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Coherence imaging spectroscopy (CIS) measures the two-dimensional profiles of both ion temperature and ion velocity in plasmas. The interferometric technique is realized by a certain relation between the phase and the wavelength of light emerging from a birefringent crystal. The calibration for the CIS system requires monochromatic and tunable light sources near the He II line (468.6 nm) or C III line (465 nm) where the CIS measures. In this research, the CIS system has been upgraded by implementing an electron multiplier CCD and a CIS cell. A monochromator validates the linearity of the phase relation on the wavelength near the He II line. As an in situ calibration at the Ring Trap 1 plasma device, two spectral lines of Ti and Zn lamps obtain the accurate dispersion function of phase. It is found that a simple method with two spectral lines is reliable and sufficient for the calibration.

An analytic estimate of the lower bounds on zonal enstrophy has been studied for the beta-plane model of two-dimensional barotropic flow. The estimate provides exact lower bounds on the zonal enstrophy, which hence must be satisfied regardless of the dynamics. The energy, impulse, circulation as well as the total enstrophy are invoked as constraints for the minimization of the zonal enstrophy. The corresponding variational principle has an unusual mathematical structure (primarily because the target functional is not a coercive form), by which the constraints work out in an interesting way. A discrete set of zonal enstrophy levels is generated by the energy constraint; each level is specified by an eigenvalue that represents the meridional mode number of zonal flow. However, the value itself of the zonal enstrophy level is a function of only impulse and circulation, being independent of the energy (and total enstrophy). Instead, the energy works in selecting the ‘level’ (eigenvalue) of the relaxed state. The relaxation occurs by emitting small-scale wavy enstrophy, and continues as far as the nonlinear effect, scaled by the energy, can create wavy enstrophy. Comparison to numerical simulations shows that the theory gives a consistent estimate of the zonal enstrophy in the relaxed state.

The dynamics of plasma can be formulated as a subalgebra of the Poisson manifold of the Clebsch fields. In this work, we extend this formulation to a Lorentz covariant form. We show that the generalized enstrophy, which means the "charge" of the Clebsch field, is no longer conserved by the relativistic effect, implying that the conservation of circulation is broken. Instead, we formulate a relativistically modified generalized enstrophy that is conserved in the relativistic model., Comment: 12 pages, 2 figures

The Kadomtsev–Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes ‘scattering’ of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are ‘ambient’ because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painleve test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.

Linearization of a Hamiltonian system around an equilibrium point yields a set of Hamiltonian-symmetric spectra: If $\lambda$ is an eigenvalue of the linearized generator, $-\lambda$ and $\bar{\lambda}$ (hence, $-\bar{\lambda}$) are also eigenvalues -- the former implies a time-reversal symmetry, while the latter guarantees the reality of the solution. However, linearization around a singular equilibrium point (which commonly exists in noncanonical Hamiltonian systems) works out differently, resulting in breaking of the Hamiltonian symmetry of spectra; time-reversal asymmetry causes chirality. This interesting phenomenon was first found in analyzing the chiral motion of the rattleback, a boat-shaped top having misaligned axes of inertia and geometry [Phys. Lett. A 381 (2017), 2772--2777]. To elucidate how chiral spectra are generated, we study the 3-dimensional Lie-Poisson systems, and classify the prototypes of singularities that cause symmetry breaking. The central idea is the deformation of the underlying Lie algebra; invoking Bianchi's list of all 3-dimensional Lie algebras, we show that the so-called class-B algebras, which are produced by asymmetric deformations of the simple algebra so(3), yield chiral spectra when linearized around their singularities. The theory of deformation is generalized to higher dimensions, including the infinite-dimensional Poisson manifolds relevant to fluid mechanics.

A coherence-imaging spectroscopy (CIS) technique was developed to investigate plasma confinement in a dipole system that imitates a planetary magnetosphere. Optical interference generated using birefringent crystals enables two-dimensional Doppler spectroscopy to measure ion temperatures and flow velocities in plasmas. CIS covers the entire dynamics of the pole areas as well as of the core and edge areas on a dipole confinement device. The two-dimensional visualization of these quantities in the magnetospheric-plasma device RT-1 was demonstrated using CIS.

