Charged Particle In Magnetic Field Research Articles

Non-stationary quasi-classical states of a charged particle in a strong magnetic field under conditions of the dissipative medium

Based on the quasi-classical approximation, a general approach is proposed for constructing non-stationary quantum states of a charged particle in a magnetic field, when the dissipative forces of viscous friction and drag, proportional to the velocity and the square of the velocity, respectively, are also significant. The corresponding quasi-classical Green’s function is found, with the help of which the squeezed and coherent states of the particle are studied. It is shown that the dissipation and a magnetic field suppress the quantum properties of the particle. This is especially true for the transverse motion with respect to the magnetic field. Over time, the coherent and squeezed states transform into the same static state, which is characterized by a zero uncertainty of the transverse coordinates and an uncertainty of the longitudinal coordinate, which contains information about the initial velocity of the particle.

Observation of universal Hall response in strongly interacting Fermions.

The Hall effect, which originates from the motion of charged particles in magnetic fields, has deep consequences for the description of materials, extending far beyond condensed matter. Understanding such an effect in interacting systems represents a fundamental challenge, even for small magnetic fields. In this work, we used an atomic quantum simulator in which we tracked the motion of ultracold fermions in two-leg ribbons threaded by artificial magnetic fields. Through controllable quench dynamics, we measured the Hall response for a range of synthetic tunneling and atomic interaction strengths. We unveil a universal interaction-independent behavior above an interaction threshold, in agreement with theoretical analyses. The ability to reach hard-to-compute regimes demonstrates the power of quantum simulation to describe strongly correlated topological states of matter.

SYNCA: A Synthetic Cyclotron Antenna for the Project 8 Collaboration

Cyclotron Radiation Emission Spectroscopy (CRES) is a technique for measuring the kinetic energy of charged particles through a precision measurement of the frequency of the cyclotron radiation generated by the particle's motion in a magnetic field. The Project 8 collaboration is developing a next-generation neutrino mass measurement experiment based on CRES. One approach is to use a phased antenna array, which surrounds a volume of tritium gas, to detect and measure the cyclotron radiation of the resulting β-decay electrons. To validate the feasibility of this method, Project 8 has designed a test stand to benchmark the performance of an antenna array at reconstructing signals that mimic those of genuine CRES events. To generate synthetic CRES events, a novel probe antenna has been developed, which emits radiation with characteristics similar to the cyclotron radiation produced by charged particles in magnetic fields. This paper outlines the design, construction, and characterization of this Synthetic Cyclotron Antenna (SYNCA). Furthermore, we perform a series of measurements that use the SYNCA to test the position reconstruction capabilities of the digital beamforming reconstruction technique. We find that the SYNCA produces radiation with characteristics closely matching those expected for cyclotron radiation and reproduces experimentally the phenomenology of digital beamforming simulations of true CRES signals.

Working principle and layout logic of closed magnetic field in sputtering

Closed magnetic field constructed by unbalanced magnetron sputtering (MS) cathodes has been a general means of developing the MS coating system. However, owing to the difficulties in characterizing the complex plasma behaviors, there are still no quantitative criteria or design bases for some critical points, such as the effective object, the working mechanism, the closure condition, the layout logic and the effectivity of the closed magnetic field. Here in this work, out of the movements of charged particles in magnetic field, the motion behaviors of electrons and ions in the vacuum chamber are studied and it is also revealed that the closed magnetic field can affect mainly the electrons and further control the distributions of ions. A Monte-Carlo collision (MCC) model of the closed magnetic field MS coating system is established by test-electron to characterize the plasma transport characteristics, and the electron constraint and coating deposition efficiency are studied by different layouts of the magnetron cathodes and the ion sources. The simulation results show that the cathode numbers and vacuum chamber size determine the constraint effect on electrons in closed magnetic field. By 8 MS cathodes and the chamber radius of 0.5 m, the proportion of the overflow electrons can decrease to 1.77%. To increase the proportion of the electrons in the coating region, four coupled magnetic fields are introduced in the center of vacuum chamber. The studies of cathode type, rotation angle and magnetic field direction reveal that the proportion of the overflow electrons is less than 3%. A local dense plasma distribution and a continuous uniform plasma distribution can be observed in the vacuum chamber, corresponding to the same and opposite layout in magnetic poles of the MS cathodes and the ion sources, and the proportion of the electrons in the coating region significantly increases to 53.41% and 42.25%, respectively.

