Parabolic Magnetic Field Research Articles

Quantifying the role of electron plateau distribution on the chorus gap formation using one-dimension PIC simulations

Although ubiquitous in the Earth’s inner magnetosphere, how chorus waves with a gap in intensity near half the electron cyclotron frequency, 0.5fce, is formed remains to be understood. One hypothesis invokes the often-observed feature in electron phase space density where two anisotropic populations of warm and hot temperatures, respectively, are separated by a relatively isotropic beam-like component, called the parallel plateau distribution. According to linear theory, its mean velocity is such that the plateau population can lead to a sufficient cyclotron damping in a narrow frequency range near 0.5fce. To test this hypothesis more quantitatively, we carry out a series of one-dimensional particle-in-cell simulations in a parabolic magnetic field with observationally constrained plateau density and mean velocity. We find that even though the chorus generation involves nonlinear physics, the gap formation is largely determined by the linear properties of plateau electrons. In addition, given a sufficiently large plateau density with a right combination of warm and/or hot source populations, our simulations were able to generate lower-band-only chorus, upper-band-only chorus, banded chorus with partial damping at the gap, and banded chorus with a strong power gap. When it comes to comparing with observations, however, we find that (1) the minimum plateau density required to generate banded chorus is somewhat larger than that observed; (2) even with the largest plateau density used, the gap formation in the simulations is not consistent; and (3) most importantly, the dependence of the gap frequency on the plateau velocity in our parametric analysis differs quite substantially from that of the recent statistical results. Provided that the simplifying assumptions in our simulations remain valid, these discrepancies would indicate that the electron plateau distribution is not the major contributor to the chorus gap formation.

Charged particles and quasiperiodic oscillations around magnetized Schwarzschild black holes

We study the motion of charged particles around Schwarzschild black holes immersed in external (i) asymptotically uniform, (ii) dipolar, and (iii) parabolic-like magnetic fields. The effect of the different magnetic-field configurations on the position of innermost stable circular orbits (ISCOs) for test-charged particles is analyzed. Furthermore, we investigated frequencies of radial and vertical oscillations of the charged particles along their stable circular orbits together with the Keplerian one. As an astrophysical application, we explore quasiperiodic oscillations (QPOs) observed in microquasars sourced by black hole candidates in the frame of the relativistic precession (RP) model. In order to obtain constraints on the values of the magnetic parameter and black hole mass for the microquasars GRO J1655-40 and GRS 1915-105, we use the method so-called chi ^2 in the Bayesian approach. Also, we get constraints on the magnetic field around the black hole in the microquasars by treating electrons and protons as oscillating test-charged particles in the accretion disc. Our performed analyses show that the masses of black hole candidates in the above-mentioned objects and magnetic parameters are different for the uniform and dipolar magnetic field configurations. However, no constraints on the magnetic field and black hole masses are obtained in the case of a parabolic magnetic field configuration. The obtained results on the black hole masses are compared with the measurements in independent astrophysical observations of these black hole masses.

Charged particle dynamics in parabolic magnetosphere around Schwarzschild black hole

The study of charged particle dynamics in the combined gravitational and magnetic field can provide important theoretical insight into astrophysical processes around black holes. In this paper, we explore the charged particle dynamics in parabolic magnetic field configuration around Schwarzschild black hole, since the paraboloidal shapes of magnetic field lines around black holes are well motivated by the numerical simulations and supported by observations of relativistic jets. Analysing the stability of bounded orbits and using the effective potential approach, we show the possibility of existence of stable circular off-equatorial orbits around the symmetry axis. We also show the influence of radiation reaction force on the dynamics of charged particles, in particular on the chaoticity of the motion and Poincaré sections, oscillatory frequencies, and emitted electromagnetic spectrum. Applied to Keplerian accretion disks, we show that in parabolic magnetic field configuration, the thin accretion configurations can be either destroyed or transformed into a thick toroidal structure given the radiation reaction and electromagnetic-disk interactions included. Calculating the Fourier spectra for radiating charged particle trajectories, we find that the radiation reaction force does not affect the main frequency peaks, however, it lowers the higher harmonics making the spectrum more flat and diluted in high frequency range.

