Drift Velocity of a Charged Particle in an Inhomogeneous Magnetic Field

1961 ◽  
Vol 32 (11) ◽  
pp. 2368-2369 ◽  
Author(s):  
James Hurley
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Drift Velocity ◽  
Inhomogeneous Magnetic Field

Non-linear oscillations

2020 ◽  
pp. 45-47
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Simple Model ◽  
Mechanical Model ◽  
Inhomogeneous Magnetic Field ◽  
Fermi Resonance ◽  
Forced Oscillations ◽  
Linear Coupling ◽  
Parametric Resonances ◽  
Non Linear

This chapter addresses the distortion in the free and forced oscillations of a harmonic oscillator caused by the presence of the anharmonic terms in the potential energy, a simple model related to the coupling of the longitudinal and flexural oscillations inmolecules, and two oscillators with a weak non-linear coupling (the so-called Fermi resonance). The chapter also examines non-linear resonances, the parametric resonances, drift of the orbit centre for a charged particle in the weakly inhomogeneous magnetic field, and a mechanical model of phase transitions of the second kind.

scholarly journals Drift of a Charged Particle in a Static Magnetic Field Having a Power Law Dependence

1975 ◽  
Vol 28 (3) ◽  
pp. 289 ◽  
Author(s):  
M Headland ◽  
PW Seymour
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Exact Solutions ◽  
Drift Velocity ◽  
Static Magnetic Field ◽  
Special Solutions ◽  
Complete Elliptic Integrals ◽  
Bound Orbits ◽  
Constant Gradient ◽  
Velocity Region

As a generalization of Seymour's (1959) exact solution for the drift velocity of a charged particle in a static magnetic field of constant gradient, exact solutions are obtained for charged particle drift in a static magnetic field represented by B. = AX', where A and IX are constants. Four cases of bound orbits are analysed. Exact solutions in terms of hypergeometric, confluent hypergeometric and gamma functions are obtained for the displacement Ay per cycle, the periodic time T and the drift velocity Vd. The special solutions in terms of complete elliptic integrals obtained by Seymour (1959) are also recovered. Calculated exact drift velocity characteristics for representative conditions are presented, and the manner in which the exact curves merge into the Alfven approximate drift velocity region is indicated.

Drift of a Charged Particle in a Magnetic Field of Constant Gradient

1959 ◽  
Vol 12 (4) ◽  
pp. 309 ◽  
Author(s):  
PW Seymour
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Small Perturbation ◽  
Drift Velocity ◽  
Order Theory ◽  
Simple Expression ◽  
Uniform Field ◽  
First Order ◽  
First Order Theory ◽  
Constant Gradient

A simple expression for the drift velocity of a charged particle moving in an inhomo, geneous magnetic field has been obtained by Alfven, who, in his first-order theory, considered the inhomogeneity as a small perturbation of a uniform field,

Non-linear oscillations

2020 ◽  
pp. 265-278
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Simple Model ◽  
Mechanical Model ◽  
Inhomogeneous Magnetic Field ◽  
Fermi Resonance ◽  
Forced Oscillations ◽  
Linear Coupling ◽  
Parametric Resonances ◽  
Non Linear

This chapter addresses the distortion in the free and forced oscillations of a harmonic oscillator caused by the presence of the anharmonic terms in the potential energy, a simple model related to the coupling of the longitudinal and flexural oscillations inmolecules, and two oscillators with a weak non-linear coupling (the so-called Fermi resonance). The chapter also examines non-linear resonances, the parametric resonances, drift of the orbit centre for a charged particle in the weakly inhomogeneous magnetic field, and a mechanical model of phase transitions of the second kind.

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