Complete separability of the Hamilton–Jacobi equation for the charged particle orbits in a Liénard–Wiechert field

2020 ◽  
Vol 61 (12) ◽  
pp. 122903
Author(s):  
Raymond G. McLenaghan ◽  
Giovanni Rastelli ◽  
Carlos Valero
Keyword(s):  
Charged Particle ◽  
Jacobi Equation ◽  
Particle Orbits ◽  
Charged Particle Orbits ◽  
Hamilton Jacobi Equation

5.—Adiabatic Motion in a Charged Particle Trap

1972 ◽  
Vol 70 ◽  
pp. 47-61 ◽  
Author(s):  
J. Byrne
Keyword(s):  
Charged Particle ◽  
Electromagnetic Fields ◽  
Jacobi Equation ◽  
Charged Particles ◽  
Adiabatic Invariants ◽  
Reflection Symmetry ◽  
Adiabatic Conditions ◽  
Adiabatic Motion ◽  
Particle Trap ◽  
Hamilton Jacobi Equation

SynopsisThe adiabatic invariants associated with the motion of charged particles, trapped in electromagnetic fields with rotational and reflection symmetry, have been studied using classical methods based on the Hamilton-Jacobi equation. It has been shown that results, valid for trapping in purely magnetic configurations, may be applied in the analysis of electromagnetic charged particle traps, provided that suitably modified expressions are used for the angular frequencies in the various dynamical modes. Attention is drawn to circumstances in which the adiabatic conditions may be violated because of cancellation of electric and magnetic terms in the equations.

scholarly journals Charged-particle orbits near a magnetic null point

2000 ◽  
Vol 64 (3) ◽  
pp. 255-262
Author(s):  
K. JAROENSUTASINEE ◽  
G. ROWLANDS
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Analytical Formula ◽  
Null Point ◽  
Zero Magnetic Field ◽  
Approximate Analytical Expression ◽  
Particle Orbits ◽  
Long Time ◽  
Charged Particle Orbits ◽  
Magnetic Null

An approximate analytical expression is obtained for the orbits of a charged particle moving in a cusp magnetic field. The particle orbits pass close to or through a region of zero magnetic field before being reflected in regions where the magnetic field is strong. Comparison with numerically evaluated orbits shows that the analytical formula is surprisingly good and captures all the main features of the particle motion. A map describing the long-time behaviour of such orbits is obtained.

The Hamilton-Jacobi Equation for a Charged Particle in a Combined Gravitational and Electromagnetic Field

1963 ◽  
Vol 6 (3) ◽  
pp. 351-358
Author(s):  
D. K. Sen
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Jacobi Equation ◽  
Jacobi Form ◽  
Equation Of Motion ◽  
Planetary Motion ◽  
Schwarzschild Metric ◽  
Special Case ◽  
Hamilton Jacobi Equation

The equation of motion of a charged particle in a combined gravitational and electromagnetic field is cast in the classical Hamilton-Jacobi form and then applied to the special case of a Schwarzschild metric, leading to the well established equation of planetary motion.

Simulation of Charged Particle Orbits in the Classroom

1971 ◽  
Vol 39 (7) ◽  
pp. 843-844
Author(s):  
G. J. Vanpraet ◽  
K. J. Van Camp
Keyword(s):  
Charged Particle ◽  
Particle Orbits ◽  
Charged Particle Orbits
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