Vertical Magnetic Field Research Articles

Three-dimensional simulation of film boiling on a horizontal surface with magnetic field

This study conducts a numerical investigation into the three-dimensional film boiling of liquid under the influence of external magnetic fields. The numerical method incorporates a sharp phase-change model based on the volume-of-fluid approach to track the liquid–vapour interface. Additionally, a consistent and conservative scheme is employed to calculate the induced current densities and electromagnetic forces. We investigate the magnetohydrodynamic effects on film boiling, particularly examining the pattern transition of the vapour bubble and the evolution of heat transfer characteristics, exposed to either a vertical or horizontal magnetic field. In single-mode scenarios, film boiling under a vertical magnetic field displays an isotropic flow structure, forming a columnar vapour jet at higher magnetic field intensities. In contrast, horizontal magnetic fields result in anisotropic flow, creating a two-dimensional vapour sheet as the magnetic strength increases. In multi-mode scenarios, the patterns observed in single-mode film boiling persist, with the interaction of vapour bubbles introducing additional complexity to the magnetohydrodynamic flow. More importantly, our comprehensive analysis reveals how and why distinct boiling effects are generated by various orientations of magnetic fields, which induce directional electromagnetic forces to suppress flow vortices within the cross-sectional plane.

Influence of the turbulent magnetic pressure on isothermal jet emitting disks

The theory of jet emitting disks (JEDs) provides a mathematical framework for a self-consistent treatment of steady-state accretion and ejection. A large-scale vertical magnetic field threads the accretion disk where magnetic turbulence occurs in a strongly magnetized plasma. A fraction of mass leaves the disk and feeds the two laminar super-Alfv\'enic jets. In previous treatments of JEDs, the disk turbulence has been considered to provide only anomalous transport coefficients, namely magnetic diffusivities and viscosity. However, 3D numerical experiments show that turbulent magnetic pressure also sets in. We analyze how this turbulent magnetic pressure modifies the classical picture of JEDs and their parameter space. We included this additional pressure term using a prescription that is consistent with the latest 3D global (and local) simulations. We then solved the complete system of self-similar magnetohydrodynamic (MHD) equations, accounting for all dynamical terms. The magnetic surfaces are assumed to be isothermal, limiting the validity of our results to cold outflows. We explored the effects of the disk thickness and the level of magnetic diffusivities on the JED response to turbulent magnetic pressure. The disk becomes puffier and less electrically conductive, causing radial and toroidal electric currents to flow at the disk surface. Field lines within the disk become straighter, with their bending and shearing occurring mainly at the surface. Accretion remains supersonic, but becomes faster at the disk surface. Large values of both turbulent pressure and magnetic diffusivities allow powerful jets to be driven, and their combined effects have a constructive influence. Nevertheless, cold outflows do not seem to be able to reproduce mass-loss rates as large as those observed in numerical simulations. Our results are a major upgrade of the JED theory, allowing a direct comparison with full 3D global numerical simulations. We argue that JEDs provide a state-of-the-art mathematical description of the disk configurations observed in numerical simulations, commonly referred to as magnetically arrested disks (MADs). However, further efforts from both theoretical and numerical perspectives are needed to firmly establish this point.

Structure, morphology and crystallization behavior of PVDF/Co nanowire nanocomposites under horizontal and vertical magnetic fields

So far, very limited research has been carried out on the fabrication of polyvinylidene fluoride (PVDF) composited with anisotropic magnetic nanostructures such as nanowires or nanorods, which can potentially provide specific reactions to magnetic fields. Here, single crystal Co nanowires (CNWs) with an average length and diameter of about 220 and 12 nm, respectively, are synthesized using a solvothermal method, followed by adding them to PVDF matrix in order to prepare flexible PVDF/CNW nanocomposites by solvent casting and solution crystallization processes at room temperature. The nucleation and growth of PCNW nanocomposites are investigated in the absence and presence of horizontal and vertical magnetic fields. According to FESEM images, in addition to the direction of the applied magnetic field, the presence or absence of CNWs induces different effects on the size of spherulites and the configuration of polymer chains. By adding CNW to the PVDF matrix in the absence of a magnetic field and under a horizontal magnetic field, the size of the spherulites in the pure PVDF film increases about 67 % (from 3 to 5 μm) and 300 % (from 3 to 12 μm), respectively. Under a vertical magnetic field, the addition of CNW reduces the size of the spherulites to 1 μm, thereby forming a film with a combination of spherulites and filamentary structure likely due to the nanowire-nanowire, nanowire-chain and chain-chain interactions. Also non-contact flexible triboelectric nanogenerators of magnetic force are fabricated.

