Exact Resonance Condition Research Articles

Electron nonlinear dynamics in a compact accelerator based on the circular rotating TM110 mode

The present study investigates the electron autoresonant acceleration using the rotating transverse magnetic mode TM110 microwave field within an inhomogeneous magnetostatic field. Differential equations governing the evolution of the phase shift between the electron’s angular position and the angle at which transferred power is maximized, the total electron energy, and the longitudinal electron velocity are derived. Magnetic field profiles required to sustain electron acceleration are determined. The results demonstrate that an electron injected along the cavity axis with an energy of 30keV can be accelerated up to approximately 200keV, using an electric field amplitude of 20kV/cm, a frequency of 8GHz, and a linear magnetic field profile. Additionally, we consider the case of electron acceleration under exact resonance conditions, and the corresponding magnetic field profile predicted by the model is obtained.The findings presented in this paper are valuable for the design of RF accelerators utilizing the circular rotating TM110 mode, particularly in applications such as x-ray sources for medical purposes, airport security, and various other fields.

Nondiffusive Pitch‐Angle Scattering of a Distribution of Energetic Particles by Coherent Whistler Waves

AbstractWhether or not coherent magnetospheric whistler waves play important roles in the pitch‐angle scattering of energetic particles is a crucial question in magnetospheric physics. The interaction of a thermal distribution of energetic particles with coherent whistler waves is thus investigated. The distribution is prescribed by the Maxwell‐Jüttner distribution, which is a relativistic generalization of the Maxwell‐Boltzmann distribution. Coherent whistler waves are modeled by circularly polarized waves propagating parallel to the background magnetic field. It is shown that for parameters relevant to magnetospheric chorus, a significant fraction (1–5%) of the energetic particle population undergoes drastic, nondiffusive pitch‐angle scattering by coherent chorus. The scaling of this fraction with the wave amplitude may also explain the association of relativistic microbursts to large‐amplitude chorus. A much improved condition for large pitch‐angle scattering is presented that is related to, but may or may not include the exact resonance condition depending on the particle's initial conditions. The theory reveals a critical mechanism not contained in the widely used second‐order trapping theory.

Discriminating electromagnetically induced transparency from Autler–Townes splitting in a Ξ system

In this work, we report on experimentally discerning Autler–Townes splitting (ATS) from electromagnetically induced transparency (EIT). Our findings are based on a Ξ (ladder) transition 5S1/2→5P3/2→5D5/2 of 87Rb atoms under different laser detuning combinations. Based on the ratio of power levels of two individual and counter-propagating lasers through a room temperature Rb vapor cell, we experiment on two different categories of Ξ configuration: types I and II. For type I, 5P3/2→5D5/2 transition is strongly driven, and we observe EIT. Type II (5S1/2→5P3/2 strongly coupled) exhibits pure ATS. Under two different two-photon detuning conditions, ATS and EIT are studied. While ATS becomes stronger near exact two-photon resonance condition, the EIT weakens. This is supported by the analysis of blue light emanating from 5D5/2→6P3/2→5S1/2 decay. The complete opposite behavior of these two phenomena at exact two-photon resonance condition can be used to clearly discern EIT from ATS.

Maximization of Acoustic Levitating Force for a Single-Axis Acoustic Levitation System Using the Finite Element Method**Supported by the Science and Engineering Research Board under Grant No YSS/2015/001245.

We investigate single-axis acoustic levitation using standing waves to levitate particles freely in a medium bounded by a driver and a reflector. The acoustic pressure at the pressure antinode of the standing wave counteracts the downward gravitational force of the levitating object. The optimal relationship between the air gap and the driving frequency leads to resonance and hence maximization of the levitating force. Slight deviation from the exact resonance condition causes a reduction in acoustic pressure at the pressure antinodes. This results in a significant reduction of the levitating force. The driving frequency is kept constant while the air gap is varied for different conditions. The optimal air gap for maximizing the levitation force is studied for first three resonance modes. Furthermore, a levitating particle is introduced between the driver and the reflector. The dependence of the resonance condition on the size of the levitating particle as well as the position of the particle between the driver and the reflector has also been studied. As the size of the levitating particle increases, the resonance condition also gets modified. Finite element results show a good agreement with the validated results available in the literature. Furthermore, the finite element approach is also used to study the variation of acoustic pressure at the pressure antinode with respect to the size of the reflector. The optimum diameter of the reflector is calculated for maximizing the levitating force for three resonance modes.