A new Nd:YAG laser Thomson scattering (TS) system has been developed to explore the mechanism of high-beta plasma formation in the RT-1 device. The TS system is designed to measure electron temperatures (Te) from 10 eV to 50 keV and electron densities (ne) of more than 1.0 × 1017 m−3. To measure at the low-density limit, the receiving optics views the long scattering length (60 mm) using a bright optical system with both a large collection window (260-mm diameter) and large collection lenses (300-mm diameter, a solid angle of ∼68 × 10−3 str). The scattered light of the 1.2-J Nd:YAG laser (repetition frequency: 10 Hz) is detected with a scattering angle of 90° and is transferred via a set of lenses and an optical fiber bundle to a polychromator. After Raman scattering measurement for the optical alignment and an absolute calibration, we successfully measured Te = 72.2 eV and ne = 0.43 × 1016 m−3 for the coil-supported case and Te = 79.2 eV and ne = 1.28 × 1016 m−3 for the coil-levitated case near the inner edge in the magnetospheric plasmas.

Topological constraints are the key to an understanding of how a macrosystem can be different from the simple sum of microelements. The emergence of a macrostructure is a reflection of reduced degr...

When particles are magnetized, a diffusion process is influenced by the ambient magnetic field. While the entropy increases, the constancy of the magnetic moment puts a constraint. Here, we compare the E-cross-B diffusion caused by random fluctuations of the electric field in two different systems, the Penning-Malmberg trap and the magnetic dipole trap. A Fokker-Planck equation is derived by applying the ergodic ansatz on the invariant measure of the system. In the dipole magnetic field particles diffuse inward and accumulate in the higher magnetic field region, while, in a homogeneous magnetic field, particles diffuse out from the confinement region. The properties of analogous transport in a more general class of magnetic fields are also briefly discussed., Comment: 10 pages, 5 figures

The Ring Trap 1 (RT-1) device creates a laboratory magnetosphere, that is motivated by the Jovian magnetosphere, which contains self-organized, high-beta plasmas. In the RT-1 plasmas, the density limit for 8.2 GHz electron cyclotron heating (ECH) occurs at the electron densities 8.0×1017 m−3 and for 2.45 GHz ECH, 1.6×1017 m−3. We have used full-wave simulations to study the propagation and absorption of electromagnetic waves in the RT-1 plasmas in an effort to understand the observed density limits as well as the over-dense state in which the actual density exceeds the cutoff density of the magnetospheric plasma. The simulation results cannot explain the experimentally observed over-dense states and density limits in the view of the power absorption. We discuss possible reasons for the gap between the experiments and the simulation results.

We have developed a tomographic reconstruction method using a conditional Generative Adversarial Network to obtain local-intensity profiles from imaging-diagnostic data. To train the network we prepared pairs of local-emissivity and line-integrated images that simulate the experimental system. After validating the accuracy of the trained network, we used it to reconstruct a local image from a measured line-integrated image. We applied this procedure to the He II-emission imaging diagnostic for RT-1 magnetospheric plasmas, including the effects of stray light within the measured image to remove reflections from the chamber walls in the reconstruction. The local intensity profiles we obtain clearly elucidate the effect of ion-cyclotron-resonance heating. This method is a powerful tool for systems where it is difficult to solve the inversion problem due to the involved contributions of nonlocal optical effects or measurement restrictions.

A singularity of a system of differential equations may produce “intrinsic” solutions that are independent of initial or boundary conditions—such solutions represent “irregular behavior” uncontrolled by external conditions. In the recently formulated non-linear model of Alfven/Beltrami waves [Commum Nonlinear Sci Numer Simulat 17 (2012) 2223], we find a singularity occurring at the resonance of the Alfven velocity and sound velocity, from which pulses bifurcate irregularly. By assuming a stationary waveform, we obtain a sufficient number of constants of motion to reduce the system of coupled ordinary differential equations (ODEs) into a single separable ODE that is readily integrated. However, there is a singularity in the separable equation that breaks the Lipschitz continuity, allowing irregular solutions to bifurcate. Apart from the singularity, we obtain solitary wave solutions and oscillatory solutions depending on control parameters (constants of motion).