On the Complex-Valued Distribution Function of Charged Particles in Magnetic Fields

In this work, we revisit Boltzmann’s distribution function, which, together with the Boltzmann equation, forms the basis for the kinetic theory of gases and solutions to problems in hydrodynamics. We show that magnetic fields may be included as an intrinsic constituent of the distribution function by theoretically motivating, deriving and analyzing its complex-valued version in its most general form. We then validate these considerations by using it to derive the equations of ideal magnetohydrodynamics, thus showing that our method, based on Boltzmann’s formalism, is suitable to describe the dynamics of charged particles in magnetic fields.

Rising and lowering operator approach to the problem of a charged particle in a uniform magnetic field

In this paper, we analyse the quantization of cyclotron orbits for a 2D non-relativistic and spinless charged particle under the influence of a static and uniform magnetic field, the Landau problem. We follow the algebraic approach of rising and lowering operators. The Hamiltonian is expressed in terms of the usual rising and lowering operators of an isotropic quantum oscillator. Through a Bogoliubov transformation, we show that the Hamiltonian may be reduced to the one of a quantum oscillator that accounts for the formation of infinitely degenerate Landau levels. The explicit form of the position-space wave functions of Fock–Darwin states for a vanishing parabolic confinement potential is worked out by applying the techniques of ladder operators and the induction method. To explore the internal dynamics of the electron states, we compute the Fock–Darwin states’ density currents expressing them in terms of the ladder operators. In the supplementary material, we provide the reader with Mathematica algorithm that can help perform some of the calculations exposed in the paper. The charged particle in a magnetic field is used to explore some of the fundamental concepts of quantum mechanics as commuting operators, simultaneous eigenstates, degeneracy, rising and lowering operators, etc. This approach can be used as supplementary material in undergraduate final-year courses like quantum mechanics or solid state physics.

On the dynamics of a charged particle in magnetic fields with cylindrical symmetry

We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance r from the symmetry axis of the form 1+Ar−γ as r→∞, with A≠0 and γ>1. With perturbative-variational techniques, we can prove the existence of infinitely many trajectories whose projection on a plane orthogonal to the direction of the field describe bounded curves given by the superposition of two motions: a rotation with constant angular speed at a unit distance about a point which moves along a circumference of large radius ρ with a slow angular speed ε. The values ρ and ε are suitably related to each other. This problem has some interest also in the context of planar curves with prescribed curvature.

Multi-step Boris rotation schemes for Lorentz force equation of charged particles

A numerical procedure for integrating the rotation equations of electrically charged particles in magnetic fields with higher accuracy is provided. The proposed n-step rotation schemes have the same accuracy with the standard Boris rotation with 1∕2n−1 time step.

A three-step Boris integrator for Lorentz force equation of charged particles

This paper provides a numerical procedure for integrating the equations of motion for electrically charged particles in magnetic fields with higher accuracy than the conventional Boris integrator. It is confirmed by both of numerical test and theoretical analysis that the proposed three-step integrator has the same accuracy as the standard (two-step) Boris integrator with a half time step.

Coherent and Semiclassical States of a Charged Particle in Electromagnetic Fields

In the present article we extend our study (BJP 45 (2015) 369) of generalized coherent states (GCS) of a one-dimensional particle considering such important physical system as a 3-dimensional charged particle in electric and magnetic fields. Constructing GCS in many-dimensional case, we meet nontrivial technical complications that make the consideration nontrivial and instructive. The GCS of a system under consideration are constructed. We study properties of these GCS such as completeness relations, minimization of uncertainty relations and so on. We point out which family of the obtained GCS of a charged particle in magnetic field is related with the CS constructed first by Malkin and Man'ko. We obtain conditions under which some of the GCS can be considered as semiclassical states.

