Toroidal eddy currents induced in the tokamak vacuum vessel play a critical role in plasma startup, volt-second consumption, and magnetic field configuration. However, the direct and accurate measurement of these currents is challenged by the presence of strong background magnetic fields—on the order of several Tesla—generated by the central solenoid (CS) and poloidal field (PF) coils, with currents often exceeding several mega-ampere-turns. This paper presents a novel dual-loop fiber optic current sensor (FOCS) system developed specifically for the EXL-50U spherical tokamak to directly measure toroidal eddy currents. The diagnostic setup includes an inner FOCS loop dedicated to measuring the plasma current (I p), and an outer loop for detecting the total enclosed toroidal current, which comprises contributions from the plasma, all external coils, and the eddy currents. A specially designed hardware compensation coil physically cancels the dominant magnetic flux generated by the CS leads in real time, significantly enhancing the signal-to-noise ratio. Experimental results demonstrate that the system is capable of measuring eddy currents even under strong background fields. The measured waveforms are in good agreement with numerical simulations, validating both the diagnostic approach and the electromagnetic model of the device. The proposed diagnostic system offers a robust and reliable tool for optimizing plasma startup scenarios in spherical tokamaks.

More often than not, mean-field descriptions for random composites neglect microscopic interactions between elastic and plastic processes. They do so by homogenizing purely elastic and purely plastic deformations separately to compound them additively. While appealing simplifications in the structure of macroscopic constitutive relations naturally ensue, discomforting complications in accompanying aspects of the descriptions unfortunately arise. When cast within the framework of generalized standard materials, the problem is to seek approximate mean-field potentials based on reduced sets of effective internal variables that provide a partial but hopefully accurate characterization of the evolving microscopic state of the composite and that, at the same time, comply with the generalized standard structure. One of the simplest approximations compatible with this line of thinking consists in assuming intraphase plastic homogeneity and then identifying effective internal variables with the plastic deformation within each constituent phase. Experience has recurrently shown, however, that intraphase plastic heterogeneity is an ineludible ingredient of any worthy approximation. Against this state of affairs, a formalism leading to mean-field potentials for random composites that account for elastic and plastic deformations concomitantly is elaborated. Deformations within constituent phases are described by archetypical potentials for rate-dependent elastoplasticity with combined isotropic and kinematical hardening. Plastic deformation fields are then additively decomposed into irrotational and solenoidal fields in such a way that variational approximations available for purely elastic and purely plastic potentials become applicative to elastoplastic potentials. The resulting mean-field potentials exhibit a generalized standard structure with a finite set of effective internal variables containing the phase averages of the irrotational and solenoidal fields. Crucially, these potentials are sensitive to intraphase plastic heterogeneities. Illustrative results for particulate composites with isotropic phases are presented to highlight the role of these effective internal variables in elastoplastic transitions and residual stresses.

ABSTRACT Cardiac arrests are common worldwide due to unhealthy lifestyles and food habits. Cardiopulmonary Resuscitation (CPR) is an effective way of saving patients immediately after cardiac arrest. Manual CPR is traditionally more popular, wherein chest compressions are given by a single or double rescuer. This involves adequate training to do CPR, and manual fatigue is also unavoidable. Even qualified professionals may struggle to perform chest compressions at the CPR‐recommended depth and rate. Thus, robotic chest compression manipulators are explored to improve resuscitation. The combination of robotics and automation may improve patient survival rates. Our aim is to develop a device to perform high‐quality compressions per minute up to 50 mm depth as per the American Heart Association (AHA) protocol. The device consists of three pneumatically soft‐actuated air muscles that are designed to work together to compress between 80 and 120 times/min at 260 N. A solenoid valve regulates airflow while a microprocessor controls compression. The solenoid coil's deactivation duration is precisely controlled to 50 ms to create compression depth equivalent to one‐third of the manikin's chest breadth. Our test results showed that the developed device's performance on the specialized CPR manikin (Resusci Anne QCPR, Norway) is comparable to manual compression readings as per AHA protocols. Thus, we propose it as a new suitable concept and design for a mechanical CPR device for hospital and out‐of‐hospital environments.

