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At least 703 records · Page 39

HOT ELECTROMAGNETIC OUTFLOWS. I. ACCELERATION AND SPECTRA

The theory of cold, relativistic, magnetohydrodynamic outflows is generalized by the inclusion of an intense radiation source. In some contexts, such as the breakout of a gamma-ray burst (GRB) jet from a star, the outflow is heated to a high temperature at a large optical depth. Eventually it becomes transparent and is pushed to a higher Lorentz factor by a combination of the Lorentz force and radiation pressure. We obtain its profile, both inside and outside the fast magnetosonic critical point, when the poloidal magnetic field is radial and monopolar. Most of the energy flux is carried by the radiation field and the toroidal magnetic field that is wound up close to the rapidly rotating engine. Although the entrained matter carries little energy, it couples the radiation field to the magnetic field. Then the fast critical point is pulled inward from infinity and, above a critical radiation intensity, the outflow is accelerated mainly by radiation pressure. We identify a distinct observational signature of this hybrid outflow: a hardening of the radiation spectrum above the peak of the seed photon distribution, driven by bulk Compton scattering. The non-thermal spectrum-obtained by a Monte Carlo method-is most extended when the Lorentz force dominates the acceleration, and the seed photon beam is wider than the Lorentz cone of the MHD fluid. This effect is a generic feature of hot, magnetized outflows interacting with slower relativistic material. It may explain why some GRB spectra appear to peak at photon energies above the original Amati et al. scaling. A companion paper addresses the case of jet breakout, where diverging magnetic flux surfaces yield strong MHD acceleration over a wider range of Lorentz factor.

79 ASTRONOMY AND ASTROPHYSICS↗

Propagation And Damping Of High Harmonic Fast Waves And Electron Cyclotron Waves In The Nstx-U-Device

For the spherical torus and for conventional tokamaks to be viable means of producing fusion energy there are two important requirements. The first is to heat the plasma in the experimental devices to high temperatures; preferably, to fusion relevant temperatures. The second is to drive a current in the plasma so that the fusion device operates in a steady-state mode. A pulsed fusion reactor for energy production is not desirable. A favored means to achieve both of these requirements is through the use of microwaves, commonly referred to as radio frequency waves. This proposal was to understand observations from the National Spherical Torus Experiment Upgrade (NSTX-U) device on radio frequency wave heating of the confined plasma during operations with high harmonic fast waves. The proposed research was also directed toward assisting in the optimization of the experimental modes of operation so as to maximize the heating efficiency. A detailed analysis of the experiments has shown that about one-third of the input radio frequency power does not make it into the core region of the plasma where heating is required. The losses are believed to occur primarily in the edge region where the radio frequency power is initially coupled into the plasma. Using sophisticated computational codes and theoretical models, that have been developed for the NSTX-U experimental program, this research quantified the physical processes which occur in the edge plasma and lead to a decrease in the heating efficiency. The effect of edge turbulence on the scattering of radio frequency waves was studied for waves in the ion cyclotron and electron cyclotron range of frequencies. For high harmonic fast waves in the ion cyclotron range of frequencies, simulations were carried out using a full-wave solver that was extended to the vacuum vessel wall. These simulations successfully reproduced trends that were observed experimentally. This simulation capability was also used to study the interaction of high harmonic fast waves with the scrape-off layer plasma. More recently, a new technique has been developed for the calculation of radio frequency waves in toroidal geometry that enables the simultaneous incorporation of antenna geometry, plasma facing components, the scrape off-layer, and core propagation in the high harmonic fast wave regime. The effect of turbulent plasmas on the mode conversion of extraordinary electromagnetic waves in the electron cyclotron range of frequencies in the NSTX-U plasma has been studied theoretically. In the over-dense plasmas of NSTX-U, the traditional electromagnetic waves are not effective for delivering energy and momentum to the core plasma. However, electron Bernstein waves generated by mode conversion are efficient carriers of wave energy and momentum to the core. The mode conversion occurs in the turbulent edge region. A theory for mode conversion in such plasmas has been developed. The parameters that can optimize the mode conversion can be readily determined. Also, the model is useful for experimentalists to analyze observation on a shot-to-shot basis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Propagation And Damping Of High Harmonic Fast Waves And Electron Cyclotron Waves In The Nstx-U-Device

