Critical Examination of a Proposed Charged-Particle Stern–Gerlach Experiment

1972 ◽  
Vol 50 (3) ◽  
pp. 185-195
Author(s):  
Thomas F. Knott
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Phase Space ◽  
Initial Phase ◽  
Initial Conditions ◽  
Transverse Velocity ◽  
Charged Particles ◽  
Transverse Magnetic ◽  
Critical Examination ◽  
Focusing Effect

It has been proposed by Enga and Bloom that combined electric and magnetic helical quadrupole fields may be used to perform a Stern–Gerlach experiment on charged particles. A detailed investigation shows that the longitudinal Lorentz force due to coupling of the transverse velocity of the particles to the transverse magnetic field produces an additional focusing effect which masks the Stern–Gerlach force in large regions of initial phase space. Consideration of uncompensated magnetic fields, produced by small random variations in conductor dimensions and location, shows that the tolerances required to preserve spin separation in the useful range of initial conditions are several orders of magnitude higher than can be achieved at this time.

scholarly journals DIRAC BRACKETS FROM MAGNETIC BACKGROUNDS

2007 ◽  
Vol 04 (04) ◽  
pp. 523-532 ◽  
Author(s):  
JOSÉ M. ISIDRO
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Phase Space ◽  
Symplectic Form ◽  
Weak Magnetic Field ◽  
Complex Geometry ◽  
Poisson Brackets ◽  
Generalized Complex ◽  
Dirac Brackets ◽  
Classical Phase Space

In symplectic mechanics, the magnetic term describing the interaction between a charged particle and an external magnetic field has to be introduced by hand. On the contrary, in generalized complex geometry, such magnetic terms in the symplectic form arise naturally by means of B-transformations. Here we prove that, regarding classical phase space as a generalized complex manifold, the transformation law for the symplectic form under the action of a weak magnetic field gives rise to Dirac's prescription for Poisson brackets in the presence of constraints.

scholarly journals Magnetic motion of spherical frictional charged particles on the unit sphere

2019 ◽  
Vol 65 (5 Sept-Oct) ◽  
pp. 496 ◽  
Author(s):  
Talat Körpınar ◽  
Ridvan Cem Demirkol
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Potential Energy ◽  
Frictional Force ◽  
Poynting Vector ◽  
Positive Curvature ◽  
Charged Particles ◽  
Energy Functional ◽  
Ordinary Space ◽  
Potential Energy Functional

Mathematically, the sphere unit S² is described to be a 2-sphere in an ordinary space with a positive curvature. In this study, we aim to present the manipulation of a spherical charged particle in a continuous motion with a magnetic field on the sphere S² while it is exposed to a frictional force. In other words, we effot to derive the exact geometric characterization for the spherical charged particle under the influence of a frictional force field on the unit 2-sphere. This approach also helps to discover some physical and kinematical characterizations belonging to the particle such as the magnetic motion, the torque, the potential energy functional, and the Poynting vector.

Orbits of magnetized charged particles in parabolic and inverse electrostatic potentials

2016 ◽  
Vol 82 (1) ◽  
Author(s):  
P. M. Bellan
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Charged Particle ◽  
Penning Trap ◽  
Axial Magnetic Field ◽  
Charged Particles ◽  
Analytic Solutions ◽  
The Other ◽  
Particle Orbit ◽  
Slow Frequency

Analytic solutions are presented for the orbit of a charged particle in the combination of a uniform axial magnetic field and parabolic electrostatic potential. These trajectories are shown to correspond to the sum of two individually rotating vectors with one vector rotating at a constant fast frequency and the other rotating in the same sense but with a constant slow frequency. These solutions are related to Penning trap orbits and to stochastic orbits. If the lengths of the two rotating vectors are identical, the particle has zero canonical angular momentum in which case the particle orbit will traverse the origin. If the potential has an inverse dependence on distance from the source of the potential, the particle can impact the source. Axis-encircling orbits are where the length of the vector associated with the fast frequency is longer than the vector associated with the slow frequency. Non-axis-encircling orbits are the other way around.

scholarly journals CHARGED PARTICLES WITH SPIN IN A GRAVITATIONAL WAVE AND A UNIFORM MAGNETIC FIELD

2006 ◽  
Vol 15 (01) ◽  
pp. 121-130 ◽  
Author(s):  
MORTEZA MOHSENI
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Gravitational Wave ◽  
Uniform Magnetic Field ◽  
Charged Particles ◽  
Space Time ◽  
Pp Wave

We study the motion of a pseudo-classical charged particle with spin in the space–time of a gravitational pp wave in the presence of a uniform magnetic field.

scholarly journals Distribution of the charged particles of a gas-discharge laser plasma in a transverse magnetic field. I. Calculation model

2021 ◽  
Vol 2059 (1) ◽  
pp. 012013
Author(s):  
S A Martsinukov ◽  
D K Kostrin
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Charged Particles ◽  
Transverse Magnetic ◽  
Gas Discharge ◽  
Calculation Model ◽  
Independent Components ◽  
Electrons And Ions ◽  
Weakly Ionized ◽  
Discharge Laser

Abstract The paper considers a physical and mathematical model describing the influence of an external transverse magnetic field on the distribution of charged particles in a positive column of a gas discharge. This model is developed in relation to the weakly ionized plasma of a gas-discharge laser. In this case, the plasma flow is considered as an analog of a liquid consisting of two practically independent components – electrons and ions.

scholarly journals Distribution of the charged particles of a gas-discharge laser plasma in a transverse magnetic field. II. Experimental study

2021 ◽  
Vol 2059 (1) ◽  
pp. 012014
Author(s):  
S A Martsinukov ◽  
D K Kostrin
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Experimental Study ◽  
Transverse Magnetic Field ◽  
Positive Column ◽  
Charged Particles ◽  
Transverse Magnetic ◽  
Gas Discharge ◽  
Gas Mixture ◽  
Discharge Laser

Abstract The paper presents an experimental verification of the adequacy of a physical and mathematical model describing the influence of an external transverse magnetic field on the distribution of the charged particles in a positive column of a gas discharge. A gas-discharge laser located in a transverse magnetic field was used to conduct the study. The vacuum installation allows pumping out the system and feeding the gas mixture into it under a certain pressure. The data obtained during the experiments differ from the calculated ones by no more than 4–5 %.

scholarly journals Coherent State Quantization and Moment Problem

10.14311/1185 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
J. P. Gazeau ◽  
M. C. Baldiotti ◽  
D. M. Gitman
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Energy Spectrum ◽  
Phase Space ◽  
Coherent State ◽  
Moment Problem ◽  
Coherent States ◽  
Uniform Magnetic Field ◽  
Classical Motion ◽  
Negative Numbers

Berezin-Klauder-Toeplitz (“anti-Wick”) or “coherent state” quantization of the complex plane, viewed as the phase space of a particle moving on the line, is derived from the resolution of the unity provided by the standard (or gaussian) coherent states. The construction of these states and their attractive properties are essentially based on the energy spectrum of the harmonic oscillator, that is on natural numbers. We follow in this work the same path by considering sequences of non-negative numbers and their associated “non-linear” coherent states. We illustrate our approach with the 2-d motion of a charged particle in a uniform magnetic field. By solving the involved Stieltjes moment problem we construct a family of coherent states for this model. We then proceed with the corresponding coherent state quantization and we show that this procedure takes into account the circle topology of the classical motion.

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