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.

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 Motion of a Charged Particle in an Axially Symmetric Magnetic Field

1971 ◽  
Vol 26 (12) ◽  
pp. 2068-2070
Author(s):  
V. L. Bharadwaj
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Configuration Space ◽  
Plasma Stream ◽  
Axially Symmetric ◽  
Interaction Forces ◽  
Transverse Pressure ◽  
Steady Current ◽  
Test Charge ◽  
The Magnetic Field

The object of this note is to study the motion of a charged particle entering the magnetic field due to a steady current inside a plasma column. Even if the particles of the plasmas stream mutually interact, their distribution across the stream can be such that the interaction forces are balanced by the transverse pressure gradient in the plasma 1. It is shown here that the test charge entering the plasma stream remains bounded to the stream between two coaxial cylindrical surfaces and further that under suitable conditions it may remain trapped inside a cylindrical box. FISSER and KIPPENHAHN 2 have discussed the general problem of the motion of a charged particle in an axially symmetric magnetic field in configuration space. The following is a particular case of that problem. HERTWECK 3 has investigated the motion of a test charge in the magnetic field due to a line current. His results are applicable here if the test charge remains outside the plasma stream

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.

Modeling the magnetic structure of CMEs in the inner heliosphere based on data-driven time-dependent simulations of active region evolution

2021 ◽  
Author(s):  
Jens Pomoell ◽  
Emilia Kilpua ◽  
Daniel Price ◽  
Eleanna Asvestari ◽  
Ranadeep Sarkar ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Active Region ◽  
Magnetic Structure ◽  
Interplanetary Space ◽  
Coronal Magnetic Field ◽  
Time Dependent ◽  
Data Driven ◽  
Dependent Data ◽  
Heliospheric Physics ◽  
The Magnetic Field

&lt;p&gt;Characterizing the detailed structure of the magnetic field in the active corona is of crucial importance for determining the chain of events from the formation to the destabilisation and subsequent eruption and propagation of coronal structures in the heliosphere. A comprehensive methodology to address these dynamic processes is needed in order to advance our capabilities to predict the properties of coronal mass ejections (CMEs) in interplanetary space and thereby for increasing the accuracy of space weather predictions. A promising toolset to provide the key missing information on the magnetic structure of CMEs are time-dependent data-driven simulations of active region magnetic fields. This methodology permits self-consistent modeling of the evolution of the coronal magnetic field from the emergence of flux to the birth of the eruption and beyond.&amp;#160;&lt;/p&gt;&lt;p&gt;In this presentation, we discuss our modeling efforts in which time-dependent data-driven coronal modeling together with heliospheric physics-based modeling are employed to study and characterize CMEs, in particular their magnetic structure, at various stages in their evolution from the Sun to Earth.&amp;#160;&lt;/p&gt;

scholarly journals Two-fluid simulations of the magnetic field evolution in neutron star cores in the weak-coupling regime

2020 ◽  
Vol 498 (2) ◽  
pp. 3000-3012 ◽  
Author(s):  
F Castillo ◽  
A Reisenegger ◽  
J A Valdivia
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Charged Particles ◽  
Stable Stratification ◽  
Composition Gradient ◽  
Axially Symmetric ◽  
Drag Forces ◽  
Degeneracy Pressure ◽  
The Magnetic Field ◽  
Two Fluid

ABSTRACT In a previous paper, we reported simulations of the evolution of the magnetic field in neutron star (NS) cores through ambipolar diffusion, taking the neutrons as a motionless uniform background. However, in real NSs, neutrons are free to move, and a strong composition gradient leads to stable stratification (stability against convective motions) both of which might impact on the time-scales of evolution. Here, we address these issues by providing the first long-term two-fluid simulations of the evolution of an axially symmetric magnetic field in a neutron star core composed of neutrons, protons, and electrons with density and composition gradients. Again, we find that the magnetic field evolves towards barotropic ‘Grad–Shafranov equillibria’, in which the magnetic force is balanced by the degeneracy pressure gradient and gravitational force of the charged particles. However, the evolution is found to be faster than in the case of motionless neutrons, as the movement of charged particles (which are coupled to the magnetic field, but are also limited by the collisional drag forces exerted by neutrons) is less constrained, since neutrons are now allowed to move. The possible impact of non-axisymmetric instabilities on these equilibria, as well as beta decays, proton superconductivity, and neutron superfluidity, are left for future work.

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