Bending Of Field Lines Research Articles

Hybrid Simulations of the Martian Magnetotail Twist

Three-dimensional global hybrid simulations are performed to explore how the interplanetary magnetic field (IMF), the Martian crustal fields, and planetary pickup ions affect the twisting of the Martian magnetotail. The results agree with previous studies that the crustal magnetic fields cause the Martian magnetotail to twist counterclockwise or clockwise depending on the sign of the IMF Y-component in the Mars solar orbital coordinates. However, the twist is more pronounced when the crustal fields are on the nightside, contradicting the early explanation that the crustal fields affect the twist through dayside magnetic reconnection between the crustal fields and the draped IMF. Additionally, planetary pickup ions also contribute to the twist because their mass loading slows down the plasma flow and leads to the bending of the magnetic field lines in the magnetotail. It is demonstrated that the twist inside Mars’ shadow in the near magnetotail region (at X = −1.5 R M, where R M is Mars’ radius) is mainly attributable to the crustal fields, while the influence of planetary pickup ions starts to dominate outside Mars’ shadow and in regions further away from Mars.

Photoresponse performance of Au (nanocluster and nanoparticle) TiO2: Photosynthesis, characterization and mechanism studies

In this study, gold (Au), nanoclusters (NC) and heterogeneous titanium dioxide (TiO2) were successfully synthesized by low-temperature photoelectron spectroscopy. The chemical structure of Au-TiO2 was characterized by XRD, EDX, XPS and HR-TEM. Optical properties were evaluated using PL and UV–Vis, and electrical properties were evaluated using CV, CP, UPS and EIS parameters. The results showed that Au nanocluster (NCs) were converted into Au nanoparticles (NPs) during high sunlight, and the transfer mechanism was examined. In addition, the produced nanoparticles can form a Schottky barrier with TiO2, which affects the band structure. Moreover, the simultaneous synthesis of nanoparticles and nanoclusters adds an extra dimension to the understanding of the photoelectronic behavior of structured photoelectrodes. Moreover, this research shows that good control of the photography process can result in more photos. This improvement is related to several factors, including the plasmonic field and coupling line bending.

Effect of hyper-resistivity on ballooning modes with resonant magnetic perturbations

The impact of hyper-resistivity on non-ideal ballooning modes (BMs) is studied in the presence of resonant magnetic perturbation (RMP) through considering the hyper-resistivity, resistivity and diamagnetic effect in the BM model with an equilibrium distorted by RMP, which is stable for ideal BMs. Similar to the resistivity, the hyper-resistivity is also destabilizing for the BMs, but RMPs make the mode spectrum of the BMs destabilized by the hyper-resistivity move towards the low toroidal mode number side on the flux surface with a safety factor slightly larger than the RMP resonance safety factor, where the growth rates of the BMs destabilized by the resistivity decrease due to RMP. When both the hyper-resistivity and the resistivity are considered, there is a sort of competitive relationship between them in determining the properties of BMs. If either of the hyper-resistivity term and the resistivity term is much larger than the other one, the instability of BMs is mainly determined by the larger one, and the effect of the smaller one is masked. The destabilizing mechanisms of the hyper-resistivity and the resistivity on BMs are similar, namely, the diffusion and dissipation of current and magnetic field weaken the stabilizing effect of magnetic field line bending. The research results may be important for understanding the enhancement of plasma transport and the mechanism of small edge localized mode (ELM) during ELM control with RMP.

Nonlinear interaction between double tearing mode and Kelvin–Helmholtz instability with different shear flows

The nonlinear interaction between the double tearing mode (DTM) and Kelvin–Helmholtz (KH) instabilities with different shear flow profiles has been numerically investigated via the use of a compressible magnetohydrodynamics (MHD) model. We focus on KH instabilities in weak and reversed magnetic shear plasmas with strong stabilizing effect of field line bending. Results show that KH instabilities coupled with DTMs occur in these plasmas and the KH mode dominates the instability dynamics, suggesting the crucial role of weak magnetic shear in the formation of high-mode harmonics. For symmetric flows, an asymmetric forced magnetic reconnection configuration is maintained during the growth phase, leading to interlocking of the modes. Additionally, this investigation of the DTM-KH instability interaction contributes to our understanding of the nonlinear reconnection mechanism in the regime of weak and reversed magnetic shear plasmas, which is relevant for astrophysical and fusion studies.