Upstream Shift of Generation Region of Whistler‐Mode Rising‐Tone Emissions in the Magnetosphere

AbstractWe have performed a series of simulation runs for whistler‐mode wave‐particle interaction in a parabolic magnetic field with 12 different frequencies of triggering waves and 3 different plasma frequencies specifying cold plasma densities. Under a given plasma condition, a specific frequency range of the triggering wave exists that can generate rising‐tone emissions. The generation region of rising‐tone emission shifts upstream. The velocity of the wave generation region is dependent on duration of the subpacket, which is controlled by the formation of the resonant current in the generation region. When the source velocity, which is a sum of the resonance and group velocities, is approximately the same as the velocity of the wave generation region, a long‐sustaining rising‐tone emission is generated. When the spatial and temporal gap between subpackets exists due to damping phase of short subpacket generation, resonant electrons in the gap of the subpackets are carried at the resonance velocity to the upstream region, and the velocity of the wave generation region becomes large in magnitude. When formation of resonant currents is delayed, the velocity of the generation region becomes smaller than the source velocity in magnitude. Below one quarter of the cyclotron frequency, coalescence of subpackets takes place, suppressing formation of the resonant current in the generation region. Since gradual upstream shift of the generation region is necessary for the wave to grow locally, the source velocity should be a small negative value.

Full Particle Simulation of Whistler‐Mode Triggered Falling‐Tone Emissions in the Magnetosphere

AbstractWe perform a one‐dimensional electromagnetic full particle simulation for triggered falling‐tone emissions in the Earth's magnetosphere. The equatorial region of the magnetosphere is modeled with a parabolic magnetic field approximation. The short whistler‐mode waves with a large amplitude are excited and propagate poleward from an artificial current oscillating with a constant frequency and amplitude. Following the excited waves, clear emissions are triggered with a falling frequency. Without the inhomogeneity of the background magnetic field, no triggered emission appears. The falling tone has several subpackets of amplitude and decreases the frequency in a stepwise manner. The positive resonant current formed by resonant electrons in the direction of the wave magnetic field clearly shows that an electron hill is formed in the phase space and causes the frequency decrease. The entrapping of the resonant electrons at the front of the packets and the decrease of the amplitude at the end of packets are essential for the generation of falling‐tone emissions. Each wavefront of the emission has a strongly negative resonant current −JE, which results in the wave growth. In the formation process of the resonant currents, we investigate the inhomogeneous factor S, which controls the nonlinear motion of the resonant electrons interacting with waves. The factor S consists of two terms, a frequency sweep rate and a gradient of the background magnetic field. The resonant current JE in the wave packet changes its sign from negative to positive as the packet moves away from the equator, terminating the wave growth.

Distortion of Magnetic Fields in the Dense Core SL 42 (CrA-E) in the Corona Australis Molecular Cloud Complex

Abstract The detailed magnetic field structure of the dense core SL 42 (CrA-E) in the Corona Australis molecular cloud complex was investigated based on near-infrared polarimetric observations of background stars to measure dichroically polarized light produced by magnetically aligned dust grains. The magnetic fields in and around SL 42 were mapped using 206 stars, and curved magnetic fields were identified. On the basis of simple hourglass (parabolic) magnetic field modeling, the magnetic axis of the core on the plane of the sky was estimated to be 40° ± 3°. The plane-of-sky magnetic field strength of SL 42 was found to be 22.4 ± 13.9 μG. Taking into account the effects of thermal/turbulent pressure and the plane-of-sky magnetic field component, the critical mass of SL 42 was obtained to be M cr = 21.2 ± 6.6 M ⊙, which is close to the observed core mass of M core ≈ 20 M ⊙. We thus conclude that SL 42 is in a condition close to the critical state if the magnetic fields lie near the plane of the sky. Because there is a very low-luminosity object toward the center of SL 42, it is unlikely that this core is in a highly subcritical condition (i.e., the magnetic inclination angle is significantly deviated from the plane of the sky). The core probably started to collapse from a nearly kinematically critical state. In addition to the hourglass magnetic field modeling, the Inoue & Fukui mechanism may explain the origin of the curved magnetic fields in the SL 42 region.

