Resonant Velocity Research Articles

Comparison of parallel group velocity of ECH waves with electron resonant velocity: Implication for electron diffusion by ECH waves

We have investigated the role of group velocity in the calculation of pitch-angle diffusion coefficients by electron cyclotron harmonic (ECH) waves in planetary magnetospheres. The assumption which is generally made that the parallel group velocity can be neglected in comparison with particle parallel velocity is examined in detail. It is found that for lowest harmonic band this assumption is quite good. It is found that in general it is not possible to ignore the parallel group velocity. However, for lowest harmonic band this assumption is quite good at low electron temperatures.

Guided waves analysis using multiemitter and multireceiver arrays.

Structural and material properties of elastic waveguides can be characterized by fitting measured to theoretical guided wave phase velocities. Here emitters and receivers are placed in contact on the same side of the waveguide (i.e., axial transmission geometry). Multireceiver arrays allow the determination of phase velocities using two‐dimensional spatial‐temporal Fourier transform, which requires a large distance probed by the receivers. Practical constraints, as in clinical inspection of cortical bones, may reduce the inspected spatial length and therefore the efficiency of this technique. We propose a technique which takes benefit of using both multiple emitters and multiple receivers. This approach derived from the DORT method adapted to the transmission problem. The singular values decomposition at different frequencies of the transmission matrix between the arrays give the invariants of transmission, which are linked with the guided modes. First, experiments carried out on different metallic plates are shown. Experimental velocities are in good agreement with Lamb waves theoretical values. In particular, zero group velocity resonance and negative phase velocities are shown. These results allows a good evaluation of the thickness and the transverse and longitudinal bulk waves velocities. Further applications concerning evaluation of elastic properties of cortical bone are finally mentioned.

Theory of current-free double layers in plasmas

The existence of current-free double layers in unmagnetized plasma is studied by means of the quasipotential method applied to the Vlasov–Poisson system. Crucial for its existence are trapped particle populations that are characterized by notches (dips) in the velocity distribution functions at resonant velocity becoming flat at large amplitude limit. The potential drop across the double layer, or its amplitude ψ, can be arbitrarily strong covering the whole range 0<ψ<∞. Both the small and large amplitude limit are worked out explicitly, inclusively effective kinetic temperatures and pressures. It is, hence, the effective electron (ion) temperature increase (decrease) with increasing potential, caused by the trapped particles, which is responsible for the existence of this two-parameter family of solutions.

Wave-particle interaction at double resonance

This paper is devoted to studying wave-particle interaction at "double resonance" condition, i.e., when two waves interact resonantly with the same group of charged particles. A theoretical Hamiltonian model and a symplectic numerical code are built to describe the three-dimensional interactions of wave spectra with resonant electrons in a magnetized plasma. Related simulations on the evolution of two waves of close parallel phase velocities interacting resonantly with particles' fluxes have been performed, which reveal some common features which do not depend on the kind of waves, instabilities, and particles' distributions: after the stage of linear instability, when the waves' amplitudes saturate due to particle trapping, a nonlinear process takes place which is characterized by a quasiperiodical exchange of energy between the waves, depending in particular on the value of the mismatch between the waves' resonant velocities. In order to explain such observations, a simple Hamiltonian model describing the interaction of two different waves of close resonant velocities with a periodical train of bunches of trapped particles moving synchronously has been built. It allows one to describe the nonlinear characteristics of this process as well as to estimate analytically its time scale and shows a good agreement with the numerical simulation results.

Observation of Hamiltonian chaos in wave–particle interaction

The motion of charged particle in longitudinal waves is a paradigm for the transition to large scale chaos in Hamiltonian systems. Recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s) in a specially designed Traveling Wave Tube (TWT). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The resonant velocity domain associated to a single wave is observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a “devil’s staircase” behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons to escape from a given velocity region as well as its robustness are also successfully tested. Thus generic features of Hamiltonian chaos have been experimentally observed.

