Nonlinear Theory of the Instability of a Modulated Electron Beam of Low Density in a Plasma. III. Derivation of Nonlinear Equations for the Time- and Space-Problems (Single Wave Model)

1983 ◽  
Vol 23 (4) ◽  
pp. 381-397 ◽  
Author(s):  
K. J. G. Kruscha ◽  
A. N. Kondratenko
Keyword(s):  
Electron Beam ◽  
Nonlinear Equations ◽  
Nonlinear Theory ◽  
Wave Model ◽  
Low Density ◽  
Time And Space ◽  
Single Wave

The onset of meandering in a barotropic jet

2001 ◽  
Vol 449 ◽  
pp. 85-114 ◽  
Author(s):  
N. J. BALMFORTH ◽  
C. PICCOLO
Keyword(s):  
Nonlinear Theory ◽  
Stability Boundary ◽  
Wave Model ◽  
Inviscid Limit ◽  
Reduced Model ◽  
Mean Flow ◽  
Single Wave ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
The Stability

This study explores the dynamics of an unstable jet of two-dimensional, incompressible fluid on the beta-plane. In the inviscid limit, standard weakly nonlinear theory fails to give a low-order description of this problem, partly because the simple shape of the unstable normal mode is insufficient to capture the structure of the forming pattern. That pattern takes the form of ‘cat's eyes’ in the vorticity distribution which develop inside the modal critical layers (slender regions to either side of the jet's axis surrounding the levels where the modal wave speed matches the mean flow). Asymptotic expansions furnish a reduced model which is a version of what is known as the single-wave model in plasma physics. The reduced model predicts that the amplitude of the unstable mode saturates at a relatively low level and is not steady. Rather, the amplitude evolves aperiodically about the saturation level, a result with implications for Lagrangian transport theories. The aperiodic amplitude ‘bounces’ are intimately connected with sporadic deformations of the vortices within the cat's eyes. The theory is compared with numerical simulations of the original governing equations. Slightly asymmetrical jets are also studied. In this case the neutral modes along the stability boundary become singular; an extension of the weakly nonlinear theory is presented for these modes.

Application of Improved Voltage Compensation in the SEM to Imaging of Organic Materials

1973 ◽  
Vol 31 ◽  
pp. 444-445
Author(s):  
P.J. Killingworth ◽  
M. Warren
Keyword(s):  
Electron Beam ◽  
Organic Materials ◽  
Operating Parameters ◽  
Low Density ◽  
Beam Diameter ◽  
Incident Electron Beam ◽  
Specimen Material ◽  
Voltage Compensation ◽  
Selection Of ◽  
Scanning Electron

Ultimate resolution in the scanning electron microscope is determined not only by the diameter of the incident electron beam, but by interaction of that beam with the specimen material. Generally, while minimum beam diameter diminishes with increasing voltage, due to the reduced effect of aberration component and magnetic interference, the excited volume within the sample increases with electron energy. Thus, for any given material and imaging signal, there is an optimum volt age to achieve best resolution.In the case of organic materials, which are in general of low density and electric ally non-conducting; and may in addition be susceptible to radiation and heat damage, the selection of correct operating parameters is extremely critical and is achiev ed by interative adjustment.

scholarly journals Low-dimensional chaos in the single wave model for self-consistent wave–particle Hamiltonian

2021 ◽  
Vol 31 (8) ◽  
pp. 083104
Author(s):  
J. V. Gomes ◽  
M. C. de Sousa ◽  
R. L. Viana ◽  
I. L. Caldas ◽  
Y. Elskens
Keyword(s):  
Wave Model ◽  
Single Wave ◽  
Self Consistent ◽  
Low Dimensional

Nonlinear theory of the orotron with inclined electron beam

2006 ◽  
Vol 13 (12) ◽  
pp. 123104 ◽  
Author(s):  
G. S. Nusinovich ◽  
O. V. Sinitsyn
Keyword(s):  
Electron Beam ◽  
Nonlinear Theory
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