Solar active region evolution and imminent flaring activity through color-coded visualization of photospheric vector magnetograms

Context. The emergence of magnetic flux, its transition to complex configurations, and the pre-eruptive state of active regions are probed using photospheric magnetograms. Aims. Our aim is to pinpoint different evolutionary stages in emerging active regions, explore their differences, and produce parameters that could advance flare prediction using color-coded maps of the photospheric magnetic field. Methods. The three components of the photospheric magnetic field vector are combined to create color-combined magnetograms (COCOMAGs). From these, the areas occupied by different color hues are extracted, creating appropriate time series (color curves). These COCOMAGs and color curves are used as proxies of the active region evolution and its complexity. Results. The morphology of COCOMAGs showcases typical features of active regions, such as sunspots, plages, and sheared polarity inversion lines. The color curves represent the area occupied by photospheric magnetic field of different orientation and contain information pertaining to the evolutionary stages of active regions. During emergence, most of the region area is dominated by horizontal or highly inclined magnetic field, which is gradually replaced by more vertical magnetic field. In complex regions, large parts are covered by highly inclined magnetic fields, appearing as abrupt color changes in COCOMAGs. The decay of a region is signified by a domination of vertical magnetic field, indicating a gradual relaxation of the magnetic field configuration. The color curves exhibit a varying degree of correlation with active region complexity. Particularly the red and magenta color curves, which represent strong, purely horizontal magnetic field, are good indicators of future flaring activity. Conclusions. Color-combined magnetograms facilitate a comprehensive view of the evolution of active regions and their complexity. They offer a framework for the treatment of complex observations and can be used in pattern recognition, feature extraction, and flare-prediction schemes.

Shear-driven magnetic buoyancy in the solar tachocline: Dependence of the mean electromotive force on diffusivity and latitude

Abstract The details of the dynamo process that is responsible for driving the solar magnetic activity cycle are still not fully understood. In particular, whilst differential rotation provides a plausible mechanism for the regeneration of the toroidal (azimuthal) component of the large-scale magnetic field, there is ongoing debate regarding the process that is responsible for regenerating the Sun’s large-scale poloidal field. Our aim is to demonstrate that magnetic buoyancy, in the presence of rotation, is capable of producing the necessary regenerative effect. Building upon our previous work, we carry out numerical simulations of a local Cartesian model of the tachocline, consisting of a rotating, fully compressible, electrically conducting fluid with a forced shear flow. An initially weak, vertical magnetic field is sheared into a strong, horizontal magnetic layer that becomes subject to magnetic buoyancy instability. By increasing the Prandtl number we lessen the back reaction of the Lorentz force onto the shear flow, maintaining stronger shear and a more intense magnetic layer. This in turn leads to a more vigorous instability and a much stronger mean electromotive force, which has the potential to significantly influence the evolution of the mean magnetic field. These results are only weakly dependent upon the inclination of the rotation vector, i.e. the latitude of the local Cartesian model. Although further work is needed to confirm this, these results suggest that magnetic buoyancy in the tachocline is a viable poloidal field regeneration mechanism for the solar dynamo.

Manipulating Charge-to-Spin conversion via insertion layer control at the interface of topological insulator and ferromagnet

Strong spin–orbit coupling and highly spin-polarized surface states in topological insulators (TIs) are key parameters that explain their extremely high charge-to-spin conversion (CSC) efficiency at interfaces with ferromagnetic materials (FMs). This study focused on the influence of the insertion layer on the proximity effect occurring in a Co4Fe4B2/Bi2Se3 interface. Various insertion layers, including Au, MgO, and Se, were introduced to modulate the proximity effect from TI to FM and vice versa. X-ray photoelectron spectroscopy and transmission electron microscopy revealed that the Se insertion layer effectively suppresses the formation of an additional Bi layer, reducing intermixing against Co4Fe4B2. Electrical transport properties such as RXX and RXY under a vertical magnetic field show that the Se-inserted structure features the lowest anomalous Hall angle and exhibits a pristine topological surface state, indicating its potential for improving CSC efficiency. The Se-inserted structure exhibits the highest spin Hall angle among various heterostructures, according to results obtained from spin-torque ferromagnetic resonance. These findings highlight the importance of selecting an insertion layer and controlling the interface to optimize the spin-transport properties of TI-based spintronic devices and provide insights into the design of future spin devices.

