Magnetic Field Decay Research Articles

Electron and muon dynamics in neutron stars beyond chemical equilibrium

A neutron star harbors 𝒪(1056) electrons in its core, and almost the same number of muons, with muon decay prohibited by Pauli blocking. However, as macroscopic properties of the star such as its mass, rotational velocity, or magnetic field evolve over time, the equilibrium lepton abundances (dictated by the weak interactions) change as well. Scenarios where this can happen include spin-down, accretion, magnetic field decay, and tidal deformation. We discuss the mechanisms by which a star disrupted in one of these ways re-establishes lepton chemical equilibrium. In most cases, the dominant processes are out-of-equilibrium Urca reactions, the rates of which we compute for the first time. If, however, the equilibrium muon abundance decreases, while the equilibrium electron abundance increases (or decreases less than the equilibrium muon abundance), outward diffusion of muons plays a crucial role as well. This is true in particular for stars older than about 104 yrs whose core has cooled to ≲ 20 keV. The muons decay in a region where Pauli blocking is lifted, and we argue that these decays lead to a flux of 𝒪(10 MeV) neutrinos. Realistically, however, this flux will remain undetectable for the foreseeable future.

The Galactic population of canonical pulsar. II. Taking into account several evolutionary paths: Interstellar medium interaction, Galactic potential, and a death valley

Pulsars are highly magnetised rotating neutron stars, emitting in a broad electromagnetic energy range. These objects were discovered more than 55 years ago and are astrophysical laboratories for studying physics at extreme conditions. Reproducing the observed pulsar population helps refine our understanding of their formation and evolution scenarios, as well as their radiation processes and geometry. In this paper, we improve our previous population synthesis by focusing on both the radio and gamma -ray pulsar populations, investigating the impact of the Galactic gravitational potential and of the radio emission death line. To elucidate the necessity of a death line, we implemented our refined initial distributions of the spin period and spacial position at birth. This approach allowed us to elevate the sophistication of our simulations to the most recent state-of-the-art approaches. The motion of each individual pulsar was tracked in the Galactic potential by a fourth-order symplectic integration scheme. Our pulsar population synthesis took into account the secular evolution of the force-free magnetosphere and magnetic field decay simultaneously and self-consistently. Each pulsar was evolved from birth to the present time. The radio and gamma -ray emission locations were modelled by the polar cap geometry and striped wind model, respectively. By simulating ten million pulsars, we found that including a death line allows us to better reproduce the observational trend. However, when simulating one million pulsars, we obtained an even more realistic $P- P $ diagram, whether or not a death line was included. This suggests that the ages of the detected pulsars might be overestimated and so, it sets the need for a death line in pulsar population studies into question. Kolmogorov-Smirnov tests confirm the statistical similarity between the observed and simulated $P- P $ diagram. Additionally, simulations with increased gamma -ray telescope sensitivities hint at a significant contribution coming from the gamma -ray pulsars to the GeV excess in the Galactic centre.

Magnetic coupling through flux branching of adjacent type-I and -II superconductors in a neutron star

Abstract The inner and outer cores of neutron stars are believed to contain type-I and -II proton superconductors, respectively. The type-I superconductor exists in an intermediate state, comprising macroscopic flux-free and flux-containing regions, while the type-II superconductor is flux-free, except for microscopic, quantized flux tubes. Here, we show that the inner and outer cores are coupled magnetically, when the macroscopic flux tubes subdivide dendritically into quantized flux tubes, a phenomenon called flux branching. An important implication is that up to ∼1012(r1/106 cm) erg of energy are required to separate a quantized flux tube from its progenitor macroscopic flux tube, where r1 is the length of the macroscopic flux tube. Approximating the normal-superconducting boundary as sharp, we calculate the magnetic coupling energy between a quantized and macroscopic flux tube due to flux branching as a function of, f1, the radius of the type-I inner core divided by the radius of the type-II outer core. Strong coupling delays magnetic field decay in the type-II superconductor. For an idealised inner core containing only a type-I proton superconductor and poloidal flux, and in the absence of ambipolar diffusion and diamagnetic screening, the low magnetic moments (≲ 1027 G cm3) of recycled pulsars imply f1 ≲ 10−1.5.

