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 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.

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.

scholarly journals THIN LAYERS IN MICROMAGNETISM

2001 ◽  
Vol 11 (09) ◽  
pp. 1529-1546 ◽  
Author(s):  
G. CARBOU
Keyword(s):  
Magnetic Field ◽  
Magnetic Moment ◽  
Thin Layers ◽  
Time Dependent ◽  
Thin Domain ◽  
Dependent Case ◽  
The Magnetic Field

In this paper we study the solutions of micromagnetism equation in thin domain both in the stationary and in the time-dependent case. We prove that the magnetic field induced by the magnetisation behaves like the projection of the magnetic moment on the normal to the domain, both for a flat and a non-flat domain.

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.

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents

1968 ◽  
Vol 2 (2) ◽  
pp. 189-195
Author(s):  
D. N. Burghes ◽  
R. C. Hewson-Browne
Keyword(s):  
Magnetic Field ◽  
General Problem ◽  
Time Dependent ◽  
Special Case ◽  
The Magnetic Field

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents are considered. The general problem is formulated and solved in the case of an initially flat-faced cloud of flux approaching and passing the magnetic field of n line currents. The special case of a line dipole is analysed in some detail.

scholarly journals Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines

2020 ◽  
Vol 86 (2) ◽  
Author(s):  
Elena Elbarmi ◽  
Wrick Sengupta ◽  
Harold Weitzner
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Particle Dynamics ◽  
Closed Field ◽  
Symmetric Vacuum ◽  
Field Lines ◽  
Particle Confinement ◽  
Special Case ◽  
The Magnetic Field

Understanding particle drifts in a non-symmetric magnetic field is of primary interest in designing optimized stellarators in order to minimize the neoclassical radial loss of particles. Quasisymmetry and omnigeneity, two distinct properties proposed to ensure radial localization of collisionless trapped particles in stellarators, have been explored almost exclusively for magnetic fields with nested flux surfaces. In this work, we examine radial particle confinement when all field lines are closed. We then study charged particle dynamics in the special case of a non-symmetric vacuum magnetic field with closed field lines obtained recently by Weitzner & Sengupta (Phys. Plasmas, vol. 27, 2020, 022509). These magnetic fields can be used to construct magnetohydrodynamic equilibria for low pressure. Expanding in the amplitude of the non-symmetric fields, we explicitly evaluate the omnigeneity and quasisymmetry constraints. We show that the magnetic field is omnigeneous in the sense that the drift surfaces coincide with the pressure surfaces. However, it is not quasisymmetric according to the standard definitions.

scholarly journals Moving Pearl Vortices in Thin-Film Superconductors

2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Vladimir Kogan ◽  
Norio Nakagawa
Keyword(s):  
Magnetic Field ◽  
Thin Film ◽  
Time Dependent ◽  
Superconducting Thin Film ◽  
Self Energy ◽  
London Equation ◽  
The Magnetic Field

The magnetic field hz of a moving Pearl vortex in a superconducting thin-film in (x,y) plane is studied with the help of the time-dependent London equation. It is found that for a vortex at the origin moving in +x direction, hz(x,y) is suppressed in front of the vortex, x>0, and enhanced behind (x<0). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.

Motion of a charged particle in superposed Heliotron and biconical cusp fields

1969 ◽  
Vol 3 (2) ◽  
pp. 255-267 ◽  
Author(s):  
M. P. Srivastava ◽  
P. K. Bhat
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Moment ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Neutral Point ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Hybrid Type

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

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