First adiabatic invariant of a charged particle modified in a time-dependent magnetic field

1999 ◽  
Vol 6 (2) ◽  
pp. 425-434
Author(s):  
S. Olszewski ◽  
T. Roliński
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Adiabatic Invariant ◽  
Time Dependent

scholarly journals A Quantum Charged Particle under Sudden Jumps of the Magnetic Field and Shape of Non-Circular Solenoids

2019 ◽  
Vol 1 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Viktor V. Dodonov ◽  
Matheus B. Horovits
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Electric Fields ◽  
Cross Sections ◽  
Magnetic Moment ◽  
Landau Gauge ◽  
Time Dependent ◽  
The Mean ◽  
The Magnetic Field

We consider a quantum charged particle moving in the x y plane under the action of a time-dependent magnetic field described by means of the linear vector potential of the form A = B ( t ) − y ( 1 + β ) , x ( 1 − β ) / 2 . Such potentials with β ≠ 0 exist inside infinite solenoids with non-circular cross sections. The systems with different values of β are not equivalent for nonstationary magnetic fields or time-dependent parameters β ( t ) , due to different structures of induced electric fields. Using the approximation of the stepwise variations of parameters, we obtain explicit formulas describing the change of the mean energy and magnetic moment. The generation of squeezing with respect to the relative and guiding center coordinates is also studied. The change of magnetic moment can be twice bigger for the Landau gauge than for the circular gauge, and this change can happen without any change of the angular momentum. A strong amplification of the magnetic moment can happen even for rapidly decreasing magnetic fields.

Resonance behavior of a charged particle in presence of a time dependent magnetic field

2015 ◽  
Vol 142 (15) ◽  
pp. 154122 ◽  
Author(s):  
Somrita Ray ◽  
Madhumita Rano ◽  
Bidhan Chandra Bag
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Time Dependent ◽  
Resonance Behavior

Geometrical squeezed states of a charged particle in a time-dependent magnetic field

1994 ◽  
Vol 188 (3) ◽  
pp. 232-238 ◽  
Author(s):  
V.V. Dodonov ◽  
V.I. Man'ko ◽  
P.G. Polynkin
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Time Dependent ◽  
Squeezed States

scholarly journals Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1579
Author(s):  
Viktor V. Dodonov ◽  
Matheus B. Horovits
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Electric Fields ◽  
Magnetic Moment ◽  
Classical Equation ◽  
Time Dependent ◽  
Gauge Parameter ◽  
Mean Values ◽  
Sudden Jump ◽  
The Magnetic Field

We consider a quantum spinless nonrelativistic charged particle moving in the xy plane under the action of a time-dependent magnetic field, described by means of the linear vector potential A=B(t)−y(1+α),x(1−α)/2, with two fixed values of the gauge parameter α: α=0 (the circular gauge) and α=1 (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for α=0 and straight lines for α=1. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function B(t). They are expressed in terms of solutions to the classical equation of motion ε¨+ωα2(t)ε=0, with ω1=2ω0. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions B(t), when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value.

Die „adiabatische Invarianz“ des magnetischen Bahnmomentes geladener Teilchen

1957 ◽  
Vol 12 (10) ◽  
pp. 844-849 ◽  
Author(s):  
F. Hertweck ◽  
A. Schlüter
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Moment ◽  
Relative Rate ◽  
Rate Of Change ◽  
Time Dependent ◽  
Constant Field ◽  
Relative Change ◽  
Special Case ◽  
The Magnetic Field

In einem Magnetfeld ist das magnetische Bahnmoment μ* eines geladenen Teilchens annähernd eine Konstante der Bewegung, wenn das Magnetfeld nur schwach variiert. Für den Spezialfall eines homogenen, zeitabhängigen Magnetfeldes wird gezeigt, daß die relative Änderung in μ* zwischen zwei verschiedenen Zuständen, in denen das Magnetfeld konstant ist, mindestens exponentiell in h/a gegen Null geht. Hierin ist α ein Maß für die relative Feldänderungsgeschwindigkeit und mit h ist die Gyro-Frequenz bezeichnet.The magnetic moment μ of the motion of a charged particle in a magnetic field is an approximate constant of motion in moderately varying magnetic fields. For the special case of a homgeneous time-dependent magnetic field, it is shown that the relative change in μ between two different states of constant field decreases at least exponentially in h/α if α/h tends to zero, where a represents the relative rate of change of the magnetic field and h denotes the gyro-frequency.

scholarly journals Charged Particle Motion in a Time?Dependent Axially Symmetric Magnetic Field

1965 ◽  
Vol 18 (6) ◽  
pp. 553 ◽  
Author(s):  
PW Seymour ◽  
RB Leipnik ◽  
AF Nicholson
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Constant Velocity ◽  
Short Review ◽  
Time Dependent ◽  
Radial Compression ◽  
Axially Symmetric ◽  
Cylindrical Coordinates ◽  
Drift Theory ◽  
The Magnetic Field

Following a short review of the drift theory of plasma radial compression, an exact solution for the motion of a charged particle in an axially symmetric time-dependent magnetic field is� obtained. The method gives forms for the cylindrical coordinates rand B of the charged particle that have a simple interpretation, the z-motion being of constant velocity. As examples, the exact results are discussed for a simple power law and an exponential time dependence of the magnetic field and, using the latter results, the drift theory of plasma radial compression is qualitatively verified.

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