Indication of rapid magnetic field decay in X-ray Dim Isolated Neutron Star RX J0720.4-3125

Indication of rapid magnetic field decay in X-ray Dim Isolated Neutron Star RX J0720.4-3125

Practical twin-field quantum key distribution parameter optimization based on quantum annealing algorithm

Abstract Twin-field quantum key distribution (TF-QKD) is widely studied since it can surpass the key capacity of repeaterless QKD, whereas electromagnetic interference (EMI) is one of the main challenges in its practical applications. This study is based on the Faraday–Michelson TF-QKD. Analyze the effect of EMI on the rotation angle of the Faraday mirror causing an additional quantum bit error rate (QBER). Moreover, the quantum annealing algorithm (QA) based on quantum tunneling mechanism is applied to the optimization of practical TF-QKD. Mapping the secure key rate of TF-QKD into the evaluation function of QA and the transverse magnetic field is introduced to construct the kinetic energy term, which can realize the quantum tunneling effect. Meanwhile, the QA is improved in terms of chaotic optimization to obtain the dynamic initial value of the algorithm, the design of a perturbation method to skip the locally optimal solution, and the use of suitable temperature and magnetic field decay functions. Optimizing TF-QKD with QA, the standard deviation of QBER fluctuation caused by EMI is reduced to 0.206, the mean square error of the signal-state pulse intensity is only 3.38 × 10 − 4 , and the optimization accuracy of the secure key rate can reach 99.8 % . Additionally, this optimization method shortens the runtime and reduces computational resource consumption, making it highly efficient for practical implementations.

Collisionless Shock in a Relativistically Hot Unmagnetized Electron–Positron Plasma

In this work, we investigate collisionless shocks propagating in a relativistically hot unmagnetized electron–positron plasma. We estimate the dissipation fraction at shocks in the relativistically hot plasma, showing that it is sufficiently large to explain the observation of gamma-ray bursts even when the shock is not highly relativistic. It is shown by two-dimensional particle-in-cell simulations that magnetic fields are generated around the shock front by the Weibel instability, as in the cold upstream plasma. However, in contrast to the cold upstream plasma, no particles are accelerated at the shock in the simulation time of t=3600ωp−1 . The decay of the magnetic field in the downstream region is slower for slower shock velocities in the hot plasma cases. Applying the slow decay of the downstream magnetic field, we propose a model that generates magnetic fields in the large downstream region, which is required from the standard model of the gamma-ray burst afterglow.

Isolated Pulsar Population Synthesis with Simulation-based Inference

We combine pulsar population synthesis with simulation-based inference (SBI) to constrain the magnetorotational properties of isolated Galactic radio pulsars. We first develop a framework to model neutron star birth properties and their dynamical and magnetorotational evolution. We specifically sample initial magnetic field strengths, B, and spin periods, P, from lognormal distributions and capture the late-time magnetic field decay with a power law. Each lognormal is described by a mean, μlogB,μlogP , and standard deviation, σlogB,σlogP , while the power law is characterized by the index, a late. We subsequently model the stars’ radio emission and observational biases to mimic detections with three radio surveys, and we produce a large database of synthetic P– Ṗ diagrams by varying our five magnetorotational input parameters. We then follow an SBI approach that focuses on neural posterior estimation and train deep neural networks to infer the parameters’ posterior distributions. After successfully validating these individual neural density estimators on simulated data, we use an ensemble of networks to infer the posterior distributions for the observed pulsar population. We obtain μlogB=13.10−0.10+0.08 , σlogB=0.45−0.05+0.05 and μlogP=−1.00−0.21+0.26 , σlogP=0.38−0.18+0.33 for the lognormal distributions and alate=−1.80−0.61+0.65 for the power law at the 95% credible interval. We contrast our results with previous studies and highlight uncertainties of the inferred a late value. Our approach represents a crucial step toward robust statistical inference for complex population synthesis frameworks and forms the basis for future multiwavelength analyses of Galactic pulsars.

