Interactions of spin waves with a magnetic vortex

We have investigated azimuthal spin-wave modes in magnetic vortex structures using time-resolved Kerr microscopy. Spatially resolved phase and amplitude spectra of ferromagnetic disks with diameters from 5 microm down to 500 nm reveal that the lowest order azimuthal spin-wave mode splits into a doublet as the disk size decreases. We demonstrate that the splitting is due to the coupling between spin waves and the gyrotropic motion of the vortex core.     

Comparison of frequency,field, and time domain ferromagnetic resonance methods

We present vector network analyzer ferromagnetic resonance measurements of epitaxial Fe films having a thickness of 16 monolayers. Our objective is to test the reliability of this novel frequency domain technique with respect to frequency and damping. For this purpose we compare vector network analyzer ferromagnetic resonance to pulsed inductive microwave magnetometry, time resolved magneto-optic Kerr effect (both methods in the time domain), and conventional ferromagnetic resonance (measured in the field domain) in terms of position and width of the ferromagnetic resonance. In addition, we compare the various techniques with respect to the signal to noise ratio of the raw data. All data is obtained using the same well characterized ultrathin magnetic Fe/GaAs (0 0 1) film. Finally, we demonstrate the potential of the vector network analyzer ferromagnetic resonance technique for the investigation of nano-structured magnetic elements having nonuniform magnetization configuration. The absorption spectrum of Permalloy disks with a diameter of 200 nm and a thickness of 15 nm shows up to eight distinct resonance peaks. The spatial structure of the corresponding modes was derived from numerical calculations and reveals that azimuthal modes up to the fifth order have been observed inductively.     

Dynamics of Magnetic Skyrmions in Nanodots

Bloch and Neel magnetic skyrmions have been studied in systems of confined geometry (nanodots, a linear array of nanodots). The spectra of low- and high-frequency excitation modes of a skyrmion state have been calculated. It has been shown that skyrmion spectrum asymmetry, namely, the characteristic difference between the frequencies of the azimuthal modes of the azimuthal skyrmion modes rotating clockwise and counterclockwise, is associated with asymmetry in the magnetization profiles of high-frequency spin waves propagating on the background of a skyrmion state in a nanodot. The low-frequency spectrum contains the only gyrotropic mode localized near the center of a nanodot. The gyrotropic frequency depends on the material parameters of a nanodot and the size of a skyrmion. The eigenfrequency of the gyrotropic mode of an isolated skyrmion in a nanodot in ultrathin films (L ~ 1 nm) does not depend on the internal structure of a skyrmion and is the same for Bloch and Neel skyrmions. The interaction of skyrmions, in particular, in a linear chain of nanodots with the ground skyrmion state, leads to distinctions in low-frequency spectra. The structure of a skyrmion (of Bloch or Neel type) is exhibited as a shift of dispersion curves and a difference between the frequencies of ferromagnetic resonance in a system of interacting skyrmions.     

Spin-wave interference in microscopic rings

We have studied the spin excitations of ferromagnetic rings and observed a distinct series of quantized modes in the vortex state. We attribute them to spin waves that circulate around the ring and interfere constructively. They form azimuthal eigenmodes of a magnetic ring resonator which we resolve up to the fourth order. The eigenfrequencies are calculated semianalytically and classified as a function of magnetic field by a quantization rule which takes into account a periodic boundary condition. Strikingly each mode exists only below a characteristic field.     

Calculations,in the three-dimensional approximation,for a half-symmetric unstable resonator with internal axicon (HSURIA) in the three-dimensional diffraction approximation with annular shape of the active medium

6. Conclusions 1. It was shown that, compared with other methods, realization of the analytic Prony method increases strongly the effective establishment of the radiation of the mode structure of the radiation field in an empty cavity having o complex configuration, such as the HSURIA resonator. 2. We investigated the dependence of the losses of various azimuthal and radial modes in an empty HSURIA resonator on the value of N_eq. We have shown that in the region N_eq=20−25 and at M=2 the losses of the highest-Q zeroth and first azimuthal modes amount to ≈0.65 and ≈0.70 respectively, which ensures lasing in the single-mode regime in the case of a sufficiently homogeneous active medium. 3. We found the field distributions of various azimuthal and radial modes in the HSURIA resonator in the absence of a medium. 4. We have shown that in the case of lasing on one highest-Q mode the radiation intensity on the tip of a W-axicon is not more than 2–3 times larger than the average over the central region of the W-axicon. Translated from Preprint No. 31 of the Lebedev Physics Institute, Russian Academy of Sciences, Moscow, 1991.     

