scholarly journals Short-Wave Asymptotics for Gaussian Beams and Packets and Scalarization of Equations in Plasma Physics

Physics ◽  
2019 ◽  
Vol 1 (2) ◽  
pp. 301-320
Author(s):  
Anatoly Yu. Anikin ◽  
Sergey Yu. Dobrokhotov ◽  
Alexander I. Klevin ◽  
Brunello Tirozzi
Keyword(s):  
Wave Packet ◽  
High Frequency ◽  
Classical Mechanics ◽  
Short Wave ◽  
Lower Hybrid ◽  
Focal Points ◽  
Complex Germ ◽  
High Frequency Waves ◽  
Arbitrary Frequency ◽  
Main Ideas

We study Gaussian wave beam and wave packet types of solutions to the linearized cold plasma system in a toroidal domain (tokamak). Such solutions are constructed with help of Maslov’s complex germ theory (short-wave or semi-classical asymptotics with complex phases). The term “semi-classical” asymptotics is understood in a broad sense: asymptotic solutions of evolutionary and stationary partial differential equations from wave or quantum mechanics are expressed through solutions of the corresponding equations of classical mechanics. This, in particular, allows one to use useful geometric considerations. The small parameter of the expansion is h = λ / 2 π L where λ is the wavelength and L the dimension of the system. In order to apply the asymptotic algorithm, we need this parameter to be small, so we deal only with high-frequency waves, which are in the range of lower hybrid waves used to heat the plasma. The asymptotic solution appears to be a Gaussian wave packet divided by the square root of the determinant of an appropriate Jacobi matrix (“complex divergence”). When this determinant is zero, focal points appear. Our approach allows one to write out asymptotics near focal points. We also claim that this approach is very practical and leads to formulas that can be used for numerical simulations in software like Wolfram Mathematica, Maple, etc. For the particular case of high-frequency beams, we present a recipe for constructing beams and packets and show the results of their numerical implementation. We also propose ideas to treat the more difficult general case of arbitrary frequency. We also explain the main ideas of asymptotic theory used to obtain such formulas.

The Interaction Between Steep Waves and a Vertical, Surface-Piercing Column

2005 ◽  
Vol 127 (1) ◽  
pp. 31-38 ◽  
Author(s):  
Rizwan Sheikh ◽  
Chris Swan
Keyword(s):  
High Frequency ◽  
Impact Damage ◽  
Wave Interaction ◽  
Scattered Wave ◽  
Short Wave ◽  
Vertical Surface ◽  
Wave Impact ◽  
Single Column ◽  
High Frequency Waves ◽  
Incident Waves

This paper describes new laboratory observations concerning the interaction between a series of steep incident waves and a vertical, surface-piercing, column. The motivation for the study arose as a result of wave impact damage sustained to the undersides of several concrete gravity-based structures in the northern North Sea. Earlier work, [Swan et al. Appl. Ocean. Res. 19, pp. 309–327 (1997)], demonstrated that in the case of multiple column structures, the individual diameters of which lie outside the typical (linear) diffraction regime, there exists a new and previously unexpected mechanism leading to the scattering of high-frequency waves. Although the implications of this effect was carefully documented, not least because it explained the occurrence of wave impacts in relatively moderate seas, its physical origins remained unclear. In particular, it was uncertain whether this type of scattering would be observed in the case of a single column, or whether it results from the transmission of wave modes trapped between the legs of a multiple column structure. In the case of a single column, if the diameter, D, is such that the flow lies within the drag-inertia regime, D/λ<0.2, where λ is the corresponding wavelength, linear diffraction theory suggests there will be little or no scattered wave energy. The present laboratory observations demonstrate that this is not, in fact, the case. If the incident waves are steep, a strong and apparently localized interaction is clearly observed at the water surface. This, in turn, leads to the scattering of high-frequency waves. Although these waves are relatively small in amplitude, their subsequent interaction with other steep incident waves takes the form of a classic long-wave short-wave interaction and can produce a significant increase in the maximum crest elevation relative to those recorded in the absence of the structure. The present paper will demonstrate that the scattering of these high-frequency waves, and their subsequent nonlinear interaction with other incident waves, has significant implications for the specification of an effective air-gap and hence for the setting of deck elevations.

