Magnetic Mirror Research Articles

Design and construction of the magnetic mirror magnets of the space plasma environment research facility (SPERF)

The Space Plasma Environment Research Facility aims to research the space plasma physics in the laboratory. Two elliptical magnets are used to form a magnetic mirror field simulating the interplanetary magnetic field to investigate the magnetic reconnection at the magnetopause and magnetotail of the earth on the ground. To perform the research, the issues facing the magnets in terms of high pulsed current, vacuum, plasma, and mechanical support must be resolved. The paper presents their design and construction process to settle these issues. A series of measures are adopted to enhance insulation, reduce the gas leakage, and avoid tip discharge, ranging from the dielectric layers to the Inconel spraying. A transition structure considering the effect of the strong pulsed current is designed for connecting the magnet's leads to the cables of its pulsed power supply. In addition, a supporting and motion mechanism is proposed to hold the magnets and drive them to move. The strength of the mechanism is assessed by the static mechanical analysis for the extreme magnetic force load. Meanwhile, a connection scheme compatible with the supporting and motion mechanism is proposed to guide the cables through the vacuum vessel. The great mechanical stress occurring at the interface between the cables and the stainless-steel blocks due to the sheared magnetic force is reduced considerably by a fixing plate. The results in the paper are valuable for designing the magnet conducting a large pulsed current in the vacuum environment for plasma applications.

The 3D magnetic topology and plasma dynamics in open stochastic magnetic field lines

The thermal quench triggered by locked modes is known to be mainly due to open stochastic magnetic field lines connected to the wall boundary. It is essential to understand the 3D structure of open stochastic field lines since it determines the overall plasma dynamics in the system. In this study, we analyze the 3D magnetic topology for two key concepts, the connection length Lc and the effective magnetic mirror ratio Meff, and present a comprehensive picture of electron and ion dynamics related to the magnetic topology. The connection length determines the 3D structure of the ambipolar potential, and a sharp potential drop across distinct Lc regions induces the E × B transport and mixing across the field line. The confinement of electrons and ions along the field line is determined by the ambipolar potential and Meff configuration. Electron and ion temperatures in magnetic hills (Meff<1) are lower than in magnetic wells (Meff>1) because particles in magnetic hills are more likely to escape toward the wall boundary along the field line. The mixing between the magnetic wells and hills by E × B and magnetic drift motions results in collisionless detrapping of electrons and ions, which reduces their temperature efficiently. Numerical simulations of two different magnetic configurations demonstrate the importance of the collisionless detrapping mechanism, which could be the main cause of plasma temperature drop during the thermal quench.

Plasma diagnosis of an unclosed E × B drift thruster with a visible ionization zone

The traditional annular closed-loop E × B drifting Hall thruster is limited by its compact structure. Two-dimensional (2D) distribution of the plasma parameters inside the discharge channel cannot be accurately measured, thus directly hindering further understanding of the discharge process. In this paper, we propose to employ an unclosed E × B drift thruster with a visible (UDTv) ionization zone to conduct research into the effects of the crossed electric field and magnetic field on the plasma distribution inside the discharge channel. Experiments showed that the UDTv presented discharge similar to a Hall thruster, especially the low-frequency oscillation related to the discharge voltage. A 2D symmetrically crescent-shaped distribution of plasma inside the channel with a hollow zone located near the maximum of the magnetic field was clearly captured by optical imaging and an emission spectrometer. Correlation between the location of the maximal magnetic gradient and the 2D ionization zone configuration was verified. A decreased magnetic mirror effect at the location of the maximum magnetic field enhanced the electron–wall interaction, inducing near-wall conduction and secondary electron emission. The electron temperature presented a canyon distribution, resulting in a bimodal configuration of the plasma density. Increased flowrate lowered the ionization inside the channel and transformed the plasma distribution into a unimodal structure because of enhanced electron conduction and the lower electron temperature. Generally, the ability to capture the correlation between 2D plasma distribution and the magnetic field inside the discharge channel was successfully demonstrated, thus proposing new ideas for further research into the internal plasma of Hall thrusters.