Comparison of natural convection in liquid gallium under horizontal and vertical magnetic fields

The dynamics of two-dimensional natural convection in liquid metal under the influence of magnetic fields within a confined square enclosure are numerically investigated using a high-accuracy method. The study focuses on the flow transition process influenced by both horizontal and vertical magnetic fields, examining the impacts of temperature difference, magnetic field strength, and orientation on flow characteristics and heat transfer. The range of Rayleigh numbers (Ra) explored is from 104 to 106, while Hartmann numbers (Ha) vary from 0 to 100. Liquid gallium is used as the working fluid with a Prandtl number (Pr) of 0.025. Our investigation reveals rich variations in flow patterns, categorized into unsteady periodic, steady “two-in-one” vortex, and steady single vortex states. As Rayleigh numbers increase, a complex series of flow transitions is observed, leading to enhanced flow dynamics. The transition from a steady state to periodic motion is accompanied by a notable increase in heat transfer efficiency. However, increasing the strength of the magnetic field suppresses the flow. A sufficiently strong suppression transitions the flow from periodic motion back to a steady state, resulting in a gradual decrease in heat transfer efficiency. For the parameters considered, the suppression efficiency of horizontal magnetic fields is stronger than that of vertical ones, especially when Ra>6×105 and Ha=100, with a 14% greater suppression efficiency. A scaling law for heat transfer is also identified: Nu:Ra/Ha2γ, where 14≤γ≤12, independent of the magnetic field orientation.

Case Studies on Pre-eruptive X-class Flares using R-value in the Lower Solar Atmosphere

The R-value is a measure of the strength of photospheric magnetic polarity inversion lines in active regions (ARs). This work investigates the possibility of a relation between R-value variations and the occurrence of X-class flares in ARs, not in the solar photosphere, as usual, but above it in regions closer to where flares occur. The modus operandi is to extrapolate the Solar Dynamic Observatory’s Helioseismic and Magnetic Imager magnetogram data up to a height of 3.24 Mm above the photosphere and then compute the R-value based on the extrapolated magnetic field. Recent studies have shown that certain flare-predictive parameters such as the horizontal gradient of the vertical magnetic field and magnetic helicity may improve flare prediction lead times significantly if studied at a specific height range above the photosphere, called the optimal height range (OHR). Here, we define the OHR as a collection of heights where a sudden but sustained increase in R-value is found. For the eight case studies discussed in this paper, our results indicate that it is possible for OHRs to exist in the low solar atmosphere (between 0.36 and 3.24 Mm), where R-value spikes occur 48–68 hr before the first X-class flare of an emerging AR. The temporal evolution of R-value before the first X-class flare for an emerging AR is also found to be distinct from that of nonflaring ARs. For X-class flares associated with nonemerging ARs, an OHR could not be found.

Diagnosis Method of Failure in PEMFC Using Magnetic Fields

Proton exchange membrane fuel cells (PEMFCs) are currently used in various applications because they are compact, lightweight, and easy to start up. One of the challenges in PEMFCs is the improvement of gas diffusion. To overcome this challenge, appropriate water management in the gas diffusion layer and flow channels is necessary. Therefore, PEMFC diagnostic techniques are needed to detect flooding and plugging, which affect performance and efficiency. In this study, the magnetic field inside a PEMFC was analyzed to evaluate the changes caused by the internally generated water. Three cell types were used in the experiments: normal, channel-modified, and membrane–electrode assembly-modified cells. The results showed that the current was diverted because of the channel modification and water content, which resulted in a significant difference in the vertical magnetic field. This indicates that power generation inhibition due to flooding can be detected using vertical magnetic fields.

Diagnosis Method of Failure in PEMFC Using Magnetic Fields

Proton exchange membrane fuel cells (PEMFCs) are currently used in various applications because they are compact, lightweight, and easy to start up. One of the challenges in PEMFCs is the improvement of gas diffusion. To overcome this challenge, appropriate water management in the gas diffusion layer and flow channels is necessary. Therefore, PEMFC diagnostic techniques are needed to detect flooding and plugging, which affect performance and efficiency. In this study, the magnetic field inside a PEMFC was analyzed to evaluate the changes caused by the internally generated water. Three cell types were used in the experiments: normal, channel-modified, and membrane–electrode assembly-modified cells. The results showed that the current was diverted because of the channel modification and water content, which resulted in a significant difference in the vertical magnetic field. This indicates that power generation inhibition due to flooding can be detected using vertical magnetic fields.

