Further analysis of nonlinear, periodic, highly superluminous waves in a magnetized plasma

1982 ◽  
Vol 27 (1) ◽  
pp. 177-187 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Magnetic Field ◽  
Power Series ◽  
Periodic Solutions ◽  
Wave Speed ◽  
Nonlinear Differential Equations ◽  
Plane Waves ◽  
Electron Plasma ◽  
Finite Amplitude ◽  
Magnetized Plasma ◽  
Cold Electron

A perturbation method is applied to the pair of second-order, coupled, nonlinear differential equations that describe the propagation, through a cold electron plasma, of plane waves of fixed profile, with direction of propagation and electric vector perpendicular to the ambient magnetic field. The equations are expressed in terms of polar variables π, φ, and solutions are sought as power series in the small parameter n, where c/n is the wave speed. When n = 0 periodic solutions are represented in the (π,φ) plane by circles π = constant, and when n is small it is found that there are corresponding periodic solutions represented to order n2 by ellipses. It is noted that further investigation is required to relate these finite-amplitude solutions to the conventional solutions of linear theory, and to determine their behaviour in the vicinity of certain resonances that arise in the perturbation treatment.

On nonlinear circularly polarized Alfvén waves

1988 ◽  
Vol 40 (2) ◽  
pp. 281-287 ◽  
Author(s):  
G. Mann
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Periodic Solutions ◽  
Type Equation ◽  
Finite Amplitude ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Circularly Polarized ◽  
Ambient Magnetic Field ◽  
Nonlinear Schrödinger

Finite-amplitude circularly polarized Alfvén waves propagating along the ambient magnetic field are described by a derivative nonlinear Schrödinger-type equation. It leads to stationary, solitary and periodic solutions with phase modulations. The amplitude–width relation for these solitons is shown to be an inequality. The relevance of the results is briefly discussed for particular phenomena in the solar wind.

Nonlinear behaviour of a finite amplitude electron plasma wave - IV. Decay to ion cyclotron waves

1978 ◽  
Vol 363 (1715) ◽  
pp. 547-557
Keyword(s):  
Magnetic Field ◽  
Low Frequency ◽  
Electron Plasma ◽  
Finite Amplitude ◽  
Nonlinear Behaviour ◽  
Electron Plasma Wave ◽  
Ion Cyclotron Waves ◽  
Ion Cyclotron ◽  
Low Frequency Mode ◽  
The Magnetic Field

Plasma in a magnetic field displays low frequency modes near the ion cyclotron frequency for waves propagating at an angle to the magnetic field. These modes are only slightly modified in a bounded plasma, and therefore can be excited by nonlinear decay of electron plasma waves which also propagate at an angle to the magnetic field. The nonlinearly generated low frequency mode has been identified experimentally as an ion cyclotron wave by stimulating the decay. The resonant matching conditions have also been demonstrated.

scholarly journals Relativistic longitudinal self-compression of ultra-intense Gaussian laser pulses in magnetized plasma

2020 ◽  
Vol 38 (3) ◽  
pp. 188-196
Author(s):  
Gunjan Purohit ◽  
Priyanka Rawat ◽  
Pradeep Kothiyal ◽  
Ramesh Kumar Sharma
Keyword(s):  
Magnetic Field ◽  
Laser Pulse ◽  
Nonlinear Differential Equations ◽  
Radial Distance ◽  
Laser Pulses ◽  
Magnetized Plasma ◽  
Fourth Power ◽  
Initial Pulse ◽  
Incident Laser Intensity ◽  
Paraxial Ray

AbstractThis article presents a preliminary study of the longitudinal self-compression of ultra-intense Gaussian laser pulse in a magnetized plasma, when relativistic nonlinearity is active. This study has been carried out in 1D geometry under a nonlinear Schrodinger equation and higher-order paraxial (nonparaxial) approximation. The nonlinear differential equations for self-compression and self-focusing have been derived and solved by the analytical and numerical methods. The dielectric function and the eikonal have been expanded up to the fourth power of r (radial distance). The effect of initial parameters, namely incident laser intensity, magnetic field, and initial pulse duration on the compression of a relativistic Gaussian laser pulse have been explored. The results are compared with paraxial-ray approximation. It is found that the compression of pulse and pulse intensity of the compressed pulse is significantly enhanced in the nonparaxial region. It is observed that the compression of the high-intensity laser pulse depends on the intensity of laser beam (a0), magnetic field (ωc), and initial pulse width (τ0). The preliminary results show that the pulse is more compressed by increasing the values of a0, ωc, and τ0.

Padé approximants and nonlinear waves

1979 ◽  
Vol 21 (3) ◽  
pp. 549-571 ◽  
Author(s):  
F. J. Romerias ◽  
J. P. Dougherty
Keyword(s):  
Differential Equations ◽  
Asymptotic Expansions ◽  
Nonlinear Waves ◽  
Wave Amplitude ◽  
Plane Waves ◽  
Electron Plasma ◽  
Cold Electron ◽  
Small Wave ◽  
The Waves ◽  
Approximant Method

The perturbation solution of the ordinary differential equations that describe exact nonlinear travelling plane waves leads to asymptotic expansions in powers of the (small) wave amplitude for both the proffle and the frequency of the waves. This paper shows how the Padé approximant method can be used to extend the validity of those expansions to larger amplitudes. The method is applied to the Duffing equation and to two types of nonlinear waves in a cold electron plasma: longitudinal oscillations and coupled transverse–longitudinal relativistic waves.