Explicit observation of tertiary magnetic field in TDEM transients; plausible explanation towards induced polarization effect in geophysical prospecting

In time domain electromagnetic central loop sounding or coincidence loop measurements often a sign reversal is observed in the recorded decay transients. These negative decay transients are generally attributed to induced polarization effect. We observed a similar sign reversal in the decay transients recorded with SQUID as a receiver in central loop sounding measurements at later decay times. The magnitude of the secondary magnetic field observed in the negative decay transients is considerably high and the SQUID output never reaches its noise floor even at decay times of >155 ms. This observation stimulated us to record the current flow in the transmitter loop and therefore a small resistor is connected in series with the transmitter loop. Decay transients have been recorded simultaneously across the resistor and the SQUID which is located at the centre of the transmitter loop. To our surprise, the time at which the sign reversal occurred in the recorded decay transients with SQUID and across the resistor confirmed that the SQUID is recording the magnetic field produced by the flow of the induced current in the transmitter loop in addition to the decay of the secondary magnetic field from the ground. A novel hypothesis has been proposed to explain the flow of induced current in the transmitter loop and extensive laboratory experimental simulations have been performed to prove it. The proposed novel hypothesis explains the occurrence of sign reversal in TEM systems not only in single loop but also in coincidence loop and central loop TEM configurations. In all cases, the sign reversal is due to the self induced tertiary magnetic fields. In this work, a set of transient measurements have been carried out with different targets and different thicknesses. The experiments have been repeated by locating the targets at different depths in order observe the response of the tertiary magnetic field in the decay transients. The experimental data and subsequent analysis confirmed our hypothesis that the self induced tertiary magnetic field is responsible for the sign reversals rather than the induced polarization effects.

Heating of millisecond pulsars by magnetic field decay

AbstractMillisecond pulsars (MSPs) are believed to be very old neutron stars (NSs) whose age may exceed significantly years. Although cooling scenarios of isolated NSs predict for that age a surface temperature K, observations of the nearest MSP J0437‐4715 indicate well above that value. Besides the heating of the polar cap surface by backflowing charged particles, Joule heating in the crust can contribute to the overall heat budget of MSPs. Because the dipolar field component, derived from and measurements, is much too weak for remarkable heating, smaller‐scale structures should be analyzed to understand whether they can supply the demanded heat. For this purpose, we study the small‐scale field structure of radio pulsars. Magnetic field components, significantly stronger than the dipolar one, may exist especially at the surface of MSPs. We assign upper limits to the strength of single‐field components up to a multipolarity of and the corresponding deviations from axial symmetry . Arguments are provided that the decay of the small‐scale components with or of the crustal magnetic field may cause the relatively high surface temperature of isolated MSPs.

Formation of long-period radio pulsars

Abstract This study investigates the influence of different braking mechanisms on the formation of three long-period radio pulsars (PSRs J0250 + 5854, J2251-3711, and J0901-4046): plasma-filled magnetosphere in combination with magnetic field decay, fall-back disc, and r-mode instability. These braking mechanisms can also affect the thermal evolution of pulsars. By comparing the model-predicted values with observational data such as spin periods, period derivatives, and upper limits of the bolometric luminosity of these pulsars, we find that these three braking mechanisms can reasonably explain the spin period and the period derivative within a certain range of parameters for these sources. The model-predicted bolometric luminosity associated with magnetic field dissipation exceeds the upper limit for PSR J0901-4046 but falls below the upper limits for PSR J0250 + 5854 and PSR J2251-3711. The model-predicted bolometric luminosity within the fall-back disc model exceeds the observed results, whereas the luminosity within the r-mode instability falls below the observed upper limit for these three pulsars. However, a conflict arises when we consider the pulsar radio activity and the accretion phases within the fall-back disc model simultaneously. By combining data from radio and X-ray observations, along with precise measurements of surface thermal emissions, we can enhance our understanding of the braking mechanisms involved in the formation of long-period radio pulsars or constrain key model parameters. Finding more long-period pulsars in the future and conducting multi-band observations will enhance our understanding of the formation and nature of long-period radio pulsars.