Simulation of the fluid–structure-interaction of steam generator tubes and bluff bodies

The accuracy of computational fluid dynamics in simulating the cross-flow around a steam generator and the feasibility of a full scale coupled CFD/FEA fluid–structure-interaction (FSI) analysis is examined through successive validations. The study begins with a comparison between experiment and computation of flow within a stationary tube bank. Results from the simulation of an individual tube experiencing two-degree-of-freedom flow-induced vibration (at a Reynolds number of 3800) are then shown to compare favorably to experimental results. Finally, free vibration of a single cantilevered hydrofoil is simulated with comparison of mean square acceleration at resonant and non-resonant velocities, respectively. The magnitudes and frequencies of vibration are shown to be accurately captured.

Ground-state pump-probe spectroscopy

The absorption/gain spectrum of a weak probe field is theoretically analyzed for an atomic three-level Λ system driven by a strong pump field and perturbed by collisions with buffer-gas atoms. It is assumed that both pump and probe drive the same transition. When the dark state is sufficiently long lived, the probe spectrum exhibits an extremely narrow (possibly subnatural-width) resonance. It is shown that coherence-preserving collisions drastically (both qualitatively and quantitatively) change the probe absorption spectrum even at a low collision frequency, when Dicke narrowing is negligible. Strong coherence effects on the resonance structure at low gas pressures is explained by a change in refractive index due to coherence-preserving collisions for particles in the resonant velocity group.

Observation of Hamiltonian chaos and its control in wave–particle interaction

Wave–particle interactions are central in plasma physics. They can be studied in a traveling wave tube (TWT) to avoid intrinsic plasma noise. This led to detailed experimental analysis of the self-consistent interaction between unstable waves and an either cold or warm beam. More recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed. The resonant velocity domain associated with a single wave is also observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a ‘devil's staircase’ behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons from escaping from a given velocity region as well as its robustness are successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics.

Dispersion properties of electromagnetically induced transparency under the Doppler broadening

The influence of heat motion of atoms in gaseous media on the features of manifestation of electromagnetically induced transparency is investigated. Taking into account elastic and inelastic collisions, fairly general and compact analytical relations are derived for the absorption and refraction coefficients of the probe wave in the presence of high-power inducing radiation, resonant to the adjacent atomic transition. It is shown, that occurrence of narrow resonance structures in the Doppler absorption and refraction profile is due to “overlap” of effective resonance velocities of atoms. The atomic level splitting in the strong wave field is uniformly analyzed in the entire intensity range. Interference transparency in a particular region of the Doppler profile is found to be accompanied by high resonance dispersion of the refraction coefficient, which is important for generating slow radiation and controlling its parameters.

Heavy ion acceleration in the divergent solar wind

We study the heavy ion acceleration due to cyclotron interaction with both right‐ and left‐hand polarized MHD waves propagating along the magnetic field in the outward direction in the divergent solar wind. It is shown in test‐particle approximation that heavy ions can overcome the gap between the maximum resonant velocity for left‐handed waves and minimum resonant velocity for right‐handed waves and acquire the average parallel velocity on the order of local Alfven speed relative to the protons.

Rapidly moving sources of upper band ELF/VLF chorus near the magnetic equator

Multiple simultaneous wideband (Gurnett et al., 2001) measurements on the Cluster spacecraft of upper band chorus emissions near the magnetic equator (at magnetic latitudes between −20° and 10° and L shells ranging between L = 4 and L = 5) are used to deduce the properties of the compact source regions of ELF/VLF chorus emissions. The frequency differences exhibited by the same chorus emissions observed on different spacecraft are interpreted (Inan et al., 2004) in terms of a differential Doppler shift, using a simple model involving rapidly moving sources traveling at speeds comparable to the parallel resonant velocity of counter‐streaming gyroresonant electrons. Cluster observations are used to determine the location and extent along the Earth's magnetic field lines of the source of chorus. Frequency and time differences between spacecraft are interpreted as a direct consequence of the rapid motion of highly localized source regions of chorus. In this paper, we examine the previously presented model of rapid motion of sources of chorus, extending the calculations to a three‐dimensional space, using measurements of the four Cluster spacecraft. These calculations of source location and velocity as a function of frequency indicate that chorus sources move a distance of ∼6000 km along the field lines. The emitted chorus waves at the source are assumed to have a wide range of wave normal angles, but the rays reaching the spacecraft seem to be the ones with lower angles (with some exceptions). The ranges of velocity obtained vary with frequency around values ranging from ∼0.01c to ∼0.04c.

