The effects of trapped and untrapped particles on an electrostatic wave packet

We present a procedure to solve the Vlasov–Poisson equations for electrostatic wave packets. We obtain a Schrödinger type of wave equation, taking the wave– particle interaction into account. We use this equation to study the propagation of one finite-amplitude wave packet. We find a change in amplitude caused by interaction between the packet and particles propagating near to the group velocity. Also, we find a modulation of the plasma in the front of the packet, caused by trapping effects.

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Local Finite-Amplitude Wave Activity as a Diagnostic for Rossby Wave Packets

Monthly Weather Review ◽

10.1175/mwr-d-18-0068.1 ◽

2018 ◽

Vol 146 (12) ◽

pp. 4099-4114 ◽

Cited By ~ 4

Author(s):

Paolo Ghinassi ◽

Georgios Fragkoulidis ◽

Volkmar Wirth

Keyword(s):

Rossby Wave ◽

Model Simulation ◽

Wave Packets ◽

Meridional Wind ◽

Finite Amplitude ◽

Wave Activity ◽

Amplitude Wave ◽

High Impact Weather ◽

Finite Amplitude Wave Activity ◽

Isentropic Coordinates

AbstractUpper-tropospheric Rossby wave packets (RWPs) are important dynamical features, because they are often associated with weather systems and sometimes act as precursors to high-impact weather. The present work introduces a novel diagnostic to identify RWPs and to quantify their amplitude. It is based on the local finite-amplitude wave activity (LWA) of Huang and Nakamura, which is generalized to the primitive equations in isentropic coordinates. The new diagnostic is applied to a specific episode containing large-amplitude RWPs and compared with a more traditional diagnostic based on the envelope of the meridional wind. In this case, LWA provides a more coherent picture of the RWPs and their zonal propagation. This difference in performance is demonstrated more explicitly in the framework of an idealized barotropic model simulation, where LWA is able to follow an RWP into its fully nonlinear stage, including cutoff formation and wave breaking, while the envelope diagnostic yields reduced amplitudes in such situations.

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Optical wave-packet with nearly-programmable group velocities

Communications Physics ◽

10.1038/s42005-020-00481-4 ◽

2020 ◽

Vol 3 (1) ◽

Author(s):

Zhaoyang Li ◽

Junji Kawanaka

Keyword(s):

Wave Packet ◽

Group Velocity ◽

Wave Packets ◽

Bessel Beam ◽

Propagation Path ◽

Uniform Motion ◽

Optical Wave ◽

Straight Line ◽

Line Trajectory ◽

Group Velocities

AbstractDuring the process of Bessel beam generation in free space, spatiotemporal optical wave-packets with tunable group velocities and accelerations can be created by deforming pulse-fronts of injected pulsed beams. So far, only one determined motion form (superluminal or luminal or subluminal for the case of group velocity; and accelerating or uniform-motion or decelerating for the case of acceleration) could be achieved in a single propagation path. Here we show that deformed pulse-fronts with well-designed axisymmetric distributions (unlike conical and spherical pulse-fronts used in previous studies) allow us to obtain nearly-programmable group velocities with several different motion forms in a single propagation path. Our simulation shows that this unusual optical wave-packet can propagate at alternating superluminal and subluminal group velocities along a straight-line trajectory with corresponding instantaneous accelerations that vary periodically between positive (acceleration) and negative (deceleration) values, almost encompassing all motion forms of the group velocity in a single propagation path. Such unusual optical wave-packets with nearly-programmable group velocities may offer new opportunities for optical and physical applications.

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Longitudinal wave instability due to rotating beam-plasma interaction in weakly turbulent astrophysical plasmas

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2281 ◽

2019 ◽

Vol 489 (3) ◽

pp. 3059-3065

Author(s):

S M Khorashadizadeh ◽

Sh Abbasi Rostami ◽

A R Niknam ◽

S Vasheghani Farahani ◽

R Fallah

Keyword(s):

Distribution Function ◽

Longitudinal Wave ◽

Electron Distribution ◽

Electron Distribution Function ◽

Particle Interaction ◽

Magnetoactive Plasma ◽

Plasma Region ◽

Wave Instability ◽

Electrostatic Wave ◽

Wave Particle Interaction

ABSTRACTThe aim of this study is to highlight the temporal evolution of the longitudinal wave instability due to the interaction between a rotating electron beam and the magnetoactive plasma region in space plasma structures. The plasma structure which could be either in the solar atmosphere or any active plasma region in space is considered weakly turbulent, where the quasi-linear theory is implemented to enable analytic insight on the wave–particle interaction in the course of the event. It is found that in a weakly turbulent plasma, quasi-linear saturation of the longitudinal wave is accompanied by a significant alteration in the distribution function in the resonant region. In case of a pure electrostatic wave, the wave amplitude experiences elevation due to the energy transfer from the plasma particles. This causes flattening of the bump on tail (BOT) in the electron distribution function. If the gradient of the distribution function is positive, the chance that the beam would excite the wave is probable. In such a situation a plateau on the distribution function (∂f/∂v ≈ 0) is formed that will stop the diffusion of beam particles in the velocity space. Evolution of the electron distribution function experiences a decreases of the instability of the longitudinal wave. It is deduced that the growth rate of the wave instability is inversely proportional to the wave energy. Regarding the Sun, in addition to creating micro-turbulence due to wave–particle interaction, as the wave elevates to higher altitudes it enters a saturated energy state before releasing energy that may be a candidate for the generation of radio bursts.

