Strong Toroidal Magnetic Field Research Articles

Three-dimensional magnetothermal evolution of off-centred dipole magnetic field configurations in neutron stars

ABSTRACT Off-centred dipole configurations have been suggested to explain different phenomena in neutron stars, such as natal kicks, irregularities in polarization of radio pulsars and properties of X-ray emission from millisecond pulsars. Here, for the first time, we model magnetothermal evolution of neutron stars with crust-confined magnetic fields and off-centred dipole moments. We find that the dipole shift decays with time if the initial configuration has no toroidal magnetic field. The decay time-scale is inversely proportional to magnetic field. The octupole moment decreases much faster than the quadrupole. Alternatively, if the initial condition includes strong dipolar toroidal magnetic field, the external poloidal magnetic field evolves from centred dipole to off-centred dipole. The surface thermal maps are very different for configurations with weak B = 1013 G and strong B = 1014 G magnetic fields. In the former case, the magnetic equator is cold while in the latter case, it is hot. We model light curves and spectra of our magnetothermal configurations. We found that in the case of cold equator, the pulsed fraction is small (below a few per cent in most cases) and spectra are well described with a single blackbody. Under the same conditions, models with stronger magnetic fields produce light curves with pulsed fraction of tens of per cent. Their spectra are significantly better described with two blackbodies. Overall, the magnetic field strength has a more significant effect on bulk thermal emission of neutron stars than does the field geometry.

Saturation of the magnetorotational instability and the origin of magnetically elevated accretion discs

ABSTRACT We propose that the strength of angular momentum transport in accretion discs threaded by net vertical magnetic field is determined by a self-regulation mechanism: the magnetorotational instability (MRI) grows until its own turbulent resistivity damps the fastest growing mode on the scale of the disc thickness. Given weak assumptions as to the structure of MRI-derived turbulence, supported by prior simulation evidence, the proposed mechanism reproduces the known scaling of the viscous α-parameter, $\alpha \propto \beta _z^{-1/2}$. Here, $\beta _z = 8\pi p_{\rm g}/B_{z0}^2$ is the initial plasma β-parameter on the disc mid-plane, Bz0 is the net field, and pg is the mid-plane gas pressure. We generalize the argument to discs with strong suprathermal toroidal magnetic fields, where the MRI growth rate is modified from the weak-field limit. Additional sources of turbulence are required if such discs are to become magnetically elevated, with the increased scale heights near the mid-plane that are seen in simulations. We speculate that tearing modes, associated with current sheets broadened by the effective resistivity, are a possible source of enhanced turbulence in elevated discs.

Time-extended inductive tokamak discharges with differentially-tilted toroidal field coils

The strong toroidal magnetic field required for plasma confinement in tokamaks is generated by a set of D-shaped coils lying equidistant on meridian planes toroidally located around the central axis of the device. A major technological challenge tied to this configuration is represented by the large Lorentz force acting on the coils and arising from the interaction of the coils’ currents with the magnetic field generated by the coil system itself. As this force is given by the cross product of the coil current and the magnetic field, various kinds of coil geometry modification have been proposed to alleviate this problem, from an inclination of the entire coil in order to maintain its planarity, to azimuthal tilting of all, or parts of, the coil profile. When the inner legs of the coils are tilted, apart from a reduction of the electromagnetic forces, a solenoid-like structure is formed which introduces additional magnetic flux linked to the plasma. Considering compact, high field devices, it is shown that when this additional flux is exploited, totally or in part, to ramp up the plasma current, the discharge time can be extended by a significant amount without resorting to noninductive current drive systems. Operational scenarios with inner-leg-tilted toroidal field coils are presented.

Numerical MHD Simulation of Laboratory Jets in a Toroidal Magnetic Field

The results of MHD modeling of the formation and collimation of laboratory jets with a toroidal magnetic field are presented. We showed that in the absence of a magnetic field, a significant expansion of the jet occurs in the computational region. In the presence of a strong toroidal magnetic field, the jet expands insignificantly, which confirms the possibility of a magnetic mechanism of collimation of astrophysical jets. The opening angle of the jet cone depends on the magnitude of the magnetic field induction. The larger Bϕ, the smaller the angle of deflection of the flow. For certain values of Bϕ on the detector, the occurrence of ring structures in the density distribution is possible, the characteristics of which depend on the magnitude of the field. The simulation results are compared with the laboratory jets generated in the experiment at the Neodim laser facility and with the previously obtained results of the MHD simulation of the formation of jets in a poloidal magnetic field.