The conservation of the enstrophy (\(L^2\) norm of the vorticity \(\omega \)) plays an essential role in the physics and mathematics of two-dimensional (2D) Euler fluids. Generalizing to compressible ideal (inviscid and barotropic) fluids, the generalized enstrophy \(\int _{\varSigma (t)}\) f(\(\omega /\rho )\rho \mathrm {d}^2 x\) (f an arbitrary smooth function, \(\rho \) the density, and \(\varSigma (t)\) an arbitrary 2D domain co-moving with the fluid) is a constant of motion, and plays the same role. On the other hand, for the three-dimensional (3D) ideal fluid, the helicity \(\int _{M}\) V \(\cdot \varvec{\omega }\,\mathrm {d}^3x\) (\(\varvec{V}\) the flow velocity, \(\varvec{\omega }=\nabla \times \varvec{V}\), and M the three-dimensional domain containing the fluid) is conserved. Evidently, the helicity degenerates in a 2D system, and the (generalized) enstrophy emerges as a compensating constant. This transition of the constants of motion is a reflection of an essential difference between 2D and 3D systems, because the conservation of the (generalized) enstrophy imposes stronger constraints, than the helicity, on the flow. In this paper, we make a deeper inquiry into the helicity-enstrophy interplay: the ideal fluid mechanics is cast into a Hamiltonian form in the phase space of Clebsch parameters, generalizing 2D to a wider category of epi-2D flows (2D embedded in 3D has zero-helicity, while the converse is not true – our epi-2D category encompasses a wider class of zero-helicity flows); how helicity degenerates and is substituted by a new constant is delineated; and how a further generalized enstrophy is introduced as a constant of motion applying to epi-2D flow is described.

Bifurcation of equilibrium points in fluids or plasmas is studied using the notion of Casimir foliation that occurs in the noncanon- ical Hamiltonian formalism of the ideal dynamics. The nonlinearity of the system makes the Poisson operator inhomogeneous on phase space (the function space of the state variable), and creates a singularity where the nullity of the Poisson operator changes. The problem is an infinite-dimensional generalization of the theory of singular differential equations. Singular Casimir elements stemming from this singularity are unearthed using a generalization of the functional derivative that occurs in the Poisson bracket.

It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here we investigate a different type: the topological constraint imposed on "space." Such a constraint emerges from the null space of the Poisson operator linking an energy gradient to phase space velocity and appears as an adiabatic invariant altering the preserved phase space volume at the core of statistical mechanics. The correct measure of entropy, built on the distorted invariant measure, behaves consistently with the second law of thermodynamics. The opposite behavior (decreasing entropy and negative entropy production) arises in arbitrary coordinates. An ensemble of rotating rigid bodies is worked out. The theory is then applied to up-hill diffusion in a magnetosphere.

We formulate a nonlinear wave equations that describe amplitude and pitch modulations of one-dimensional Alfven waves propagating on a dispersive nonlinear plasma. The well-known fact that the ideal Alfven wave can propagate on a homogeneous ambient magnetic field with conserving an arbitrary wave shape of any amplitude is explained by invoking the Casimirs stemming from a “topological defect” (or, a kernel) in the Poisson bracket operator of the ideal magnetohydrodynamic (MHD) system. Including the Hall term, however, the Alfven waves are affected by the dispersive effect, and the aforementioned simplicity of the ideal Alfven waves is greatly lost; an arbitrary wave can no longer propagate with a constant shape. Yet, we observe an integrable structure in the nonlinear modulation (induced by a compressible motion) of the Alfven waves, which is described as nonlinear deformation of “Beltrami vortex” pertaining to the Casimirs.

The Ring Trap 1 (RT-1) device produces a magnetospheric configuration for the confinement of a high- β plasma with a Bi-2223 high-temperature superconducting magnet. Here we report the results of emergency demagnetization of the superconducting coil, where we could not connect current leads, temperature measurement connectors, and connectors for a persistent-current switch (PCS) heater to the coil. The spontaneous warming of the coil caused a rise in the flux-flow resistance of the superconducting coil, and the persistent current slowly decreased as coil resistance increased. Approximately 98% of the total stored magnetic energy was safely released before the quenching of the PCS, and there was no substantial damage to the superconducting coil.