Direct observation of a “devil’s staircase” in wave-particle interaction

We report the experimental observation of a "devil's staircase" in a time-dependent system considered as a paradigm for the transition to large-scale chaos in the universality class of Hamiltonian systems. A test electron beam is used to observe its non-self-consistent interaction with externally excited wave(s) in a traveling wave tube (TWT). A trochoidal energy analyzer records the beam energy distribution at the output of the interaction line. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The resonant velocity domain associated to a single wave is observed, as well as the transition to large-scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a "devil's staircase" behavior for increasing excitation amplitude, due to the nonlinear forcing by the second wave on the pendulum-like motion of a charged particle in one electrostatic wave.

Internal gravity wave resonance of thermal convection fields in a square cavity with heat‐flux vibration

AbstractIn this paper, the thermal convection field and its resonance phenomena in a square cavity with sinusoidal heat‐flux vibration were numerically investigated. As the angular velocity ω is changed, the thermal convection field at Pr = 0.71,Ra = 106 is found to be classified into 5 regions. In particular, the field has the local maximum relative amplitude of midplane Nusselt's number at ωc = 350, which corresponds to the angular velocity of internal gravity wave ωr estimated by a theoretical equation proposed by Thorpe. This shows that the local enhancement is induced by internal gravity wave resonance. Such correspondence is observed for Ra ≥ 105,Ra ≥ 106 for Pr = 0.71, 7.1, respectively. For these ranges of Ra we propose a correlation equation, a function of Pr and Gr only, to estimate the resonant angular velocity. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(5): 309–322, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20122

Wave-particle interaction and Hamiltonian dynamics investigated in a traveling wave tube

For wave-particle interaction studies, the one-dimensional (1-D) beam-plasma system can be advantageously replaced by a Traveling Wave Tube (TWT). This led us to a detailed experimental analysis of the self-consistent interaction between unstable waves and a small either cold or warm beam. More recently, a test electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is investigated with a trochoidal energy analyzer that records the beam energy distribution at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed. The resonant velocity domain associated to a single wave is also observed, as well as the transition to large-scale chaos when the resonant domains of two waves and their secondary resonances overlap leading to a typical “devil’s staircase” behavior. A new strategy for the control of chaos is tested.

Dispersion Management Using Betatron Resonances in an Ultracold-Atom Storage Ring

Particles circulating at specific velocities in a storage ring can undergo betatron resonances at which static perturbations of the particles' orbit yield large transverse (betatron) oscillations. We have observed betatron resonances in an ultracold-atom storage ring and found these resonances to cause the near-elimination of the longitudinal dispersion of atomic beams propagating at resonant velocities. This effect can improve atom-interferometric devices. Both the resonant velocities and the resonance strengths were varied by deliberate modifications to the storage ring.

Characterization of FGM monomorph actuators fabricated using EPD

Piezoelectric FGM monomorph actuators fabricated using electrophoretic deposition (EPD) were investigated. Both the physical and electromechanical properties were examined. The high voltage performance of the actuator in both static and dynamic state was focused. It was found that the monomorph exhibits tetragonal phase perovskite structure and the gradient variation of microstructure was observed over the cross section. The displacement keeps a wide range of linearity in the static state. In the dynamic state, the vibration displacement is both frequency and voltage dependent. The resonant frequency shifts to lower frequency range due to the higher vibration loss at higher voltages. This results in the frequency dependence of the vibration limitations. The vibration limitation is also voltage dependent. Above a cutoff voltage, the displacement may not increase. To obtain a higher resonant displacement or velocity, the frequency and voltage should match well. Temperature rise or heat generation is caused by vibration loss. The maximum temperature happens at the clamped end of the monomorph.