Particle simulations on propagation and resonance of lower hybrid wave launched by phased array antenna in linear devices

In this work, we performed first-principles electromagnetic-kinetic simulations to study a phased antenna array and its interaction with deuterium plasmas within the lower hybrid range of frequency. We first gave wave accessibility and resonance results, which agree well with theoretical prediction. In addition, we further investigated the antenna power spectrum with different antenna phases in the presence of the plasma and compared it with that in a vacuum, which directly indicates wave coupling and plasma absorption. Furthermore, for the case with zero phasing difference, our simulation results show that, albeit the launch is away from the accessibility region, tunneling effect and mode conversion occurred, which enhanced coupling and absorption. Moreover, consistent interactions between the injected wave and the plasma concerning various antenna phase differences are shown. We presented the inchoate response of the plasma in terms of the launching directions. Our results could be favorable for the engineering design of wave heating experiments with a tunable phased antenna array in linear devices, such as simple magnetic mirrors or tandem mirrors.

Tunable bilayer dielectric metasurface via stacking magnetic mirrors.

Functional tunability, environmental adaptability, and easy fabrication are highly desired properties in metasurfaces. Here we provide a tunable bilayer metasurface composed of two stacked identical dielectric magnetic mirrors. The magnetic mirrors are excited by the interaction between the interference of multipoles of each cylinder and the lattice resonance of the periodic array, which exhibits nonlocal electric field enhancement near the interface and high reflection. We achieve the reversible conversion between high reflection and high transmission by manipulating the interlayer coupling near the interface between the two magnetic mirrors. Controlling the interlayer spacing leads to the controllable interlayer coupling and scattering of meta-atom. The magnetic mirror effect boosts the interlayer coupling when the interlayer spacing is small. Furthermore, the high transmission of the bilayer metasurface has good robustness due to the meta-atom with interlayer coupling can maintain scattering suppression against positional perturbation. This work provides a straightforward method to design tunable metasurface and sheds new light on high-performance optical switches applied in communication and sensing.

Spatially selective excitation of spin dynamics in magneto-photonic crystals by spectrally tunable ultrashort laser pulses

Abstract In this work, we tackle the problem of the spatially selective optical excitation of spin dynamics in structures with multiple magnetic layers. The 120 fs circularly polarized laser pulses were used to launch magnetization precession in an all-dielectric magneto-photonic crystals (MPC) formed by magnetic layers sandwiched between and inside two magnetic Bragg mirrors. Optical pump-probe experiments reveal magnetization precession triggered via ultrafast inverse Faraday effect with an amplitude strongly dependent on the pump central wavelength: maxima of the amplitude are achieved for the wavelength tuned at the cavity resonance and at the edge of the photonic bandgap. The optical impact on the spins caused by the inverse Faraday effect and spectrum of this effect are found to correlate mostly to the direct Faraday effect. We show that even though the pump laser pulses propagate along the whole structure tuning their wavelength allows localization of a larger spin precession either in the cavity layer or in the Bragg mirror layers selectively. The results pave the way to the ultrafast optical control of magnetization dynamics at a sub-wavelength scale that is vital for modern magneto-photonics and magnonics.

Ion temperature effects on plasma flow in the magnetic mirror configuration

Effects of finite ion temperature on the plasma flow in the converging–diverging magnetic field, the magnetic mirror, or equivalently, magnetic nozzle configuration are studied using a quasineutral paraxial two-fluid MHD model with isothermal electrons and warm magnetized ions. The ion acceleration was studied with an emphasis on the role of the singularity at the sonic point transition. It is shown that the regularity of the sonic point defines a global solution describing plasma acceleration from subsonic to supersonic velocity. Stationary accelerating solutions were obtained and compared with the time dependent dynamics, confirming that the solutions of the time-dependent equations converge to the stationary solutions and, therefore, are stable. The effects of the ion pressure anisotropy were analyzed using the Chew–Golberger–Low model and its generalization. It is shown that the mirror force (manifested by the perpendicular ion pressure) enhances plasma acceleration. The role of ionization and charge exchange on plasma flow acceleration have been investigated.