Semi-classical description of electrostatics and quantization of electric charge

Abstract In this work, we present an explanation of the electric charge quantization based on a semi-classical model of electrostatic fields. We claim that in electrostatics, an electric charge must be equal to a rational multiple of the elementary charge of an electron. However, the charge is quantized if the system has certain boundary conditions that force the wavefunction representing an electric field to vanish at specific surfaces. Next, we develop the corresponding model for the electric displacement vector. It is demonstrated that a number of classical results, e.g. bending of field lines at the interface of two dielectric media, method of images, etc are all consistent with the predictions of this model. We also present the possible form of Gauss's law (or Poisson's equation), to find the wavefunctions of the field from a source charge distribution, in this model.

Bending of electric field lines and light-ray trajectories in a static gravitational field

It is well known that the light-ray trajectories follow a curved path in a gravitational field. This has been confirmed observationally where light rays coming from distant astronomical objects are seen to get bent in Sun’s gravitational field. We explore here the bending of electric field lines due to gravity. We determine, from a theoretical perspective, not only the exact shapes of the bent trajectories of light rays, emitted isotropically by a source supported in a gravitational field, but also demonstrate that the electric field lines of a charge, supported in a gravitational field, follow exactly the trajectories of light rays emitted isotropically from a source at the charge location. From a detailed examination of the electrostatic field of a charge accelerated uniformly in the instantaneous rest frame, exploiting the strong principle of equivalence, we determine the bending of the electric field lines of a charge in a gravitational field. The fraction of electric field lines crossing a surface, stationary above or below the charge in the gravitational field, are shown to be exactly similar to the fraction of light-ray trajectories intersecting that surface, emanating from a source lying at the charge location. On the other hand, for a freely falling charge in the gravitational field there is no such bending of electric field lines. The field lines continue to extend in radial straight lines from the instantaneous ‘present’ position of the charge, as do the trajectories of light rays spreading away from the instantaneous position of a freely falling source in the gravitational field. The electric field configuration of a freely falling charge in the gravitational field is shown to be exactly the same as that of a charge moving uniformly in an inertial frame with velocity equal to the instantaneous ‘present’ velocity of the freely falling charge.

Theoretical study of effect of hyper-resistivity on linear stability of ballooning mode

The coupling of ballooning mode and peeling mode forms the so-called peeling-ballooning mode, which is widely used in the physical explanation of the edge localized mode (ELM). The nonlinear platform simulation based on the non-ideal peeling-ballooning mode model successfully explained the ELM experimental results. Therefore, exploring the influences of various non-ideal effects on the ballooning mode in the edge transport barrier is very important in controlling the ELM in the future fusion reactors. Among the reports on non-ideal effects, there are few reports involving the effect of hyper-resistivity caused by anomalous electron viscosity on ballooning mode. It has been found that the hyper-resistivity has a destabilizing effect on the ballooning mode, but the associated physical mechanism is still unclear. Therefore, it is necessary to systematically explore the influence of hyper-resistivity on the ballooning mode theoretically by introducing hyper-resistivity into the ballooning mode model. The linear growth rate of ideal and non-ideal ballooning mode are solved by the shooting method for the derived eigenvalue equation of non-ideal ballooning mode containing hyper-resistivity, finite resistivity and diamagnetic drift effects, and the dependence of ballooning mode on hyper-resistivity is also explored under different conditions. The results show that the hyper-resistivity may destabilize the ballooning mode, and the physical mechanism is that the current diffusion effect caused by the hyper-resistivity weakens the stabilizing effect of the magnetic field line bending on the ballooning mode. When both the resistivity and hyper-resistivity are considered, they are in a competitive relationship. When the ratio of hyper-resistivity to resistivity is relatively high, hyper-resistivity plays a dominant role, and the destabilizing effect of resistivity will be shielded by hyper-resistivity, and vice versa. The destabilization effect of hyper-resistivity on ballooning modes is enhanced with the increase of the toroidal mode number. The hyper-resistivity will destabilize the original stable modes once the toroidal mode number exceeds a certain threshold. Further studies show that the threshold is inversely proportional to the ratio of hyper-resistivity to resistivity. The research results have important reference value for the control of edge localized modes in low-collisionality edge plasma in future fusion reactors.

Elongation effect on beta-induced Alfvén eigenmode

Beta induced Alfvén eigenmode (BAE) can be an important candidate for ion loss in burning plasmas. Elongation effect on BAE has been investigated by the gyrokinetic eigenvalue code DAEPS in this work. We construct a shaped equilibrium model by modifying local s − α model with which the capability of the DAEPS code has been extended to study the elongation effect. It is discovered that the BAE growth rate first increases with elongation factor κ, reaches a maximum and then decreases. This trend occurs for many different values of η i. We find that, in the weak or moderate elongation region, the BAE instability is reactive type and mainly determined by the fluid/MHD effects, namely the combination of stabilizing field line bending term and destabilizing interchange drive in the vorticity equation. However, in the strong elongation region, the BAE instability becomes dissipative and is mainly driven by the wave–particle resonance effect embedded in δW k since the fluid driving damps away. It is also discovered that the wave–particle resonance decreases with elongation in this region, which is due to the decrease of the geodesic curvature with elongation and leads to the decrease in the growth rate of BAE.