Is short-offset frequency-domain controlled-source electromagnetic survey using an equatorial configuration a good choice on land?

The frequency-domain controlled-source electromagnetic (FD-CSEM) method can be used to collect data in both the large-offset plane-wave zones and the short-offset zone using an axial configuration within conductive marine environments. In contrast, the equatorial configuration is more commonly adopted for field surveys on land. However, selecting a suitable offset using an equatorial configuration on land remains a challenge. Therefore, the primary objective of this study was to choose a reasonable offset using an equatorial configuration on land. To this end, we compared the distribution and decay characteristics of the horizontal electric field. Additionally, we analyzed the detectability of the horizontal electric field to targets based on the root mean square (RMS) misfit and three-dimensional (3D) simulation at different offsets. The 3D simulation results show that the maximum normalized response at different offsets is similar, indicating that electric fields at different offsets share similar resolution limits. However, the horizontal electric field at small offsets (less than 3 times the target depth) only have the detectability for the target resistivity and are unable to make more precise distinctions on the target thickness. The detectability for the target thickness at very small offsets (about one time the target depth) is limited, as frequency sounding cannot be effectively established. A larger offset distance (larger than 4 to 6 times the target depth) is required when observing the vertical magnetic field compared to the horizontal electric field. Finally, we observed the electric field data at different offsets in the Kalatongke nickel–copper deposit in Xinjiang, China, which verifies our theoretical analysis.

Evolution of Characteristics of Vertical Electric Current and Magnetic Field in Active Regions of the Sun and their Relation to Powerful Flares

The study of evolution of magnetic field and electric currents in active regions of the Sun over a long-time interval is of interest for understanding the processes of accumulation and release of energy in them, leading to various phenomena that affect space weather. In this work, based on the photospheric vector magnetograms of the Helioseismic and Magnetic Imager instrument aboard the Solar Dynamics Observatory, an analysis was made of the evolution of a number of characteristics of the magnetic field and vertical electric current in three active regions 11158, 11675, and 12673 that produced class M and X flares, during the time from their origin in the Eastern hemisphere, during the passage through the solar disk, and until the disappearance near the Western limb with a step of 2 hours. The characteristics under consideration included: the power-law exponent of the probability density function of the absolute value of the vertical electric current density, the maximum of the absolute value of the vertical current density, the signed and unsigned total vertical currents and the unsigned total vertical and horizontal magnetic fluxes, the energy of the nonlinear force-free and potential magnetic fields, the free magnetic energy, and the number of islands with strong vertical current. Some regularities in the behaviour of the characteristics under consideration are found, in particular regarding the occurrence of solar flares. The correlation coefficients between pairs of these characteristics are calculated. Additionally, M. Aschwanden’s approach is shown to be promising for predicting the maximum X-ray class of a flare based on the calculation of the energy of the potential magnetic field in active regions. The results obtained can be used to predict powerful solar flares.

Numerical analysis of stacked HTS tapes in rotating magnetic fields using H and T-A formulations

Superconducting windings in rotating electrical machines and multi-phase transformers are subject to rotating magnetic fields. Most existing studies on the electromagnetic characteristics of stacked high-temperature superconducting (HTS) tapes focus on the influence of vertical magnetic field (VMF) and the transport current. The numerical study on characteristics of HTS stacked tapes in rotating magnetic fields (RMFs) has received less research attention. This paper presents two-dimensional models of stacked HTS tapes in RMF based on H and T-A formulations. AC losses obtained by the two formulations agree well in a single tape configuration but significantly differ in a stack configuration. The discrepancy increases as the number of stack layers and the stack interval increase. Under the same magnetic field amplitude, the RMF penetration depth in stacked tapes is higher than those of VMF and parallel magnetic field (PMF), and the parallel component of RMF causes higher AC loss in the end tapes of a stack. While the applied current increases the overall AC loss, it can significantly decrease the AC loss of the end tape. It is found that reducing the stack interval and replacing end tapes with tapes of higher critical current can significantly reduce the overall AC loss of stacked tapes in an RMF. These results are crucial for modeling superconducting machines and offer valuable insights into characterizing superconducting tapes in RMFs using numerical methods.

