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MODE COUPLING IN A BEAM PLASMA
Title
MODE COUPLING IN A BEAM PLASMA.
Creator
FREDERICK, LAWRENCE WILLIAM, Florida Atlantic University
Abstract/Description
The collective coordinate treatment of mode coupling in a beam plasma is investigated by computer simulation. Two methods are derived generalized and programmed. The programming is done for a two mode, one species, stationary plasma. The first method integrates the second order collective Lagrangian equations for the mode amplitudes. This method neglects the plasma temperature and coupling is not observed. The second method integrates the first order Hamiltonian equations for the mode...
Show moreThe collective coordinate treatment of mode coupling in a beam plasma is investigated by computer simulation. Two methods are derived generalized and programmed. The programming is done for a two mode, one species, stationary plasma. The first method integrates the second order collective Lagrangian equations for the mode amplitudes. This method neglects the plasma temperature and coupling is not observed. The second method integrates the first order Hamiltonian equations for the mode amplitudes and their canonical momentum. This takes account of the plasma temperature and coupling is observed. A perturbation theory approach is then suggested which would smooth out the detail of the mode interactions and shorten the calculation time.
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Date Issued
1972
PURL
http://purl.flvc.org/fcla/dt/13485
Subject Headings
Coupled mode theory
Format
Document (PDF)
MODE-MODE COUPLING IN AN ELECTRON BEAM PLASMA
Title
MODE-MODE COUPLING IN AN ELECTRON BEAM PLASMA.
Creator
ELKMAN, WILLIAM ROBERT., Florida Atlantic University
Abstract/Description
A coherent nonlinear wave-wave coupling effect which is consistent with a more complete description of damping effects of a plane wave disturbance of a finite plasma initially spatially uniform and Maxwellian in velocity space is considered. A smeared out ion background is assumed and the coupling between the ions and electrons is neglected. A self consistent field and collective coordinate approach is used to obtain a dispersion relation for mode coupling in a plasma. The equations for the...
Show moreA coherent nonlinear wave-wave coupling effect which is consistent with a more complete description of damping effects of a plane wave disturbance of a finite plasma initially spatially uniform and Maxwellian in velocity space is considered. A smeared out ion background is assumed and the coupling between the ions and electrons is neglected. A self consistent field and collective coordinate approach is used to obtain a dispersion relation for mode coupling in a plasma. The equations for the amplitudes and the frequencies are solved numerically both by direct time integration and by a perturbation method for two and three modes. The perturbation method solutions are obtained for the n mode equations. The perturbation equations for two modes are solved analytically. For the two mode case the resulting coupling shows that the energy oscillates between the modes and that the periodicity of the amplitudes and the frequencies is associated with the initial parameters. Energy feeding between the modes is also observed for three or more modes. However, phase mixing occurs for more than two modes.
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Date Issued
1973
PURL
http://purl.flvc.org/fcla/dt/13593
Subject Headings
Coupled mode theory, Electron beams
Format
Document (PDF)
MODE-MODE COUPLING OF PLASMA WAVES IN SYSTEMS WITH STRONG NON-LINEARITIES
Title
MODE-MODE COUPLING OF PLASMA WAVES IN SYSTEMS WITH STRONG NON-LINEARITIES.
Creator
LODDEN, JAMES ALAN, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
The coupled equations of motion describing electrostatic plasma oscillations are derived using a collective coordinate approach. The boundary between the physical and nonphysical regions of phase space is discussed. The two mode case is studied in detail for both small and large initial disturbances. For small initial disturbances the motion was found to be periodic. For large initial disturbances, non-periodic growing solutions were found that approached one of two asymptotic limits. For...
Show moreThe coupled equations of motion describing electrostatic plasma oscillations are derived using a collective coordinate approach. The boundary between the physical and nonphysical regions of phase space is discussed. The two mode case is studied in detail for both small and large initial disturbances. For small initial disturbances the motion was found to be periodic. For large initial disturbances, non-periodic growing solutions were found that approached one of two asymptotic limits. For these solutions, the variables became infinitely large in a finite time.
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Date Issued
1976
PURL
http://purl.flvc.org/fcla/dt/13828
Subject Headings
Coupled mode theory, Plasma waves
Format
Document (PDF)
The influence of connectivity on the global dynamics of nonlinear oscillator ensembles
Title
The influence of connectivity on the global dynamics of nonlinear oscillator ensembles.
Creator
Rogers, Jeffrey L., Florida Atlantic University, Wille, Luc T.
Abstract/Description
In this thesis we have studied the global dynamics which spontaneously emerge in ensembles of interacting disparate nonlinear oscillators. Collective phenomena exhibited in these systems include synchronization, quasiperiodicity, chaos, and death. Exact analytical solutions are presented for two and three coupled oscillators with phase and amplitude variations. A phenomenon analogous to a phase-transition is found as a function of interaction-range in a one-dimensional lattice: for coupling...
Show moreIn this thesis we have studied the global dynamics which spontaneously emerge in ensembles of interacting disparate nonlinear oscillators. Collective phenomena exhibited in these systems include synchronization, quasiperiodicity, chaos, and death. Exact analytical solutions are presented for two and three coupled oscillators with phase and amplitude variations. A phenomenon analogous to a phase-transition is found as a function of interaction-range in a one-dimensional lattice: for coupling exponents larger than some critical value, alpha c, synchronization is shown to be impossible. Massively parallel computer simulations in conjunction with finite-size scaling were used to extrapolate to the infinite-size limit.
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Date Issued
1994
PURL
http://purl.flvc.org/fcla/dt/15031
Subject Headings
Nonlinear oscillators, Coupled mode theory, Physics--Data processing, Parallel processing (Electronic computers)
Format
Document (PDF)