Destabilization of low-frequency modes (LFMs) driven by a thermal pressure gradient in EAST plasmas with q min ⩽ 2

Mode structures and excitation conditions for the low-frequency modes (LFMs) have been investigated in experimental advanced superconducting tokamak (EAST) plasmas with q min ⩽ 2. Two different stages/categories of the LFM instabilities are observed during the oscillation of annular/central collapse events: (I) the upward sweeping frequency of LFMs; (II) the upward frequency jumpsof LFMs. The annular/central events are triggered by the m/n = 2/1 double tearing modes with different q-profiles, while the LFMs are characterized by higher mode numbers m/n = 4/2, 6/3, …, where m and n are the poloidal and toroidal mode numbers, respectively. The maximum radial coverage of the LFMs is located in the annular region of 1.97 2.07 m with the normalized minor radius 0.2 0.4, while the higher-frequency (or upward sweeping frequency) branch is more localized to the radial position of 2 2.02 m (q min). The frequency characteristics of upward sweeps or upward jumps of the LFMs are mainly attributed to the change in the q-profile, e.g. the upward sweeping frequency in stage I is caused by q min decreasing. Accordingly, the linear wave properties of LFMs in EAST with weak/reversed magnetic shear are studied numerically and analytically based on a general fishbone-like dispersion relation. Without considering the contribution of energetic ions, it is shown that the LFM with Alfvénic polarization is an MHD-unstable kinetic ballooning mode with frequency of the order of the ion diamagnetic drift frequency. Several important factors for the excitation of LFM instability are analyzed: (1) the role of energetic ions is unimportant, and the LFMs can be excited under the two conditions of with/without energetic ions; (2) the higher τ = T e/T i with larger η i = L ni /L Ti are required, namely the normalized pressure gradient α ∝ (1 + τ)(1 + η i) should be large enough to overcome the stability effect of finite field line bending; (3) the weak/reversed shear q-profile with q min ⩽ 2 and suitable S ≡ (r/q)(q″)1/2 are required.

Studies of inter-pad distance in Low Gain Avalanche Detectors

The effective inter-pad distance of low gain avalanche detector prototypes for ATLAS-HGTD from two producers were investigated. The dependence of the effective inter-pad distance on bias voltage and fluence was systematically measured with Transient Current Technique using different laser wavelengths. Bending of the electric field lines at the edges of the electrodes was found to be the reason for the difference between measured and nominal inter-pad distances. The effective inter-pad distances were also simulated and compared to the measurements.

A 3D magnetohydrodynamic simulation of the propagation of a plasma plume transverse to applied magnetic field

We have carried out a 3D ideal-MHD (magnetohydrodynamic) simulation to study the evolution of a laser-generated plasma plume in a moderate external magnetic field (0.13 T) oriented perpendicular to the flow direction of the plasma plume. The simulation shows that the plasma plume pushes the external magnetic field lines outward in the direction of the expansion. This leads to the compression and bending of the magnetic field lines. The force resulting from the change in shape and the density of the magnetic field lines opposes the expansion of the plume. An elliptic layer of shocked plasma is formed at the plasma/external field interface leaving a cavity in the plume core due to the outward expansion and the inertia of the plume. As the plasma pressure drops due to expansion, the imbalance between the magnetic energy and the internal energy results in the collapse of the cavity. These observations have striking similarities with the observations of the experiments (Behera et al 2017 Phys. Plasmas 24 033511) performed recently to study the plasma plume expansion in the presence of an external transverse magnetic field. This similarity indicates that the physical mechanisms dominantly governing the plasma plume expansion in the moderate magnetic field are aptly described in the ideal MHD regime. The studies thus show that the laser-generated plasma plume can be utilized to carry out interesting experiments on MHD phenomena in a simple laboratory setup.