Randomized Controlled Trial of the Effects of Repetitive Transcranial Magnetic Stimulation and Mirror Therapy on Phantom Limb Pain in Amputees

To investigate the effect of repetitive transcranial magnetic stimulation (rTMS) on phantom limb pain (PLP) in amputees, and to compare the therapeutic effect with that of mirror therapy (MT). The study was designed as a randomized controlled trial. The evaluators were blinded, while the subjects and the therapists were unblinded. Subjects were randomly assigned to either the rTMS group or the MT group with a computer-generated random number table. From June 2018 to December 2020, from out of 45 amputee patients screened for the study, 30 who met the inclusion criteria were recruited for the study. All patients were recruited from the Rehabilitation Medicine Center, West China Hospital, Sichuan University. In the end, 4 patients withdrew from the study and 26 patients (12 in the rTMS group and 14 in the MT group) completed the prescribed treatment and evaluation. The rTMS group was given rTMS (1 Hz, 15 min, 5 d/week) for 2 weeks in addition to conventional rehabilitation therapy, while the MT group received MT (corresponding movements of limbs, 15 min, 5 d/week) for 2 weeks in addition to conventional rehabilitation therapy. PLP was evaluated by the Visual Analogue Scale (VAS) and Douleur Neuropathique 4 Questions (DN-4). Subjects were assessed before treatment ( t 0), immediately after the completion of the treatment ( t 1) and 3 months after the completion of the treatment ( t 2). The mean age of the 26 patients was 39.73±12.64. There were 15 males and 11 females. According to the reported description of the characteristics of the PLP by the patients, the characteristics with the highest incidence were tingling, stabbing, numbing, electric shocks and burning in descending order. There was no significant difference in the incidence of PLP characteristics between the two groups ( P>0.05). The two groups had comparable baseline data, showing no significant difference in VAS and DN-4 between the two groups at t 0 ( P>0.05). At t 1 and t 2, the VAS and DN-4 scores were decreased from those of t 0, showing statistically significant difference in both groups ( P<0.01 for both scores). In the rTMS group, there was no significant difference between VAS and DN-4 scores at t 1 and those at t 2 ( P>0.05). In the MT group, the VAS and DN-4 scores at t 2 were significantly lower than those of t 1 ( P<0.05). There was no statistically significant difference between the rTMS group and MT group in the changes in pain measurements, i.e., VAS and DN-4 scores, before and after the intervention ( P>0.05). The 26 patients who completed the experiment showed no dizziness, headache, or other abnormalities during the study. The results of this study indicate that repetitive transcranial magnetic stimulation could improve PLP in amputees, and the improvement effect was comparable to that of mirror therapy.

Influence of the upstream axial magnetic mirror field on the plume characteristics in the full cylindrical Hall thruster

Full cylindrical Hall thruster holds considerable promise in terms of its low wall erosion rate and long-lifetime performance advantages. As far as we know, its upstream magnetic mirror field plays a fundamental role in the determination of plasma behavior and hence the thruster performance. In this paper, a series of upstream axial magnetic mirror fields with different axial gradient values were generated by adjusting the inverse-electromagnetic coil currents near the upstream channel and its effect on the plume characteristics were investigated. The experiment results indicate that under a low magnetic mirror field with 44.8 G/mm gradient value, a bulb-like plasma discharge region emitting a visible high-intensity light is discovered near the thruster exhaust, its plume manifests a hollow profile with a plume angle of 77°. In contrast, as the axial gradient value of magnetic mirror field increases from 44.8 G/mm to 72.5 G/mm, this bulb-like plasma region near exhaust shrink gradually to disappear along with the plume angle decreasing to 65°. Meanwhile, the anode efficiency enhances significantly (from 16% to 28%) correspondingly. According to the analysis of ion current, electron current and ion energy distribution, the observed strong plasma discharge near the thruster exhaust should be intimately related with the extension of the ionization region towards exit due to the weak electron confinement under the low magnetic mirror field. However, the larger upstream magnetic mirror field could diminish the leaking of local electrons towards the anode efficiently, which could not only intensify the ionization, but also induce the shrink of the ionization region axially towards the upstream channel and the clearer separation of acceleration region from the ionization region. Ultimately, the enhanced propellant utilization and current utilization, higher ion energy and the collimated plume are achieved. This work provides a feasible way to recognize the ionization and acceleration process under the mirror-like magnetic field of the miniaturized full cylindrical Hall thruster.

