Energy inequalities for a model of wave propagation in cold plasma

Energy inequalities are derived for an elliptic-hyperbolic operator arising in plasma physics. These inequalities imply the existence of distribution and weak solutions to various closed boundary-value problems. An existence theorem is proven for a related class of Keldysh equations, and the failure of expected methods for obtaining uniqueness is discussed. The proofs use ideas recently introduced by Lupo, Morawetz, and Payne for a generalized Tricomi operator. The existence of strong solutions under open boundary conditions is also proven.Comment: 33 page

Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations

We study the long-time asymptotic of the solutions to Maxwell's equation in the case of a upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Despr\'es, L.M. Imbert-G\'erard and R. Weder, J. Math. Pures Appl. {\bf 101} ( 2014) 623-659, where the singular solutions to Maxwell's equations in the frequency domain were constructed by means of a limiting absorption principle and a formula for the heating of the plasma in the limit of vanishing collision frequency was obtained. Currently there is considerable interest in these problems, in particular, because upper-hybrid resonances are a possible scenario for the heating of plasmas, and since they can be a model for the diagnostics involving wave scattering in plasmas.Comment: This published version has been edited to improve the presentation of the result

A boundary-value problem for cold plasma dynamics

A weak Guderley-Morawetz problem is formulated for a mixed elliptic-hyperbolic system that arises in models of wave propagation in cold plasma. Weak solutions are shown to exist in a weighted Hilbert space. This result extends work by Yamamoto.Comment: 18 pages, tcilate

Rapidly solidified titanium alloys by melt overflow

A pilot plant scale furnace was designed and constructed for casting titanium alloy strips. The furnace combines plasma arc skull melting techniques with melt overflow rapid solidification technology. A mathematical model of the melting and casting process was developed. The furnace cast strip of a suitable length and width for use with honeycomb structures. Titanium alloys Ti-6Al-4V and Ti-14Al-21 Nb were successfully cast into strips. The strips were evaluated by optical metallography, microhardness measurements, chemical analysis, and cold rolling

The Hydromagnetic Interior of a Solar Quiescent Prominence. I. Coupling between Force-balance and Steady Energy-transport

This series of papers investigates the dynamic interior of a quiescent prominence revealed by recent {\it Hinode} and {\it SDO/AIA} high-resolution observations. This first paper is a study of the static equilibrium of the Kippenhahn-Schl\"{u}ter diffuse plasma slab, suspended vertically in a bowed magnetic field, under the frozen-in condition and subject to a theoretical thermal balance among an optically-thin radiation, heating, and field-aligned thermal conduction. The everywhere-analytical solutions to this nonlinear problem are an extremely restricted subset of the physically admissible states of the system. For most values of the total mass frozen into a given bowed field, force-balance and steady energy-transport cannot both be met without a finite fraction of the total mass having collapsed into a cold sheet of zero thickness, within which the frozen-in condition must break down. An exact, resistive hydromagnetic extension of the Kippenhahn-Schl\"{u}ter slab is also presented, resolving the mass-sheet singularity into a finite-thickness layer of steadily-falling dense fluid. Our hydromagnetic result suggests that the narrow, vertical prominence $H_{\alpha}$ threads may be falling across magnetic fields, with optically-thick cores much denser and ionized to much lower degrees than conventionally considered. This implication is discussed in relation to (i) the recent {\it SDO/AIA} observations of quiescent prominences that are massive and yet draining mass everywhere in their interiors, (ii) the canonical range of $5-60 G$ determined from spectral-polarimetric observations of prominence magnetic fields over the years and (iii) the need for a more realistic multi-fluid treatment.Comment: 45 pages, 14 figure

Multi-filament structures in relativistic self-focusing

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review

Self-similar solution of fast magnetic reconnection: Semi-analytic study of inflow region

An evolutionary process of the fast magnetic reconnection in ``free space'' which is free from any influence of outer circumstance has been studied semi-analytically, and a self-similarly expanding solution has been obtained. The semi-analytic solution is consistent with the results of our numerical simulations performed in our previous paper (see Nitta et al. 2001). This semi-analytic study confirms the existence of self-similar growth. On the other hand, the numerical study by time dependent computer simulation clarifies the stability of the self-similar growth with respect to any MHD mode. These results confirm the stable self-similar evolution of the fast magnetic reconnection system.Comment: 15 pages, 7 figure