One-dimensional ion-acoustic modes of bounded plasmas

1970 ◽  
Vol 4 (1) ◽  
pp. 195-203 ◽  
Author(s):  
Rui Rosa ◽  
J. E. Allen
Keyword(s):  
Spatial Structure ◽  
Normal Modes ◽  
Characteristic Frequencies ◽  
One Dimensional ◽  
Acoustic Modes ◽  
Ion Acoustic

One-dimensional ion-acoustic normal modes of bounded plasmas are theoretically investigated in plane, cylindrical and spherical geometries. The characteristic frequencies, damping constants and spatial structure of the oscillatory modes are obtained.

scholarly journals Теплопроводность цепочки ротаторов с двухбарьерным потенциалом взаимодействия

2021 ◽  
Vol 63 (7) ◽  
pp. 975
Author(s):  
А.П. Клинов ◽  
М.А. Мазо ◽  
В.В. Смирнов
Keyword(s):  
Thermal Conductivity ◽  
Heat Conductivity ◽  
Normal Modes ◽  
Double Barrier ◽  
One Dimensional ◽  
Internal Barrier ◽  
Local Fluctuations ◽  
Small Height ◽  
Coefficient Of Thermal Conductivity ◽  
Height Dependence

The thermal conductivity of a one-dimensional chain of rotators with a double-barrier interaction potential of nearest neighbors has been studied numerically. We show that the height of the "internal" barrier, which separates topologically nonequivalent degenerate states, significantly affects the temperature dependence of the heat conductivity of the system. The small height of this barrier leads to the dominant contribution of the non-linear normal modes at low temperatures. In such a case the coefficient of thermal conductivity turns out to be the risen function of the temperature. The growth of the coefficient is limited by local fluctuations corresponding to jumps over the barriers. At higher values of the internal barrier height, dependence of the heat conductivity on temperature is similar to that of classical rotators.

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

2019 ◽  
Vol 878 ◽  
pp. 190-220 ◽  
Author(s):  
Francesca M. Sogaro ◽  
Peter J. Schmid ◽  
Aimee S. Morgans
Keyword(s):  
Time Domain ◽  
Time Scale ◽  
Initial Conditions ◽  
Normal Modes ◽  
Time Domain Analysis ◽  
Normal Behaviour ◽  
Optimal Perturbation ◽  
Acoustic Modes ◽  
Energy Growth ◽  
The Time Domain

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.

Vibration of an elastic strip with varying curvature

1992 ◽  
Vol 339 (1655) ◽  
pp. 587-625 ◽  
Keyword(s):  
Total Internal Reflection ◽  
Normal Modes ◽  
Mode Shapes ◽  
Elastic Strip ◽  
Interesting Phenomenon ◽  
One Dimensional ◽  
End Conditions ◽  
The One ◽  
Fixed End ◽  
Good Agreement

The vibrational behaviour of an elastic strip with varying curvature is investigated. The case of vibration which is predominantly transverse is considered, and it is shown that when the strip is S-shaped, certain of the normal modes may be confined to the vicinity of the inflection point of the S by a process of total internal reflection from points where the curvature reaches critical values. This confinement can produce modes with extraordinarily low damping factors. Asymptotic analysis is compared with experimental measurements on a strip in several S-shaped configurations, and very good agreement is demonstrated for modal frequencies and shapes. Mathematically, the lower modes turn out to be analogous to those of the one-dimensional harmonic oscillator in quantum mechanics. This mode confinement behaviour occurs for all waveguide branches except the lowest, ‘bending beam ’, branch. In this particular case, wave propagation is insensitive to curvature. However, an interesting phenomenon associated with curvature is found : the successive mode shapes do not display the normal alternation of symmetry and antisymmetry with respect to the centre of the strip. The effect is shown to result from the constraint on axial movement produced by fixed end conditions. For the geometry of the experiments, this constraint raises the frequencies of antisymmetric modes in a characteristic way while leaving the symmetric modes unaltered, thus changing the mode sequence. Theory is developed which gives reasonable quantitive agreement with the observations.

Multi-field characteristics and eigenmode spatial structure of geodesic acoustic modes in DIII-D L-mode plasmas

2013 ◽  
Vol 20 (9) ◽  
pp. 092501 ◽  
Author(s):  
G. Wang ◽  
W. A. Peebles ◽  
T. L. Rhodes ◽  
M. E. Austin ◽  
Z. Yan ◽  
...  
Keyword(s):  
Spatial Structure ◽  
Acoustic Modes

The Cauchy problem for the system of Zakharov equations arising from ion-acoustic modes

1996 ◽  
Vol 126 (4) ◽  
pp. 811-820 ◽  
Author(s):  
Guo Boling ◽  
Yuan Guangwei
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Cauchy Data ◽  
Continuous Method ◽  
Initial Value ◽  
Acoustic Modes ◽  
Ion Acoustic ◽  
The Cauchy Problem

In this paper the initial value problem for a class of Zakharov equations arising from ion-acoustic modes is discussed. Without assuming the Cauchy data are small, we prove the existence and uniqueness of the global smooth solution for the problem via the so-called continuous method and delicate a priori estimates.

scholarly journals Coherent Mechanisms of Pulsar Radio Emission

2000 ◽  
Vol 177 ◽  
pp. 389-392
Author(s):  
Maxim Lyutikov ◽  
Roger Blandford ◽  
George Machabeli
Keyword(s):  
Radio Emission ◽  
Normal Modes ◽  
Relativistic Plasma ◽  
Primary Beam ◽  
Dimensional Electron ◽  
Pulsar Radio ◽  
One Dimensional ◽  
Electron Positron ◽  
Pulsar Radio Emission

AbstractRelativistic plasma masers operating on the anomalous cyclotron-Cherenkov resonanceω−k||υ||+ωB/ϒres= 0 and the Cherenkov-drift resonanceω−k||υ||−kx/ud= 0, are capable of explaining the main observational characteristics of pulsar radio emission. Both electromagnetic instabilities are due to the interaction of the fast particles from the primary beam and from the tail of the secondary pairs distribution with the normal modes of a strongly magnetized one-dimensional electron-positron plasma. In a typical pulsar both resonances occur in the outer parts of magnetosphere atrres≈ 109cm.

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