Electrically tunable artificial gauge potential for polaritons

Neutral particles subject to artificial gauge potentials can behave as charged particles in magnetic fields. This fascinating premise has led to demonstrations of one-way waveguides, topologically protected edge states and Landau levels for photons. In ultracold neutral atoms, effective gauge fields have allowed the emulation of matter under strong magnetic fields leading to realization of Harper-Hofstadter and Haldane models. Here we show that application of perpendicular electric and magnetic fields effects a tunable artificial gauge potential for two-dimensional microcavity exciton polaritons. For verification, we perform interferometric measurements of the associated phase accumulated during coherent polariton transport. Since the gauge potential originates from the magnetoelectric Stark effect, it can be realized for photons strongly coupled to excitations in any polarizable medium. Together with strong polariton–polariton interactions and engineered polariton lattices, artificial gauge fields could play a key role in investigation of non-equilibrium dynamics of strongly correlated photons.

Drift velocity of charged particles in magnetic fields and its relation to the direction of the source current

Integrable motion of charged particles in magnetic fields produced by stationary current distributions is investigated. We treat motion in the magnetic field from an infinite flat current sheet, a Harris current sheath, an infinite rectilinear current, and a dipole in its equatorial plane. We find that positively charged particles as a rule will drift in the same direction as the current that is the source of the magnetic field in question. The conclusion is that charged particles moving under the influence of current distributions tend to enhance the current and that this indicates current self-amplification.

SU‐F‐J‐152: Accuracy of Charge Particle Transport in Magnetic Fields Using EGSnrc

Purpose:Determine accuracy of the current implementation of electron transport under magnetic fields in EGSnrc by means of single scattering (SS) and Fano convergence tests, and establish quantitatively the electron step size restriction required to achieve a desired level of accuracy for ionization chamber dosimetry.Methods:Condensed history (CH) dose calculations are compared to SS results for a PTW30013 ionization chamber irradiated in air by a 60Co photon beam. CH dose results for this chamber irradiated in a water phantom by a source of mono‐energetic electrons are compared to the prediction of Fano's theorem for step size restrictions EM ESTEPE from 0.01 to 0.1 and strengths of 0.5 T, 1.0 T, and 1.5 T.Results:CH calculations in air for 60Co photons using an EM ESTEPE of 0.25 overestimate SS values by 6% for a 1.5 T field and by 1.5% for a 0.5 T field. Agreement improves with decreasing EM ESTEPE reducing this difference at 0.02 to 0.13% and 0.04% for 1.5 T and 0.5 T respectively. CH results converge with decreasing EM ESTEPE reaching an agreement of 0.2% at a value of EM ESTEPE of 0.01 for 100 keV electrons. SS results at 100 keV for 1.5 T show the same EM ESTEPE dependency as the CH results.Conclusion:Accurate transport of charged particles in magnetic fields is only possible if the step size is significantly restricted. An EM ESTEPE value of 0.02 is required to reproduce SS results at the 0.1% level for a calculation in air. The EM ESTEPE dependency of the SS results suggests SS is bypassed when simulating the transport of charged particles in magnetic fields. Fano test results for in water calculation suggest that only a 0.2% accuracy can be achieved with the current implementation.

Fractional dynamics of charged particles in magnetic fields

In many physical applications the electrons play a relevant role. For example, when a beam of electrons accelerated to relativistic velocities is used as an active medium to generate Free Electron Lasers (FEL), the electrons are bound to atoms, but move freely in a magnetic field. The relaxation time, longitudinal effects and transverse variations of the optical field are parameters that play an important role in the efficiency of this laser. The electron dynamics in a magnetic field is a means of radiation source for coupling to the electric field. The transverse motion of the electrons leads to either gain or loss energy from or to the field, depending on the position of the particle regarding the phase of the external radiation field. Due to the importance to know with great certainty the displacement of charged particles in a magnetic field, in this work we study the fractional dynamics of charged particles in magnetic fields. Newton’s second law is considered and the order of the fractional differential equation is [Formula: see text]. Based on the Grünwald–Letnikov (GL) definition, the discretization of fractional differential equations is reported to get numerical simulations. Comparison between the numerical solutions obtained on Euler’s numerical method for the classical case and the GL definition in the fractional approach proves the good performance of the numerical scheme applied. Three application examples are shown: constant magnetic field, ramp magnetic field and harmonic magnetic field. In the first example the results obtained show bistability. Dissipative effects are observed in the system and the standard dynamic is recovered when the order of the fractional derivative is 1.