Effects of vertical magnetic field on natural convection of magnetic nanoscale fluid in a sinusoidal curved cavity partially filled with porous medium

In order to enhance heat dissipation effect of electronic components, this paper studied the cooling performance of a sinusoidal bending cavity partially filled with porous media under a vertical magnetic field, the main variables included nanofluids concentration (wt%=0.0, 0.1, 0.3, 0.5 %), magnetic strength (B=0.0, 0.01, 0.02, 0.03, 0.04 T), power (Q=10, 15, 20, 25 W), magnetic space layout (single-sided vertical, double sides vertical corresponding, bilateral vertical staggered), conclusion is that the double side vertical staggered magnetic field possesses better heat transfer, compared with deionized water, the Nu can be increased by 9.04 % at most under the double side vertical magnetic field, which provides some guidance for the heat transfer by convection in the heat exchange model of electronic equipment filled with some pore structure under the interference of external magnetic field.

Experimental investigation on magneto-convective flows around two differentially heated horizontal cylinders

Liquid metal buoyant flow around two differentially heated horizontal cylinders in the presence of a uniform vertical magnetic field is investigated experimentally. While magneto-convection in pipes or ducts has been studied theoretically and experimentally in recent years, data for heat transfer at immersed obstacles are rare and, to our knowledge, detailed experimental investigations on this fundamental magnetohydrodynamic problem do not exist. In the present work, two horizontal cylinders inserted into an adiabatic rectangular cavity filled with gallium–indium–tin are kept at constant temperatures to establish a driving temperature gradient in the surrounding liquid metal. The buoyancy-driven flow, quantified by the Grashof number $Gr$ , is varied in the range ${10^{6} \leq Gr \leq ~5\times 10^{7}}$ . With increasing magnetic field, expressed via the Hartmann number $Ha$ , different flow regimes are identified from measurements for $0 \leq Ha \leq ~3000$ . The effect of the electromagnetic force primarily consists in suppressing turbulence and damping the convective flow. The heat transfer is quantified in terms of the non-dimensional Nusselt number $Nu$ , and its dependence on $Gr/{Ha}^{2}$ , which is identified as the important group governing the flow, is discussed.

Overview of physics results from the ADITYA-U tokamak and future experiments

The ADITYA upgrade (ADITYA-U), a medium-sized (R0=75 cm,a=25 cm) conventional tokamak facility in India, has been consistently producing experiments findings by using circular and shaped-plasmas. Recognizing the plasma parameters aligning closely with the design parameters of circular limited plasmas, ADITYA-U shifted its focus toward exploring the operational regime for experimentation on saw-tooth and MHD phenomena. Moreover, ADITYA-U has made consistent advancements toward conducting preliminary plasma shaping experiments through the activation of top and bottom divertor coils utilizing hydrogen as well as deuterium fuels. Confinement is improved by a factor of ∼1.5 in D2 plasmas when compared to H 2 plasmas of ADITYA-U. Further, ADITYA-U operations emphasize preventing disruptions and runaway electrons (REs) to ensure safe operations for future fusion devices. Significant suppression of REs has been achieved in ADITYA-U with the application of pulsed localized vertical magnetic field (LVF) perturbation, thereby establishing the technique’s independence from the tokamak device. The successful RE mitigation requires a critical threshold of LVF pulse magnitude, which is approximately 1% of the toroidal magnetic field, and a minimum duration of ∼5 ms. Apart from this, several novel findings have been achieved in the ADITYA-U experiments, including the modification of sawtooth duration through gas-puff, the emergence of MHD-induced geodesic acoustic mode-like oscillations, the propagation of fast heat pulses induced by MHD activity, the control of RE dynamics through Gas-puffs, the propagation of pinch-driven cold-pulses, the transport and core accumulations of argon impurities, the mass dependency of plasma toroidal rotation and the detection of ‘RICE’ scaling, as well as the characterization of edge plasma using wall conditioning methods, such as glow discharge cleaning using a combination of Ar-H 2 mixture, localized wall cleaning by electron cyclotron resonant plasma, and the development of machine learning-based disruption predictions, will be discussed in this paper.