Structure of a nonparaxial gaussian beam near the focus: III. Stability,eigenmodes, and vortices

Exact analytical structurally stable solutions of the Maxwell equations for singular mode beams propagating in free space or a uniform isotropic medium are obtained. Approximate boundary conditions are chosen in the form of the requirement that in the paraxial approximation the fields of nonparaxial mode beams in the waist plane are transformed into the fields of eigenmodes and vortices of weakly guiding optical fibers with the axial symmetry of refractive index. It is shown that optical vortices, in spite of a rather complex structure of field distribution, do not experience substantial changes in the beam form and reproduce, in general features, the field of paraxial vortices. Linear perturbations of the characteristic parameters of mode beams do not change the structure of their electromagnetic field. Nonparaxial singular beams have one more important property, in addition to the fact that the structure of these beams in the paraxial approximation is similar to the structure of the fields of eigenmodes in a fiber. The propagation constants of eigenmodes of a fiber exactly coincide (in the first approximation of perturbation theory) with the projection of the wave vector of a mode beam on the optical axis (an analog of the propagation constant). The possibility of the paraxial transition for nonparaxial mode beams with arbitrary values of azimuthal and radial indices is shown. The properties of nonparaxial modes are illustrated by numerous examples. The solutions obtained and the results of their analysis can be used for exact matching optical fibers and laser beams in various applications.     

The Radial-Azimuthal Instability of a Radiation-Pressure-Dominated Accretion Disk with Advection

A radial-azimuthal instability analysis of a radiation-pressure-dominated accretion disk with advection is presented. We find that the including of a very little advection has significant effect on two acoustic modes, which are no longer complex conjugates of each other. With the increase of azimuthal perturbations, the thermal mode becomes more unstable and the viscous mode more stable, but there has no effect on acoustic mode. For geometrically slim and advection-dominated disks, the azimuthal perturbation and increasing of advection do not affect the stability of all the modes.     

Azimuthal-order variations of surface-roughness-induced mode splitting and scattering loss in high-Q microdisk resonators

We report an experimental observation of strong variations of quality factor and mode splitting among whispering-gallery modes with the same radial order and different azimuthal orders in a scattering-limited microdisk resonator. A theoretical analysis based on the statistical properties of the surface roughness reveals that mode splittings for different azimuthal orders are uncorrelated, and variations of mode splitting and quality factor among the same radial mode family are possible. Simulation results agree well with the experimental observations.     

Unstable twisted modes in interpenetrating space plasmas containing superthermal species

The electrostatic twisted modes with orbital angular momentum and associated kinetic instability are studied in a permeating space plasma containing streaming particle species. The plasma containing superthermal electrons and ions is modeled by using a non-gyrotropic Kappa distribution function which penetrates through a relatively slow moving (static) plasma and gives rise to dispersion, damping and growth of ion-acoustic mode under various conditions. Using the Vlasov-Poisson model, the solutions of twisted modes are defined by Laguerre-Gaussian mode functions, which decompose the plasma distribution function and electric field into components characterized by the axial and azimuthal wave numbers. The dielectric constant is derived and analyzed for threshold condition of wave dispersion and instability in the presence of helical electric field with illustrations. The wave excitations due to penetration of solar wind into cometary clouds or interstellar electron-ion plasmas is examined.     