For the spherical torus and for conventional tokamaks to be viable means of producing fusion energy there are two important requirements. The first is to heat the plasma in the experimental devices to high temperatures; preferably, to fusion relevant temperatures. The second is to drive a current in the plasma so that the fusion device operates in a steady-state mode. A pulsed fusion reactor for energy production is not desirable. A favored means to achieve both of these requirements is through the use of microwaves, commonly referred to as radio frequency waves. This proposal was to understand observations from the National Spherical Torus Experiment Upgrade (NSTX-U) device on radio frequency wave heating of the confined plasma during operations with high harmonic fast waves. The proposed research was also directed toward assisting in the optimization of the experimental modes of operation so as to maximize the heating efficiency. A detailed analysis of the experiments has shown that about one-third of the input radio frequency power does not make it into the core region of the plasma where heating is required. The losses are believed to occur primarily in the edge region where the radio frequency power is initially coupled into the plasma. Using sophisticated computational codes and theoretical models, that have been developed for the NSTX-U experimental program, this research quantified the physical processes which occur in the edge plasma and lead to a decrease in the heating efficiency. The effect of edge turbulence on the scattering of radio frequency waves was studied for waves in the ion cyclotron and electron cyclotron range of frequencies. For high harmonic fast waves in the ion cyclotron range of frequencies, simulations were carried out using a full-wave solver that was extended to the vacuum vessel wall. These simulations successfully reproduced trends that were observed experimentally. This simulation capability was also used to study the interaction of high harmonic fast waves with the scrape-off layer plasma. More recently, a new technique has been developed for the calculation of radio frequency waves in toroidal geometry that enables the simultaneous incorporation of antenna geometry, plasma facing components, the scrape off-layer, and core propagation in the high harmonic fast wave regime. The effect of turbulent plasmas on the mode conversion of extraordinary electromagnetic waves in the electron cyclotron range of frequencies in the NSTX-U plasma has been studied theoretically. In the over-dense plasmas of NSTX-U, the traditional electromagnetic waves are not effective for delivering energy and momentum to the core plasma. However, electron Bernstein waves generated by mode conversion are efficient carriers of wave energy and momentum to the core. The mode conversion occurs in the turbulent edge region. A theory for mode conversion in such plasmas has been developed. The parameters that can optimize the mode conversion can be readily determined. Also, the model is useful for experimentalists to analyze observation on a shot-to-shot basis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Extreme ultraviolet resonant inelastic X-ray scattering (RIXS) at a seeded free-electron laser

In the past few years, we have been witnessing an increased interest for studying materials properties under non-equilibrium conditions. Several well established spectroscopies for experiments in the energy domain have been successfully adapted to the time domain with sub-picosecond time resolution. Here we show the realization of high resolution resonant inelastic X-ray scattering (RIXS) with a stable ultrashort X-ray source such as an externally seeded free electron laser (FEL). We have designed and constructed a RIXS experimental endstation that allowed us to successfully measure the d-d excitations in KCoF 3 single crystals at the cobalt M 2,3-edge at FERMI FEL (Elettra-Sincrotrone Trieste, Italy). The FEL-RIXS spectra show an excellent agreement with the ones obtained from the same samples at the MERIXS endstation of the MERLIN beamline at the Advanced Light Source storage ring (Berkeley, USA). We established experimental protocols for performing time resolved RIXS experiments at a FEL source to avoid X ray-induced sample damage, while retaining comparable acquisition time to the synchrotron based measurements. Finally, we measured and modelled the influence of the FEL mixed electromagnetic modes, also present in externally seeded FELs, and the beam transport with ~120 meV experimental resolution achieved in the presented RIXS setup.