Particle Simulation of the Generation of Plasmaspheric Hiss

AbstractWe have conducted a one‐dimensional electromagnetic particle simulation with a parabolic magnetic field to reproduce whistler‐mode hiss emissions in the plasmasphere. We assume a bi‐Maxwellian distribution with temperature anisotropy for energetic electrons injected into the plasmasphere and find that hiss emissions are generated with spectrum characteristics typical of those observed by spacecraft near the magnetic equator. The hiss emissions contain fine structures involving rising tone and falling tone elements with variation in frequencies. The amplitude profile of the spectra agrees with the optimum wave amplitude derived from the nonlinear wave growth theory. The simulation demonstrates that hiss emissions are generated locally near the magnetic equator through linear and nonlinear interactions with energetic electrons with temperature anisotropy. The coherent hiss emissions efficiently scatter resonant electrons of 2.5–80 keV into the loss cone.

Effects of Different Magnetic Field Profiles on Output Power and Efficiency of a Second-Harmonic Gyrotron

As the magnetic field used in nuclear magnetic resonance (NMR) research increases (up to 23 T), the irradiation frequency of the electromagnetic field used for dynamic nuclear polarization (DNP) needs to be in the terahertz band (140–600 GHz). This article analyzed and compared the influence of different external magnetic field profiles on start current and beam–wave interaction of a 394-GHz gyrotron. As the simulation results show, the minimum start current corresponding to the linear and parabolic external magnetic field profile is lower than that corresponding to the uniform magnetic field. The minimum start current in the case of parabolic magnetic field profile is a little lower than that in the case of a linear magnetic field profile. Based on the nonlinear self-consistent calculation, it is observed that the optimum output powers in both linear and parabolic magnetic field profile cases are nearly equal when the beam current is 0.25 A and both of them are larger than the optimum output power when the magnetic field is uniform. In the calculation of orbital efficiency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta _{\bot } $ </tex-math></inline-formula> , the maximum orbital efficiency in the soft-excitation region in the inhomogeneous magnetic field profile cases is larger than that in the case of uniform magnetic field profile. After comprehensive consideration of beam voltage, beam current, and efficiency, the final operation point is located in the place where the beam current is 0.25 A and the beam voltage is 15 kV. The output power is more than 300 W and meets the requirements of DNP-NMR experiment.

General analytical method of designing shielded coils for arbitrary axial magnetic field**Project supported by the National Natural Science Foundation of China (Grant Nos. 61701515 and 61671458), the Postdoctoral Science Foundation, China (Grant No. 2017M613367), the Natural Science Foundation of Hunan Province, China (Grant No. 2018JJ3608), and the Research Project of National University of Defense Technology, China (Grant No. ZK170204).

Magnetic coils for specific requirements are widely used in modern quantum physics. In this study, a general analytical method of designing the shielded coils for generating an arbitrary axial magnetic field is proposed. The theoretical formula for an axial magnetic field generated by a single shielded coil is obtained and used to construct specific coils. The structural parameters of these coils are determined by fitting the theoretical formula with their specific requirements. The feasibility of this method is proved by realizing four concrete kinds of coils: uniform magnetic field generating coils, gradient magnetic field generating coils, asymmetrical uniform magnetic field generating coils, and parabolic magnetic field generating coils. The correctness of these theoretical results is demonstrated by both the finite element simulations and the relevant experimental results. Furthermore, the application of this method is of great significance for developing the quantum physics and quantum devices in future.

Magnetospheric chorus wave simulation with the TRISTAN-MP PIC code

We present the results of particle-in-cell simulations of the whistler anisotropy instability that results in magnetospheric chorus wave excitation. The simulations were carried out using, for the first time for this problem, the 2D TRISTAN-massively parallelized code, widely used before in the modeling of astrophysical shocks. The code has been modified to allow for two populations of electrons: cold electrons (which maintain the wave propagation) and hot electrons (which provide the wave growth). For the hot electrons, the anisotropic form of the relativistic Maxwell–Jüttner distribution is implemented. We adopt the standard approximation of a parabolic magnetic field to simulate the Earth's magnetic field close to the equator. Simulations with different background magnetic field inhomogeneity strengths demonstrate that higher inhomogeneity yields lower frequency chirping rates and, eventually, it suppresses chorus generation. The results are in agreement with other numerical simulations and the theoretical predictions for the frequency chirping rates.