The Interaction Between Steep Waves and a Vertical, Surface-Piercing Column

2003 ◽  
Author(s):  
Rizwan Sheikh ◽  
Chris Swan
Keyword(s):  
High Frequency ◽  
Impact Damage ◽  
Wave Interaction ◽  
Scattered Wave ◽  
Short Wave ◽  
Vertical Surface ◽  
Wave Impact ◽  
Single Column ◽  
High Frequency Waves ◽  
Incident Waves

The paper describes new laboratory observations concerning the interaction between a series of steep incident waves and a vertical, surface-piercing, column. The motivation for the study arose as a result of wave impact damage sustained to the undersides of several concrete gravity-based structures in the northern North Sea. Earlier work, Swan et al. [1], demonstrated that in the case of multiple column structures, the individual diameters of which lie outside the typical (linear) diffraction regime, there exists a new and previously unexpected mechanism leading to the scattering of high-frequency waves. Although the implications of this effect was carefully documented, not least because it explained the occurrence of wave impacts in relatively moderate seas, its physical origins remained unclear. In particular, it was uncertain whether this type of scattering would be observed in the case of a single column, or whether it results from the transmission of wave modes trapped between the legs of a multiple column structure. In the case of a single column, if the diameter, D, is such that the flow lies within the drag-inertia regime, D/λ &lt; 0.2, where λ is the corresponding wavelength, linear diffraction theory suggests there will be little or no scattered wave energy. The present laboratory observations demonstrate that this is not, in fact, the case. If the incident waves are steep, a strong and apparently localised interaction is clearly observed at the water surface. This, in turn, leads to the scattering of high-frequency waves. Although these waves are relatively small in amplitude, their subsequent interaction with other steep incident waves takes the form of a classic long-wave short-wave interaction and can produce a significant increase in the maximum crest elevation relative to those recorded in the absence of the structure. The present paper will demonstrate that the scattering of these high-frequency waves, and their subsequent nonlinear interaction with other incident waves, has significant implications for the specification of an effective air-gap and hence for the setting of deck elevations.

Anomalous transport and anomalous heating due to lower-hybrid wave fields

1988 ◽  
Vol 39 (3) ◽  
pp. 447-474 ◽  
Author(s):  
M. Krämer ◽  
N. Sollich ◽  
J. Dietrich
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Field Energy ◽  
Lower Hybrid ◽  
Hybrid Wave ◽  
Heating Rates ◽  
Lower Hybrid Wave ◽  
Drift Wave Turbulence ◽  
Frequency Fluctuations ◽  
High Frequency Waves

The microscopic and macroscopic behaviours of a linear reflex discharge in the presence of low-frequency turbulence are investigated under the action of moderate lower-hybrid wave power. The frequency and wavenumber spectra of both the low-frequency fluctuations and the high-frequency waves are measured using a correlation-analysis technique with two probes. The low-frequency fluctuations may be attributed to drift-wave turbulence. The fluctuation level is raised when RF power is coupled to the plasma, thus leading to considerably enhanced radial transport. The coupling between low-frequency fluctuations and high-frequency waves can be seen clearly from the spectra. The high-frequency wavenumber spectra measured inside the antenna are in reasonable agreement with the lower-hybrid wave dispersion. However, the wavenumbers observed in the lower-hybrid resonance region outside the antenna are – in contrast with expectation – not larger than in the plasma edge region. From the electric-field energy-density spectra and from measurements of the density and the temperatures, a detailed energy balance can be performed. The calculated heating rates are anomalously large for both the electrons and the ions. The absorption processes, relevant for the present experiment, are discussed.

scholarly journals Cluster observations of high-frequency waves in the exterior cusp

2004 ◽  
Vol 22 (7) ◽  
pp. 2403-2411 ◽  
Author(s):  
Y. Khotyaintsev ◽  
A. Vaivads ◽  
Y. Ogawa ◽  
B. Popielawska ◽  
M. André ◽  
...  
Keyword(s):  
High Frequency ◽  
Plasma Frequency ◽  
Electron Beams ◽  
Broad Band ◽  
Generation Mechanism ◽  
Lower Hybrid ◽  
Short Time Scale ◽  
Current Sheets ◽  
Spectral Peaks ◽  
High Frequency Waves

Abstract. We study wave emissions, in the frequency range from above the lower hybrid frequency up to the plasma frequency, observed during one of the Cluster crossings of a high-beta exterior cusp region on 4 March 2003. Waves are localized near narrow current sheets with a thickness a few times the ion inertial length; currents are strong, of the order of 0.1-0.5μA/m2 (0.1-0.5mA/m2 when mapped to ionosphere). The high frequency part of the waves, frequencies above the electron-cyclotron frequency, is analyzed in more detail. These high frequency waves can be broad-band, can have spectral peaks at the plasma frequency or spectral peaks at frequencies below the plasma frequency. The strongest wave emissions usually have a spectral peak near the plasma frequency. The wave emission intensity and spectral character change on a very short time scale, of the order of 1s. The wave emissions with strong spectral peaks near the plasma frequency are usually seen on the edges of the narrow current sheets. The most probable generation mechanism of high frequency waves are electron beams via bump-on-tail or electron two-stream instability. Buneman and ion-acoustic instability can be excluded as a possible generation mechanism of waves. We suggest that high frequency waves are generated by electron beams propagating along the separatrices of the reconnection region.