Deconfinement of runaway electrons by local vertical magnetic field perturbation

Runaway electron (RE) deconfinement and subsequent suppression is of prime importance for successful long-term operation of any tokamak. In this work, to deconfine and mitigate REs, the efficacy of local vertical field (LVF) perturbation has been explored numerically. LVF perturbation-assisted RE loss studies are carried out by simulating the drift orbits of the REs in magnetostatic perturbed fields and estimating the resulting orbit losses for different initial energies and magnitudes of LVF perturbation. To this end, the pre-existing PARTICLE code has been extended to the relativistic full-orbit-following code PARTICLE-3D (P3D) integrated with the magnetic field calculation code EFFI and plasma equilibrium field calculation code IPREQ to include the required fields for studying particle dynamics in general; this is then used to numerically model LVF perturbation-assisted RE deconfinement experiments conducted in the ADITYA tokamak. Simulation results show a significant (∼90%) deconfinement of REs with the application of LVF perturbation of a suitable amplitude (∼0.1% of the total magnetic field) in a preferred direction. The existence of a threshold magnitude of the applied field is also established, which is observed to be dependent on the energy of the REs. The simulation results reproduce all the experimental observations and reveal other interesting features of RE mitigation using LVF perturbation. The temporal map of orbiting time of REs shows that REs originating from the inboard side edge region ( ψ N > 0.5) of the plasma are relatively more prone to be lost with the application of suitable LVF perturbation than those originating from the plasma core. Interestingly, the simulation results demonstrate the existence of strong correlation between the safety factor (q) profile in the plasma edge region ( ψ N > 0.7) and the level of RE deconfinement using LVF perturbation.

Instability of double-diffusive magnetoconvection in a non-Newtonian fluid layer with cross-diffusion effects

The study explores the initiation of two-dimensional double-diffusive convection in a horizontal layer of an electrically conducting non-Newtonian Navier–Stokes–Voigt fluid, subjected to a uniform vertical magnetic field and cross-diffusion effects. The numerical results are presented by obtaining the analytical solutions for both steady and oscillatory onset scenarios. The viscoelastic nature of the fluid either delays or hastens the onset of oscillatory convection depending on the strength of solute concentration. The analysis also uncovers contradictions in the linear instability characteristics with and without cross-diffusion terms, even when other input parameters are identical. Under specific conditions, three novel phenomena are observed that are not typically seen in double-diffusive cases: (i) an electrically conducting Navier–Stokes–Voigt fluid layer, initially linearly stable in the presence of a magnetic field, can become destabilized with the addition of a heavy solute to the fluid's bottom; (ii) a stable double-diffusive electrically conducting Navier–Stokes–Voigt fluid layer can be destabilized by the application of a magnetic field; and (iii) the requirement of three critical values of the thermal Rayleigh number to determine linear instability, as opposed to the usual single value owing to the existence of disconnected closed convex oscillatory neutral curves. The results are shown to align with previously published findings in the limiting cases.

Design of a combined X–Y scanning magnet with high field uniformity for pencil beam scanning proton therapy

In proton therapy, scanning magnets play a crucial role in the treatment equipment. Specifically, in pencil beam scanning, these magnets are responsible for deflecting the proton beam, thereby enabling the illumination of the tumor’s precise location. To reduce the size of the scanning system, a combined X–Y scanning magnet is used instead of separate scanning magnets, which can reduce the overall size of the gantry. The design in this paper combines a window-shaped yoke and three sets of elephant-ear-shaped coils, and one of the coils generates a horizontal magnetic field while the other two coils generate a vertical magnetic field. By adjusting the distance between the coils and the shape of the coils at both ends, the magnetic integral field exhibits higher uniformity compared to other combined scanning magnets. The simulation results show that the integrated field achieves a uniformity of 0.84% in the horizontal direction and 0.60% in the vertical direction. Particle tracking simulation and steady-state thermal analysis were also conducted. After cutting a certain number of slits with the same size at the ends of the magnetic yoke, the magnet can meet the requirements of a suitable working temperature. This magnet design has the capability to effectively decrease the space utilized by the scanning system, consequently reducing the rotational radius of the frame and minimizing the equipment required.

Experimental confirmation of the linear relation between plasma current and external vertical magnetic field in EXL-50 spherical torus energetic electron plasmas

A three-fluid equilibrium plasma with bulk plasma and energetic electrons has been observed on the Xuanlong-50 (EXL-50) spherical torus, where the energetic electrons play a crucial role in sustaining the plasma current and pressure. In this study, the equilibrium of a multi-fluid plasma was investigated by analyzing the relationship between the external vertical magnetic field (B V), plasma current (I p), the poloidal ratio (β p) and the Shafranov formula. Remarkably, our research demonstrates some validity of the Shafranov formula in the presence of multi-fluid plasma in EXL-50 spherical torus. This finding holds significant importance for future reactors as it allows for differentiation between alpha particles and background plasma. The study of multi-fluid plasma provides a significant reference value for the equilibrium reconstruction of burning plasma involving alpha particles.