Strong toroidal magnetic fields sustained by the elastic crust in a neutron star

ABSTRACT We investigate new solutions for magnetized neutron stars with a barotropic core in magnetohydrodynamic (MHD) equilibrium and a magnetoelastic crust, which was neglected by previous studies concerning stars in MHD equilibrium. The Lorentz force of the barotropic star is purely irrotational and the structures of magnetic fields are constrained. By contrast, a solenoidal component of the Lorentz force exists in the elastic crust and the structures of the magnetic fields are less restricted. We find that the minor solenoidal component in the elastic crust is important for sustaining the strong magnetic field in the core. Unlike previous studies, the toroidal magnetic field exists in the entire region of the core, and we obtain equilibrium states with large toroidal magnetic fields, where the toroidal magnetic energy is larger than the poloidal magnetic energy. The elastic force of the crust sustains an order of 1015 G toroidal magnetic field in the core, and the maximum strength of the toroidal magnetic field is approximately proportional to the crust thickness.

Continuous Gravitational Wave Emissions from Neutron Stars with Pinned Superfluids in the Core

We investigate the effect of a pinned superfluid component on the gravitational wave emissions of a rotating neutron star. The pinning of superfluid vortices to the flux-tubes in the outer core (where the protons are likely to form a type-II superconductor) is a possible mechanism to sustain long-lived and non-axisymmetric neutron currents in the interior, which break the axial symmetry of the unperturbed hydrostatic configuration. We consider pinning-induced perturbations to a stationary corotating configuration and determine the upper limits on the strength of gravitational wave emissions due to the pinning of vortices with a strong toroidal magnetic field of the kind predicted by recent magneto-hydrodynamic simulations of neutron star interiors. We estimate the contributions to gravitational wave emissions from both the mass and current multipole generated by the pinned vorticity in the outer core and find that the mass quadrupole can be large enough for gravitational waves to provide the dominant spindown torque in millisecond pulsars.

Magnetically confined mountains on accreting neutron stars with multipole magnetic fields

ABSTRACT Magnetically confined mountains on accreting neutron stars are candidates for producing continuous gravitational waves. We formulate a magnetically confined mountain on a neutron star with strong multipole magnetic fields and obtain some sequences of numerical solutions. We find that the mass ellipticity of the mountain increases by one order of magnitude if the neutron star has strong multipole magnetic fields. As matter accretes on to the magnetic pole, the size of the mountain increases and the magnetic fields are buried. If the neutron star has a dipole magnetic field, the dipole magnetic field is buried and transformed into multipole components. By contrast, if the neutron star has both dipole and strong multipole magnetic fields, the multipole magnetic fields are buried and transformed into a negative dipole component. We also calculate magnetically confined mountains with toroidal magnetic fields and find that the ellipticity becomes slightly smaller when the mountain has toroidal magnetic fields. If the multipole magnetic fields are buried, they sustain the intense toroidal magnetic field near the stellar surface, and the ratio of the toroidal magnetic field to the poloidal magnetic field is close to 100. The hidden strong toroidal magnetic fields are sustained by the buried multipole magnetic fields.

3D RMHD simulations of jet-wind interactions in high-mass X-ray binaries

Context. Relativistic jets are ubiquitous in the Universe. In microquasars, especially in high-mass X-ray binaries, the interaction of jets with the strong winds driven by the massive and hot companion star in the vicinity of the compact object is fundamental for understanding the jet dynamics, nonthermal emission, and long-term stability. However, the role of the jet magnetic field in this process is unclear. In particular, it is still debated whether the magnetic field favors jet collimation or triggers more instabilities that can jeopardize the jet evolution outside the binary. Aims. We study the dynamical role of weak and moderate to strong toroidal magnetic fields during the first several hundred seconds of jet propagation through the stellar wind, focusing on the magnetized flow dynamics and the mechanisms of energy conversion. Methods. We developed the code Lóstrego v1.0, a new 3D relativistic magnetohydrodynamics code to simulate astrophysical plasmas in Cartesian coordinates. Using this tool, we performed the first 3D relativistic magnetohydrodynamics numerical simulations of relativistic magnetized jets propagating through the clumpy stellar wind in a high-mass X-ray binary. To highlight the effect of the magnetic field in the jet dynamics, we compared the results of our analysis with those of previous hydrodynamical simulations. Results. The overall morphology and dynamics of weakly magnetized jet models is similar to previous hydrodynamical simulations, where the jet head generates a strong shock in the ambient medium and the initial overpressure with respect to the stellar wind drives one or more recollimation shocks. On the timescales of our simulations (i.e., t < 200 s), these jets are ballistic and seem to be more stable against internal instabilities than jets with the same power in the absence of fields. However, moderate to strong toroidal magnetic fields favor the development of current-driven instabilities and the disruption of the jet within the binary. A detailed analysis of the energy distribution in the relativistic outflow and the ambient medium reveals that magnetic and internal energies can both contribute to the effective acceleration of the jet. Moreover, we verified that the jet feedback into the ambient medium is highly dependent on the jet energy distribution at injection, where hotter, more diluted and/or more magnetized jets are more efficient. This was anticipated by feedback studies in the case of jets in active galaxies.