Study on the Correlation between Magnetic Field Structure and Cold Electron Transport in Negative Hydrogen Ion Sources

In most negative hydrogen ion sources, an external magnet is installed near the extraction region to reduce the electron temperature. In this paper, the self-developed CHIPIC code is used to simulate the mechanism of a magnetic filter system, in the expansion region of the negative hydrogen ion source, on “hot” electrons. The reflection and the filtering processes of “hot” electrons are analyzed in depth and the energy distribution of electrons on the extraction surface is calculated. Moreover, the effects of different collision types on the density distribution of “cold” electrons along the X-axis and the spatial distribution of “cold” electrons on the X−Z plane are discussed. The numerical results show that the electron reflection is caused by the magnetic mirror effect. The filtering of “hot” electrons is due to the fact that the magnetic field constrains most of the electrons from reaching the vicinity of the extraction surface, being that collisions cause a decay in electron energy. Excitation collision is the main decay mechanism for electron energy in the chamber. The numerical results help to explain the formation process of “cold” electrons at the extraction surface, thus providing a reference for reducing the loss probability of H−.

Perfect magnetic mirror based on magnetic dipole scattering in all-dielectric resonators

Perfect magnetic mirrors are important optical devices for the development of novel optical detectors, solar cells, and imaging devices. They have the property of only reversing the magnetic field of a light wave upon reflection, for instance, in functional optical metasurfaces. To design an optical magnetic mirror, high-refractive-index dielectric nanostructures that support strong magnetic dipole (MD) response in the optical wavelength range are used. However, the spectral overlap between the MD and electric dipole in dielectric resonators degrades the magnetic mirror reflection. Here, we propose and demonstrate a perfect optical magnetic mirror metasurface that totally reflects an incident wave without electric field phase change. In this perfect magnetic mirror, the electric dipole radiation is completely suppressed by the radiation of the anapole mode in the spectral range where the destructive interference between the electric dipole and toroidal dipole occurs. By fine-tuning the size parameters of the dielectric resonators, we show near-perfect MD scattering as a result of the spectral overlap between MD resonance and anapole mode. The optical magnetic mirror can be tuned from the visible to near-infrared range by scaling the sizes of the resonators. The MD scattering resonators promote the perfect magnetic mirror, a promising platform for designing photodetectors, biological sensors, and reflected waveplates.

Electron beam-plasma discharge in GDT mirror trap: experiments on plasma start-up with electron gun

The paper describes experiments on the injection of an electron beam into a gas at the gas dynamic trap (GDT) and develops a technique for creating a starting plasma with parameters sufficient for its subsequent heating by neutral beams. It is found that a relatively thin electron beam is capable of ionizing plasma in the entire volume of the trap, and the plasma turbulence it excites is capable of accelerating some of the electrons to energies tens of times higher than the initial energy of the beam. It is shown that, in contrast to early experiments on tabletop open traps, collective beam relaxation under GDT conditions occurs in the vicinity of the entrance magnetic mirror. Since the electron cyclotron frequency in this region significantly exceeds the plasma frequency, it is necessary to study the mechanism of a beam-plasma discharge under these conditions. As a first step along this path, we measure the radial diffusion coefficient of fast particles, as well as the rate at which they gain energy.

Energy distribution and bremsstrahlung spectra of energetic electrons escaping from the ECR plasma with high energy input

Electron energy distribution function (EEDF) is an important characteristic that defines the processes of plasma confinement and ionization. Understanding such processes is crucial for the proper tuning of ion sources. In the ECR plasma, the EEDF is significantly non-Maxwellian, and the exact shape remains still unknown. As the initial step towards the EEDF resolving, the energy distribution of the electrons lost from the magnetic mirror trap was directly measured in a wide range of neutral gas pressures and gyrotron powers along with bremsstrahlung spectra. A series of experiments were performed on the newly constructed Gasdynamic Ion Source for Multipurpose Operation (GISMO) facility allowing record-breaking specific energy input into the plasma. Obtained distributions showed unconventional behavior as the function of source parameters. The EEDF shape and the bremsstrahlung spectra showed a threshold qualitative change with the gyrotron power presumably as a result of the development of kinetic instabilities.