Start-up scenario in gyrotrons with a nonstationary microwave-field structure

Megawatt class gyrotrons operate in very high-order modes. Therefore, control of a gyrotron oscillator's start-up is important for excitation of the desired mode in the presence of the many undesired modes. Analysis of such scenario using the self-consistent code MAGY [M. Botton, IEEE Trans. Plasma Sci. 26, 882 (1998)10.1109/27.700860] reveals that during start-up not only mode amplitudes vary in time, but also their axial structure can be time dependent. Simulations done for a 1.5 MW gyrotron show that the excitation of a single operating mode can exhibit a sort of intermittency when, first, it is excited as a mode whose axial structure extends outside the interaction cavity, then it ceases and then reappears as a mode mostly localized in the cavity. This phenomenon makes it necessary to analyze start-up scenarios in such gyrotrons with the use of codes that account for the possible evolution of field profiles.     

Axial mode locking in a harmonic-multiplying, inverted gyrotwystron

When in microwave sources, an open waveguide operating at frequencies close to cutoff is used as a resonator, a number of modes with the same transverse structure, but different axial distribution can be excited by an electron beam. The width of the resonance curves of these modes broadens as the number of axial variations grows. This leads to overlapping of these curves at large axial indexes. As a result, phase locking of such modes may occur. A theory describing axial mode locking in gyrodevices is developed. The results of theoretical analysis are compared to a harmonic-multiplying, inverted gyrotwystron experiment. It is shown that such phase-locked operation in a set of modes with overlapping resonance curves can significantly enlarge the bandwidth of gyrodevices. Furthermore, this technique may be broadly applicable to other devices, which employ cavities with overlapping modes     

Observation of a free-Shercliff-layer instability in cylindrical geometry

We report on observations of a free-Shercliff-layer instability in a Taylor-Couette experiment using a liquid metal over a wide range of Reynolds numbers, Re～10(3)-10(6). The free Shercliff layer is formed by imposing a sufficiently strong axial magnetic field across a pair of differentially rotating axial end cap rings. This layer is destabilized by a hydrodynamic Kelvin-Helmholtz-type instability, characterized by velocity fluctuations in the r-θ plane. The instability appears with an Elsasser number above unity, and saturates with an azimuthal mode number m which increases with the Elsasser number. Measurements of the structure agree well with 2D global linear mode analyses and 3D global nonlinear simulations. These observations have implications for a range of rotating MHD systems in which similar shear layers may be produced.     

Spin orientation and excitation of magnetic nanocluster on metal surface

The spin orientation and excitation of the ferromagnetic nanocluster on the magnetic metal surface are studied numerically. We show that localized magnetic excitation modes are generated by the spin fluctuation of the cluster, when the ferromagnetic interaction J′ between the cluster and the metal surface is small and the spins in the cluster are oriented in the opposite direction with those of the metal surface by the external field. This magnetic structure is similar to the domain wall (DW) structure of a ferromagnetic wire, both sides of which connect with metal surfaces. As the interaction J′ increases, the sign of the thermal average of the spins in the cluster changes, i.e., the spin-flip takes place. In this time, the magnetic fluctuation of the cluster becomes large and the magnetic excitation energies, except for that of one excitation mode, overlap with the excitation spectrum of the spin wave. We also show that, by the overlap, sharp peaks and dips occur in the excitation spectrum of the spin wave.     

Magnetostatic modes of a lateral ferromagnetic/ferromagnetic superlattice

In this Letter, we calculate the magnetostatic modes of a semi-infinite lateral ferromagnetic/ferromagnetic superlattice with the effective-medium theory and present the general features of the modes. The numerical calculations for Co/Ni superlattice show some interesting properties which different from the lateral ferromagnetic/nonmagnetic superlattice. Two branches of the surface modes appear for the superlattice. Comparing with the surface magnetostatic modes of bulk Ni, one branch of the mode is of high frequency; the other branch of mode is of low frequency.     

Directly mapping whispering gallery modes in a microsphere through modal coupling and directional emission

We fabricate slightly deformed fused-silica microspheres in which whispering gallery modes possess remarkably directional escape emission from the microsphere boundary. With efficient flee-space excitation and collection, the lateral spatial distribution of whispering gallery modes with different azimuthal mode numbers, rn, is directly observed through modal coupling and directional emission. Excellent agreement with theory is obtained.     