The Permanent Downshifting at Later Stages of Benjamin–Feir Instability of Waves

Some of the prominent features in later stages of the Benjamin–Feir (BF) instability development are still not well clarified: What are the conditions for a permanent downshifting in the wave energy spectrum, is this process inevitable accompanied by wave breaking dissipation? What is the mechanism of multiple downshifting and discrete energy spreading to higher frequencies, how does it depend on the initial steepness and frequency space of waves? We conducted experimental and theoretical studies on this issue and revealed a number of new features of the development of instability in the late stages of wave’s evolution. We employ the reduced (truncated) version of Zakharov equations, the multi-wave near-neighbor resonance model (NN model), which takes into account the most effective quasi-resonances with minimum detuning from the exact resonance conditions. We show that the near-neighbor model of wave interactions can adequately describe the number of new characteristic features of BF instability. NN model is much simpler than Zakharov equation for computation and analysis. The dissipation version of Zakharov equations based on the Tulin’s semi-empirical model is employed for the description of breaking wave’s propagation. We verify the new characteristic features of BFI for various initial wave conditions by experiments conducted in Tainan Hydraulics Laboratory and confirm the theoretical predictions of NN model. A strong permanent downshifting of the spectral maximum for gentle waves without wave breaking is revealed for initially two-time narrower spectral width in comparison with the most unstable case. For steep waves, a multiple downshifting regime is detected, accompanied by a wave breaking. The discrete energy flow to higher spectral components takes place in the breaking and no-breaking regimes. Results of numerical simulations of Zakharov and NN models reasonably correspond to each other and to our experimental and field observations on wave modulation.

Design and Simulation of Compact Band-Pass Filter Using Stub Loaded Plasmonic Mim Waveguide

In this article, plasmonic band-pass filters (BPF) have been studied and numerically analyzed. This filter has been designed based on the two-stubs. Pass-band can be realized by appropriately adjusting the lengths and width of the resonator. Based on the ideal characteristics of the proposed two stubs BPF is allowing the band at THz frequencies. Multiple transmission zeros are generated to improve the selectivity of the filter. All simulated results have been studied using CST Microwave studio suite. Usually, the transmission effectiveness is revealed by the exact resonance condition, whichwill confirmalong with the numerical simulation or theoretical analysis. This article delivers a promising application for plasmonic BPFsin addition to plasmonic integrated circuits (PICs).

Dynamics of a Dipolariton Optical Parametric Oscillator in a Semiconductor Microcavity

The dynamics of dipolariton states in a planar microcavity has been studied upon pumping of a state corresponding to the middle dipolariton branch. It has been shown that, under exact resonance conditions, both periodic and aperiodic regimes of conversion of pump dipolaritons to dipolaritons of idler and signal modes occur. The periodic regime of conversion of signal and idler dipolaritons without involving pump dipolaritons on the middle branch has also been analyzed.

Non-exponential decoherence of radio-frequency resonance rotation of spin in storage rings

Precision experiments, such as the search for electric dipole moments of charged particles using radiofrequency spin rotators in storage rings, demand for maintaining the exact spin resonance condition for several thousand seconds. Synchrotron oscillations in the stored beam modulate the spin tune of off-central particles, moving it off the perfect resonance condition set for central particles on the reference orbit. Here we report an analytic description of how synchrotron oscillations lead to non-exponential decoherence of the radiofrequency resonance driven up-down spin rotations. This non-exponential decoherence is shown to be accompanied by a nontrivial walk of the spin phase. We also comment on sensitivity of the decoherence rate to the harmonics of the radiofreqency spin rotator and a possibility to check predictions of decoherence-free magic energies.

Dynamics of an optical parametric oscillator based on dipolaritons

The dynamics of dipolariton states in a planar microcavity under pumping of the state corresponding to the intermediate dipolariton branch has been studied. Aperiodic conversion of pump dipolaritons into dipolaritons of idler and signal modes is shown to occur under exact-resonance conditions.

Nonlinear internal resonance of functionally graded cylindrical shells using the Hamiltonian dynamics

Internal resonance in nonlinear vibration of functionally graded (FG) circular cylindrical shells in thermal environment is studied using the Hamiltonian dynamics formulation. The material properties are considered to be temperature-dependent. Based on the Kármán-Donnell's nonlinear shell theory, the kinetic and potential energy of FG cylindrical thin shells are formulated. The primary target is to investigate the two-mode internal resonance, which is triggered by geometric and material parameters of shells. Following a secular perturbation procedure, the underlying dynamic characteristics of the two-mode interactions in both exact and near resonance cases are fully discussed. It is revealed that the system will undergo a bifurcation in near resonance case, which induces the dynamic response at high energy level being distinct from the motion at low energy level. The effects of temperature and volume fractions of composition on the exact resonance condition and bifurcation characteristics of FG cylindrical shells are also investigated.

