameterization are worked out.

math-ph↗

arXiv2015

Thermal equilibrium of non-neutral plasma in dipole magnetic field

Self-organization of a long-lived structure is one of the remarkable characteristics of macroscopic systems governed by long-range interactions. In a homogeneous magnetic field, a non-neutral plasma creates a "thermal equilibrium" which is a Boltzmann distribution on a rigidly rotating frame. Here, we study how a non-neutral plasma self-organizes in inhomogeneous magnetic field; as a typical system we consider a dipole magnetic field. In this generalized setting, the plasma exhibits its fundamental mechanism that determines the relaxed state. The scale hierarchy of adiabatic invariants is the determinant; the Boltzmann distribution under the topological constraint by the robust adiabatic invariants (hence, the homogeneous distribution with respect to the fragile invariant) is the relevant relaxed state, which turns out to be a rigidly rotating clump of particles (just same as in a homogeneous magnetic field), while the density is no longer homogeneous.

physics.plasm-ph↗

arXiv2015

Hamiltonian Formalism of Extended Magnetohydrodynamics

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 infinite-dimensional 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.

physics.plasm-ph↗

arXiv2014

A Stochastic Model of Inward Diffusion in Magnetospheric Plasmas

The inward diffusion of particles, often observed in magnetospheric plasmas (either naturally created stellar ones or laboratory devices) creates a spontaneous density gradient, which seemingly contradicts the entropy principle. We construct a theoretical model of diffusion that can explain the inward diffusion in a dipole magnetic field. The key is the identification of the proper coordinates on which an appropriate diffusion operator can be formulated. The effective phase space is foliated by the adiabatic invariants; on the symplectic leaf, the invariant measure (by which the entropy must be calculated) is distorted, by the inhomogeneous magnetic field, with respect to the conventional Lebesgue measure of the natural phase space. The collision operator is formulated to be consistent to the ergodic hypothesis on the symplectic leaf, i.e., the resultant diffusion must diminish gradients on the proper coordinates. The non-orthogonality of the cotangent vectors of the configuration space causes a coupling between the perpendicular and parallel diffusions, which is derived by applying Ito's formula of changing variables. The model has been examined by numerical simulations. We observe the creation of a peaked density profile that mimics radiation belts in planetary magnetospheres as well as laboratory experiments.

physics.plasm-ph↗

arXiv2014

Relabeling symmetry in relativistic fluids and plasmas

The conservation of the recently formulated relativistic canonical helicity [Yoshida Z, Kawazura Y, and Yokoyama T 2014 J. Math. Phys. 55 043101] is derived from Noether's theorem by constructing an action principle on the relativistic Lagrangian coordinates (we obtain general cross helicities that include the helicity of the canonical vorticity). The conservation law is, then, explained by the relabeling symmetry pertinent to the Lagrangian label of fluid elements. Upon Eulerianizing the Noether current, the purely spatial volume integral on the Lagrangian coordinates is mapped to a space-time mixed three-dimensional integral on the four-dimensional Eulerian coordinates. The relativistic conservation law in the Eulerian coordinates is no longer represented by any divergence-free current; hence, it is not adequate to regard the relativistic helicity (represented by the Eulerian variables) as a Noether charge, and this stands the reason why the "conventional helicity" is no longer a constant of motion. We have also formulated a relativistic action principle of magnetohydrodynamics (MHD) on the Lagrangian coordinates, and have derived the relativistic MHD cross helicity.

physics.plasm-ph↗

arXiv2014

Numerical study on a canonized Hamiltonian system representing reduced magnetohydrodynamics and its comparison with two-dimensional Euler system

Introducing a Clebsch-like parameterization, we have formulated a canonical Hamiltonian system on a symplectic leaf of reduced magnetohydrodynamics. An interesting structure of the equations is in that the Lorentz-force, which is a quadratic nonlinear term in the conventional formulation, appears as a linear term -ΔQ, just representing the current density (Q is a Clebsch variable, and Δ is the two-dimensional Laplacian); omitting this term reduces the system into the two-dimensional Euler vorticity equation of a neutral fluid. A heuristic estimate shows that current sheets grow exponentially (even in a fully nonlinear regime) together with the action variable P that is conjugate to Q. By numerical simulation, the predicted behavior of the canonical variables, yielding exponential growth of current sheets, has been demonstrated.

physics.plasm-ph↗

arXiv2013

Singular Casimir Elements of the Euler Equation and Equilibrium Points

The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal fluid and plasma dynamics, is addressed in the context of the Euler equation for an incompressible inviscid fluid. The problem is traced to a Casimir deficit, where Casimir elements constitute the center of the Lie-Poisson algebra underlying the Hamiltonian formulation, and this leads to a study of the symplectic operator defining the Poisson bracket. The kernel of the symplectic operator, for this typical example of an infinite-dimensional Hamiltonian system for media in terms of Eulerian variables, is analyzed. For two-dimensional flows, a rigorously solvable system is formulated. The nonlinearity of the Euler equation makes the symplectic operator inhomogeneous on phase space (the function space of the state variable), and it is seen that this creates a singularity where the nullity of the symplectic operator (the "dimension" of the center) changes. Singular Casimir elements stemming from this singularity are unearthed using a generalization of the functional derivative that occurs in the Poisson bracket.

math-ph↗

arXiv2011

Comparison of Entropy Production Rates in Two Different Types of Self-organized Flows: Bénard Convection and Zonal flow

Entropy production rate (EPR) is often effective to describe how a structure is self-organized in a nonequilibrium thermodynamic system. The "minimum EPR principle" is widely applicable to characterizing self-organized structures, but is sometimes disproved by observations of "maximum EPR states." Here we delineate a dual relation between the minimum and maximum principles; the mathematical representation of the duality is given by a Legendre transformation. For explicit formulation, we consider heat transport in the boundary layer of fusion plasma [Phys. Plasmas {\bf 15}, 032307 (2008)]. The mechanism of bifurcation and hysteresis (which are the determining characteristics of the so-called H-mode, a self-organized state of reduced thermal conduction) is explained by multiple tangent lines to a pleated graph of an appropriate thermodynamic potential. In the nonlinear regime, we have to generalize Onsager's dissipation function. The generalized function is no longer equivalent to EPR; then EPR ceases to be the determinant of the operating point, and may take either minimum or maximum values depending on how the system is driven.

physics.plasm-ph↗

arXiv2011

Beltrami-like fields created by baroclinic effect in two-fluid plasmas

A theory of two-dimensional plasma evolution with Beltrami-like flow and field due to baroclinic effect has been presented. Particular solution of the nonlinear two-fluid equations is obtained. This simple model can explain the generation of magnetic field without assuming the presence of a seed in the system. Coupled field and flow naturally grow together. The theory has been applied to estimate B-field in laser-induced plasmas and the result is in good agreement with experimental values.

physics.plasm-ph↗

arXiv2002

Generation of Flows in the Solar Chromosphere Due to Magnetofluid Coupling

It is shown that a generalized magneto-Bernoulli mechanism can effectively generate high velocity flows in the Solar chromosphere by transforming the plasma pressure energy into kinetic energy. It is found that at reasonable heights and for realistic plasma parameters, there is a precipitous pressure fall accompanied by a sharp amplification of the flow speed.

astro-ph↗

arXiv2001

Magneto-Fluid Coupling - Eruptive Events in the Solar Corona

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.

astro-ph↗