Interaction of radio frequency waves with cylindrical density filaments: scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

End Effects and Geometric Compensation in Linear Permanent Magnet Synchronous Generators with Different Topologies

Electricity production from ocean waves with different solutions is a topic of major research interest. Many of such designs are based on linear generators that inherently introduce end forces. In this paper, detent force using Maxwell Stress Tensor and induced voltage is initially investigated for two different winding patterns for a generator topology with buried magnets in a finite element software. Two ways of overcoming the end forces are further examined: the first method reduces the magnetic flux variations of the translator between stator and air. The second method aims at countering the end forces at both ends for full active stator area. A comparison is then made between buried and surface-mounted topologies for the second end effect compensation method. Both no-load and load conditions are investigated in the comparison. The end effect compensation shows promising results for both topologies. Some clear similarities of the extended stator used to counter the end forces are also apparent, where the stator extensions completely cover the outer poles of both topologies. The results also indicate a longer full active stator area for the buried topology for the same pole-pitch and stroke length, resulting in a higher average voltage for partial stator overlap.

Unifying Theory for Casimir Forces: Bulk and Surface Formulations

The principles of the electromagnetic fluctuation-induced phenomena such as Casimir forces are well understood. However, recent experimental advances require universal and efficient methods to compute these forces. While several approaches have been proposed in the literature, their connection is often not entirely clear, and some of them have been introduced as purely numerical techniques. Here we present a unifying approach for the Casimir force and free energy that builds on both the Maxwell stress tensor and path integral quantization. The result is presented in terms of either bulk or surface operators that describe corresponding current fluctuations. Our surface approach yields a novel formula for the Casimir free energy. The path integral is presented both within a Lagrange and Hamiltonian formulation yielding different surface operators and expressions for the free energy that are equivalent. We compare our approaches to previously developed numerical methods and the scattering approach. The practical application of our methods is exemplified by the derivation of the Lifshitz formula.

Vibration Mechanism and Compensation Strategy of Magnetic Suspension Rotor System under Unbalanced Magnetic Pull

The existing imbalance compensation strategies for magnetic suspension motors mainly focus on the mass unbalance force, ignoring the effects of the unbalanced magnet pull (UMP). This paper studied the vibration mechanism and compensation strategy of magnetic suspended permanent magnet synchronous motor (PMSM) under the influence of UMP. Firstly, an analytical model of the flux density was established based on equivalent magnetic circuit method, then the analytical expressions of UMP was deduced by Maxwell stress tensor method. Furthermore, an unbalanced compensation method based on hypothetical reference frame (HRF) transformation was proposed. The stability of the closed-loop system with compensation was analyzed based on the complex-coefficients theory. The proposed model and compensation strategy were verified by the simulations and experiments. The results indicate that the proposed compensation strategy can achieve effective suppression of the magnetic rotor vibration.

3D Simulations of Oxygen Shell Burning with and without Magnetic Fields

We present a first 3D magnetohydrodynamic (MHD) simulation of convective oxygen and neon shell burning in a non-rotating 18 M⊙ star shortly before core collapse to study the generation of magnetic fields in supernova progenitors. We also run a purely hydrodynamic control simulation to gauge the impact of the magnetic fields on the convective flow and on convective boundary mixing. After about 17 convective turnover times, the magnetic field is approaching saturation levels in the oxygen shell with an average field strength of $\mathord {\sim }10^{10}\, \mathrm{G}$, and does not reach kinetic equipartition. The field remains dominated by small to medium scales, and the dipole field strength at the base of the oxygen shell is only 109 G. The angle-averaged diagonal components of the Maxwell stress tensor mirror those of the Reynolds stress tensor, but are about one order of magnitude smaller. The shear flow at the oxygen-neon shell interface creates relatively strong fields parallel to the convective boundary, which noticeably inhibit the turbulent entrainment of neon into the oxygen shell. The reduced ingestion of neon lowers the nuclear energy generation rate in the oxygen shell and thereby slightly slows down the convective flow. Aside from this indirect effect, we find that magnetic fields do not appreciably alter the flow inside the oxygen shell. We discuss the implications of our results for the subsequent core-collapse supernova and stress the need for longer simulations, resolution studies, and an investigation of non-ideal effects for a better understanding of magnetic fields in supernova progenitors.