Mode transition of the cylindrical Hall thruster with the near-anode cusp magnetic field

There are two distinct discharge modes in a 200 W cylindrical Hall thruster with the near-anode cusp magnetic field. In mode I, a divergent plume is observed at a low discharge voltage. When the discharge voltage rises over 280 V, an apparent discharge mode transition occurs along with the sharp decreasing of discharge current (by 9.9%) and electron current (by 26%) and apparent narrowing of plume angle (by 12%), bringing a convergent plume (mode II). In mode I, the most probable ion energy of ion energy distribution function declines monotonically with the increasing of plume angle. However, a non-monotonic variation characteristic of most probable ion energy is indicated in mode II, which suggests that there are two ionization regions in this mode. These novel mode transition phenomena should be attributed to the unique near-anode cusp magnetic field. In low discharge voltage conditions (mode I), as the energies of the electron population are low, they are trapped in the near-axial magnetic mirror field, and a cylindrical ionization region along thruster axis is established. When the discharge voltage rises over the threshold voltage occurring mode transition, the energies of the electron population are enhanced and the energetic electrons could escape from the mirror field and reach the upstream crossed electric and magnetic fields. As a result, an additional ionization region related to E × B drift is formed in the upstream region. The competitive relationship between the upstream ionization related to E × B drift and the near-axial ionization related with magnetic mirror field should be the leading cause of mode transition.

High-voltage breakdown in the injection-extraction region of the CANREB EBIS: A possible mechanism

OmniTrak simulations were performed in the 40°K injection-extraction region near the collector trumpet of the CANREB EBIS to understand the nature of chronic electrical breakdowns of PEEK feedthroughs. These feedthroughs are designed to route high-voltage wires (up to +15 kV) from room temperature to each drift-tube at 4°K, while operating in the strong superconducting semi-Helmholtz field. The electric field strength |E| at the PEEK feedthroughs are ∼ 7 × 105 V/m within about 2-3 mm of the surroundings at ground potential. When simulating only bare wires (with no PEEK feedthroughs), |E| increases by about 1 order-of-magnitude to > 106 V/m in the same region. Assuming a 3 Tesla magnetic field, electrons starting with 0 eV near the PEEK feedthroughs undergo helical motions due to -drift and demonstrate reflections from magnetic mirror effects. A combination of this helical motion, reflecting mirror trajectories, and attraction of electrons to exposed HV wires may be responsible for the ongoing HV breakdown of insulating feedthroughs in this region of the EBIS. Solving this problem requires complete ground-shielding of all HV wiring to eliminate |E| and should encapsulate all wires to prevent breakdown paths.

Bulk and surface electronic structure of Bi4Te3 from GW calculations and photoemission experiments

We present a combined theoretical and experimental study of the electronic structure of stoichiometric Bi$_4$Te$_3$, a natural superlattice of alternating Bi$_2$Te$_3$ quintuple layers and Bi bilayers. In contrast to the related semiconducting compounds Bi$_2$Te$_3$ and Bi$_1$Te$_1$, density functional theory predicts Bi$_4$Te$_3$ to be a semimetal. In this work, we compute the quasiparticle electronic structure of Bi$_4$Te$_3$ in the framework of the $GW$ approximation within many-body perturbation theory. The quasiparticle corrections are found to modify the dispersion of the valence and conduction bands in the vicinity of the Fermi energy, leading to the opening of a small indirect band gap. Based on the analysis of the eigenstates, Bi$_4$Te$_3$ is classified as a dual topological insulator with bulk topological invariants $\mathbb{Z}_2$ (1;111) and magnetic mirror Chern number $n_M=1$. The bulk $GW$ results are used to build a Wannier-functions based tight-binding Hamiltonian that is further applied to study the electronic properties of the (111) surface. The comparison with our angle-resolved photoemission measurements shows excellent agreement between the computed and measured surface states and indicates the dual topological nature of Bi$_4$Te$_3$.