A full wave model of high-harmonic EMIC wave propagation in sheared magnetic fields

ABSTRACT A new dispersion relation, with finite Larmor orbit effects, for oblique propagating electromagnetic ion cyclotron (EMIC) waves in a magnetized plasma medium, is derived including the magnetic shear effect. The approximate, yet accurate, dispersion relation is used to implement the ray tracing model. A parabolic magnetic field is considered to model the geomagnetic field in the magnetosphere. Energetic protons are also considered as resonant particles. The propagation characteristics of EMIC waves in the vicinity of the ion cyclotron resonances are investigated in some detail. The results reveal adiabatic oscillating motion for wave and magnetic field fluctuations where high harmonics limit the wave damping and confines the magnetic fluctuations. For inward propagating EMIC waves we find (1) turning points which depend on the wave launch position, and (2) wave trapped areas playing a role in quasi-coherent wave-particle interaction in agreement with the observational and theoretical studies. This wave trapping is an effective process for particle acceleration in the context of space plasmas.

A computational and theoretical investigation of nonlinear wave‐particle interactions in oblique whistlers

AbstractMost previous work on nonlinear wave‐particle interactions between energetic electrons and VLF waves in the Earth's magnetosphere has assumed parallel propagation, the underlying mechanism being nonlinear trapping of cyclotron resonant electrons in a parabolic magnetic field inhomogeneity. Here nonlinear wave‐particle interaction in oblique whistlers in the Earth's magnetosphere is investigated. The study is nonself‐consistent and assumes an arbitrarily chosen wave field. We employ a “continuous wave” wave field with constant frequency and amplitude, and a model for an individual VLF chorus element. We derive the equations of motion and trapping conditions in oblique whistlers. The resonant particle distribution function, resonant current, and nonlinear growth rate are computed as functions of position and time. For all resonances of order n, resonant electrons obey the trapping equation, and provided the wave amplitude is big enough for the prevailing obliquity, nonlinearity manifests itself by a “hole” or “hill” in distribution function, depending on the zero‐order distribution function and on position. A key finding is that the n = 1 resonance is relatively unaffected by moderate obliquity up to 25°, but growth rates roll off rapidly at high obliquity. The n = 1 resonance saturates due to the adiabatic effect and here reaches a maximum growth at ~20 pT, 2000 km from the equator. Damping due to the n = 0 resonance is not subject to adiabatic effects and maximizes at some 8000 km from the equator at an obliquity ~55°.

Magnetoresistance induced by rare strong scatterers in a high-mobility two-dimensional electron gas

We observe a strong negative magnetoresistance at non-quantizing magnetic fields in a high-mobility two-dimensional electron gas (2DEG). This strong negative magnetoresistance consists of a narrow peak around zero magnetic field and a huge magnetoresistance at larger fields. The peak shows parabolic magnetic field dependence and is attributed to the interplay of smooth disorder and rare strong scatterers. We identify the rare strong scatterers as macroscopic defects in the material and determine their density from the peak curvature.

Relativistic electron microbursts due to nonlinear pitch angle scattering by EMIC triggered emissions

We show that the anomalous cyclotron resonance between relativistic electrons and electromagnetic ion cyclotron (EMIC) triggered emissions takes place very effectively near the magnetic equator because of the variation of the ambient magnetic field. Efficient precipitations are caused by nonlinear trapping of relativistic electrons by electromagnetic wave potentials formed by EMIC triggered emissions. We derive the necessary conditions of the wave amplitude, kinetic energies, and pitch angles that must be satisfied for the nonlinear wave trapping. We have conducted test particle simulations with a large number of relativistic electrons trapped by a parabolic magnetic field near the magnetic equator. In the presence of coherent EMIC‐triggered emissions with increasing frequencies, a substantial amount of relativistic electrons is trapped by the wave, and the relativistic electrons at high pitch angles are guided to lower pitch angles within a short time scale much less than a second, resulting in rapid precipitation of relativistic electrons or relativistic electron microbursts.