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A Nonlinear Multiscale Theory of Atmospheric Blocking: Eastward and Upward Propagation and Energy Dispersion of Tropospheric Blocking Wave Packets

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-20-0153.1 ◽

2020 ◽

Vol 77 (12) ◽

pp. 4025-4049

Author(s):

Dehai Luo ◽

Wenqi Zhang

Keyword(s):

Group Velocity ◽

Growth Phase ◽

Wave Packets ◽

Finite Amplitude ◽

Wave Activity ◽

Amplitude Equation ◽

Planetary Waves ◽

Decay Phase ◽

Upper Troposphere ◽

Envelope Amplitude

AbstractIn this paper, a nonlinear multiscale interaction model is used to examine how the planetary waves associated with eddy-driven blocking wave packets propagate through the troposphere in vertically varying weak baroclinic basic westerly winds (BWWs). Using this model, a new one-dimensional finite-amplitude local wave activity flux (WAF) is formulated, which consists of linear WAF related to linear group velocity and local eddy-induced WAF related to the modulus amplitude of blocking envelope amplitude and its zonal nonuniform phase. It is found that the local eddy-induced WAF reduces the divergence (convergence) of linear WAF in the blocking upstream (downstream) side to favor blocking during the blocking growth phase. But during the blocking decay phase, enhanced WAF convergence occurs in the blocking downstream region and in the upper troposphere when BWW is stronger in the upper troposphere than in the lower troposphere, which leads to enhanced upward-propagating tropospheric wave activity, though the linear WAF plays a major role. In contrast, the downward propagation of planetary waves may be seen in the troposphere for vertically decreased BWWs. These are not seen for a zonally uniform eddy forcing. A perturbed inverse scattering transform method is used to solve the blocking envelope amplitude equation. It is found that the finite-amplitude WAF represents a modified group velocity related to the variations of blocking soliton amplitude and zonal wavenumber caused by local eddy forcing. Using this amplitude equation solution, it is revealed that, under local eddy forcing, the blocking wave packet tends to be nearly nondispersive during its growth phase but strongly dispersive during the decay phase for vertically increased BWWs, leading to strong eastward and upward propagation of planetary waves in the downstream troposphere.

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Phase and group velocity tracing analysis of projected wave packet motion along oblique radar beams – qualitative analysis of QP echoes

Annales Geophysicae ◽

10.5194/angeo-25-77-2007 ◽

2007 ◽

Vol 25 (1) ◽

pp. 77-86 ◽

Cited By ~ 1

Author(s):

F. S. Kuo ◽

H. Y. Lue ◽

C. L. Fern

Keyword(s):

Wave Packet ◽

Group Velocity ◽

Gravity Waves ◽

Theoretical Calculations ◽

Wave Packets ◽

Wave Length ◽

Wave Period ◽

Horizontal Distance ◽

Characteristic Wave ◽

Horizontal Wave

Abstract. The wave packets of atmospheric gravity waves were numerically generated, with a given characteristic wave period, horizontal wave length and projection mean wind along the horizontal wave vector. Their projection phase and group velocities along the oblique radar beam (vpr and vgr), with different zenith angle θ and azimuth angle φ, were analyzed by the method of phase- and group-velocity tracing. The results were consistent with the theoretical calculations derived by the dispersion relation, reconfirming the accuracy of the method of analysis. The RTI plot of the numerical wave packets were similar to the striation patterns of the QP echoes from the FAI irregularity region. We propose that the striation range rate of the QP echo is equal to the radial phase velocity vpr, and the slope of the energy line across the neighboring striations is equal to the radial group velocity vgr of the wave packet; the horizontal distance between two neighboring striations is equal to the characteristic wave period τ. Then, one can inversely calculate all the properties of the gravity wave responsible for the appearance of the QP echoes. We found that the possibility of some QP echoes being generated by the gravity waves originated from lower altitudes cannot be ruled out.

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Self-modulation of a nonlinear ion wave packet

Journal of Plasma Physics ◽

10.1017/s0022377800020754 ◽

1977 ◽

Vol 17 (3) ◽

pp. 487-501 ◽

Cited By ~ 63

Author(s):

S. Watanabe

Keyword(s):

Wave Packet ◽

Modulational Instability ◽

Wave Packets ◽

Broad Band ◽

Particle Interaction ◽

Voltage Response ◽

Monochromatic Wave ◽

Linear Dispersion ◽

Step Voltage ◽

Positive Step

The modulational instability of the ion wave is observed experimentally. Two kinds of wave packets are launched in the plasma by means of a grid. One is a broad-band wave packet excited by a positive step voltage. The other is a quasi-monochromatic wave packet modulated by a pulse. For the step voltage response, we observe a large oscillation in the wave front which evolves to Korteveg–de Vries solitons and a small amplitude wave packet in the tail. The wave packet becomes modulationally unstable and divides into smaller wave packets. Whenever the wave packet is modulated, the spread of the packet is suppressed and is much smaller than is expected from linear dispersion. For the quasi-monochromatic wave packet, we also observe the modulational instability if the carrier frequency is high. The frequency of the carrier is shifted by the instability. The result of the quasi-monochromatic wave packet is qualitatively explained by the modified nonlinear Schrödinger equation taking account of the wave-particle interaction at the group velocity.