Low cost demonstration experiment Lorentz force: Change in path of charged particles in magnetic field

The path of charged particles is affected when they enter a magnetic field. This change of path largely depends on the angle between the applied magnetic field and the direction of motion of the charged particle (and its velocity) entering the magnetic field. This is demonstrated by means of a simple, low-cost experiment. A high voltage is used to ionize the air between a spark gap. The flow of charged particles between the spark gap is altered by applying a magnetic field from a rare earth permanent magnet having surface magnetic field induction of 0.12 T.

Question on Some Principles of Electromagnetism

In theory of electromagnetism, there are principles indicated as below: motional magnetic field shall not exist; action and reaction can be in the same direction, but differ in value; magnetic field can have an infinitely great motional speed; the same physical phenomenon can be explained conversely in different inertia systems; there is no uniform scientific explanation for deflection of high-speed charged particle in magnetic field; coexistence of static magnetic field with static electric field cannot be explained. Hence, truth of the above principles of electromagnetism is questioned here.

Gauge properties of the guiding center variational symplectic integrator

Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008); H. Qin, X. Guan, and W. Tang, Phys. Plasmas (2009); J. Li, H. Qin, Z. Pu, L. Xie, and S. Fu, Phys. Plasmas 18, 052902 (2011)]. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms, an instability arises because the discrete symplectic structure does not become the continuous structure in the t→0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the “antisymmetric discretization gauge,” in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and φ are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss’s law [J. Squire, H. Qin, and W. Tang (to be published)].

Virtual Design and Visual Simulation of Cathode Target on Magnetron Sputtering Coater

In order to solve the traditional problems such as long designing cycle and high designing cost, the research applies the virtual simulation technology to the design of cathode target on magnetron sputtering vacuum coater. Through analyzing, modeling and simulating, the process model of a typical cathode target on magnetron sputtering coater is proposed. The virtual design of cathode target framework based on distributed collaborative simulation is constructed, which provides a theorial basis for the research of virtual design on cathode target.Using Solidworks software, parts modeling and assembly modeling of cathode target are realized. Using ADAMS, the movements of charged particles in magnetic field and high frequency alternating electric field are simulated, and the visual animation simulation of particles movement is achieved. The research demonstrates the feasibility of virtual simulation technology on vacuum coater design.

Motion of Charged Particle in Electric and Magnetic Fields in 3D Noncommutative Spaces and Related Problems

In three-dimensional noncommutative phase space, the energy spectrum and wave functions for the motion of a charged particle in a magnetic field are derived. Due to the momentum–momentum noncommutativity, the particle feels an effective magnetic field in a new direction. When an external electric field perpendicular to this effective magnetic field is applied, the Hall conductivity can be calculated. To get the Hall conductivity, one should define the electric currents from the probability currents in quantum mechanics rather than extending the classical electric currents to quantum mechanics directly. When the electric field is not perpendicular to the effective magnetic field, it is difficult to define the Hall conductivity.

Geometric phase of the gyromotion for charged particles in a time-dependent magnetic field

We study the dynamics of the gyrophase of a charged particle in a magnetic field which is uniform in space but changes slowly with time. As the magnetic field evolves slowly with time, the changing of the gyrophase is composed of two parts. The first part is the dynamical phase, which is the time integral of the instantaneous gyrofrequency. The second part, called geometric gyrophase, is more interesting, and it is an example of the geometric phase which has found many important applications in different branches of physics. If the magnetic field returns to the initial value after a loop in the parameter space, then the geometric gyrophase equals the solid angle spanned by the loop in the parameter space. This classical geometric gyrophase is compared with the geometric phase (the Berry phase) of the spin wave function of an electron placed in the same adiabatically changing magnetic field. Even though gyromotion is not the classical counterpart of the quantum spin, the similarities between the geometric phases of the two cases nevertheless reveal the similar geometric nature of the different physics laws governing these two physics phenomena.