Design and experimental verification of the quench detection system for the CFETR central solenoid model coil

Abstract The next generation tokamak aiming to carry out D-T experiments and to demonstrate power generation, is under development at the Institution of Plasma Physics, Chinese Academy of China (ASIPP). A hybrid magnet configuration is proposed for the central solenoid (CS) coil of this tokamak, a high-temperature superconducting (HTS) coil is inserted into an outer Nb3Sn coil for increasing the flux. Minimization of the coupling losses is investigated in the Nb3Sn Cable-In-Conduit Conductor (CICC) with rectangular cross-section for the outer CS coils using numerical modeling and experimental verification. The AC loss was measured on several candidate conductors with a superconducting AC Dipole at ASIPP and the numerical modeling was performed with the JackPot-AC/DC© model, which was developed by University of Twente (UT). The data from the experiments tested in UT were used for calibrating and validating the model computations. With the model, further optimization on cable parameters was then carried out. The results show that the twist pitch of the first stage and the twist pitches ratio have an important impact on the rectangular CICC coupling loss, and the influences of these two factors are related. In addition, the use of a rectangular cross-section CICC can have significant advantages when used in CS magnets.

Breast cancer has become the most common cancer among women worldwide. Magnetic resonance imaging (MRI) can compensate for the limitations of x-ray breast scanning and ultrasound in the early detection of patients with dense breasts. However, limited by the density of MRI units per million population and the cost of high-field MRI systems, breast MRI is not widely used in breast cancer screening. Ultra-low field MRI can potentially promote the application of MRI for breast detection, but specialized breast radio-frequency (RF) coils are required. The RF coils with a resonant frequency of 2.131MHz include a high uniformity transmit coil with a low depth-to-width ratio and a four-channel phased-array receive coil, which are designed specifically for a 50 mT runway-type lightweight magnet with a vertical static magnetic field to achieve mobile breast MRI. The transmit coil adopts the variant solenoid structure. To ensure the RF field uniformity within the target area is greater than 95%, the transmit coil's dimension parameters were calculated using a nonlinear programming algorithm. Due to the main magnetic field being a vertical field, the receive coil employs a four-channel phased-array to achieve high sensitivity, and the overlapping area between the channels was optimized to achieve decoupling by simulating the minimum mutual inductance. Finally, the RF coils' performance was verified through a phantom experiment on the self-developed mobile 50 mT breast MRI prototype. The non-uniformity of the RF field of the modified solenoid coil in the target area can reach 3.7%. The adjacent receive coils have a minimum mutual inductance of 0.232 nH, as the overlapping area is 16.12%. The performance results indicated that the designed transmit coil has a low return loss (RL) of -44.4dB and a high Q value of 46.55. The S12 value between adjacent channels of the receive coil is below -25dB, and between non-adjacent channels is about -12dB. The imaging ability of the designed RF coils was validated by the phantom experiments on the 50 mT breast MRI prototype. The designed transmit and receive coils in this paper can meet the requirements of the 50 mT mobile MRI with a vertical static magnetic field, which is expected to promote the application of ultra-low field MRI technology in breast cancer screening.

The SPring-8 Angstrom Compact free-electron LAser (SACLA) linear accelerator utilizes a dc gun with a thermionic cathode, known for delivering high beam quality, excellent operational stability, and low maintenance requirements. In the second part of our design study, we present a comprehensive beam dynamics analysis of the SACLA dc electron gun and outline a roadmap toward achieving submicrometer ( 0.1 μ m ) beam emittance. We provide both analytical and numerical estimates of four key sources contributing to emittance growth: (i) image = charge effects on the cathode, (ii) nonlinear space-charge forces arising from imperfect beam edge geometry, (iii) aberrations in the accelerating field, and (iv) solenoid field aberrations due to longitudinal–transverse momentum exchange. The analysis yields a closed-form expression for the superposition of emittance growth mechanisms, highlighting an “interference” term that amplifies the net emittance when space-charge and solenoid effects coexist. To address the challenge of emittance growth, we propose a compact hybrid magnet that ensures strong longitudinal confinement of the magnetic field. This confinement allows placement of the hybrid magnet in close proximity to the gun exit, thus mitigating emittance growth effectively, while having a negligible magnetic field on the cathode. The hybrid magnet design is achieved by symmetrically positioning permanent ring magnets on either side of a solenoid, enabling fine control over the field distribution and “squeezing in” it longitudinally. Our findings offer new insights applicable to low-voltage continuous-wave very high-frequency guns and superconducting radio-frequency electron guns.