Two-dimensional Particle-in-cell Simulation of Magnetic Reconnection in the Downstream of a Quasi-perpendicular Shock

Abstract In this paper, by performing a two-dimensional particle-in-cell simulation, we investigate magnetic reconnection in the downstream of a quasi-perpendicular shock. The shock is nonstationary, and experiences cyclic reformation. At the beginning of the reformation process, the shock front is relatively flat, and part of the upstream ions are reflected by the shock front. The reflected ions move upward in the action of the Lorentz force, which leads to the upward bending of the magnetic field lines at the foot of the shock front, and then a current sheet is formed due to the squeezing of the bending magnetic field lines. The formed current sheet is brought toward the shock front by the solar wind, and the shock front becomes irregular after interacting with the current sheet. Both the current sheet carried by the solar wind and the current sheet associated with the shock front are then fragmented into many small filamentary current sheets. Electron-scale magnetic reconnection may occur in several of these filamentary current sheets when they are convected into the downstream, and magnetic islands are generated. A strong reconnection electric field and energy dissipation are also generated around the X line, and a high-speed electron outflow is also formed.

Chromospheric plasma ejection above a pore

ABSTRACT We present high spatial resolution observations of short-lived transients, ribbons and jet-like events above a pore in Ca ii H images where fine structure, like umbral dots, light bridges and penumbral microfilaments, is present in the underlying photosphere. We found that current layers are formed at the edges of the convective fine structure, due to the shear between their horizontal field and the ambient vertical field. High vertical electric current density patches are observed in the photosphere around these events, which indicates the formation of a current sheet at the reconnection site. In the framework of past studies, low altitude reconnection could be the mechanism that produces such events. The reconnection is caused by an opposite polarity field produced by the bending of field lines by convective downflows at the edge of pore fine structure.

A three-dimensional reduced MHD model consistent with full MHD

Within the context of a viscoresistive magnetohydrodynamic (MHD) model with anisotropic heat transport and cross field mass diffusion, we introduce novel three-term representations for the magnetic field (background vacuum field, field line bending, and field compression) and velocity (E→×B→ flow, field-aligned flow, and fluid compression), which are amenable to three-dimensional treatment. Once the representations are inserted into the MHD equations, appropriate projection operators are applied to Faraday's law and the Navier-Stokes equation to obtain a system of scalar equations that is closed by the continuity and energy equations. If the background vacuum field is sufficiently strong and the β is low, MHD waves are approximately separated by the three terms in the velocity representation, with each term containing a specific wave. Thus, by setting the appropriate term to zero, we eliminate fast magnetosonic waves, obtaining a reduced MHD model. We also show that the other two velocity terms do not compress the magnetic field, which allows us to set the field compression term to zero within the same reduced model. Dropping also the field-aligned flow, a further simplified model is obtained, leading to a fully consistent hierarchy of reduced and full MHD models for 3D plasma configurations. Finally, we discuss the conservation properties and derive the conditions under which the reduction approximation is valid. We also show that by using an ordering approach, reduced MHD equations similar to what we got from the ansatz approach can be obtained by means of a physics-based asymptotic expansion.

The structure of magnetically dominated energy-extracting black hole magnetospheres: Dependencies on field line angular velocity

Abstract If a magnetically dominated magnetosphere is to extract a black hole’s rotational energy and transmit it to distant regions, then the inner light surface of that magnetosphere must lie within the ergoregion. That inner light surface condition limits the angular velocity of magnetic field lines. We take the distribution of magnetic field line angular velocity on the horizon to be a useful proxy for inner light surface location and study how different distributions affect the structure of energy-extracting magnetospheres. Within magnetospheres that exhibit differential field line bending towards both the azimuthal axis and the equatorial plane, we find that the total Poynting flux energy directed outward along the azimuthal axis can vary by over a factor of 100 for a single value of black hole spin.

Dynamics of ideal modes and subsequent ELM crashes in 3D tokamak geometry from external magnetic perturbations

The impact of three-dimensional (3D) tokamak geometry from external magnetic perturbations on edge instabilities has been examined in high confinement mode plasmas with edge localised modes (ELMs) in ASDEX Upgrade. The 3D geometry has been probed using rigidly rotating MP fields. The measured distortions of the plasma boundary are compared to single-fluid ideal magnetohydrodynamic (MHD) equilibria using VMEC and MARS-F applying ideal and resistive MHD, whereas VMEC uses only ideal MHD. Both codes accurately reproduce the measured radial displacements of the edge density and temperature profiles in amplitude, toroidal phase and their dependence on the applied poloidal mode spectrum.The induced 3D geometry distorts the local magnetic shear, which locally reduces the stabilising effect from field-line bending at certain most unstable field lines. Around these field lines, we observe additional stable ideal MHD modes with clear ballooning structure in-between ELMs. After their immediate appearance, they saturate and then grow on timescales of the pedestal pressure recovery. The subsequent ELMs show strongly localised magnetic perturbations of the initial crash and accompanied energetic electrons around the same most unstable field lines. These are strong signatures that filaments at the ELM onset preferentially erupt on these most unstable (‘bad’) field lines with their unfavourable 3D geometry where preceding ballooning modes are observed.