36 MATERIALS SCIENCE↗

Optical properties of titanium dioxide nanotube arrays

We present experimental measurements and a theoretical analysis of the near UV to NIR optical properties of free standing titania nanotube arrays. An improved understanding of the optical physics of this type of nanostructure is important to several next generation solar energy conversion technologies. We measured the transmission, reflection, and absorption of the electromagnetic spectrum from 300 nm to 1000 nm (UV to NIR) of titania nanotube arrays. We measured the total, specular, and diffuse reflection and transmission using both single point detection and an integrating sphere spectrometer. We find that the transmission, but not the reflection, of light (UV to NIR) through the nanotube array is well-explained by classic geometric optics using an effective medium model taking into account the conical geometry of the nanotubes. For wavelengths shorter than ∼500 nm, we find the surprising result that the reflection coefficient for light incident on the open side of the nanotube array is greater than the reflection coefficient for light incident on the closed “floor” of the nanotube array. We consider theoretical models based on the eikonal approximation, photonic crystal band theory, and a statistical treatment of scattering to explain the observed data. We attribute the fact that light with wavelengths shorter than 500 nm is more highly reflected from the open than the closed tube side as being due to disorder scattering inside the nanotube array.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Fast modulations of pulsating proton aurora related to subpacket structures of Pc1 geomagnetic pulsations at subauroral latitudes

To understand the role of electromagnetic ion cyclotron (EMIC) waves in determining the temporal features of pulsating proton aurora (PPA) via wave-particle interactions at subauroral latitudes, high-time-resolution (1/8 s) images of proton-induced N 2 >+ emissions were recorded using a new electron multiplying charge-coupled device camera, along with related Pc1 pulsations on the ground. The observed Pc1 pulsations consisted of successive rising-tone elements with a spacing for each element of 100 s and subpacket structures, which manifest as amplitude modulations with a period of a few tens of seconds. In accordance with the temporal features of the Pc1 pulsations, the auroral intensity showed a similar repetition period of 100 s and an unpredicted fast modulation of a few tens of seconds. Furthermore, these results indicate that PPA is generated by pitch angle scattering, nonlinearly interacting with Pc1/EMIC waves at the magnetic equator.

58 GEOSCIENCES↗

Physics‐Informed Machine Learning for Inverse Design of Optical Metamaterials

Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.

Sarkar, Sulagna↗

Meson Photo-Production in GEANT4 for $E_\gamma = 0.225$ E γ = 0 . 225 -3.0 GeV using the $\gamma + p \rightarrow p + \pi^{0}$ reaction

The study of nuclear resonances in the intermediate energy regime requires accurate modeling of the experimental physics background. The cross sections in the GEANT4 toolkit do not adequately treat meson photo-production. The purpose of this study is to compare experimental data and theoretical models implemented in version 9.6.p02 of the GEANT4 Monte Carlo simulation toolkit for the exclusive and differential cross sections of $\pi^0$ photo-production. Two models were studied: the Chiral Invariant Phase Space (CHIPS) and Bertini Cascade (BERT). The cross section data from the models were compared to the experimental data from the CEBAF Large Acceptance Spectrometer (CLAS) of Jefferson Lab and the phenomenological Scattering Analysis Interactive Dial-in (SAID) model. Relativistic Breit-Wigner fits were used to compare the $\Delta(1232)$, N*(1520), N*(1650) and N*(1875) resonances from SAID, CLAS and CHIPS, giving agreements to within 3% for the mass of each resonance. The limited tabulated data set of BERT does not allow for an accurate description of the energy distribution, even following its improvement in version 10p02. The angular distributions of the cross sections show significant differences between CHIPS and both CLAS and SAID data, the latter being the most accurate model to describe the $\gamma p\rightarrow p\pi ^0$ exclusive cross section. Finally, the physics in CHIPS appears to be correct but it needs further development for the individual resonances contributions that could be useful since it is also the only model able to treat electromagnetically induced meson production for $A>1$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Role of surface electromagnetic waves in metamaterial absorbers