Field recordings of transcranial magnetic stimulation in human brain postmortem models.

The ability of repetitive transcranial magnetic stimulation (rTMS) to deliver a magnetic field (MF) in deep brain targets is debated and poorly documented. To quantify the decay of MF in the human brain. Magnetic field was generated by single pulses of TMS delivered at maximum intensity using a flat or angulated coil. Magnetic field was recorded by a 3D-magnetic probe. Decay was measured in the air using both coils and in the head of 10 postmortem human heads with the flat coil being positioned tangential to the scalp. Magnetic field decay was interpreted as a function of distance to the coil for 6 potential brain targets of noninvasive brain stimulation: the primary motor cortex (M1, mean depth: 28.5 mm), dorsolateral prefrontal cortex (DLPFC: 28 mm), secondary somatosensory cortex (S2: 35.5 mm), posterior and anterior insulae (PI: 38.5 mm; AI: 43.5 mm), and midcingulate cortex (MCC: 57.5 mm). In air, the maximal MF intensities at coil center were 0.88 and 0.77 T for the flat and angulated coils, respectively. The maximal intracranial MF intensity in the cadaver model was 0.34 T, with a ∼50% decay at 15 mm and a ∼75% MF decay at 30 mm. The decay of the MF in air was similar for the flat coil and significantly less attenuated with the angulated coil (a ∼50% decay at 20 mm and a ∼75% MF decay at 45 mm). Transcranial magnetic stimulation coil MFs decay in brain structures similarly as in air, attenuation with distance being significantly lower with angulated coils. Reaching brain targets deeper than 20 mm such as the insula or Antérior Cingulate Cortex seems feasible only when using angulated coils. The abacus of MF attenuation provided here can be used to adjust modalities of deep brain stimulation with rTMS in future research protocols.

Combined magnetic field evolution in neutron star cores and crusts: ambipolar diffusion, Hall effect, and Ohmic dissipation

ABSTRACT Neutron star magnetic field evolution is mediated through the Hall effect and Ohmic dissipation in the crust while ambipolar diffusion is taking place in the core. These effects have been studied in detail in either part of the star, however, their combined, simultaneous evolution and interplay has not been explored in detail yet. Here, we present simulation results of the simultaneous evolution of the magnetic field in the core due to ambipolar diffusion and the crust due to Hall effect and Ohmic decay, under the assumption of axial symmetry. We find that a purely poloidal field generates a toroidal field in the crust, due to the Hall effect, that sinks into the core. A purely toroidal field remains toroidal and spreads into the core and the crust. Finally, for a mixed poloidal–toroidal field, the north–south symmetry is broken due to the Hall effect in the crust, however, ambipolar diffusion, tends to restore it. We examine the role of ambipolar diffusion to the magnetic field decay and we compare the rate of the conversion of magnetic field energy into heat, finding that it enhances the magnetic field decay in neutron stars.

Optimal Parameter Design and Microrobotic Navigation Control of Parallel-Mobile-Coil Systems

In this work, we study the optimal parameter design and microrobotic navigation control of the parallel-mobile-coil system (PMCS) that consists of three mobile electromagnetic coils. With motion driven by a parallel mechanism, the three coils can move in 3D large space and keep as close as possible to the controlled microrobot for magnetic actuation. Although promising for microrobotic applications, how to design such a type of system for a specific workspace requirement is untackled. Regarding this issue, we propose a computational design method, by which one can calculate the structural parameters of a PMCS starting from a required cylindrical workspace. With the derived performance metrics for motion actuation and magnetic actuation of the PMCS, the system actuation performance (composed of motion and magnetic actuation) is optimized. Utilizing the design method, we optimally construct a prototype PMCS for microrobotic navigation. We then conduct experiments to validate the demanding field/force generation capability of the PMCS and demonstrate the navigation control of different types of magnetic microrobots. In particular, we design closed-loop motion controllers for both torque and force-driven microrobots, using which automated large-workspace and high-accuracy trajectory tracking is realized. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the recent wide interest in magnetic microrobots. Driven by external magnetic fields, magnetic microrobots can navigate in a wireless manner for targeted delivery/therapy. To promote microrobot applications to the human body, a magnetic actuation system with large workspace is desirable. However, due to the fast decay of magnetic field, the commonly used stationary coil-based magnetic actuation systems have the workspace scalability problem. Thus, several mobile-coil-based systems have been designed. In this work, we propose an optimal design method for the PMCS, using which one can design a PMCS starting from a cylindrical workspace with performance being optimized. We construct a PMCS prototype with a workspace of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi 230 \times 100$</tex-math> </inline-formula> mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^3$</tex-math> </inline-formula> , and we then study the automated microrobotic navigation control methods for the PMCS. Controllers are designed for different types of magnetic microrobots, and experiments show that, using the controllers, the PMCS can perform automated large-workspace microrobotic navigation control with high accuracy.

