Cyclotron resonance in an inhomogeneous plasma

1972 ◽  
Vol 8 (2) ◽  
pp. 255-260 ◽  
Author(s):  
M. J. Laird
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Cyclotron Resonance ◽  
Uniform Magnetic Field ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Inhomogeneous Plasma ◽  
Phase Speed ◽  
Hamiltonian Form ◽  
Energy And Momentum

The motion of a charged particle in a transverse wave of varying amplitude, wavelength and phase speed βp, propagating along a uniform magnetic field, together with a longitudinal electric field, is investigated. The equations of motion, in Hamiltonian form, are reduced to a system with two degrees of freedom in which integrable cases appear naturally. It is shown that particles may be locked in resonance with the wave, and expressions are found for the energy and momentum of such particles in terms of βp.

On gyroresonance

1968 ◽  
Vol 2 (1) ◽  
pp. 59-64 ◽  
Author(s):  
M. J. Laird
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Pitch Angle ◽  
Uniform Magnetic Field ◽  
Equations Of Motion ◽  
Circularly Polarized ◽  
Simple Picture

The motion of a charged particle in the field of a plane circularly polarized wave propagating along a uniform magnetic field B0 is investigated. For the wave magnetic field small compared with B0, the equations of motion simplify to those of the pendulum, and a simple picture of what happens for particles near gyro- resonance results. Expressions are found for the amplitude and period of the pitch angle oscillations. Departures from uniformity and possible applications to the magnetosphere are briefly discussed.

Ion Acceleration by Ion-Cyclotron Resonance in Non-Uniform Magnetic Field Using the TPD-Sheet IV Linear Divertor Simulator

2013 ◽  
Vol 63 (1T) ◽  
pp. 417-419 ◽  
Author(s):  
T. Iijima ◽  
S. Hagiwara ◽  
S. Tanaka ◽  
A. Tonegawa ◽  
Kazutaka Kawamura ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Cyclotron Resonance ◽  
Uniform Magnetic Field ◽  
Ion Acceleration ◽  
Ion Cyclotron Resonance ◽  
Ion Cyclotron

Two-dimensional motion of a parabolically confined charged particle in a perpendicular magnetic field

Open Physics ◽  
2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Orion Ciftja
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Equations Of Motion ◽  
Complex Variables ◽  
Perpendicular Magnetic Field ◽  
Two Dimensional ◽  
Cyclotron Motion ◽  
Lissajous Figures ◽  
Long Time ◽  
Concentric Circles

AbstractThe classical two-dimensional motion of a parabolically confined charged particle in presence of a perpendicular magnetic is studied. The resulting equations of motion are solved exactly by using a mathematical method which is based on the introduction of complex variables. The two-dimensional motion of a parabolically charged particle in a perpendicular magnetic field is strikingly different from either the two-dimensional cyclotron motion, or the oscillator motion. It is found that the trajectory of a parabolically confined charged particle in a perpendicular magnetic field is closed only for particular values of cyclotron and parabolic confining frequencies that satisfy a given commensurability condition. In these cases, the closed paths of the particle resemble Lissajous figures, though significant differences with them do exist. When such commensurability condition is not satisfied, path of particle is open and motion is no longer periodic. In this case, after a sufficiently long time has elapsed, the open paths of the particle fill a whole annulus, a region lying between two concentric circles of different radii.

Electron whistler mode instability in an inhomogeneous thermal plasma in the presence of an inhomogeneous beam of suprathermal electrons

1983 ◽  
Vol 29 (3) ◽  
pp. 439-448 ◽  
Author(s):  
H.A. Shah ◽  
V.K. Jain
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Thermal Plasma ◽  
Uniform Magnetic Field ◽  
Inhomogeneous Plasma ◽  
Mode Instability ◽  
Whistler Mode ◽  
Suprathermal Electrons ◽  
Whistler Mode Waves

The excitation of the whistler mode waves propagating obliquely to the constant and uniform magnetic field in a warm and inhomogeneous plasma in the presence of an inhomogeneous beam of suprathermal electrons is studied. The full dispersion relation including electromagnetic effects is derived. In the electrostatic limit the expression for the growth rate is given. It is found that the inhomogeneities in both beam and plasma number densities affect the growth rates of the instabilities.

scholarly journals DOUBLE WAVE DESCRIPTION OF THE MOTION OF A CHARGED PARTICLE IN A UNIFORM MAGNETIC FIELD

1993 ◽  
Vol 42 (2) ◽  
pp. 180
Author(s):  
HUANG XIANG-YOU ◽  
LIU QUAN-HUI ◽  
TIAN XU ◽  
QIU ZHONG-PING
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Uniform Magnetic Field

The Hamiltonian equations of motion. Poisson brackets

2020 ◽  
pp. 305-316
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Hydrogen Atom ◽  
Particle Velocity ◽  
Conservation Law ◽  
Equations Of Motion ◽  
Hamiltonian Function ◽  
Poisson Brackets ◽  
Hamiltonian Equations ◽  
Hidden Symmetry

This chapter addresses invariance of the Hamiltonian function under a given transformation and the conservation law, the Hamiltonian function for the beam of light, the motion of a charged particle in a nonuniform magnetic field, and the motion of electrons in a metal or semiconductor. The chapter also discusses the Poisson brackets and the model of the electron and nuclear paramagnetic resonances, the Poisson brackets for the components of the particle velocity, and the “hidden symmetry” of the hydrogen atom.

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