Metamaterial absorbers have been demonstrated across much of the electromagnetic spectrum and exhibit both broad and narrow-band absorption for normally incident radiation. Absorption diminishes for increasing angles of incidence and transverse electric polarization falls off much more rapidly than transverse magnetic. We unambiguously demonstrate that broad-angle TM behavior cannot be associated with periodicity, but rather is due to coupling with a surface electromagnetic mode that is both supported by, and well described via the effective optical constants of the metamaterial where we achieve a resonant wavelength that is 19.1 times larger than the unit cell. Furthermore, experimental results are supported by simulations and we highlight the potential to modify the angular response of absorbers by tailoring the surface wave.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Precision Measurement of the Proton Magnetic Form Factor at High Q2

Elastic electromagnetic form factors characterize the distribution of electric charge and magnetization current inside the nucleon and reflect the internal structure determined by Quantum Chromodynamics. Existing data on the proton magnetic form factor at high Q2 (the 4-momentum transfer squared) have large statistical and systematic uncertainties. The GMp experiment E12-07-108 was one of the first set of experiments to run in Hall A at Jefferson Lab after the 12 GeV upgrade with the goal of this experiment to precisely measure the electron-proton elastic cross section for Q2 up to 17 GeV2 with an accuracy of better than 2% - several times better than existing data in this Q2 range. This will allow further tests of form factor scaling predicted by pQCD and, additionally, will be an important benchmark for many other experiments where elastic electron-proton scattering is used for normalization. Since, GMp data were taken at lower ?(virtual photon polarization) than SLAC data, the measured cross sections recieve a smaller contribution from the electric form factor. This dissertation analyzed the GMp experiment data for five different kinematic settings determining the form factor with total uncertainties nearly two times smaller than the existing data at these Q2. This dissertation also presents the results of all Fall 2016 and Spring 2016 GMp experiment data. The proton magnetic form factors were extracted using both the Rosenbluth separation method and a parameterization of the form factor ratio (?pGpE=GpM) obtained from a fit to the existing cross section data. At the end of this thesis, the extracted GMp form factor data is compared to the existing data. The results for ?pGpE=GpM from Rosenbluth separations are found to be consistent with previous extractions, but with significantly reduced uncertainties, further highlighting the discrepancy with the polarization transfer technique. This data set can provide significant additional constraints on contributions from two-photon exchange.

Narayan Gautam, Thir↗

Energetic Electron Precipitation: Multievent Analysis of Its Spatial Extent During EMIC Wave Activity

Electromagnetic ion cyclotron (EMIC) waves can drive precipitation of tens of keV protons and relativistic electrons, and are a potential candidate for causing radiation belt flux dropouts. In this study, we quantitatively analyze three cases of EMIC-driven precipitation, which occurred near the dusk sector observed by multiple Low-Earth-Orbiting (LEO) Polar Operational Environmental Satellites/Meteorological Operational satellite programme (POES/MetOp) satellites. During EMIC wave activity, the proton precipitation occurred from few tens of keV up to hundreds of keV, while the electron precipitation was mainly at relativistic energies. We compare observations of electron precipitation with calculations using quasi-linear theory. For all cases, we consider the effects of other magnetospheric waves observed simultaneously with EMIC waves, namely, plasmaspheric hiss and magnetosonic waves, and find that the electron precipitation at MeV energies was predominantly caused by EMIC-driven pitch angle scattering. Interestingly, each precipitation event observed by a LEO satellite extended over a limited L shell region (ΔL ~ 0.3 on average), suggesting that the pitch angle scattering caused by EMIC waves occurs only when favorable conditions are met, likely in a localized region. Furthermore, we take advantage of the LEO constellation to explore the occurrence of precipitation at different L shells and magnetic local time sectors, simultaneously with EMIC wave observations near the equator (detected by Van Allen Probes) or at the ground (measured by magnetometers). Our analysis shows that although EMIC waves drove precipitation only in a narrow ΔL, electron precipitation was triggered at various locations as identified by POES/MetOp over a rather broad region (up to ~4.4 hr MLT and ~1.4 L shells) with similar patterns between satellites.