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A Budget Equation for the Amplitude of Rossby Wave Packets Based on Finite-Amplitude Local Wave Activity

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-19-0149.1 ◽

2019 ◽

Vol 77 (1) ◽

pp. 277-296

Author(s):

Paolo Ghinassi ◽

Marlene Baumgart ◽

Franziska Teubler ◽

Michael Riemer ◽

Volkmar Wirth

Keyword(s):

Wave Packet ◽

Rossby Wave ◽

Wave Packets ◽

Finite Amplitude ◽

Equation Model ◽

Wave Activity ◽

Phase Dependence ◽

Local Wave ◽

Budget Equation ◽

Upper Level

Abstract Recently, the authors proposed a novel diagnostic to quantify the amplitude of Rossby wave packets. This diagnostic extends the local finite-amplitude wave activity (LWA) of N. Nakamura and collaborators to the primitive-equations framework and combines it with a zonal filter to remove the phase dependence. In the present work, this diagnostic is used to investigate the dynamics of upper-tropospheric Rossby wave packets, with a particular focus on distinguishing between conservative dynamics and nonconservative processes. For this purpose, a budget equation for filtered LWA is derived and its utility is tested in a hierarchy of models. Idealized simulations with a barotropic and a dry primitive-equation model confirm the ability of the LWA diagnostic to identify nonconservative local sources or sinks of wave activity. In addition, the LWA budget is applied to forecast data for an episode in which the amplitude of an upper-tropospheric Rossby wave packet was poorly represented. The analysis attributes deficiencies in the Rossby wave packet amplitude to the misrepresentation of diabatic processes and illuminates the importance of the upper-level divergent outflow as a source for the error in the wave packet amplitude.

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Studies of gravity wave propagation in the mesosphere observed by MU radar

Annales Geophysicae ◽

10.5194/angeo-31-845-2013 ◽

2013 ◽

Vol 31 (5) ◽

pp. 845-858 ◽

Cited By ~ 3

Author(s):

H. Y. Lue ◽

F. S. Kuo ◽

S. Fukao ◽

T. Nakamura

Keyword(s):

Wave Packet ◽

Phase Velocity ◽

Group Velocity ◽

Gravity Waves ◽

Wave Packets ◽

Wave Period ◽

Parameter Analysis ◽

Mu Radar ◽

Horizontal Wavelength ◽

Group Velocities

Abstract. Mesospheric data were analyzed by a composite method combining phase and group velocity tracing technique and the spectra method of Stokes parameter analysis to obtain the propagation parameters of atmospheric gravity waves (AGW) in the height ranges between 63.6 and 99.3 km, observed using the MU radar at Shigaraki in Japan in the months of November and July in the years 1986, 1988 and 1989. The data of waves with downward phase velocity and the data of waves with upward phase velocity were independently treated. First, the vertical phase velocity and vertical group velocity as well as the characteristic wave period for each wave packet were obtained by phase and group velocity tracing technique. Then its horizontal wavelength, intrinsic wave period and horizontal group velocity were obtained by the dispersion relation. The intrinsic frequency and azimuth of wave vector of each wave packet were checked by Stokes parameters analysis. The results showed that the waves with intrinsic periods in the range 30 min–4.5 h had horizontal wavelength ranging from 25 to 240 km, vertical wavelength from 2.5 to 12 km, and horizontal group velocities from 15 to 60 m s−1. Both upward moving wave packets and downward moving wave packets had horizontal group velocities mostly directed in the sector between directions NNE (north-north-east) and SEE in the month of November, and mostly in the sector between directions NW and SWS in the month of July. Comparing with mean wind directions, the gravity waves appeared to be more likely to propagate along with mean wind than against it. This apparent prevalence for downstream wave packets was found to be caused by a systematic filtering effect existing in the process of phase and group velocity tracing analysis: A significant portion of upstream wave packets might have been Doppler shifted out of the vertical range in phase and group velocity tracing analysis.

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Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100134144 ◽

1990 ◽

Vol 48 (2) ◽

pp. 110-111 ◽

Cited By ~ 1

Author(s):

F. Hasselbach ◽

A. Schäfer

Keyword(s):

Group Velocity ◽

Wave Packets ◽

Index Of Refraction ◽

Electron Wave ◽

Fringe Contrast ◽

Faraday Cage ◽

Optical Index ◽

Wien Filter ◽

Coherent Wave ◽

Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

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