Hamiltonian theory of adiabatic motion of relativistic charged particles

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.

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E×B guiding-centre motion in three electrostatic waves: statistics of separatrix crossings

Journal of Plasma Physics ◽

10.1017/s0022377898006679 ◽

1998 ◽

Vol 59 (4) ◽

pp. 761-772

Author(s):

B. WEYSSOW

Keyword(s):

Phase Space ◽

Low Frequency ◽

Integration Scheme ◽

Symplectic Integrator ◽

Third Order ◽

Special Configuration ◽

Electrostatic Waves ◽

Hamiltonian Theory ◽

Numerical Integration Methods ◽

Adiabatic Motion

E×B guiding-centre (GC) motion in a special configuration of three low-frequency electrostatic waves can be considered as a paradigmatic Hamiltonian system for studying adiabatic motion and separatrix crossings. A peculiarity of this system is that a single initial condition gives rise to two stroboscopic phase-space trajectories. According to the classical Hamiltonian theory, the proportion of points on the stroboscopic trajectories is a function of the time evolution of the surfaces enclosed by the separatrices in the phase space. This behaviour is qualitatively observed in test-particle numerical experiments. The ability of numerical integration methods like the ‘classical’ fourth-order Runge–Kutta integration scheme or a third-order symplectic integrator to reproduce the statistics is analysed.

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The Adiabatic Motion of Charged Particles

American Journal of Physics ◽

10.1119/1.1969867 ◽

1964 ◽

Vol 32 (10) ◽

pp. 807-807 ◽

Cited By ~ 32

Author(s):

Theodore G. Northrop ◽

F. R. Scott

Keyword(s):

Charged Particles ◽

Adiabatic Motion

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The adiabatic motion of charged particles

Journal of the Franklin Institute ◽

10.1016/0016-0032(64)90357-6 ◽

1964 ◽

Vol 278 (1) ◽

pp. 61

Author(s):

Ernest C. Ray

Keyword(s):

Charged Particles ◽

Adiabatic Motion

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EVIDENCE FOR QUASI-ADIABATIC MOTION OF CHARGED PARTICLES IN STRONG CURRENT SHEETS IN THE SOLAR WIND

The Astrophysical Journal ◽

10.3847/1538-4357/834/1/34 ◽

2016 ◽

Vol 834 (1) ◽

pp. 34 ◽

Cited By ~ 11

Author(s):

H. V. Malova ◽

V. Yu. Popov ◽

E. E. Grigorenko ◽

A. A. Petrukovich ◽

D. Delcourt ◽

...

Keyword(s):

Solar Wind ◽

Charged Particles ◽

Current Sheets ◽

Strong Current ◽

Adiabatic Motion

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Molecular quantum electrodynamics

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1971.0049 ◽

1971 ◽

Vol 321 (1547) ◽

pp. 557-572 ◽

Cited By ~ 138

Keyword(s):

Electromagnetic Field ◽

Quantum Electrodynamics ◽

Unitary Transformation ◽

Charged Particles ◽

Gauge Condition ◽

Binding Energies ◽

Quantum Mechanical ◽

Supplementary Condition ◽

Molecular Systems ◽

Hamiltonian Theory

A comparison is made of the conventional quantum mechanical hamiltonian for the interaction of molecular systems with the electromagnetic field and the alternative multipole formulation given recently (Atkins & Woolley 1970). The conventional hamiltonian is first derived by using Dirac’s generalized hamiltonian theory in which the Coulomb gauge condition is introduced as a supplementary condition. We analyse further the interpretation of the unitary transformation that connects the two hamiltonians in terms of the arbitrariness of the phase of the wavefunctions of charged particles in the presence of the electromagnetic field, and finally examine the problem of exhibiting explicitly the binding energies of the molecular systems.

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