Form Drag Caused by Topographically Forced Waves in a Barotropic β Channel: Effect of Higher Mode Resonance

The relationship between form drag and the zonal mean velocity of steady states is investigated in a very simple system; a barotropic quasi-geostrophic β channel with sinusoidal topography. When a steady solution is calculated by the modified Marquardt method, keeping the zonal mean velocity constant as a parameter, the characteristic of the solution changes at a phase speed of a wave with a wavenumber higher than that of the bottom topography. For velocities smaller than this critical value, there exists a stable quasi-linear solution similar to the linear solution. For larger velocities, there exist three solutions whose form drag is very large. In addition, the resonant velocity of the mode, whose wavenumber is the same as the bottom topography, has no effect on these solutions. When the quiescent fluid is accelerated by a constant wind stress, acceleration stops around the critical velocity for a wide range of the wind stress. If the wind stress is too large for the acceleration to stop, the zonal current speed continues to increase infinitely. It is implied that the zonal velocity of equilibrium is mainly determined, not by the wind stress, but by the amplitude of the bottom topography and the viscosity coefficient.

Coherent resonant tunneling time and velocity in finite periodic systems

The velocity ${v}_{\mathrm{res}}$ of resonant tunneling electrons in finite periodic structures is analytically calculated in two ways. The first method is based on the fact that a transmission of unity leads to a coincidence of all still-competing tunneling time definitions. Thus, having an indisputable resonant tunneling time ${\ensuremath{\tau}}_{\mathrm{res}}$, we apply the natural definition ${v}_{\mathrm{res}}=L∕{\ensuremath{\tau}}_{\mathrm{res}}$ to calculate the velocity. For the second method, we combine Bloch's theorem with the transfer matrix approach to decompose the wave function into two Bloch waves. The expectation value of the velocity is then calculated. Both approaches lead to the same result, showing their physical equivalence. The obtained resonant tunneling velocity ${v}_{\mathrm{res}}$ is smaller than or equal to the group velocity times the magnitude of the complex transmission amplitude of the unit cell. Only at energies at which the unit cell of the periodic structure has a transmission of unity does ${v}_{\mathrm{res}}$ equal the group velocity. Numerical calculations for a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ superlattice are performed. For typical parameters, the resonant velocity is below one-third of the group velocity.

Kinetic theory of periodic hole and double layer equilibria in pair plasmas

The existence of manifestly nonlinear electrostatic modes in pair plasmas is shown analytically by means of the quasi-potential method applied to the Vlasov–Poisson system. These modes owe their existence to the trapping of particles in the potential trough(s) and are typically characterized by a notch in the particle distribution functions at resonant velocity, forming vortices in phase space. Both entities, wave structure Φ(x) and phase velocity v0, are uniquely characterized by two parameters, the periodicity parameter k0 and the spectral parameter B. Whereas k0 = 0 describes double layers, with a phase velocity in the thermal range, k0 ≠ 0 represents a periodic wave train which can propagate with two rather distinct phase velocities. One is related to the fast plasma wave, the other one to the slow acoustic mode.

Vertical dynamic responses of a simply supported bridge subjected to a moving train with two-wheelset vehicles using modal analysis method

The vertical dynamic responses of a simply supported bridge subjected to a moving train are investigated by means of the modal analysis method. Each vehicle of train is modelled as a four-degree-of-freedom mass–spring–damper multi-rigid body system with a car body and two wheelsets. The bridge, together with track, is modelled as a simply supported Bernoulli–Euler beam. The deflection of the beam is described by superimposing modes. The train and the beam are regarded as an entire dynamic system, in which the contact forces between wheelset and beam are considered as internal forces. The equations of vertical motion in matrix form with time-dependent coefficients for this system are directly derived from the Hamilton's principle. The equations of motion are solved by Wilson-θ method to obtain the dynamic responses for both the support beam and the moving train. Compared with the results previous reported, good agreement between the proposed method and the finite element method is obtained. Finally, the effects of beam mode number, vehicle number, beam top surface, and train velocity on the dynamic responses of the entire train and bridge coupling system are studied, and the dynamic responses of beam are given under the train moving with resonant velocity. Copyright © 2005 John Wiley & Sons, Ltd.