Numerical simulation of adiabatons in electromagnetically induced transparency under quasi-resonance conditions

The evolution of adiabatons in electromagnetically induced transparency in the scheme of degenerate quantum transitions with Doppler broadening of spectral lines has been numerically simulated taking into account the effect of resonance detunings. It is shown that, in the case of linearly polarised fields, an increase in the probe-field resonance detuning (under exact-resonance conditions for the control radiation) leads to a transformation of electromagnetically induced transparency into electromagnetically induced absorption at certain stages. When the control-field resonance detuning is varied, the transparency of the medium for the probe (exactly resonant) radiation monotonically decreases with increasing detuning because of the rising role of single-photon absorption. In the case of circularly polarised control radiation and linearly polarised input probe field, a probe pulse propagating in the medium splits into two pulses with oppositely directed circular polarisations. An increase in the probe pulse resonance detuning (under exact-resonance conditions for the control radiation) leads primarily to an increase in the absorption by the medium of the probe pulse, the direction of circular polarisation for which coincides with the circular-polarisation direction for the control radiation.

Generation of an acoustic-gravity wave by two gravity waves, and their subsequent mutual interaction

AbstractThe nonlinear triad interaction of two opposing gravity waves with almost identical frequencies and one much longer acoustic-gravity wave is studied for non-resonance, as well as for exact resonance conditions. For non-resonance conditions the previously known results for a ‘bound’ acoustic-gravity wave are recovered. For resonance, or near-resonance conditions, where all three waves are ‘free waves’, the interaction is recurrent and the amplitude of the free acoustic-gravity wave turns out to be much larger than that known for the bound wave. The results for the recurrent evolution are given analytically, in terms of Jacobian elliptic functions and elliptic integrals.

Controlled engineering of extended states in disordered systems

We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suitably chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.

Transient Magnetoresponse of Photoexcited Electrons: Oscillating Conductivity and Negative Cyclotron Absorption

The nonlinear transient magnetoresponse of two-dimensional (2D) electrons is studied theoretically. Transient conductivity is calculated under exact cyclotron resonance condition. Two cases are considered: (a) the electrons excited by an ultrashort optical pulse, and isotropy of the initial distribution is expected; (b) dc electric field impose strongly anisotropic initial distribution. In case (b), evolution is strongly dependent on the initial phase of a circularly polarized wave. After the streaming distribution is formed, the magnetoresponse demonstrates periodically oscillating conductivity for both cases. The negative cyclotron absorption caused by the transient absolute negative conductivity effect is predicted for a certain range of parameters.

Parametric instability in a rotating cylinder of gas subject to sinusoidal axial compression. Part 1. Linear theory

An analysis is presented of parametric instability in a finite-length rotating cylinder subject to periodic axial compression by small sinusoidal oscillations of one of its ends (the ‘piston’). The instability is due to resonant interactions between inertial-wave (Kelvin) modes of the cylinder and the oscillatory compression and is resisted by viscosity, acting both through thin boundary layers and throughout the volume, the two mechanisms proving crucial for a satisfactory description. Instability is found to take the form of either a single axisymmetric mode with frequency near to half that of compression, or a pair of non-axisymmetric modes of the same azimuthal and axial orders and oppositely signed frequencies, whose difference is close to the compression frequency. Thus, in the axisymmetric case, instability leads to spontaneous growth of a system of one or more oscillating toroidal vortices encircling the cylinder axis, while the differing frequencies of the two modes of non-axisymmetric instability implies an oscillatory aperiodic flow. The neutral curves giving the threshold for instability are determined for all modes/mode pairs. For a given mode or mode pair, the neutral curve shows a critical piston amplitude dependent on rotational Reynolds number and cylinder aspect ratio, below which instability does not occur, and above which there is instability provided the compression frequency is chosen to lie in a band centred on the exact resonance condition.

Broadband rotational resonance in solid state NMR spectroscopy.

