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.

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.

On the stability of parallel flows with parallel magnetic fields

1966 ◽  
Vol 293 (1434) ◽  
pp. 342-358 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Parallel Magnetic Field ◽  
Parallel Flows ◽  
The Mean ◽  
The Stability ◽  
The Magnetic Field ◽  
Parallel Magnetic Fields

The first part of the paper is a physical discussion of the way in which a magnetic field affects the stability of a fluid in motion. Particular emphasis is given to how the magnetic field affects the interaction of the disturbance with the mean motion. The second part is an analysis of the stability of plane parallel flows of fluids with finite viscosity and conductivity under the action of uniform parallel magnetic fields. We show that, in general, three-dimensional disturbances are the most unstable, thus disagreeing with the conclusion of Michael (1953) and Stuart (1954). We show how results obtained for two-dimensional disturbances can be used to calculate the most unstable three-dimensional disturbances and thence we prove that a parallel magnetic field can never completely stabilize a parallel flow.

Suppression of runaway of electrons in a Lorentz plasma. II. crossed electric and magnetic fields

1970 ◽  
Vol 4 (3) ◽  
pp. 441-450 ◽  
Author(s):  
Barbara Abraham-Shrauner
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Electric Fields ◽  
Cyclotron Frequency ◽  
Collision Frequency ◽  
Uniform Electric Field ◽  
Drift Motion ◽  
Electric And Magnetic Fields ◽  
The Magnetic Field

Suppression of runaway of electrons in a weak, uniform electric field in a fully ionized Lorentz plasma by crossed magnetic and electric fields is analysed. A uniform, constant magnetic field parallel to a constant or harmonically time varying electric field does not alter runaway from that in the absence of the magnetic field. For crossed, constant fields the passage to runaway or to free motion as described by constant drift motion and spiral motion about the magnetic field is lengthened in time for strong magnetic fields. The new ‘runaway’ time scale is roughly the ratio of the cyclotron frequency to the collision frequency squared for cyclotron frequencies much greater than the collision frequency. All ‘runaway’ time scales may be given approximately by t2E Teff where tE is the characteristic time of the electric field and Teff is the ffective collision time as estimated from the appropriate component of the electrical conductivity.

scholarly journals Modified Adiabatic Approximation for A Hydrogen Atom Moving in A Magnetic Field

1994 ◽  
Vol 147 ◽  
pp. 555-559
Author(s):  
V.G. Bezchastnov ◽  
A.Y. Potekhin
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Magnetic Fields ◽  
Density Distribution ◽  
Cross Sections ◽  
Electron Density Distribution ◽  
Adiabatic Approximation ◽  
Strong Magnetic Fields ◽  
Radiative Transitions ◽  
The Magnetic Field

AbstractMotion of a hydrogen atom across the magnetic field shifts center of electron density distribution. For strong magnetic fields, the radiative transitions can be considered in the modified adiabatic approximation in which the shifts are taken into account. The method is illustrated by calculating the photoionization cross sections.

scholarly journals A dynamo amplifying the magnetic field of a Milky-Way-like galaxy

2020 ◽  
Vol 641 ◽  
pp. A165
Author(s):  
Evangelia Ntormousi ◽  
Konstantinos Tassis ◽  
Fabio Del Sordo ◽  
Francesca Fragkoudi ◽  
Rüdiger Pakmor
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Spiral Galaxies ◽  
Mean Field ◽  
Dark Matter Halo ◽  
Random Component ◽  
Galactic Magnetic Field ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Field Dynamo

Context. The magnetic fields of spiral galaxies are so strong that they cannot qualify as primordial. Their typical values are over one billion times higher than any value predicted for the early Universe. Explaining this immense growth and incorporating it in galaxy evolution theories is one of the long-standing challenges in astrophysics. Aims. So far, the most successful theory for the sustained growth of the galactic magnetic field is the alpha-omega dynamo. This theory predicts a characteristic dipolar or quadrupolar morphology for the galactic magnetic field, which has been observed in external galaxies. So far, however, there has been no direct demonstration of a mean-field dynamo operating in direct, multi-physics simulations of spiral galaxies. We carry out such a demonstration in this work. Methods. We employed numerical models of isolated, star-forming spiral galaxies that include a magnetized gaseous disk, a dark matter halo, stars, and stellar feedback. Naturally, the resulting magnetic field has a complex morphology that includes a strong random component. Using a smoothing of the magnetic field on small scales, we were able to separate the mean from the turbulent component and analyze them individually. Results. We find that a mean-field dynamo naturally occurs as a result of the dynamical evolution of the galaxy and amplifies the magnetic field by an order of magnitude over half a Gyr. Despite the highly dynamical nature of these models, the morphology of the mean component of the field is identical to analytical predictions. Conclusions. This result underlines the importance of the mean-field dynamo in galactic evolution. Moreover, by demonstrating the natural growth of the magnetic field in a complex galactic environment, it brings us a step closer to understanding the cosmic origin of magnetic fields.

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.

OPTICAL PROPERTIES OF ACCEPTORS IN SEMIMAGNETIC QUANTUM WELL SYSTEMS

2002 ◽  
Vol 16 (25) ◽  
pp. 3737-3757 ◽  
Author(s):  
Sr. GERARDIN JAYAM ◽  
K. NAVANEETHAKRISHNAN
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Quantum Well ◽  
Cross Sections ◽  
Empirical Relationship ◽  
Phonon Interaction ◽  
Shallow Acceptor ◽  
Electron Phonon Interaction ◽  
The Magnetic Field ◽  
Confined Phonons

The binding energy of a shallow acceptor in an isolated quantum well of the CdTe / Cd 1-x Mn x Te system has been investigated in an external magnetic field, assuming an empirical relationship between the barrier height and the magnetic field. Photoionization cross-sections for different magnetic fields have been estimated. Taking into account the confined phonons in the electron-phonon interaction, carrier capture times for various magnetic fields and different hydrostatic pressures have been computed. The results obtained are discussed in the light of the existing literature.

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