A second order calculation of the adiabatic invariant of a charged particle spiraling in a longitudinal magnetic field

1978 ◽  
Vol 19 (5) ◽  
pp. 937-941 ◽  
Author(s):  
R. Chehab
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Longitudinal Magnetic Field ◽  
Second Order ◽  
Adiabatic Invariant ◽  
Order Calculation

scholarly journals Lie transforms and motion of a charged particle in a periodic magnetic field

1984 ◽  
Vol 7 (1) ◽  
pp. 159-169
Author(s):  
Sikha Bhattacharyya ◽  
R. K. Roy Choudhury
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Averaging Method ◽  
Second Order ◽  
Lie Series ◽  
Periodic Magnetic Field ◽  
First Order ◽  
Order Solution ◽  
Lie Transforms ◽  
Spatially Periodic

We use the Lie series averaging method to obtain a complete second order solution for motion of a charged particle in a spatially periodic magnetic field. A comparison is made with the first order solution obtained previously by Coffey.

THE EXPERIMENTALLY OBSERVED OPTICAL COTTON–MOUTON EFFECT: EVIDENCE FOR THE PHOTON'S LONGITUDINAL MAGNETIC FIELD, B(3)

1993 ◽  
Vol 07 (19) ◽  
pp. 1247-1251 ◽  
Author(s):  
M. W. EVANS
Keyword(s):  
Magnetic Field ◽  
Laser Beam ◽  
Flux Density ◽  
Experimental Observation ◽  
Longitudinal Magnetic Field ◽  
Laser Intensity ◽  
Longitudinal Component ◽  
Second Order ◽  
Permanent Magnetic Field ◽  
Classical Counterpart

The recent experimental observation of the optical Cotton–Mouton effect is consistent with the induction of magnetization by the longitudinal component of the photon's magnetic field, whose classical counterpart is the equivalent flux density B(3). In the optical Cotton–Mouton effect observed by Zon et al.,16 the field B(3) acts at second order and is independent of the polarization of the inducing laser beam propagating parallel to a permanent magnetic field. The optical Cotton–Mouton effect is therefore proportional to the laser intensity as observed.16

Calculation of the Adiabatic Invariant for Magnetized Intensive Relativistic Beams

2010 ◽  
Vol 3 (2) ◽  
pp. 76-79
Author(s):  
Andrey V. Ivanov ◽  
Mikhail A. Tiunov
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Cross Section ◽  
Transverse Energy ◽  
Longitudinal Magnetic Field ◽  
Adiabatic Invariant ◽  
Drift Motion ◽  
Relativistic Beam ◽  
Magnetic Field Transverse

The technique of adiabatic invariant calculation in cross-section of magnetized intensive relativistic beam with consideration of drift motion of beam particles centers of rotation is suggested. Example of adiabatic invariant calculation of electrons of intensive beam in electrostatic accelerating system with longitudinal magnetic field is presented. It was shown that in strong enough magnetic field transverse energy of electrons preserves even at abrupt alteration of electric field.

scholarly journals General formulas for adiabatic invariants in nearly periodic Hamiltonian systems

2020 ◽  
Vol 86 (6) ◽  
Author(s):  
J. W. Burby ◽  
J. Squire
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Hamiltonian System ◽  
Particle Dynamics ◽  
Adiabatic Invariant ◽  
Adiabatic Invariants ◽  
Coordinate Transformations ◽  
Popular Method ◽  
Field Lines ◽  
Periodic Hamiltonian System

While it is well known that every nearly periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely defined scalar. A less well-known method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to charged-particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed.

Anomale Diffusion in der positiven Säule im longitudinalen Magnetfeld1

1962 ◽  
Vol 17 (11) ◽  
pp. 937-962
Author(s):  
K. H. Wöhler
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Positive Column ◽  
Longitudinal Magnetic Field ◽  
Diffusion Theory ◽  
Low Pressure ◽  
Gas Discharge ◽  
Critical Magnetic Field ◽  
Anomalous Behaviour

The positive column of a low pressure stationary gas discharge in a longitudinal magnetic field is investigated. Above a critical magnetic field the charged particle losses of the discharge increase rapidly in contradiction to the diffusion theory of the positive column. This effect has become known as LEHNERT-effect. Different theories and hypothesis are investigated and compared with the experiments to explain this phenomenon. It is shown that all experiments are most compatible with a theory of KADOMTSEV which states the anomalous behaviour of the positive column to be a turbulence like instability.

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