High-β plasma is stably confined in the Ring Trap 1 (RT-1) device, a magnetospheric configuration with a levitated dipole field magnet. The plasma pressure is mainly resulted from high temperature electrons generated by electron cyclotron resonance heating (ECH), whose bremsstrulung was observed by an X-ray CCD camera. The coil support structure is the main loss route of the hot electrons, and higher-β discharge is realized by coil levitation. Confinement properties of charged particles in the magnetospheric configuration were investigated by using toroidal non-neutral plasma. Fluctuation-induced inward particle diffusion into the strong magnetic field region was realized due to the onset of diocotron (Kelvin–Helmholtz) instability.

The Ring Trap-1 (RT-1) device confines a high- β plasma in a magnetospheric configuration which is generated by a high-temperature-superconducting coil levitated in a vacuum chamber. The levitated coil is unstable with respect to the vertical motion when it is attracted from above. The vertical motion has been analyzed from the equation of motion and the flux conservation law and the response of the P D (proportional–derivative) feedback system of RT-1 has been formulated by using a transfer function. The result of the model analysis has shown sufficient agreement with experiments. To meet the various requirements in order to conduct the plasma experiments and measurement, the feedback gains are optimized to suppress a feedback noise in parallel with ensuring the stability of the system.

In a weakly ionized plasma, the evolution of the magnetic field is described by a "generalized Ohm's law" that includes the Hall effect and the ambipolar diffusion terms. These terms introduce additional spatial and time scales which play a decisive role in the cascading and the dissipation mechanisms in magnetohydrodynamic turbulence. We determine the Kolmogorov dissipation scales for the viscous, the resistive and the ambipolar dissipation mechanisms. The plasma, depending on its properties and the energy injection rate, may preferentially select one of the these dissipation scales. thus determining the shortest spatial scale of the supposedly self-similar spectral distribution of the magnetic field. The results are illustrated taking the partially ionized part of the solar atmosphere as an example. Thus the shortest spatial scale of the supposedly self-similar spectral distribution of the solar magnetic field is determined by any of the four dissipation scales given by the viscosity, the Spizer resistivity (electron-ion collisions), the resistivity due to electron-neutral collisions and the ambipolar diffusivity. It is found that the ambipolar diffusion dominates for resonably large energy injection rate. The robustness of the magnetic helicity in the partially ionized solar atmosphere would facilitate the formation of self-organized vortical structures., 6 pages

A thin disk accompanied by spindle-like jet, created commonly near massive central objects, exhibits a topologically singular aspect when viewed from an ideal macroscopic theory. The accreting inflow and jet's outflow are singular perturbation on the ambient Keplerian rotation, which are generated by some nonideal higher order (in the order of derivatives) effects. The Hall effect can generate such a structure in a weakly ionized plasma of a protostellar disk. Numerical estimate of the characteristic length scale defined by the singular perturbation justifies the precedence of the Hall effect.

The high temperature superconducting (HTS) floating magnet of the ring trap 1 (RT-1) reached the first experiment on levitation and plasma. The magnet using an HTS coil was levitated stably by levitation coil, and plasma was produced around the ring-shaped HTS magnet by electron cyclotron heating with 8.2 GHz microwave. This novel plasma device was constructed at the University of Tokyo to explore means of achieving the advanced-fuel fusion. The plasma confinement mechanism is based on the concept of high-beta relaxed state that is self-organized within flowing plasma. The HTS magnet is operated in a persistent-current mode and magnetically levitated in a plasma vacuum chamber. The weight of the HTS magnet is about 110 kg. Initially the HTS coil is cooled below 20 K by an external cooling system with detachable transfer tubes. After the transfer tubes are detached, an experiment of levitation and plasma is conducted while the HTS coil temperature remains within the range of 20 K-32 K without cooling. This paper describes the HTS coil design and test results of the HTS magnet as follows; an initial cooling, a persistent-current operation without cooling and the first levitation and the first plasma experiment.

The center of a Keplerian disk is an irregular singularity for the eigenfunctions of magnetorotational instabilities. The system is studied using the small-radius approximation, which by no means implies that the analysis is valid only in the vicinity of the center of the astrophysical disks. In fact, the singularity has an effect on the entire disk and yields continuous eigenvalues (growth rates in the unstable regime and real frequencies in the stable regime) with rather intriguing implications for the non-Hermitian nature of the rotating plasmas. Through the Laplace transform, as well as numerical simulations, interesting long-term behavior of the instability has been found.