A THREE‐DIMENSIONAL SEISMIC WAVE MODEL WITH BOTH ELECTRICAL AND VISUAL OBSERVATION OF WAVES

Geophysics ◽  
1954 ◽  
Vol 19 (2) ◽  
pp. 220-236 ◽  
Author(s):  
J. F. Evans ◽  
C. F. Hadley ◽  
J. D. Eisler ◽  
D. Silverman
Keyword(s):  
High Frequency ◽  
Three Dimensional ◽  
Wave Model ◽  
Short Wave ◽  
Visual Observation ◽  
Sound Waves ◽  
Transient Wave ◽  
Symmetric Wave ◽  
Theoretical Predictions ◽  
High Frequency Waves

The short wave lengths required in a seismic model to give wave‐front patterns geometrically similar to those in a large prototype (the earth) can only be obtained by using high frequency sound waves. As sources and detectors of such high frequency waves, piezoelectric crystals are used, primarily because under identical stimuli they are capable of almost perfect duplication. Such duplication is made use of in displaying on an oscilloscope stationary patterns which are characteristic of transient particle motion at a point in the model. Also, it has made possible the direct visual observation of transient wave fronts in transparent models, techniques for which are described, and sample photographs given. As an example of quantitative use of the described model techniques, the results are presented showing symmetric and anti‐symmetric wave propagation in a free elastic plate. Good agreement is found between many features of the experimental record and theoretical predictions.

First VIKING results: high frequency waves

1988 ◽  
Vol 37 (3) ◽  
pp. 469-474 ◽  
Author(s):  
A Bahnsen ◽  
M Jespersen ◽  
E Ungstrup ◽  
R Pottelette ◽  
M Malingre ◽  
...  
Keyword(s):  
High Frequency ◽  
High Frequency Waves

Scattering of electromagnetic waves by hybrid waves in a two-electron-temperature plasma

1991 ◽  
Vol 46 (1) ◽  
pp. 99-106 ◽  
Author(s):  
S. K. Sharma ◽  
A. Sudarshan
Keyword(s):  
Growth Rate ◽  
Electron Temperature ◽  
High Frequency ◽  
Electromagnetic Waves ◽  
Low Frequency ◽  
Lower Hybrid ◽  
Stimulated Scattering ◽  
Coupled Modes ◽  
Temperature Plasma ◽  
Electrostatic Perturbation

In this paper, we use the hydrodynamic approach to study the stimulated scattering of high-frequency electromagnetic waves by a low-frequency electrostatic perturbation that is either an upper- or lower-hybrid wave in a two-electron-temperature plasma. Considering the four-wave interaction between a strong high-frequency pump and the low-frequency electrostatic perturbation (LHW or UHW), we obtain the dispersion relation for the scattered wave, which is then solved to obtain an explicit expression for the growth rate of the coupled modes. For a typical Q-machine plasma, results show that in both cases the growth rate increases with noh/noc. This is in contrast with the results of Guha & Asthana (1989), who predicted that, for scattering by a UHW perturbation, the growth rate should decrease with increasing noh/noc.

Preferential acceleration of heavy ions from thermal velocities

1968 ◽  
Vol 46 (10) ◽  
pp. S638-S641 ◽  
Author(s):  
D. B. Melrose
Keyword(s):  
Frequency Spectrum ◽  
High Frequency ◽  
Heavy Ions ◽  
Crab Nebula ◽  
Low Frequency ◽  
High Frequency Waves ◽  
Hydromagnetic Waves ◽  
The Crab Nebula ◽  
Low Frequency Waves

The acceleration of ions from thermal velocities is analyzed to determine conditions under which heavy ions can be preferentially accelerated. Two accelerating mechanisms involving high-and low-frequency hydromagnetic waves respectively are considered. Preferential acceleration of heavy ions occurs for high-frequency waves if the frequency spectrum falls off faster than (frequency)−1. For the low-frequency waves heavy ions are less effectively accelerated than lighter ions. However, very heavy ions can be preferentially accelerated, the abundances of the very heavy ions being enhanced by a factor Ai over the thermal abundances. Acceleration of ions in the envelope of the Crab nebula is considered as an example.

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