Yohei Kawazura

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 Jacobis 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.

High-β plasma formation and observation of peaked density profile in RT-1

High-β ECH plasma is generated and stably sustained in a magnetospheric configuration, the Ring Trap 1 (RT-1) device, generated by a levitated dipole field magnet. Geomagnetic-field compensation and optimized operation have realized drastic improvements in plasma properties. The maximum local β value has reached 70% and the pressure profiles have a rather steep gradient near the superconducting magnet. Electrons of the high-β plasma typically consist of 70% hot (~50 keV) and the rest of cold populations. Confinement time of the hot component plasma is 0.5 s with the optimized neutral gas pressure. By removing the coil support structure, the peaked density profile is observed in the strong field region.

Relativistic helicity and link in Minkowski space-time

A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves.

Improved beta (local beta >1) and density in electron cyclotron resonance heating on the RT-1 magnetosphere plasma

This study reports the recent progress in improved plasma parameters of the RT-1 device. Increased input power and the optimized polarization of electron cyclotron resonance heating (ECRH) with an 8.2 GHz klystron produce a significant increase in electron beta, which is evaluated by an equilibrium analysis of the Grad–Shafranov equation. The peak value of the local electron beta βe is found to exceed 1. In the high-beta and high-density regime, the density limit is observed for H, D and He plasmas. The line-averaged density is close to the cutoff density for 8.2 GHz ECRH. When the filling gas pressure is increased, the density limit still exists even in the low-beta region. This result indicates that the density limit is caused by the cutoff density rather than the beta limit. From the analysis of interferometer data, we found that inward diffusion causes a peaked density profile beyond the cutoff density.

Comparison of entropy production rates in two different types of self-organized flows: Bénard convection and zonal flow

Two different types of self-organizing and sustaining ordered motion in fluids or plasmas—one is a Benard convection (or streamer) and the other is a zonal flow—have been compared by introducing a thermodynamic phenomenological model and evaluating the corresponding entropy production rates (EP). These two systems have different topologies in their equivalent circuits: the Benard convection is modeled by parallel connection of linear and nonlinear conductances, while the zonal flow is modeled by series connection. The “power supply” that drives the systems is also a determinant of operating modes. When the energy flux is a control parameter (as in usual plasma experiments), the driver is modeled by a constant-current power supply, and when the temperature difference between two separate boundaries is controlled (as in usual computational studies), the driver is modeled by a constant-voltage power supply. The parallel (series)-connection system tends to minimize (maximize) the total EP when a constant-curr...

The complete set of Casimirs in Hall-magnetohydrodynamics

A procedure for determining all the Casimir constants of motion in magnetohydrodynamics (MHD) [E. Hameiri, Phys. Plasmas 11, 3423 (2004)] is extended to Hall-MHD. We obtain and solve differential equations for the variational derivatives of all the Casimirs, which must be satisfied for any dynamically accessible motion in Hall-MHD. In an extension of the more commonly considered Hall-MHD model, we also include the electron fluid entropy. The most interesting case for plasma confinement, which is usually true for axisymmetric configurations but desirable in general, is when both the magnetic field and the ion velocity field form the two separate families of nested toroidal surfaces. The Casimirs are then three functionals for each surface, involving the fluxes of certain vector fields and the number of particles contained in each. We also determine a family of independent Casimirs in a general configuration.

Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models

Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to [Comisso \textit{et al.}, Phys. Rev. Lett. {\bf 113}, 045001 (2014)] for the electron--positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked contrast to nonrelativistic Hall MHD that does satisfy the frozen-in condition. We also find violation of the frozen-in condition is accompanied by freezing-in of an alternative flux determined by a generalized vector potential. Finally, we derive a more general 3+1 Poisson bracket for nonrelativistic extended MHD, one that does not assume smallness of the electron ion mass ratio.

Observation of a new high-β and high-density state of a magnetospheric plasma in RT-1

A new high-β and high-density state is reported for a plasma confined in a laboratory magnetosphere. In order to expand the parameter regime of an electron cyclotron resonance heating experiment, the 8.2 GHz microwave power of the Ring Trap 1 device has been upgraded with the installation of a new waveguide system. The rated input power launched from a klystron was increased from 25 to 50 kW, which enabled the more stable formation of a hot-electron high-β plasma. The diamagnetic signal (the averaged value of four magnetic loops signals) of a plasma reached 5.2 mWb. According to a two-dimensional Grad-Shafranov analysis, the corresponding local β value is close to 100%.

Two-photon ionization of atoms by ultrashort laser pulses

Based on the direct solution of the time-dependent Schrödinger equation (TDSE), we theoretically study two-photon ionization (TPI) of a hydrogen atom by ultrashort vacuum ultraviolet (VUV) laser pulses with a photon energy close to the ionization threshold and a pulse width from 10 fs down to subfemtoseconds, for which the distinction between stepwise and direct processes becomes subtle. Our analysis on TPI by a double pulse reveals that direct processes are classified into two categories: a purely direct process with no real intermediate levels, and the one via Rydberg or continuum states, which rapidly escape from the nucleus. Our results also show that TPI becomes stepwise for subfemtosecond VUV pulses even for a wavelength corresponding to a direct process in the long pulse limit, since the broad spectrum of the pulse overlaps several discrete bound levels and excites them resonantly. This also leads to a phenomenon peculiar to attosecond pulses, namely, a significant red shift of the photoelectron energy spectrum. The Rydberg wave packet generated by an ultrashort near-threshold laser pulse, containing low-lying levels and the continuum, rapidly disintegrates into several parts. Nevertheless, the bound parts come back to the nucleus in fragments, and each fragment returns in the Kepler orbit time corresponding to its central principal quantum number. The lower-energy part of the double-pulse TPI electron energy spectrum exhibits the effect of the interference between the returning fragments and the wave packet excited by the second pulse.

Self-Organization and Heating by Inward Diffusion in Magnetospheric Plasmas

Through the process of inward diffusion, a strongly localized clump of plasma is created in a magnetosphere. The creation of the density gradient, instead of the usual flattening by a diffusion process, can be explained by the topological constraints given by the adiabatic invariants of magnetized particles. After developing a canonical formalism for the standard guiding center dynamics in a dipole magnetic field, we complete our attempt to build a statistical mechanics on a constrained phase space by discussing the construction principles of the associated diffusion operator. We then investigate the heating mechanism associated with inward diffusion: as particles move toward regions of higher magnetic field, they experience preferential heating of the perpendicular (with respect to the magnetic field) temperature in order to preserve the magnetic moment. A relationship between conservation of bounce action and temperature isotropy emerged. We further show that this behavior is scaled by the diffusion parameter of the Fokker-Planck equation. These results are confirmed by numerical simulations.