The plasma confinement device "RT-1" which had a high temperature superconducting (HTS) floating magnet was constructed for advanced high-beta plasma and fusion research at the University of Tokyo. The high temperature superconducting (HTS) floating magnet is magnetically levitated inside the plasma vacuum vessel. Plasma is confined by a magnetic dipole field around the HTS floating magnet. The HTS floating magnet is operated in persistent-current mode and it consists of an HTS coil, an HTS persistent-current switch (PCS), a pair of demountable joints of current leads, detachable joints of a cooling tube, a thermal shield and a vacuum vessel. The HTS coil and the PCS and the thermal shield are cooled below 20 K by a flow of helium gas through the cooling tube. The floating HTS magnet is designed to operate in the temperature range from 20 K to 30 K without being cooled while it is levitated. We fabricated a persistent-current HTS coil that consists of the HTS coil and the PCS. Persistent-current operations and protection tests were conducted with the persistent-current HTS coil before it was mounted in the floating magnet cryostat. The current-decay rate was 0.9% in an 8 hour operation. The coil energy was safely discharged by inducing PCS quench in a protection test

A three-dimensional Hall-Magnetohydrodynamics (Hall-MHD) simulation code has been developed to study the self-organization process in two-fluid plasmas. An appreciable amount of flow is created in the direction perpendicular to the magnetic field, which is in a sharp contrast with the relaxed states in single-fluid MHD.

The cooperation of nonlinearity (producing collapsed characteristics) and dispersion (unfolding singularities) underlies a robust mechanism that imparts two distinct scales (L measuring the system size, and δi typically of the order of the ion skin depth) to the double Beltrami states of a two-fluid plasma. It is shown that the conventional single-fluid model [magnetohydrodynamic (MHD)] seemingly valid for a large system (δi/L≈0), fails to capture the small scale that is created by the singular perturbation of the two-fluid effect (dispersion). The small-scale component plays an important role in various plasma phenomena, such as coronal heating. The double Beltrami model is compared and contrasted with the standard MHD pathway (Parker’s model of current sheet, for instance).

The present study examined the electric field structure in a magnetized plasma in a prototype ring trap (Proto-RT) device with an internal ring electrode. A radial electric field of up to 3 kV m−1 was produced in the broad region between the electrode and vessel wall when the ring electrode was negatively biased. The resultant E×B toroidal rotational speed is comparable to the ion sound speed. Positive biasing, however, created a gap between the plasma and the electrode, failing to produce an internal electric field.

Electrons are injected into a stochastic magnetic region (SMR) of a stellarator vacuum configuration. Remarkably, when the SMR is present, some field-following electrons in the SMR move inwardly across the last closed flux surface. This inward propagation occurs in a collisionless process, but it is never observed for cases where the SMR is lost, nor is the electron density small in the SMR. These suggest the existence of cross-field transport that is associated with free-streaming of electrons along the stochastically wandering field lines in the SMR.

Space potential φs of non-neutral plasmas with a low density of ne∼1012 m−3 are measured by two floating-emissive probes. Nothing is different between them except the area S of filaments. Despite the fact that the thermionic current is sufficiently emitted, floating potential φf outputted from the smaller filament is much larger than the realistic φs at some measurement points, which is contrary to the widely known relation of φf⩽φs in probe measurements. The result is attributed to the insufficient probe current Ip collected in low-ne plasmas with a large φs. This is because, in such a plasma, Ip does not always satisfy the necessary condition of Ip>φs/RHI, where RHI is a high impedance resistor, although the value of Ip required for the floating emissive method is very small. In order to correctly determine the φs of the plasmas, S must be larger than φs/ene〈ve〉RHI, where e is the electron charge and 〈ve〉 is the mean speed of electrons collected to the probe.