Wakefield Acceleration in a Jet from a Neutrino-driven Accretion Flow around a Black Hole

Abstract We have investigated electromagnetic (EM) wave pulses in a jet from a neutrino-driven accretion flow (NDAF) around a black hole (BH). NDAFs are massive accretion disks whose accretion rates are M ̇ ≈ 0.01–10 M ⊙ s−1 for stellar-mass BHs. Such an extreme accretion may produce a collimated relativistic outflow like a magnetically driven jet in active galactic nuclei and microquasars. When we consider strong toroidal magnetic field stranded in the inner region of an NDAF disk and magnetic impulses on the jet, we find that they lead to the emanation of high-energy emissions for gamma-ray bursts, as well as high-energy cosmic rays. When Alfvénic wave pulses are generated by episodic immense accretions, they propagate along the large-scale structured magnetic field in the jet. Once the Alfvénic wave pulses reach nearly the speed of light in the underdense condition, they turn into EM wave pulses, which produce plasma wakes behind them. These wakefields exert a collective accelerating force synchronous to the motion of particles. As a result, the wakefield acceleration premises various observational signatures, such as pulsating bursts of high-energy gamma rays from accelerated electrons, pulses of neutrinos from accelerated protons, and protons with maximum energies beyond 1020 eV.

The Magnetic Mechanism for Hotspot Reversals in Hot Jupiter Atmospheres

Abstract Magnetically driven hotspot variations (which are tied to atmospheric wind variations) in hot Jupiters are studied using nonlinear numerical simulations of a shallow-water magnetohydrodynamic (SWMHD) system and a linear analysis of equatorial SWMHD waves. In hydrodynamic models, mid-to-high-latitude geostrophic circulations are known to cause a net west-to-east equatorial thermal energy transfer, which drives hotspot offsets eastward. We find that a strong toroidal magnetic field can obstruct these energy transporting circulations. This results in winds aligning with the magnetic field and generates westward Lorentz force accelerations in hotspot regions, ultimately causing westward hotspot offsets. In the subsequent linear analysis we find that this reversal mechanism has an equatorial wave analogy in terms of the planetary-scale equatorial magneto-Rossby waves. We compare our findings to three-dimensional MHD simulations, both quantitatively and qualitatively, identifying the link between the mechanics of magnetically driven hotspot and wind reversals. We use the developed theory to identify physically motivated reversal criteria, which can be used to place constraints on the magnetic fields of ultra-hot Jupiters with observed westward hotspots.

Gravitational wave signature of proto-neutron star convection: I. MHD numerical simulations

ABSTRACT Gravitational waves provide a unique and powerful opportunity to constrain the dynamics in the interior of proto-neutron stars during core collapse supernovae. Convective motions play an important role in generating neutron stars magnetic fields, which could explain magnetar formation in the presence of fast rotation. We compute the gravitational wave emission from proto-neutron star convection and its associated dynamo, by post-processing three-dimensional MHD simulations of a model restricted to the convective zone in the anelastic approximation. We consider two different proto-neutron star structures representative of early times (with a convective layer) and late times (when the star is almost entirely convective). In the slow rotation regime, the gravitational wave emission follows a broad spectrum peaking at about three times the turnover frequency. In this regime, the inclusion of magnetic fields slightly decreases the amplitude without changing the spectrum significantly compared to a non-magnetized simulation. Fast rotation changes both the amplitude and spectrum dramatically. The amplitude is increased by a factor of up to a few thousands. The spectrum is characterized by several peaks associated with inertial modes, whose frequency scales with the rotation frequency. Using simple physical arguments, we derive scalings that reproduce quantitatively several aspects of these numerical results. We also observe an excess of low-frequency gravitational waves, which appears at the transition to a strong field dynamo characterized by a strong axisymmetric toroidal magnetic field. This signature of dynamo action could be used to constrain the dynamo efficiency in a proto-neutron star with future gravitational wave detections.