The Edge illumination (EI) multi-contrast imaging technique has emerged as a research focus in the fields of X-ray imaging due to its capability of simultaneously retrieving absorption, phase, and scattering images. For the classical EI method, it is essential to displace the mask in a direction perpendicular to the slits with submicron-level accuracy to obtain multiple images from which contrast information can be derived. However, this mask displacement not only adds to the complexity of the motion-control subsystems (which could also be a possible source of mechanical instability) but also increases the overhead time required for mechanical displacement, thus limiting the optimal imaging efficiency. In this study, we propose an EI imaging method that relies on electromagnetic focus displacement (EI-EFD) rather than mechanical mask displacement. Through detailed analysis, it is demonstrated that the X-ray focus displacement and the mask displacement are equivalent for sampling the illumination curve for each detector pixel under certain reasonable conditions. By utilizing an X-ray tube source with its focus position controlled by an external electromagnetic field produced by a homemade solenoid coil, we successfully captured multi-contrast images of a frozen hairtail, a pen, and a plastic rod. We believe that this proposed method will enhance the practicality of EI systems and facilitate their broader application.

The fundamental wavelength of undulator radiation and free-electron lasers depends on the period and magnetic field strength of the undulator. Shortening the undulator period and increasing the magnetic field strength are essential for achieving higher-energy radiation and increased flux. The most promising approach to date has been an undulator utilizing high-temperature superconductors (HTSs), particularly the bulk HTS staggered-array undulator (BHSAU). In this Letter, we demonstrated that adding a ring HTS can increase the magnetic field strength of the BHSAU to two to three times. It was found that the ring HTS not only provides an additional undulator magnetic field but also shields the solenoid magnetic field, allowing for stronger solenoid field variations without affecting the electron beam. This, in turn, enhances the magnetic field generated by the bulk HTS itself, resulting in an exceptionally strong undulator field. The magnetic field of the undulator is more than ten times stronger than that of in-vacuum permanent magnet-based structures of similar design, significantly enhancing the performance of synchrotron radiation and free-electron lasers.

We present a compact CPT-based atomic magnetometer utilizing a directly modulated VCSEL and phase-sensitive detection. The device achieves a static magnetic field measurement accuracy of 20 pT (1σ) with directional consistency exceeding 99.6%. Calibration using saddle and solenoidal coils yields a linear response with coil coefficients of 708.4 nT/mA and 2466.3 nT/mA, respectively, closely matching an optically pumped Mx-type magnetometer. The results validate the feasibility of portable, high-sensitivity CPT magnetometers for real-time vector magnetic field sensing.

Abstract Accurate measurement of electrical conductivity in water-based samples is essential for applications ranging from water quality monitoring to biological sensing. However, direct-contact methods are prone to electrode degradation, while indirect-contact methods often suffer from undefined current paths. This study introduces a non-invasive, non-contact technique for conductivity measurement in water-based samples using radiofrequency (RF) probe loading, leveraging inductive losses induced by eddy currents in conductive media. Changes in the quality factor of the RF probe are analyzed to establish a direct proportionality between inductive losses and sample conductivity. This relationship is validated across solenoidal, loop-gap resonator, and surface coil designs with cylindrical and planar samples. Theoretical equations, derived from classical electromagnetism and the principle of reciprocity, closely align with experimental results, revealing the critical role of probe geometry and resonant frequency in measurement sensitivity. The findings demonstrate robust performance across diverse ionic solutions including samples with flow, achieving cost-effective measurement with minimal hardware. This method allows differentiation between samples with differing conductivity, even when absolute conductivity values cannot be determined. This makes it especially suited for analyzing complex, heterogeneous materials like foods or biological samples. The radio frequency probe loading approach offers a versatile alternative to conventional conductivity measurement methods, with potential for real-time, non-invasive monitoring in dynamic systems.