Internal Shock with a Background Magnetic Field for the Prompt Emission of Gamma-Ray Bursts—A Case Study of GRB 211211A

It is proposed that the synchrotron emission from an internal shock with a decaying shock-generated magnetic field can account for the prompt emission of gamma-ray bursts (GRBs). Generally, a jet from the central engine of a GRB is launched with a significant magnetization, and thus there would be a background magnetic field, rather than only the shock-generated magnetic field, in the emission region. In this paper, we study the synchrotron emission of internal shocks with both a decaying shock-generated magnetic field and a nondecaying background magnetic field. It is found that a shoulder with spectral index −1/2 appears in the low-energy regime of the radiation spectrum. The shoulder becomes dominant by increasing the ratio of the background magnetic field energy to the initial value of the shock-generated magnetic field energy f B. Correspondingly, a radiation spectrum with two bumps or a plateau around the peak of the ν F ν −ν spectrum may appear. Owing to the decay of the shock-generated magnetic field, the radiation spectral morphology in the high-energy regime is not a power-law function even though a power-law distribution of electrons is injected. We apply our model to GRB 211211A, of which the hard main emission is suggested to originate from the synchrotron emission. Compared with the spectral fitting results with a Band function and the synchrotron emission from the standard straightforward internal shocks, our model presents a perfect fitting to the observations. The fitting results show that f B is around 0.41–0.99 for the hard main emission of this burst.

Survival of fossil fields during the pre-main sequence evolution of intermediate-mass stars

Context. Chemically peculiar Ap and Bp stars host strong large-scale magnetic fields in the range of 200 G up to 30 kG, which are often considered to be the origin of fossil magnetic fields. Aims. We assess the evolution of such fossil fields during the star formation process and the pre-main sequence evolution of intermediate stars based on: fully convective models, models including a transition to a radiative protostar, and models with a radiative core. We also examine the implications of the interaction between the fossil field and the core dynamo. Methods. We employed analytic and semi-analytic calculations, combined with current observational constraints. Results. For fully convective models, we show that magnetic field decay via convection can be expected to be very efficient for realistic parameters of turbulent resistivities. Based on the observed magnetic field strength-density relation, as well as the expected amount of flux loss due to ambipolar diffusion, it appears unlikely that convection could be suppressed via strong enough magnetic fields. On the other hand, a transition from a convective to a radiative core could very naturally explain the survival of a significant amount of flux, along with the presence of a critical mass. We show that in some cases, the interaction of a fossil field with a core dynamo may further lead to changes in the surface magnetic field structure. Conclusions. In the future, it will be important to understand in more detail how the accretion rate evolves as a function of time during the formation of intermediate-mass protostars, including its impact on the protostellar structure. The latter may even allow us to derive quantitative predictions concerning the expected population of large scale magnetic fields in radiative stars.