A shear flow in a plasma brings about the non-Hermitian property, thereby invalidating the standard normal-mode analysis or energy principle for the study of stability. The Arnold method is an effective way to analyze the stability of a shear flow system. This method can give a Lyapunov stability condition to a relaxed state of two-dimensional flow or one-fluid magnetohydrodynamics (MHD). However, the Arnold method is not valid if the functional, whose first variation characterizes the relaxed (self-organized) state, is not a coercive (convex) form. Since the functional of the two-fluid MHD is not a coercive form, the stability analysis of such a flow requires a certain stronger (more coercive) constant, which corresponds to an enstrophy order constant. However, the enstrophy is not generally a constant. For a special class of two-fluid MHD flows, an enstrophy order constant can be found and a Lyapunov function that bounds the norm of all possible perturbations can be constructed.

Fluctuations in ambient shear flow exhibit interesting transient phenomena. Shear flow produces not only Kelvin–Helmholtz modes (global exponential instabilities represented by point spectra) but also local algebraic instabilities associated with multiple continuous spectra. Since the generating operator is non-Hermitian, the orthogonality of eigenmodes is broken, and unresolvable mode couplings (resonances) bring about secular behavior (algebraic instability). We analyze electrostatic fluctuations in a magnetized non-neutral (single species) plasma where the electrostatic potential parallels the stream function. This secular behavior is reproduced by solving the initial value problem with a renormalization method.

Local currents in a turbulent toroidal discharge plasma fluctuate intermittently, suggesting that the current density has a strongly inhomogeneous distribution. A canonical statistical model of current filaments accounts well for the spectral structure of the fluctuations. An innovative aspect of the model is that the ensemble is defined by the total current, not by the energy. Filamentation of the current density is a possible mechanism of producing resistance anomaly in a turbulent plasma.

In contrast to its well-known stabilization of the low-frequency plasma motions, a shear flow may equally effectively destabilize a class of plasma modes. The latter quality of the flow is illustrated by studying an incompressible ideal plasma with a simple velocity profile (Couette flow in a finite interval); it is found that interchange modes are driven more unstable through their interactions with the shear flow. In the presence of the flow shear, the growth rate of the perturbation increases due to the coupling of the Alfven wave with a Rayleigh–Taylor-type instability drive. Marginally stable modes in the flowless equilibrium achieve their maximum growth rate when the maximum flow velocity becomes comparable to the Alfven velocity. At larger shear flow velocities, however, the stabilizing “stretching” effect becomes dominant and the instability is quenched.

Stability of a special class of flows (which we call Beltrami flows) can be analyzed by invoking a constant of motion that bounds the energy of perturbations. This stability condition (a sufficient condition) suppresses any instability including nonexponential (secular) growth due to non-Hermiticity; it also prohibits nonlinear evolution to a large amplitude. The key to prove is the “coerciveness” of the constant of motion in the topology of the energy norm. The theory has been applied for an ideal (nondissipative) magnetized plasma.

The ion cyclotron range of frequencies (ICRF) heating with 3 MHz and ∼10 kW is being prepared in RT-1. The operation regime for electron cyclotron resonance (ECR) heating is surveyed as the target plasmas. ECRH with 8.2 GHz and ∼50 kW produces the plasmas with high energy electrons in the range of a few ten keV, but the ions still remain cold at a few ten eV. Ion heating is expected to access high ion beta state and to change the aspect of plasma confinement theoretically. The ICRF heating is applied to the target plasma as an auxiliary heating. The preliminary result of ICRF heating is reported.

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.

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., Comment: 21 pages, 2 figures

The stability of Beltrami flows has been analyzed. The model equation represents the coupling of the Kelvin–Helmholtz (KH) instability with Alfven waves. In a single Beltrami flow that parallels a force-free magnetic field, the magnetic field reduces the growth rate of the KH instability, while the marginally stable wave number is unchanged. Calculating the marginally stable eigenfunction of a magnetohydrodynamic flow, the necessary and sufficient condition for the exponential stability has been derived. The stability of double Beltrami flows has also been analyzed, which is represented by linear combinations of two Beltrami flows. Coupling of two vortices yields both stabilizing and destabilizing effects depending on the amplitudes and the eigenvalues of two Beltrami functions.

The structure of Kelvin's method, which is driving great advances in the study of shear-flow systems, has been carefully re-examined. It is shown that this method is a particular case of a generalized modal approach. The generality of Kelvin's solutions, which is an essential issue in the study of stability, is also proved. The possibility of extending Kelvin's method to the treatment of systems presenting spacial inhomogeneities other than the convective is discussed.