Variational principles of nonlinear magnetoelastostatics and their correspondences

We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo certain boundary integrals or constant integrals, between these formulations using the Legendre transform and properties of Maxwell’s equations. Bifurcation equations based on the second variation are stated for the incremental fields as well for all five variational principles. When the total potential energy is defined over the infinite space surrounding the body, we find that the inclusion of certain terms in the energy principle, associated with the externally applied magnetic field, leads to slight changes in the Maxwell stress tensor and associated boundary conditions. Conversely, when the energy contained in the magnetic field is restricted to finite volumes, we find that there is a correspondence between the discussed formulations and associated expressions of physical entities. In view of a diverse set of boundary data and the nature of externally applied controls in the problems studied in the literature, along with an equally diverse list of variational principles employed in modelling, our analysis emphasises care in the choice of variational principle and unknown fields so that consistency with other choices is also satisfied.

Optical force acting on a particle in the presence of a backward energy flow near the focus of a gradient lens

We show that a 70-nm dielectric nanoparticle placed on the optical axis near the surface (at a distance less than 100 nm) of a high-NA gradient microlens made of silicon, which is illuminated by a laser beam of 1.55 μm wavelength, is attracted to the lens surface with a piconewton force. The profile of the lens refractive index is described by a hyperbolic secant function. If a cut-out is made in the lens output surface, then the nanoparticle will be pulled into this cut-out, producing a kind of 'optical magnet'. If a reverse energy flow is to be generated on the optical axis near the output surface of such a gradient lens, this will lead to an absorbing dielectric nanoparticle being pulled toward the surface with a greater force than a similar non-absorbing particle. In the absence of a reverse flow, both absorbing and non-absorbing particles will be attracted to the surface with an equal force. The electromagnetic fields involved are calculated using a finite difference time domain (FDTD) method and the acting forces are calculated using a Maxwell stress tensor.

Analytical study of air-gap surface force – application to electrical machines

The Maxwell stress tensor (MST) method is commonly used to accurately compute the global efforts, such as electromagnetic torque ripple and unbalanced electromagnetic forces in electrical machines. The MST has been extended to the estimation of local magnetic surface force for the vibroacoustic design of electrical machines under electromagnetic excitation. In particular, one common air-gap surface force (AGSF) method based on MST is to compute magnetic surface forces on a cylindrical shell in the air gap. However, the AGSF distribution depends on the radius of the cylindrical shell. The main contribution of this study is to demonstrate an analytic transfer law of the AGSF between the air gap and the stator bore radius. It allows us to quantify the error between the magnetic surface force calculated in the middle of the air gap and the magnetic force computed on the stator teeth. This study shows the strong influence of the transfer law on the computed tangential surface force distribution through numerical applications with induction and synchronous electrical machines. Finally, the surface force density at stator bore radius is more accurately estimated when applying the new transfer law on the AGSF.

Lower excitons strong light matter interaction in plasmonic tweezers

Plasmonic nanocavity has been an excellent platform to study light matter interaction under ambient conditions and within sub-diffraction volumes. However, controlled strong light matter interaction in the plasmonic system has rarely been reported. Here, we design a plasmonic tweezers, which can trap a molecular J-aggregates, and be a plasmonic cavity to investigate the strong light matter interaction. We use finite-difference time-domain methods and Maxwell stress tensor to evaluate the optical response and the trapping performance. With the help of coupled oscillator model and virtual excitons theory, we analyze the strong coupling progress in lower excitons system, we further introduce a `coupling force' parameter to characterize the relationship between the optical force and model volume in the coupling system. The proposed method offers a way to locate a molecular J-aggregates in a plasmonic tweezers for investigating optical force performance and strong light matter interaction.