Scalable engineering of multipartiteWstates in a spin chain

We propose a scalable scheme for engineering multipartite entangled $W$ states in a Heisenberg spin chain. The rather simple scheme is mainly built on the accumulative angular squeezing technique first proposed in the context of quantum kicked rotor for focusing a rotor to a delta-like angular distribution [I. Sh. Averbukh and R. Arvieu, Phys. Rev. Lett. 87, 163601 (2001)]. We show how the efficient generation of various $W$ states may be achieved by engineering the interaction between a spin chain (short or long) and a time-dependent parabolic magnetic field. Our results may further motivate the use of spin chains as a test bed to investigate complex properties of multipartite entangled states. We further numerically demonstrate that our scheme can be extended to engineer arbitrary spin chain quasimomentum states as well as their superposition states.

Dynamics of electrons in a parabolic magnetic field perturbed by an electromagnetic wave

In this paper we study the resonance interaction between monochromatic electromagnetic waves and fully magnetized electrons in a model parabolic magnetic field (like, e.g., in the Earth's magnetotail). The smallness of certain physical parameters allows us to approach this problem using perturbation theory for multiscale (slow-fast) systems: the study of the global interaction is reduced to the analysis of slow passages of particles through a resonance. At the resonance, two important phenomena occur: capture into resonance and scattering on resonance. We show that while the primary adiabatic invariant (magnetic moment or Larmor radius) remains conserved, these processes result in destruction of the second, longitudinal, adiabatic invariant. We find significant acceleration of particles by capture into resonance, while the scatterings on resonances lead to decrease in energy and chaotization of particles.

Simulation of electromagnetic ion cyclotron triggered emissions in the Earth's inner magnetosphere

[1] In a recent observation by the Cluster spacecraft, emissions triggered by electromagnetic ion cyclotron (EMIC) waves were discovered in the inner magnetosphere. We perform hybrid simulations to reproduce the EMIC triggered emissions. We develop a self-consistent one-dimensional hybrid code with a cylindrical geometry of the background magnetic field. We assume a parabolic magnetic field to model the dipole magnetic field in the equatorial region of the inner magnetosphere. Triggering EMIC waves are driven by a left-handed polarized external current assumed at the magnetic equator in the simulation model. Cold proton, helium, and oxygen ions, which form branches of the dispersion relation of the EMIC waves, are uniformly distributed in the simulation space. Energetic protons with a loss cone distribution function are also assumed as resonant particles. We reproduce rising tone emissions in the simulation space, finding a good agreement with the nonlinear wave growth theory. In the energetic proton velocity distribution we find formation of a proton hole, which is assumed in the nonlinear wave growth theory. A substantial amount of the energetic protons are scattered into the loss cone, while some of the resonant protons are accelerated to higher pitch angles, forming a pancake velocity distribution.

Communication at the quantum speed limit along a spin chain

Spin chains have long been considered as candidates for quantum channels to facilitate quantum communication. We consider the transfer of a single excitation along a spin-1/2 chain governed by Heisenberg-type interactions. We build on the work of Balachandran and Gong [V. Balachandran and J. Gong, Phys. Rev. A 77, 012303 (2008)] and show that by applying optimal control to an external parabolic magnetic field, one can drastically increase the propagation rate by two orders of magnitude. In particular, we show that the theoretical maximum propagation rate can be reached, where the propagation of the excitation takes the form of a dispersed wave. We conclude that optimal control is not only a useful tool for experimental application, but also for theoretical inquiry into the physical limits and dynamics of many-body quantum systems.

Doubly excited ferromagnetic spin chain as a pair of coupled kicked rotors

We show that the dynamics of a doubly excited Heisenberg spin chain, subject to short pulses from a parabolic magnetic field may be analyzed as a pair of quantum kicked rotors. By focusing on the two-magnon dynamics in the kicked XXZ model we investigate how the anisotropy parameter--which controls the strength of the magnon-magnon interaction--changes the nature of the coupling between the two "image" coupled kicked rotors. We investigate quantum state transfer possibilities and show that one may control whether the spin excitations are transmitted together, or separate from each other.

Electron dynamics in a parabolic magnetic field in the presence of an electrostatic wave

A study is made of the problem of electron dynamics in the presence of a plane electrostatic wave in a model in which the Earth’s magnetic field is parabolic. The problem is reduced to a Hamiltonian system with two degrees of freedom, which is investigated by the methods of perturbation theory. The structure of the phase space of the system is described, and the phenomena of capture into the resonance and scattering on the resonance are considered. It is shown that these phenomena lead to breaking of the second (longitudinal) adiabatic invariant and stochastization of the electron dynamics.