By modeling the closed field structures in the solar atmosphere 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. The analysis for predicting sudden changes is carried out through a set of algebraic equations obtained by relating the four characteristic parameters (two eigenvalues and two amplitudes) of the equilibrium to the macroscopic constants of motion (helicities and energy). It is shown that a catastrophic loss of equilibrium occurs when the macro scale of a closed structure, interacting with its local surroundings, decreases below a critical value; the catastrophe is possible only if the total energy of the structure (for given helicities) also exceeds a well-defined threshold. It is further shown that at the transition much of the magnetic energy of the original state is converted to the flow kinetic energy.

Electrostatic instabilities in electron plasmas have been studied by analyzing initial value problems. The self-electric field of a non-neutral plasma produces a flow that brings about non-Hermitian property into the generating operator. Because of the nonorthogonality of eigenmodes, the evolution of the system is rather complex. Secular behavior is a typical appearance of unresolvable mode couplings that may be cast in a representation of Jordan block. The coupling of the perpendicular (with respect to the magnetic field) electrostatic modes (Kelvin–Helmholtz or diocotron modes) and parallel plasma oscillations causes a more complex phenomena.

The Navier-Stokes (NS) system of equations is a central paradigm of nonlinear partial differential equations describing nonintegrable dynamics. The mathematical analysis of the NS system invokes a priori estimates for the energy and enstrophy. The difficulty stemming from the vortex-tube stretching effect is explained. By replacing the convective nonlinear term by a random noise term, one can develop a statistical model of turbulence. The mathematical framework of such modeling is also reviewed.

The conventional rigid rotation model of thermal equilibrium does not apply to a toroidal non-neutral plasma trap; the nonuniformity of the magnetic field produces an inhomogeneous flow. For sufficiently large ωc/ωp (ωc: cyclotron frequency; ωp: plasma frequency), the flow can be approximated by the E×B drift velocity. The toroidal equilibrium of an electron plasma has been analyzed for a rather complex geometry of magnetic shear configuration.

We have developed an ion cyclotron resonance frequency (ICRF) heating system for the Ring Trap 1 (RT-1) magnetospheric device. We excite slow waves from the polar region of the dipole magnetic field. The target helium plasma is produced by electron cyclotron heating. The electrons comprise high-temperature (>10 keV) and low-temperature (

Adiabatic invariants foliate phase space, and impart a macro-scale hierarchy by separating microscopic variables. On a macroscopic leaf, long-scale ordered structures are created while maximizing entropy. A plasma confined in a magnetosphere is invoked for unveiling the organizing principle ---in the vicinity of a magnetic dipole, the plasma self-organizes to a state with a steep density gradient. The resulting nontrivial structure has maximum entropy in an appropriate, constrained phase space. One could view such a phase space as a leaf foliated in terms of Casimir invariants ---adiabatic invariants measuring the number of quasi-particles (macroscopic representation of periodic motions) are identified as the relevant Casimir invariants. The density clump is created in response to the inhomogeneity of the energy level (frequency) of quasi-particles.

Probing of streaming electron plasmas with finite temperature is studied. For the first time, a current-voltage characteristic of an electric probe is measured in electron plasmas. Due to the fast flow of the electron plasmas, the characteristic curve spreads out significantly and exhibits a long tail. This feature can be explained calculating the currents collected to the probe. In flowing electron plasmas, the distribution function observed in the laboratory frame is non-Maxwellian even if the plasmas come to a state of thermal equilibrium. Another significant feature of the characteristic is that it determines a floating potential where the current equals zero, despite there being very few ions in the electron plasma. A high impedance probe, which is popularly used to determine the space potential of electron plasmas, outputs the potential. The method is available only for plasmas with density much smaller than the Brillouin limit.

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., Comment: 4 pages of two-column text (Latex) plus 3 pages of figures, submitted to The Astrophysical Journal Letters

The diocotron instability in a magnetized non-neutral plasma is a close cousin of the Kelvin–Helmholtz instability. A sheared magnetic field brings about coupling between the diocotron modes and the Langmuir waves that propagate along the magnetic field. The motion of electrons parallel to the magnetic field cancels the electric charge produced by the diocotron modes, resulting in stabilization of the diocotron instability.