Free-fall velocities and heat transport enhancement in liquid metal magneto-convection

Abstract

Strong toroidal magnetic fields required by quiescent X-ray emission of magnetars

Magnetars are neutron stars (NSs) with extreme magnetic fields of strength $5 \times 10^{13}$ - $10^{15}$ G. They exhibit transient, highly energetic events, such as short X-ray flashes, bursts and giant flares, all of which are powered by their enormous magnetic energy. Quiescent magnetars have X-ray luminosities between $10^{29}$ and $10^{35}$ erg/s, and are further classified as either persistent or transient magnetars. Their X-ray emission is modulated with the rotational period of the NS, with a typical relative amplitude (so-called pulsed fraction) between 10-58 per cent, implying that the surface temperature is significantly non-uniform despite the high thermal conductivity of the star's crust. Here, we present the first 3D magneto-thermal MHD simulations of magnetars with strong toroidal magnetic fields. We show that these models, combined with ray propagation in curved space-time, accurately describe the light-curves of most transient magnetars in quiescence and allow us to further constrain their rotational orientation. We find that the presence of a strong toroidal magnetic field explains the observed asymmetry in the surface temperature, and is the main cause of the strong modulation of thermal X-ray emission in quiescence.

Magnetic Field Dependence of Bipolar Magnetic Region Tilts on the Sun: Indication of Tilt Quenching

Abstract The tilt of the bipolar magnetic region (BMR) is crucial in the Babcock–Leighton process for the generation of the poloidal magnetic field in the Sun. Based on the thin flux-tube model of the BMR formation, the tilt is believed to be caused by the Coriolis force acting on the rising flux tube of the strong toroidal magnetic field from the base of the convection zone. We analyze the magnetic field dependence of BMR tilts using the magnetograms of the Michelson Doppler Imager (1996–2011) and Helioseismic and Magnetic Imager (2010–2018). We observe that the distribution of the maximum magnetic field (B max) of BMRs is bimodal. Its first peak at the low field corresponds to BMRs that do not have sunspots as counterparts in the white-light images, whereas the second peak corresponds to sunspots as recorded in both type of images. We find that the slope of Joy’s law (γ 0) initially increases slowly with the increase of B max. However, when B max ≳ 2 kG, γ 0 decreases. Scatter of the BMR tilt around Joy’s law systematically decreases with the increase of B max. The decrease of observed γ 0 with B max provides a hint to a nonlinear tilt quenching in the Babcock–Leighton process. We finally discuss how our results may be used to make a connection with the thin flux-tube model.

Performance of the ATLAS RPC first level Muon trigger during the Run-2 data taking

The first level (Level-1) muon barrel trigger is one of the main elements of the event selection of the ATLAS experiment at the Large Hadron Collider. Its input is made of an array of processors which receive the full granularity of data from Resistive Plate Chambers (RPC) in the central (“Barrel”) area of the ATLAS detector. The Barrel RPCs are arranged in three concentric shells and operate in a strong toroidal magnetic field. The RPC detectors cover the pseudo-rapidity range | η |< 1.05 for a total surface of more than 4000 m2 and about 3600 gas volumes. The Level-1 Muon Trigger in the barrel region allows to select muon candidates with respect to their transverse momentum providing also the bunch-crossing assignment. We present the performance of the Level-1 muon trigger during the LHC Run-2 data taking, in particular for the years 2015–2017.

Flow of a thin liquid-metal film in a toroidal magnetic field

We investigate the gravity-driven flow of a thin film of liquid metal on a conducting conical substrate in the presence of a strong toroidal magnetic field (transverse to the flow and parallel to the substrate). We solve the leading-order governing equations in a physically relevant asymptotic limit to find the free-surface profile. We find that the leading-order fluid flow rate is a non-monotonic bounded function of the film height, and this can lead to singularities in the free-surface profile. We perform a detailed stability analysis and identify values of the relevant geometric, hydrodynamic and magnetic parameters such that the flow is stable.

Direct Measurement of a Toroidally Directed Zonal Flow in a Toroidal Plasma.

Zonal flow appears in toroidal, magnetically confined plasmas as part of the self-regulated interaction of turbulence and transport processes. For toroidal plasmas having a strong toroidal magnetic field, the zonal flow is predominately poloidally directed. This Letter reports the first observation of a zonal flow that is toroidally directed. The measurements are made just inside the last closed flux surface of reversed field pinch plasmas that have a dominant poloidal magnetic field. A limit cycle oscillation between the strength of the zonal flow and the amplitude of plasma potential fluctuations is observed, which provides evidence for the self-regulation characteristic of drift-wave-type plasma turbulence. The measurements help advance understanding and gyrokinetic modeling of toroidal plasmas in the pursuit of fusion energy.

