51 research outputs found
Nonlinear Waves and Coherent Structures in Quasi-neutral Plasmas Excited by External Electromagnetic Radiation
Starting from the Vlasov-Maxwell equations describing the dynamics of various
species in a quasi-neutral plasma, an exact relativistic hydrodynamic closure
for a special type of water-bag distributions satisfying the Vlasov equation
has been derived. It has been shown that the set of equations for the
macroscopic hydrodynamic variables coupled to the wave equations for the
self-consistent electromagnetic field is fully equivalent to the Vlasov-Maxwell
system.
Based on the method of multiple scales, a system comprising a vector
nonlinear Schrodinger equation for the transverse envelopes of the
self-consistent plasma wakefield, coupled to a scalar nonlinear Schrodinger
equation for the electron current velocity envelope, has been derived.
Using the method of formal series of Dubois-Violette, a traveling wave
solution of the derived set of coupled nonlinear Schrodinger equations in the
case of circular wave polarization has been obtained. This solution is
represented as a ratio of two formal Volterra series. The terms of these series
can be calculated explicitly to every desired order.Comment: 10 pages, 3 figure
Formation of Patterns in Intense Hadron Beams. The Amplitude Equation Approach
We study the longitudinal motion of beam particles under the action of a
single resonator wave induced by the beam itself. Based on the method of
multiple scales we derive a system of coupled amplitude equations for the
slowly varying part of the longitudinal distribution function and for the
resonator wave envelope, corresponding to an arbitrary wave number. The
equation governing the slow evolution of the voltage envelope is show to be of
Ginzburg-Landau type.Comment: LaTeX, 12 page
Nonlinear Longitudinal Waves in High Energy Stored Beams
We solve the Vlasov equation for the longitudinal distribution function and
find stationary wave patterns when the distribution in the energy error is
Maxwellian. In the long wavelength limit a stability criterion for linear waves
has been obtained, and a Korteweg-de Vries-Burgers equation for the relevant
hydrodynamic quantities has been derived.Comment: LaTeX, 10 page
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