A new technique for restoring nuclear magnetic dipole-dipole couplings under magic-angle spinning (MAS) in solid state nuclear magnetic resonance (NMR) spectroscopy is described and demonstrated. In this technique, called broadband rotational resonance (BroBaRR), the coupling between a pair of nuclear spins with NMR frequency difference close (but not necessarily equal) to the MAS frequency is restored by the application of a train of weak radio-frequency pulses at a carrier frequency close to the average of the two NMR frequencies. Phase or amplitude modulation of the pulse train at half the MAS frequency splits the carrier into sidebands close to the two NMR frequencies. The pulse train then removes offsets from the exact rotational resonance condition, leading to dipolar recoupling over a bandwidth controlled by the amplitude of the pulse train. (13)C NMR experiments on uniformly (15)N,(13)C-labeled L-valineHClH(2)O powder validate the theoretical analysis. BroBaRR will be useful in studies of molecular structures by solid state NMR, for example in the detection of long-range couplings between carbons in uniformly labeled organic and biological materials.

The Pancharatnam phase of a two-level atom in the presence of another two-level atom in a cavity

In this paper we consider a Hamiltonian modelling a pair of two-level atoms within a perfect cavity for the case of a two-photon transition. Under the exact resonance condition and in the presence of both the Stark shift and phase shift an exact solution to the Schrodinger equation is obtained. Employing this solution gives an analytical expression for the temporal evolution of the Pancharatnam phase when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom. Numerical investigations are carried out for the phenomena of collapses and revivals for different Stark shift values, the distance between the two atoms and the phase shift. It has been shown that the Pancharatnam phase is affected by the Stark shift and the distance between the two atoms when a nonlinear two-photon process is involved

Theoretical and practical research of the use of inductors for improving DLTS characterization of semiconductors

In 1982 Broniatowki [J. Appl. Phys. 56 (1982) 2907] estimated theoretically what is the change of capacitance as seen by a capacitance meter if an inductor is set in series with a DLTS sample. To the best of our knowledge, there have been no experimental studies on the inductor coupled in series with the sample to clarify in which way the inductor would actually change the DLTS spectra.In this paper, we study for the first time theoretically and experimentally, the effects of an inductor on the capacitance of a sample, as seen by the capacitance meter. We also determine the resonance condition that increases the measured signal and we also study the separation of the signal peaks, proposing a novel way to obtain the activation energy (Ea), the capture cross-section (σ), and the density (N) of deep levels.Finally, we show our preliminary results using light in connection with the inductor in DLTS to improve the accuracy of the measurements.As an illustrative example, we have investigated the DLTS of AlxGa1−xAs, with Al molar compositions of x=0.22, 0.3, 0.4, 0.6 and 0.92. Both doped and un-doped samples are studied. AlGaAs is known to exhibit at least four DX centres [J. Appl. Phys. 67 (1990) R1; Semicond. Semimetals 38 (1993) 235; International Symposium, Mauterndorf, Austria, 1991; J. Electron. Mater. 20 (1991) 1], the properties of which depend on x, but they are found to overlap with each other, which makes it hard to determine their properties precisely. We show by computation that, adding the inductor to the sample improves the resolution of the DLTS measurement, separates the peaks and facilitates determining accurate values of Ea, σ, and N. Finally, the use of light was found to maintain the DX centres de-ionized, thus keeping the capacitance at reverse bias rather constant which, in turn, enabled us to easily achieve exact resonance conditions for the best effect.

Radiation of a charge moving over the diffraction grating

The states of a charged particle with a finite free path are determined in the field of a resonant electromagnetic wave. The exact resonance conditions, the modulation and beam instability mechanisms, the charge and current densities (Ohm's law) are obtained for the collisionless beam of resonance particles. Quantum theory of radiation is developed for the resonant adiabatic interaction between a particle and a wave taking into account the interaction with a constant magnetic field induced at the grating surface by the charge and nonresonant waves. The radiation power, the spectrum, and the range of generated frequencies are determined. The results obtained can be used in the plasma and solid-state theories and in electronics.

The electron bounce resonance in a low-pressure solenoidal inductive discharge

The electron energy distribution functions (EEDFs) are measured by a rf compensated Langmuir probe in a solenoidal inductive reactor at various frequencies and at 2 mTorr of argon. The frequency dependence of the electron energy distribution function is clearly observed. The energy diffusion coefficients against the applied frequencies are calculated from the nonlocal heating theory. It is found that the bounce resonance electrons determine the energy diffusion coefficient shape and the electron energy distribution function at the bounce resonance energy in the energy diffusion coefficient begins to flatten. The exact bounce resonance condition in solenoidal inductive discharge is presented. It is reported that the frequency dependence of the EEDFs is mainly due to the electron bounce resonance in a finite-size solenoidal inductive discharge.