North‐South Asymmetric Kelvin‐Helmholtz Instability and Induced Reconnection at the Earth's Magnetospheric Flanks

AbstractWe present a three‐dimensional study of the plasma dynamics at the flank magnetopause of the Earth's magnetosphere during mainly northward interplanetary magnetic field periods. Two‐fluid simulations show that the initial magnetic shear at the magnetopause and the field line bending caused by the dynamics itself (in a configuration taken as representative of the properties of the flank magnetopause) influence both the location where the Kelvin‐Helmholtz (KH) instability and the induced magnetic reconnection take place and their nonlinear development. The KH vortices develop asymmetrically with respect to the Earth's equatorial plane where the local KH linear growth rate is maximal. Vortex‐driven reconnection processes take place at different latitudes, ranging from the equatorial plane to midlatitude regions but only in the hemisphere that turns out to be the less KH unstable. These results suggest that KH‐induced reconnection is not limited to specific regions around the vortices (inside, below, or above) but may be triggered over a broad and continuous range of locations in the vicinity of the vortices.

MHD instabilities in astrophysical plasmas: very different from MHD instabilities in tokamaks!

The extensive studies of MHD instabilities in thermonuclear magnetic confinement experiments, in particular of the tokamak as the most promising candidate for a future energy producing machine, have led to an ‘intuitive’ description based on the energy principle that is very misleading for most astrophysical plasmas. The ‘intuitive’ picture almost directly singles out the dominant stabilizing field line bending energy of the Alfvén waves and, consequently, concentrates on expansion schemes that minimize that contribution. This happens when the wave vector of the perturbations, on average, is perpendicular to the magnetic field . Hence, all macroscopic instabilities of tokamaks (kinks, interchanges, ballooning modes, ELMs, neoclassical tearing modes, etc) are characterized by satisfying the condition , or nearly so. In contrast, some of the major macroscopic instabilities of astrophysical plasmas (the Parker instability and the magneto-rotational instability) occur when precisely the opposite condition is satisfied: . How do those instabilities escape from the dominance of the stabilizing Alfvén wave? The answer to that question involves, foremost, the recognition that MHD spectral theory of waves and instabilities of laboratory plasmas could be developed to such great depth since those plasmas are assumed to be in static equilibrium. This assumption is invalid for astrophysical plasmas where rotational and gravitational accelerations produce equilibria that are at best stationary, and the associated spectral theory is widely, and incorrectly, believed to be non-self adjoint. These complications are addressed, and cured, in the theory of the Spectral Web, recently developed by the author. Using this method, an extensive survey of instabilities of astrophysical plasmas demonstrates how the Alfvén wave is pushed into insignificance under these conditions to give rise to a host of instabilities that do not occur in laboratory plasmas.

E × B flow shear drive of the linear low-n modes of EHO in the QH-mode regime

A new model for the edge harmonic oscillations (EHOs) in the quiescent H-mode regime has been developed, which successfully reproduces the recent observations in the DIII-D tokamak. In particular, at high E × B flow shear only a few low-n kink modes remain unstable at the plasma edge, consistent with the EHO behavior, while at low E × B flow shear, the unstable mode spectrum is significantly broadened, consistent with the low-n broadband electromagnetic turbulence behavior. The model is based on a new mechanism for destabilizing low-n kink/peeling modes by the E × B flow shear, which underlies the EHOs, separately from the previously found Kelvin–Helmholtz drive. We find that the differential advection of mode vorticity by sheared E × B flows modifies the 2D pattern of mode electrostatic potential perpendicular to the magnetic field lines, which in turn causes a radial expansion of the mode structure, an increase of field line bending away from the mode rational surface, and a reduction of inertial stabilization. This enhances the kink drive as the parallel wavenumber increases significantly away from the rational surface at the plasma edge where the magnetic shear is also strong. This destabilization is also shown to be independent of the sign of the flow shear, as observed experimentally, and has not been taken into account in previous pedestal linear stability analyses. Verification of the veracity of this EHO mechanism will require analysis of the nonlinear evolution of low-n kink/peeling modes so destabilized in the linear regime.

Stabilization of numerical interchange in spectral-element magnetohydrodynamics

Auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. The projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code Sovinec et al. [17], provided that the projections introduce numerical dissipation.