79 ASTRONOMY AND ASTROPHYSICS↗

Comparison of Different Classical, Semiclassical, and Quantum Treatments of Light–Matter Interactions: Understanding Energy Conservation

The optical response of an electronic two-level system (TLS) coupled to an incident continuous wave (cw) electromagnetic (EM) field is simulated explicitly in one dimension by the following five approaches: (i) the coupled Maxwell-Bloch equations, (ii) the optical Bloch equation (OBE), (iii) Ehrenfest dynamics, (iv) the Ehrenfest+R approach, and (v) classical dielectric theory (CDT). Our findings are as follows: (i) standard Ehrenfest dynamics predict the correct optical signals only in the linear response regime where vacuum fluctuations are not important; (ii) both the coupled Maxwell-Bloch equations and CDT predict incorrect features for the optical signals in the linear response regime due to a double-counting of self-interaction; (iii) by exactly balancing the effects of self-interaction versus the effects of quantum fluctuations (and insisting on energy conservation), the Ehrenfest+R approach generates the correct optical signals in the linear regime and slightly beyond, yielding, e.g., the correct ratio between the coherent and incoherent scattering EM fields. Furthermore, Ehrenfest+R dynamics agree with dynamics from the quantum OBE, but whereas the latter is easily applicable only for a single TLS in vacuum, the former should be applicable to large systems in environments with arbitrary dielectrics. Hence, this benchmark study suggests that the Ehrenfest+R approach may be very advantageous for simulating light-matter interactions semiclassically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Photonuclear reaction studies at HIγS: Developing the science of remote detection of nuclear materials

Development of gamma-ray beam interrogation technologies for remote detection of special nuclear materials and isotope analysis requires comprehensive databases of nuclear structure information and gamma-ray induced nuclear reaction observables. Relevant nuclear structure details include the energy, spin and parity of excited states that have significant probability for electromagnetic transition from the ground state, i.e, the angular momentum transferred in the reaction is Δl ≤ 2. This talk will report recent Nuclear Resonance Fluorescence (NRF) measurements to identify and characterize new low-spin states in actinide nuclei at energies from 1 to 4 MeV, which is the energy range most important for remote analysis methods. Here, these measurements are carried out using the nearly mono-energetic linearly polarized gamma-ray beam at the High Intensity Gamma-ray Source (HIγS) at the Triangle Universities Nuclear Laboratory. Also, studies of the (γ, n) reaction on a variety of nuclei with linearly polarized beams at HIγS indicate that this reaction might be used to discern between fissile and non-fissile materials. This work will be described. In addition, an overview will be given of a concept for a next generation laser Compton-backing scattering gamma-ray source to be implemented as an upgrade to increase the beam intensity at HIγS by more than an order of magnitude.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

Spherical tokamak plasmas are typically overdense and thus inaccessible to externally-injected microwaves in the electron cyclotron range. The electrostatic electron Bernstein wave (EBW), however, provides a method to access the plasma core for heating and diagnostic purposes. Understanding the details of the coupling process to electromagnetic waves is thus important both for the interpretation of microwave diagnostic data and for assessing the feasibility of EBW heating and current drive. While the coupling is reasonably well–understood in the linear regime, nonlinear physics arising from high input power has not been previously quantified. To tackle this problem, we have performed one- and two-dimensional fully kinetic particle-in-cell simulations of the two possible coupling mechanisms, namely X-B and O-X-B mode conversion. We find that the ion dynamics has a profound effect on the field structure in the nonlinear regime, as high amplitude short-scale oscillations of the longitudinal electric field are excited in the region below the high-density cut-off prior to the arrival of the EBW. We identify this effect as the instability of the X wave with respect to resonant scattering into an EBW and a lower-hybrid wave. Finally, we calculate the instability rate analytically and find this basic theory to be in reasonable agreement with our simulation results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Programmable hyperbolic polaritons in van der Waals semiconductors