The paper considers a possibility to use the figure-8 synchrotron as a replacement of the Nuclotron for acceleration of polarized proton and deuteron beams at the NICA accelerator complex. The synchrotron arcs are placed inside the NICA collider tunnel. The presented design enables preservation of polarization for any ion species (p, d, 3He, etc.) in the entire energy range of the synchrotron. Because of its shape, the ring operates in the spin transparency mode. The direction of polarization is controlled by a spin navigator which uses weak solenoidal fields. The synchrotron can also be used as a storage ring for high precision experiments with polarized beams beyond its use as an injector to the collider. The results of numerical simulations of spin dynamics for acceleration of protons and deuterons are presented.

Abstract We describe a resonant cavity search apparatus for axion dark matter constructed by the quantum sensors for the hidden sector collaboration. The apparatus is configured to search for QCD axion dark matter, though also has the capability to detect axion-like particles, dark photons, and some other forms of wave-like dark matter. Initially, a tuneable cylindrical oxygen-free copper cavity is read out using a low noise microwave amplifier feeding a heterodyne receiver. The cavity is housed in a dilution refrigerator (DF) and threaded by a solenoidal magnetic field, nominally 8 T. The apparatus also houses a magnetic field shield for housing superconducting electronics, and several other fixed-frequency resonators for use in testing and commissioning various prototype quantum electronic devices sensitive at a range of axion masses in the range 2.0– 40 μ eV c − 2 . The apparatus as currently configured is intended as a test stand for electronics over the relatively wide frequency band attainable with the TM 010 cavity mode used for axion searches. We present performance data for the resonator, DF, and magnet, and plans for the first science run.

Abstract A new methodology for achieving the formation and compressional heating of a Field Reversed Configuration (FRC) plasmoid has been investigated both theoretically and experimentally at the University of Washington and MSNW. This approach, based on previous FRC empirical scaling, is expected to achieve fusion gain as large as 10. For the FRC, the fusion gain, G ~ φp·Be2 where φp is the FRC poloidal flux and Be the confining axial magnetic field. G is essentially independent of the FRC radial scale making feasible a small, compact reactor. The necessary φp (> 60mWb) is achieved by employing a large formation chamber (~ 0.8m radius) combined with the requisite axial magnetic field reversal time (Eθ ~ 20kV/m) for generating a high initial temperature (Ti > 1keV) FRC. By employing the dynamic formation procedure, the FRC is accelerated to ~100-150km/s. This subsonic velocity is maintained as the FRC is translated through a series of cylindrical coils of decreasing radius but of sufficient length (> LFRC) and number (~ 10) to produce essentially an isentropic and adiabatic radial wall-compression of the equilibrium FRC. The final stage is a 12cm diameter, 3-6m long confinement and burn chamber with a vacuum field of 7-9T produced by external solenoidal coils inside the flux conserving cylinder. The vacuum field is compressed by the FRC on insertion to 35 T resulting in fusion gain conditions for the 2-5 ms transit. The large ratio of FRC to inner wall radius (0.85) substantially lowers the FRC edge pressure thereby greatly reducing both particle and thermal losses. The resulting D-T fusion yield for the 3.5MJ FRC is 20-40MJ/pulse. The final ejection and expansion of the FRC into a large, low field mirror chamber provides a mechanism for FRC energy recovery. The experimental justification and the physics basis for the entire process from formation through burn of the Compact FRC Fusion Reactor (CFR2) concept is presented.

Global magnetohydrodynamic (MHD) instabilities are assessed for a reference H-mode scenario designed for the China Fusion Engineering Demo Reactor (CFEDR) with a normalized beta of and a safety factor of . For this scenario, the Troyon no-wall beta limit and ideal-wall beta limit computed by MARS-F code are and , respectively. This means that it is stable against the external kink mode for the target plasma pressure. However, even with a stable classical tearing mode (TM) via optimization of the q-profile, the 2/1 neoclassical tearing mode (NTM) remains significantly unstable and can be triggered if the seed island exceeds 5 cm in width. Therefore, electron cyclotron current drive can be employed to stabilize this mode, with the necessary driven current amounting to 1% of the plasma current. Additionally, in both the plasma ramp-up and high-confinement flat-top stages, the error field tolerance of CFEDR ( 10−5 and 10−5) is larger than that of ITER ( 10−5 and 10−5), respectively, in Ohmic cases. The positional accuracy of the poloidal field coils and center solenoid coil should be controlled within 3.5 mm for shifts in order to reduce the intrinsic error field to within the specified tolerance. This reference H-mode scenario is being designed to operate in high-q 95 and high-plasma pressure, which will reduce the error field tolerance due to the resonant field amplification effect and NTM locking, as well as the actual beta limit. Therefore, further assessments for dynamic error field correction with higher plasma pressure are required.