Influences of dynamical disruptions on the evolution of pulsars in globular clusters

ABSTRACT By comparing the physical properties of pulsars hosted by core-collapsed (CCed) and non-core-collapsed (non-CCed) globular clusters (GCs), we find that pulsars in CCed GCs rotate significantly slower than their counterparts in non-CCed GCs. Additionally, radio luminosities at 1.4 GHz in CCed GCs are higher. These findings are consistent with the scenario that dynamical interactions in GCs can interrupt angular momentum transfer processes and surface magnetic field decay during the recycling phase. Our results suggest that such effects in CCed GCs are stronger due to more frequent disruptions of compact binaries. This is further supported by the observation that both estimated disruption rates and the fraction of isolated pulsars are predominantly higher in CCed GCs.

Operation of Prototype Race-Track Closed-Loop HTS Coil With Metal-as-Insulation in Solid Nitrogen

The second generation (2G) high temperature superconductor (HTS) has excellent current-carrying density performance in strong magnetic field. Thus, the maglev system driven by 2G HTS magnets has been studied a lot. In the design of magnets, metal-as-insulation coil retains self-protection feature of the no-insulation coil, and it performs well in charging time. On the other hand, using solid nitrogen (SN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) as a “thermal battery” may effectively reduce the volume of on-board HTS magnets. In order to design on-board magnets with fast charging, small volume and self-protection, firstly a prototype coil was manufactured. Then the experiment apparatus was set up and experiments in the persistent current mode were carried out. It was obtained by fitting that the magnetic field decay rate of the prototype coil was about 0.24% per day. This paper provides a foundation for the production of real-scale on-board magnets cooled by SN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> .

Systematic investigation of a NbTi-Bi2223 hybrid low-resistive joint

In this study, a NbTi-Bi2223 hybrid low-resistive joint fabricated by the superconducting solder method was systematically investigated. The joint is a necessary component of gigahertz nuclear magnetic resonance (NMR) with Bi2223 as the insert coil. The joint resistance and current capability under different applied magnetic fields were measured, and the resistance exhibited a near-linear relationship with the applied field. Beyond the superconducting properties, the allowed mechanical criteria for the Bi2223 tape in the joint were also briefly studied. Based on the above two properties, a 1.3 GHz NMR design with a NbTi-Bi2223 hybrid low-resistive joint was shown as an application demonstration. Although the current resistance can fit the magnetic-field decay criteria, obtaining a lower resistance value was attempted by extending the joint length but failed. The main source of the resistance in NbTi-Bi2223 was studied. We attempt to show an engineering-feasible NbTi-Bi2223 hybrid low-resistive joint to help improve the development of gigahertz NMR.

The Zoo of Isolated Neutron Stars

In this brief review, I summarize our basic knowledge about different types of isolated neutron stars. I discuss radio pulsars, central compact objects in supernova remnants, magnetars, nearby cooling neutron stars (also known as the magnificent seven), and sources of fast radio bursts. Several scenarios of magneto-rotational evolution are presented. Recent observational data, such as the discovery of long-period radio pulsars, require the non-trivial evolution of magnetic fields, the spin periods of neutron stars, or both. In some detail, I discuss different models of magnetic field decay and interactions of young neutron stars with fallback matter.

Multimode Control of a Parallel-Mobile-Coil System for Adaptable Large-Workspace Microrobotic Actuation

Recent studies on magnetic microrobotics for biomedical applications have resulted in varieties of magnetic actuation systems. However, the simultaneous actuation and tracking of magnetic microrobots in large workspace (e.g., the human-body size) remains challenging due to the fast decay of magnetic fields and the contradiction between resolution and field of view of a feedback instrument. Our previous work reported the concept of the parallel-mobile-coil system (PMCS), which comprises three electromagnetic coils that can move in large 3-D space for microrobotic actuation. Here, to make the PMCS have adaptability to different actuation scenarios or microrobot types, we propose three different control modes by utilizing the mobility of the coils. The torque control, force-assisted torque control, and force control modes are designed for pure torque actuation with energy conservation, torque actuation with force assistance, and pure force actuation, respectively. Comparative simulations and experiments validate the effectiveness of the three control modes. Moreover, to endow the system with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-vivo</i> feedback capability, we implement Hall-effect sensors and demonstrate the 3-D large-workspace actuation based on magnetic localization.