Adiabatic invariant of a charged particle moving in a magnetic field with a constant gradient

2021 ◽  
Vol 28 (12) ◽  
pp. 122101
Author(s):  
K. Kabin
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Adiabatic Invariant ◽  
Constant Gradient

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.

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.

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,

scholarly journals Motion of a Charged Particle in a Non-uniform Magnetic Field

1964 ◽  
Vol 17 (4) ◽  
pp. 547 ◽  
Author(s):  
RF Mathams
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Uniform Magnetic Field ◽  
Elliptic Integrals ◽  
Constant Gradient

The motion of an electron in a magnetic field of constant gradient has been analysed by Seymour (1959), who derives expressions for the x and y coordinates of the electron in terms of elliptic integrals.

Humanity Imperiled by the Geomagnetic Field and Human Corruption

2021 ◽  
Vol 8 (1) ◽  
pp. 456-478
Author(s):  
J. Marvin Herndon
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Charged Particle ◽  
Geomagnetic Field ◽  
Paradigm Shift ◽  
Government Officials ◽  
The Public ◽  
Person Perspective ◽  
First Person Perspective ◽  
The Many

Earth’s magnetic field acts as a shield, protecting life and our electrically-based infrastructure from the rampaging, charged-particle solar wind. In the geologic past, the geomagnetic field has collapsed, with or without polarity reversal, and inevitably it will again. The potential consequences of geomagnetic collapse have not only been greatly underestimated, but governments, scientists, and the public have been deceived as to the underlying science. Instead of trying to refute or advance a paradigm shift that occurred in 1979, global geoscientists, individuals and institutions, chose to function as a cartel and continued to promote their very-flawed concepts that had their origin in the 1930s and 1940s, consequently wasting vast amounts of taxpayer-provided research money, and making no meaningful advances or understanding. Here, from a first person perspective, I describe the logical progression of understanding from that paradigm shift, review the advances made and their concomitant implications, and touch upon a few of the many efforts that were made to deceive government officials, scientists, and the public. It is worrisome that geoscientists almost universally have engaged in suppressing or ignoring sound scientific advances, including those with potentially adverse implications for humanity. All of this suggests that the entire institutional structure of the geophysical sciences, funding, institutions, and bureaucracies should be radically reformed.

scholarly journals Ion motion in the current sheet with sheared magnetic field – Part 1: Quasi-adiabatic theory

2013 ◽  
Vol 20 (1) ◽  
pp. 163-178 ◽  
Author(s):  
A. V. Artemyev ◽  
A. I. Neishtadt ◽  
L. M. Zelenyi
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Analytical Description ◽  
Particle Energy ◽  
Tangential Component ◽  
Adiabatic Invariant ◽  
Ion Motion ◽  
Adiabatic Theory ◽  
Fast Oscillations ◽  
The Magnetic Field

Abstract. We present a theory of trapped ion motion in the magnetotail current sheet with a constant dawn–dusk component of the magnetic field. Particle trajectories are described analytically using the quasi-adiabatic invariant corresponding to averaging of fast oscillations around the tangential component of the magnetic field. We consider particle dynamics in the quasi-adiabatic approximation and demonstrate that the principal role is played by large (so called geometrical) jumps of the quasi-adiabatic invariant. These jumps appear due to the current sheet asymmetry related to the presence of the dawn–dusk magnetic field. The analytical description is compared with results of numerical integration. We show that there are four possible regimes of particle motion. Each regime is characterized by certain ranges of values of the dawn–dusk magnetic field and particle energy. We find the critical value of the dawn–dusk magnetic field, where jumps of the quasi-adiabatic invariant vanish.

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