Experimental Study of a Ka-Band Cylindrical Open Resonator

A study of the electrodynamical properties of a Ka-band gyrotron open resonator was experimentally conducted. Experiments were accomplished to measure resonant frequencies and their respective loaded quality factors for TE modes in the frequency range from 26 to 40 GHz. In particular, a perturbation technique was used to determine the axial, radial and azimuthal electric field profiles, as an identification method of the TE₀₂₁ mode operating around 35 GHz. In any experimental event, good agreement with the values predicted by theory was found.     

Using large eddy simulation to explore sound-source mechanisms in jets

This paper presents an analysis of data generated by means of large eddy simulation for a single-stream, isothermal Mach 0.9 jet. The acoustic field is decomposed into Fourier modes in the azimuthal direction, and filtered by means of a continuous wavelet transform in the temporal direction. This allows the identification of temporally localised, high-amplitude events in the radiated sound field for each of the azimuthal modes. Once these events have been localised, the flow field is analysed so as to determine their cause. Results show high-amplitude, intermittent sound radiation for azimuthal modes 0 and 1. The mode-0 radiation, which dominates low-angle emission, is found to result from the temporal modulation of a basic axisymmetric wave-packet structure within the flow. Similar intermittent activity, observed, again within the flow, for azimuthal mode 1 suggests a link between the modes 0 and 1 dynamics. Both the amplitude and spatial extent of the axisymmetric wave-packet are modulated, and the strongest axisymmetric propagative disturbances are found to radiate from the downstream end of the wave-packet at moments when the wave envelope becomes truncated. The observed behaviour is modelled using a line-source wave-packet ansatz which includes parameters that account for the said modulation. Inclusion of these parameters, which allow the wave-packet to “jitter” in a manner similar to that observed, leads to good quantitative agreement (accurate to within 1.5 dB), at low emission angles, with the acoustic field of the LES. This result is in contrast with results obtained using a time-averaged wave-packet (one which does not jitter), for which a 12 dB error is observed. This result shows that the said modulations are the salient source feature for the low-angle sound emission of the jet considered. Analysis of a longer time series shows the occurrence of several similar high-amplitude bursts in the axisymmetric mode of the acoustic pressure, and a calculation of the radiated sound for this longer time-series, again using the wave-packet ansatz, once again leads to good agreement with the LES (now accurate to within 1 dB).     

Linear Theory of Radially Inhomogeneous, Unneutralized, Relativistic Electron Beams

A set of four, coupled, first-order differential equations describing the normal modes of a cylindrically symmetric, cold fluid, unneutralized, relativistic electron beam of arbitrary radial profile is derived. Effects of beam rotation and equilibrium fields are treated exactly. The differential equations are found to have singular points for a radially inhomogeneous beam wherever the eigenfrequency equals the cyclotron or Doppler resonance frequencies. The resulting branch cuts in the dispersion function give rise to secularly decaying contributions to the initial value problem. The rate of decay and the character of the eigenmode near the singularity are determined from the solution of the corresponding indicial equation. Discrete eigenmodes also exist and are obtained by numerical solution of the differential equations and boundary conditions. For realistic solid-beam equilibria, only one slow cyclotron-mode exists for any given pair of axial and azimuthal wavenumbers, and that mode is localized at the beam edge. Under identical conditions several slow space-charge modes exist and are not so distorted. However, even at the space-charge limit, the phase velocity of long-wavelength slow space-charge waves does not decrease to zero. These results are relevant to the Autoresonant and Converging Guide collective ion acceleration proposals.     

Dynamics of coupled vortices in a pair of ferromagnetic disks

We here experimentally demonstrate that gyration modes of coupled vortices can be resonantly excited primarily by the ac current in a pair of ferromagnetic disks with variable separation. The sole gyration mode clearly splits into higher and lower frequency modes via dipolar interaction, where the main mode splitting is due to a chirality sensitive phase difference in gyrations of the coupled vortices, whereas the magnitude of the splitting is determined by their polarity configuration. These experimental results show that the coupled pair of vortices behaves similar to a diatomic molecule with bonding and antibonding states, implying a possibility for designing the magnonic band structure in a chain or an array of magnetic vortex oscillators.