The plasmonic eigenvalue problem

A plasmon of a bounded domain $\Omega\subset\mathbb{R}^n$ is a non-trivial bounded harmonic function on $\mathbb{R}^n\setminus\partial\Omega$ which is continuous at $\partial\Omega$ and whose exterior and interior normal derivatives at $\partial\Omega$ have a constant ratio. We call this ratio a plasmonic eigenvalue of $\Omega$. Plasmons arise in the description of electromagnetic waves hitting a metallic particle $\Omega$. We investigate these eigenvalues and prove that they form a sequence of numbers converging to one. Also, we prove regularity of plasmons, derive a variational characterization, and prove a second order perturbation formula. The problem can be reformulated in terms of Dirichlet-Neumann operators, and as a side result we derive a formula for the shape derivative of these operators.Comment: 22 pages; replacement 8-March-14: minor corrections; to appear in Review in Mathematical Physic

Noncontacting device to indicate deflection of turbopump internal rotating parts

Phase 2 (development) which was concluded for the ultrasonic Doppler device and the light-pipe-reflectance device is reported. An ultrasonic Doppler breadboard system was assembled which accurately measured runout in the J-2 LOX pump impeller during operation. The transducer was mounted on the outside of the pump volute using a C-clamp. Vibration was measured by conducting the ultrasonic wave through the volute housing and through the fluid in the volute to the impeller surface. The impeller vibration was also measured accurately using the light-pipe probe mounted in an elastomeric-gland fitting in the pump case. A special epoxy resin developed for cryogenic applications was forced into the end of the fiber-optic probe to retain the fibers. Subsequently, the probe suffered no damage after simultaneous exposure to 2150 psi and 77 F. Preliminary flash X-radiographs were taken of the turbine wheel and the shaft-bearing-seal assembly, using a 2-megavolt X-ray unit. Reasonable resolution and contrast was obtained. A fast-neutron detector was fabricated and sensitivity was measured. The results demonstrated that the technique is feasible for integrated-time measurements requiring, perhaps, 240 revolutions to obtain sufficient exposure at 35,000 rpm. The experimental verification plans are included

Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes

We consider the following eigenvalue optimization problem: Given a bounded domain $\Omega\subset\R^n$ and numbers $\alpha\geq 0$, $A\in [0,|\Omega|]$, find a subset $D\subset\Omega$ of area $A$ for which the first Dirichlet eigenvalue of the operator $-\Delta + \alpha \chi_D$ is as small as possible. We prove existence of solutions and investigate their qualitative properties. For example, we show that for some symmetric domains (thin annuli and dumbbells with narrow handle) optimal solutions must possess fewer symmetries than $\Omega$; on the other hand, for convex $\Omega$ reflection symmetries are preserved. Also, we present numerical results and formulate some conjectures suggested by them.Comment: 24 pages; 3 figures (as separate files); (shortened previous version); to appear in Comm. Math. Phy

Storage-ring measurement of the hyperfine induced 47Ti18+(2s 2p 3P0 -> 2s2 1S0) transition rate

The hyperfine induced 2s 2p 3P0 > 2s2 1S0 transition rate AHFI in berylliumlike 47Ti18+ was measured. Resonant electron-ion recombination in a heavy-ion storage ring was employed to monitor the time dependent population of the 3P0 state. The experimental value AHFI=0.56(3)/s is almost 60% larger than theoretically predicted.Comment: 4 pages. 3 figures, 1 table, accepted for publication in Physical Review Letter

Noncontacting devices to indicate deflection and vibration of turbopump internal rotating parts

Published report discusses feasibility of ultrasonic techniques; neutron techniques; X-radiography; optical devices; gamma ray devices; and conventional displacement sensors. Use of signal transmitters in place of slip rings indicated possible improvement and will be subject of futher study

Absolute rate coefficients for photorecombination and electron-impact ionization of magnesium-like iron ions from measurements at a heavy-ion storage ring

Rate coefficients for photorecombination (PR) and cross sections for electron-impact ionization (EII) of Fe$^{14+}$ forming Fe$^{13+}$ and Fe$^{15+}$, respectively, have been measured by employing the electron-ion merged-beams technique at a heavy-ion storage ring. Rate coefficients for PR and EII of Fe$^{14+}$ ions in a plasma are derived from the experimental measurements. Simple parametrizations of the experimentally derived plasma rate coefficients are provided for use in the modeling of photoionized and collisionally ionized plasmas. In the temperature ranges where Fe$^{14+}$ is expected to form in such plasmas the latest theoretical rate coefficients of Altun et al. [Astron. Astrophys. 474, 1051 (2007)] for PR and of Dere [Astron. Astrophys. 466, 771 (2007)] for EII agree with the experimental results to within the experimental uncertainties. Common features in the PR and EII resonance structures are identified and discussed.Comment: 12 pages, 6 figures, 3 tables, submitted for publication to Physical Review

Perturbation theory for plasmonic eigenvalues

We develop a perturbative approach for calculating, within the quasistatic approximation, the shift of surface resonances in response to a deformation of a dielectric volume. Our strategy is based on the conversion of the homogeneous system for the potential which determines the plasmonic eigenvalues into an inhomogeneous system for the potential's derivative with respect to the deformation strength, and on the exploitation of the corresponding compatibility condition. The resulting general expression for the first-order shift is verified for two explicitly solvable cases, and for a realistic example of a deformed nanosphere. It can be used for scanning the huge parameter space of possible shape fluctuations with only quite small computational effort