Nonlinear, superluminous, periodic waves in a plasma with magnetic field

1977 ◽  
Vol 17 (2) ◽  
pp. 301-316 ◽  
Author(s):  
P. C. Clemmow
Keyword(s):  
Magnetic Field ◽  
Periodic Solutions ◽  
Average Rate ◽  
Plane Waves ◽  
First Integral ◽  
Laboratory Frame ◽  
Static Field ◽  
Particle Velocities ◽  
Space Dependence ◽  
The Magnetic Field

The exact theory of plane waves of fixed profile travelling with constant velocity cZ/n (0 ≤ n ≤ 1) through a uniform, cold, electron-ion plasma in a magneto-static field is examined in terms of the governing equations referred to the frame of reference in which there is no space dependence. Canonical periodic solutions are defined as those with zero average rate of flow of electrons (and a fortiori of ions) in the laboratory frame. It is shown that the equations lead to a second- order, nonlinear, ordinary vector differential equation for the reduced velocity u of the electrons. A scalar first integral is obtained, from which it is deduced that the path in u-space of any solution lies within a bounded domain. It is shown that, for propagation across the magnetic field, a polarization is possible in which the particle velocities and the electric field are orthogonal to the magnetic field. The simpler model of an electron Plasma is considered. Explicit canonical periodic solutions, with the stated polarization, are obtained for propagation across the magnetic field in the case n = 0 and the case n ≃ 1. These support the conjecture that, for any fixed value of n in [0, 1], there are two ‘modes’ of arbitrary amplitude which reduce to the familiar monochromatic waves of linear magneto-ionic theory in the small amplitude limit.

Effects of a Vertical Magnetic Field on Particle Confinement in a Magnetized Plasma Torus

2004 ◽  
Vol 93 (16) ◽  
Author(s):  
S. H. Müller ◽  
A. Fasoli ◽  
B. Labit ◽  
M. McGrath ◽  
M. Podestà ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetized Plasma ◽  
Vertical Magnetic Field ◽  
Plasma Torus ◽  
Particle Confinement

Effects of repeated interactions and correlational disintegration on kinetic and transport properties of a non-neutral plasma in strong fields

1990 ◽  
Vol 44 (1) ◽  
pp. 167-190 ◽  
Author(s):  
Alf H. Øien
Keyword(s):  
Magnetic Field ◽  
Particle Transport ◽  
Axial Magnetic Field ◽  
Debye Length ◽  
Electron Plasma ◽  
Larmor Radius ◽  
Equilibration Time ◽  
Cylindrically Symmetric ◽  
Electric Potentials ◽  
Good Agreement

Collisions in a cylindrically symmetric non-neutral (electron) plasma, where the Larmor radius is much smaller than the Debye length, and the consequent particle transport, are studied. The plasma is confined radially by a strong axial magnetic field and axially by electric potentials. Hence two particles may interact repeatedly. Eventually they drift too far away from each other poloidally to interact any more, owing to shear in the E × B drift. The consequent build-up of correlation is limited by correlational disintegration due to collisions with ‘third particles’ between the repeated interactions. A kinetic equation including these effects is derived, and the cross-field particle transport along the density gradient is found. An associated equilibration time is shown to scale as B and to be in good agreement with the experimentally obtained values of Briscoli, Malmberg and Fine.

Gas-ionizing shocks in a magnetic field

1967 ◽  
Vol 1 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. D. Cowley
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Wave Speed ◽  
Normal Velocity ◽  
Electrically Conducting ◽  
Shock Stability ◽  
The Face ◽  
Arbitrary Velocity ◽  
Flow Plane ◽  
The Magnetic Field

Ionizing shocks for plane flows with the magnetic field lying in the flow plane are considered. The gas is assumed to be electrically conducting downstream, but non-conducting upstream. Shocks whose downstream state has a normal velocity component less than the slow magneto-acoustic-wave speed and whose upstream state is supersonic are found to be non-evolutionary in the face of plane magneto-acoustic disturbances, unless the upstream electric field in a frame of reference where the gas is at rest is arbitrary. Velocity conditions are also determined for shock stability with the electric field not arbitrary.Shock structures are found for the case of large ohmic diffusion, the initial temperature rise and ionization of the gas being caused by a thin transition having the properties of an ordinary gasdynamic shock. For the case where shocks are evolutionary when the upstream electric field is arbitrary, the shock structure requirements only restrict the electric field by limiting the range of possible values. When shocks are evolutionary with the electric field not arbitrary, they can only have a structure for a particular value of the electric field. Limits to the current carried by ionizing shocks and the effects of precursor ionization are discussed qualitatively.

scholarly journals Compton and Raman free electron laser stability properties for a cold electron beam propagating through a helical magnetic wiggler

1985 ◽  
Vol 33 (3) ◽  
pp. 387-423 ◽  
Author(s):  
John A. Davies ◽  
Ronald C. Davidson ◽  
George L. Johnston
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Dispersion Relation ◽  
Free Electron ◽  
Free Electron Laser ◽  
Relativistic Electron Beam ◽  
Cold Electron ◽  
Wiggler Magnetic Field ◽  
Laser Stability

This paper gives an extensive characterization of the range of validity of the Compton and Raman approximations to the exact free electron laser dispersion relation for a cold, relativistic electron beam propagating through a constantamplitude helical wiggler magnetic field. The electron beam is treated as infinite in transverse extent. Specific properties of the exact and approximate dispersion relations are investigated analytically and numerically. In particular, a detailed numerical analysis is carried out to determine the range of validity of the Compton approximation.

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