Using solid-state MRI and a double-tuned RF coil to quantify bone matrix and mineral densities in rat bones.

Kirchhoff’s current law was originally derived for systems such as telegraphs that switch in 0.1 s. It is used widely today to design circuits in computers that switch in ~0.1 nanoseconds, one billion times faster. Current behaves differently in one second and one-tenth of a nanosecond. A derivation of a current law from the fundamental equations of electrodynamics—the Maxwell equations—is needed. Here is a derivation in one line: div curlB/μ0=0=divJ+(εr−1)ε0∂E/∂t+ε0∂E/∂t=divJtotal. Maxwell’s ‘true’ current is defined as Jtotal. The universal displacement current found everywhere is ε0∂E/∂t. The conduction current J is carried by any charge with mass, no matter how small, brief, or transient, driven by any source, e.g., diffusion. The second term (εr−1)ε0∂E/∂t is the usual approximation to the polarization currents of ideal dielectrics. The dielectric constant εr is a dimensionless real number. Real dielectrics can be very complicated. They require a complete theory of polarization to replace the (εr−1)ε0∂E/∂t term. The Maxwell current law divJtotal=0 defines the solenoidal field of total current that has zero divergence, typically characterized in two dimensions by streamlines that end where they begin, flowing in loops that form circuits. Note that the conduction current J is not solenoidal. Conduction current J accumulates significantly in many chemical and biological applications. Total current Jtotal does not accumulate in any time interval or in any circumstance where the Maxwell equations are valid. Jtotal does not accumulate during the transitions of electrons from orbital to orbital within a chemical reaction, for example. Jtotal should be included in chemical reaction kinetics. The classical Kirchhoff current law div J=0 is an approximation used to analyze idealized topological circuits found in textbooks. The classical Kirchhoff current law is shown here by mathematics to be valid only when J≫ε0∂E/∂t, typically in the steady state. The Kirchhoff current law is often extended to much shorter times to help topological circuits approximate some of the displacement currents not found in the classical Kirchhoff current law. The original circuit is modified. Circuit elements—invented or redefined—are added to the topological circuit for that purpose.

UDC 517.5 Given a PDE, in [E. López-González, E. A. Martínez-García, R.~Torres-Córdoba, Chaos, Solitons and Fractals, 73, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra $\mathbb A$ and a suitable affine vector field $\varphi$ with respect to which the components of all functions $\mathcal L\circ\varphi$ are solutions, where $\mathcal L$ is differentiable in a sense of Lorch with respect to $\mathbb A.$ If we consider the 3D cyclic algebra and a suitable 3D affine map $\varphi,$ then we get families of solutions for the Laplace equation with three independent variables.

Scattering of electron in the field of a narrow solenoid with alternating current

Abstract The high-temperature superconducting (HTS) central solenoid (CS) coil in spherical tokamaks drives the plasma current by carrying rapidly varying currents, ultimately confronting the critical challenge of severe AC losses. To reduce AC losses, an interleaved transposition winding method based on a special joint for inductive balancing is proposed. This study develops a multi-physics framework integrating an equivalent circuit model, T–A formulation, and thermal analysis. This framework is applied to study a 1/10-scale CS model coil co-wound with 36 HTS tapes, which attains a peak field-on-coil of 13.3 T at 7.2 kA terminal current and a maximum magnetic ramp rate of 70 T s −1 , thereby validating the proposed winding methodology. Numerical results demonstrate a tenfold reduction in hysteresis losses via the novel winding strategy, while the coil’s peak temperature remains below 54 K post-discharge. This method enables non-twisted stacked HTS coils to achieve both fabrication simplicity and AC losses suppression, advancing compact fusion magnet design.