Lighting a route for hyperbolic dispersion The propagation of light within a material is usually well defined, with the propagation described by scattering and dispersion. In artificially designed metamaterials and in anisotropic layered materials, the dispersion can be hyperbolic, giving rise to subwavelength confinement of the light. Sternbach et al. show that the hyperbolic dispersion can be optically switched on and off on demand in the layered transition metal dichalcogenide tungsten diselenide (see the Perspective by Deng and Chen). Illuminating the material with ultrafast pulses of sub-bandgap light creates a transient waveguide, resulting in hyperbolic dispersion in the material. The ability to tune the dispersion characteristics on demand using optical pumping is an effective approach for developing ultrafast switching photonic devices and controlling the propagation of light on the nanoscale. Science , this issue p. 617 ; see also p. 572

Science & Technology - Other Topics↗

Using electron energy-loss spectroscopy to measure nanoscale electronic and vibrational dynamics in a TEM

Electron energy-loss spectroscopy (EELS) can measure similar information to x-ray, UV–Vis, and IR spectroscopies but with atomic resolution and increased scattering cross-sections. Recent advances in electron monochromators have expanded EELS capabilities from chemical identification to the realms of synchrotron-level core-loss measurements and to low-loss, 10–100 meV excitations, such as phonons, excitons, and valence structures. EELS measurements are easily correlated with electron diffraction and atomic-scale real-space imaging in a transmission electron microscope (TEM) to provide detailed local pictures of quasiparticle and bonding states. This perspective provides an overview of existing high-resolution EELS (HR-EELS) capabilities while also motivating the powerful next step in the field—ultrafast EELS in a TEM. Ultrafast EELS aims to combine atomic-level, element-specific, and correlated temporal measurements to better understand spatially specific excited-state phenomena. Ultrafast EELS measurements also add to the abilities of steady-state HR-EELS by being able to image the electromagnetic field and use electrons to excite photon-forbidden and momentum-specific transitions. We discuss the technical challenges ultrafast HR-EELS currently faces, as well as how integration with in situ and cryo measurements could expand the technique to new systems of interest, especially molecular and biological samples.

Chemistry↗

Super-resonant four-photon collinear laser frequency multiplication in plasma

Resonant four-photon scattering could nearly double frequencies of intense laser pulses in plasma. However, transverse slippage between pulses presents a technological challenge, while collinear four-photon scattering is forbidden for classical light dispersion in plasma. Nonlinear renormalization of intense laser pulses can enable collinear four-photon resonance. However, such a very intensity-sensitive resonance is difficult to maintain for evolving pulses. Remarkably, there is a lower-dimensionality submanifold of the resonant four-photon manifold where the evolving pulses stay in resonance. Furthermore this could enable an all-optical frequency doubling of mildly relativistic-intense laser pulses in collinear geometry, advantageously free of the transverse slippage challenges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Poloidal and toroidal plasmons and fields of multilayer nanorings

Composite and janus type metallodielectric nanoparticles are increasingly considered as a means to control the spatial and temporal behavior of electromagnetic fields in diverse applications such as coupling to quantum emitters, achieving invisibility cloaks, and obtaining quantum correlations between qubits. We investigate the surface modes of a toroidal nanostructure and obtain the canonical plasmon dispersion relations and resonance modes for arbitrarily layered nanorings. Unlike particle plasmon eigenmodes in other geometries, the amplitudes of the eigenmodes of tori exhibit a distinct forward and backward coupling. We present the plasmon dispersion relations for several relevant toroidal configurations in the quasistatic limit and obtain the dominant retarded dispersion relations of a single ring for comparison, discuss mode complementarity and hybridization, and introduce two new types of toroidal particles in the form of janus nanorings. The resonance frequencies for the first few dominant modes of a ring composed of plasmon supporting materials such as gold, silver, and aluminum are provided and compared to those for a silicon ring. A generalized Green's function is obtained for multilayer tori allowing for calculation of the scattering response to interacting fields. Employing the Green's function, the scalar electric potential distribution corresponding to individual poloidal and toroidal modes in response to an arbitrarily polarized external field and the field of electrons is obtained. The results are applied to obtain the local density of states and decay rate of a dipole near the center of the torus.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