Importance of stepwise ionization from the metastable state in electron cyclotron resonance ion thrusters

In electron cyclotron resonance (ECR) thrusters, the plasma mode transition is a critical phenomenon because it determines the maximum thrust performance. In ECR ion thrusters, ionization generally occurs in the magnetic confinement region, where electrons are continuously heated by ECR and confined by magnetic mirrors. However, as the flow rate increases, ionization is also observed outside the magnetic confinement region, and this induces the plasma mode transition. In our previous work, two-photon absorption laser-induced fluorescence (TALIF) analysis revealed that the stepwise ionization from the metastable state plays an important role in the ionization process. However, the distribution of the stepwise ionization has not yet been revealed because of the long lifetime of the metastable state. In this study, this distribution was investigated using one experimental and two numerical approaches. First, TALIF was applied to two types of gas injection with clear differences in thrust performance and ground-state neutral density distribution. In the first simulation, the metastable state particle simulation was used to estimate the excitation rate distribution. In the second study, simulations of the electric field of microwaves were used to estimate the contribution of the stepwise ionization to the plasma density. The experimental and numerical results revealed that the stepwise ionization spreads outside the magnetic confinement region because of the diffusion of metastable particles, and this spread induces the plasma mode transition, explaining the difference between the two types of gas injection.

Investigation of the confinement of high energy non-neutral proton beam in a bent magnetic mirror

By using the particle-in-cell (PIC) simulation method, we studied how the proton beam is confined in a bent magnetic mirror. It is found that the loss rate of the charged particles in a bent mirror is less than that in the axi-symmetric mirror. For a special bent mirror with the deflection angle of the coils α = 45°, it is found that the loss rate reaches maximum value at certain ion number density where the ion electrostatic oscillation frequency is equal to the ion cyclotron frequency. In addition, the loss rate is irrelevant to the direction of the proton beam. Our results may be helpful to devise a mirror. In order to obtain the least loss rate, we may choose an appropriate deflection angle, and have to avoid a certain ion number density at which the ion electrostatic oscillation frequency is equal to the ion cyclotron frequency.

The Kinetic Expansion of Solar-wind Electrons: Transport Theory and Predictions for the Very Inner Heliosphere

Abstract We propose a transport theory for the kinetic evolution of solar-wind electrons in the heliosphere. We derive a gyro-averaged kinetic transport equation that accounts for the spherical expansion of the solar wind and the geometry of the Parker spiral magnetic field. To solve our three-dimensional kinetic equation, we develop a mathematical approach that combines the Crank–Nicolson scheme in velocity space and a finite-difference Euler scheme in configuration space. We initialize our model with isotropic electron distribution functions and calculate the kinetic expansion at heliocentric distances from 5 to 20 solar radii. In our kinetic model, the electrons evolve mainly through the combination of ballistic particle streaming, the magnetic mirror force, and the electric field. By applying fits to our numerical results, we quantify the parameters of the electron strahl and the core part of the electron velocity distributions. The strahl fit parameters show that the density of the electron strahl is around 7% of the total electron density at a distance of 20 solar radii, the strahl bulk velocity and strahl temperature parallel to the background magnetic field stay approximately constant beyond a distance of 15 solar radii, and β ∥s (i.e., the ratio of the strahl parallel thermal pressure to the magnetic pressure) is approximately constant with heliocentric distance at a value of about 0.02. We compare our results with data measured by the Parker Solar Probe. Furthermore, we provide theoretical evidence that the electron strahl is not scattered by the oblique fast-magnetosonic/whistler instability in the near-Sun environment.

Driven nonlinear damping and mode coupling in a superconducting levitated magnet

The magnetic flux pinning phenomenon enables high-$Q$ trapping of a magnet above a superconductor. In practice, the trapped magnet can undergo nonlinear mode coupling and dissipation as its vibration can induce variations of the magnetic field and vortex displacement on the superconductor surface. Here we study nonlinear interactions between vibrational modes of a levitated magnetic mirror above a superconducting disk in vacuum conditions. We observe that by exciting one vibrational mode of the levitated mirror, the vibrational noise of another mode can be suppressed by more than 17 dB. We attribute this unique noise suppression mechanism to the mode coupling and nonlinear dissipation caused by the driven magnetic inhomogeneity of the levitated object. The results suggest that noise reduction of a vibrational mode is possible by driving another orthogonal mode.