Poloidal eigenmode of the geodesic acoustic mode in the limit of high safety factor

2009 ◽  
Vol 75 (6) ◽  
pp. 721-729 ◽  
Author(s):  
M. SASAKI ◽  
K. ITOH ◽  
A. EJIRI ◽  
Y. TAKASE
Keyword(s):  
Spatial Structure ◽  
Phase Velocity ◽  
Group Velocity ◽  
Safety Factor ◽  
Acoustic Mode ◽  
Higher Order ◽  
Expansion Parameter ◽  
Geodesic Acoustic Mode ◽  
Analytical Expressions

AbstractThe poloidal eigenmode of the geodesic acoustic mode (GAM) is studied in the limit of high safety factor. In this limit, the poloidal gyroradius cannot be treated as a perturbation or as an expansion parameter. Analytical expressions for the poloidal structure of the GAM potential, the radial wavenumber dependence of the frequency, the phase velocity, and the group velocity are obtained. The spatial structure of the poloidal eigenmode including the higher-order gyroradius effect is revealed theoretically.

Observation of geodesic acoustic mode in SINP-tokamak and its behaviour with varying edge safety factor

2017 ◽  
Vol 24 (11) ◽  
pp. 112501 ◽  
Author(s):  
Lavkesh Lachhvani ◽  
Joydeep Ghosh ◽  
P. K. Chattopadhyay ◽  
N. Chakrabarti ◽  
R. Pal
Keyword(s):  
Safety Factor ◽  
Acoustic Mode ◽  
Geodesic Acoustic Mode

scholarly journals Spatial structure of the geodesic acoustic mode in the FT-2 tokamak by upper hybrid resonance Doppler backscattering

2013 ◽  
Vol 55 (8) ◽  
pp. 085017 ◽  
Author(s):  
A D Gurchenko ◽  
E Z Gusakov ◽  
A B Altukhov ◽  
E P Selyunin ◽  
L A Esipov ◽  
...  
Keyword(s):  
Spatial Structure ◽  
Acoustic Mode ◽  
Hybrid Resonance ◽  
Geodesic Acoustic Mode

The intermittent excitation of geodesic acoustic mode by resonant Instanton of electron drift wave envelope in L-mode discharge near tokamak edge

2021 ◽  
Author(s):  
Liu Zhao-Yang ◽  
Zhang Yang-Zhong ◽  
Swadesh Mitter Mahajan ◽  
Liu A-Di ◽  
Zhou Chu ◽  
...  
Keyword(s):  
Group Velocity ◽  
Reynolds Stress ◽  
Traveling Wave ◽  
Zonal Flow ◽  
Acoustic Mode ◽  
Flow Equation ◽  
Electron Drift ◽  
Drift Wave ◽  
Wave Phase ◽  
Geodesic Acoustic Mode

Abstract There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow. A long-lived standing wave phase, which we call the Caviton, and a short-lived traveling wave phase (in radial direction) we call the Instanton. Several abrupt phenomena observed in tokamaks, such as intermittent excitation of geodesic acoustic mode (GAM) shown in this paper, could be attributed to the sudden and fast radial motion of Instanton. The composite drift wave – zonal flow system evolves at the two well-separate scales: the micro and the meso-scale. The eigenmode equation of the model defines the zero order (micro-scale) variation; it is solved by making use of the two dimensional (2D) weakly asymmetric ballooning theory (WABT), a theory suitable for modes localized to rational surface like drift waves, and then refined by shifted inverse power method, an iterative finite difference method. The next order is the equation of electron drift wave (EDW) envelope (containing group velocity of EDW) which is modulated by the zonal flow generated by Reynolds stress of EDW. This equation is coupled to the zonal flow equation, and numerically solved in spatiotemporal representation; the results are displayed in self-explanatory graphs. One observes a strong correlation between the Caviton-Instanton transition and the zero-crossing of radial group velocity of EDW. The calculation brings out the defining characteristics of the Instanton: it begins as a linear traveling wave right after the transition. Then, it evolves to a nonlinear stage with increasing frequency all the way to 20 kHz. The modulation to Reynolds stress in zonal flow equation brought in by the nonlinear Instanton will cause resonant excitation to GAM. The intermittency is shown due to the random phase mixing between multiple central rational surfaces in the reaction region.

Experimental investigation of geodesic acoustic mode spatial structure, intermittency, and interaction with turbulence in the DIII-D tokamak

2012 ◽  
Vol 19 (2) ◽  
pp. 022301 ◽  
Author(s):  
J. C. Hillesheim ◽  
W. A. Peebles ◽  
T. A. Carter ◽  
L. Schmitz ◽  
T. L. Rhodes
Keyword(s):  
Experimental Investigation ◽  
Spatial Structure ◽  
Acoustic Mode ◽  
Geodesic Acoustic Mode

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

Effects of passing energetic particles on geodesic acoustic mode

2014 ◽  
Vol 21 (10) ◽  
pp. 102506 ◽  
Author(s):  
Haijun Ren ◽  
Chao Dong
Keyword(s):  
Energetic Particles ◽  
Acoustic Mode ◽  
Geodesic Acoustic Mode

Geodesic Acoustic Mode in Toroidal Plasma

2010 ◽  
Author(s):  
N. Chakrabarti ◽  
P. N. Guzdar ◽  
R. G. Kleva ◽  
R. Singh ◽  
P. K. Kaw ◽  
...  
Keyword(s):  
Acoustic Mode ◽  
Toroidal Plasma ◽  
Geodesic Acoustic Mode

The relationship between group velocity and phase velocity for finite, discrete observations

1977 ◽  
Vol 67 (5) ◽  
pp. 1249-1258
Author(s):  
Douglas C. Nyman ◽  
Harsh K. Gupta ◽  
Mark Landisman
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
The Other ◽  
Frequency Range ◽  
Finite Frequency ◽  
Discrete Observations ◽  
Practical Situation ◽  
Order Polynomial ◽  
Observational Errors ◽  
The Relationship

abstract The well-known relationship between group velocity and phase velocity, 1/u = d/dω (ω/c), is adapted to the practical situation of discrete observations over a finite frequency range. The transformation of one quantity into the other is achieved in two steps: a low-order polynomial accounts for the dominant trends; the derivative/integral of the residual is evaluated by Fourier analysis. For observations of both group velocity and phase velocity, the requirement that they be mutually consistent can reduce observational errors. The method is also applicable to observations of eigenfrequency and group velocity as functions of normal-mode angular order.

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

2021 ◽  
Author(s):  
Yahui Wang ◽  
Tao Wang ◽  
Shizhao Wei ◽  
Zhiyong Qiu
Keyword(s):  
Steady State ◽  
Plasma Heating ◽  
Acoustic Mode ◽  
Decay Process ◽  
Nonlinear Excitation ◽  
Parametric Decay ◽  
Geodesic Acoustic Mode ◽  
Burning Plasmas ◽  
Reversed Shear ◽  
Excitation Conditions

Abstract The parametric decay process of a reversed shear Alfv\'{e}n eigenmeode (RSAE) into a geodesic acoustic mode (GAM) and a kinetic reversed shear Alfv\'{e}n eigenmode (KRSAE) is investigated using nonlinear gyrokinetic theory. The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold, which could be readily satisfied in burning plasmas operated in steady-state advanced scenario. This decay process can contribute to thermal plasma heating and confinement improvement.

Attenuation of dispersed wave trains

1962 ◽  
Vol 52 (1) ◽  
pp. 109-112
Author(s):  
James N. Brune
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Seismic Waves ◽  
Free Oscillations ◽  
Wave Trains

Abstract It is shown that groups of seismic waves are attenuated by the factor exp −exp⁡−πXQUT where X is the distance, U the group velocity, T the period and Q−1 is a measure of the damping of free oscillations. Accordingly, observations of Q given by Ewing and Press (1954 a, b) and Sato (1958) are revised by the ratio of the phase velocity to the group velocity.

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