Shallow-water Magnetohydrodynamics for Westward Hotspots on Hot Jupiters

Abstract Westward winds have now been inferred for two hot Jupiters (HJs): HAT-P-7b and CoRoT-2b. Such observations could be the result of a number of physical phenomena such as cloud asymmetries, asynchronous rotation, or magnetic fields. For the hotter HJs magnetic fields are an obvious candidate, though the actual mechanism remains poorly understood. Here we show that a strong toroidal magnetic field causes the planetary-scale equatorial magneto-Kelvin wave to structurally shear as it travels, resulting in westward tilting eddies, which drive a reversal of the equatorial winds from their eastward hydrodynamic counterparts. Using our simplified model we estimate that the equatorial winds of HAT-P-7b would reverse for a planetary dipole field strength , a result that is consistent with three-dimensional magnetohydrodynamic simulations and lies below typical surface dipole estimates of inflated HJs. The same analysis suggests the minimum dipole field strength required to reverse the winds of CoRoT-2b is , which considerably exceeds estimates of the maximum surface dipole strength for HJs. We hence conclude that our magnetic wave-driven mechanism provides an explanation for wind reversals on HAT-P-7b; however, other physical phenomena provide more plausible explanations for wind reversals on CoRoT-2b.

Effects of Rotation and Magnetic Field on the Revival of a Stalled Shock in Supernova Explosions

Abstract We investigate axisymmetric steady solutions of (magneto)hydrodynamics equations that approximately describe accretion flows through a standing shock wave onto a protoneutron star and discuss the effects of rotation and magnetic field on the revival of the stalled shock wave in supernova explosions. We develop a new powerful numerical method to calculate the two-dimensional steady accretion flows self-consistently. We first confirm the results of preceding papers that there is a critical luminosity of irradiating neutrinos, above which there exists no steady solution in spherical models. If a collapsing star is rotating and/or has a magnetic field, the accretion flows are no longer spherical owing to the centrifugal force and/or Lorentz force, and the critical luminosity is modified. In fact, we find that the critical luminosity is reduced by about 50%–70% for very rapid rotations; the rotation frequencies are 0.2–0.45 s−1 at the radius of r = 1000 km (equivalent to spin periods ∼0.5–0.22 ms at r = 10 km) and about 20%–50% for strong toroidal magnetic fields (the strengths of which are 1.0 × 1012–3.0 × 1012 G at r = 1000 km), depending on the mass accretion rate. These results may also be interpreted as the existence of a critical specific angular momentum or critical magnetic field, above which there exists no steady solution and the standing shock wave will be revived for a given combination of mass accretion rate and neutrino luminosity.

Conductivity of neutron star crust under superhigh magnetic fields and Ohmic decay of toroidal magnetic field of magnetar

&lt;sec&gt;Magnetar is a kind of pulsar powered by magnetic field energy. Part of the X-ray luminosities of magnetars in quiescence have a thermal origin and can be fitted by a blackbody spectrum with temperature &lt;i&gt;kT&lt;/i&gt; ～ 0.2－0.6 keV, much higher than the typical values for rotation-powered pulsars. The observation and theoretical study of magnetar are one of hot topics in the field of pulsar research. The activity and emission characteristics of magnetar can be attributed to internal superhigh magnetic field. According to the work of WGW19 and combining with the equation of state, we first calculate the electric conductivity of the crust under a strong magnetic field, and then calculate the toroidal magnetic field decay rate and magnetic energy decay rate by using an eigenvalue equation of toroidal magnetic field decay and considering the effect of general relativity. We reinvestigate the &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;X&lt;/sub&gt;-&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;rot&lt;/sub&gt; relationship of 22 magnetars with persistent soft X-ray luminosities and obtain two new fitting formulas on &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;X&lt;/sub&gt;-&lt;i&gt;L&lt;/i&gt;&lt;sub&gt;rot&lt;/sub&gt;. We find that for the magnetars with &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;X&lt;/sub&gt; &lt; &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;rot&lt;/sub&gt;, the soft X-ray radiations may originate from their rotational energy loss rate, or from magneto-sphere flow and particle wind heating. For the magnetars with &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;X&lt;/sub&gt; &gt; &lt;i&gt;L&lt;/i&gt;&lt;sub&gt;rot&lt;/sub&gt;, the Ohmic decay of crustal toroidal magnetic fields can provide their observed isotropic soft X-ray radiation and maintain higher thermal temperature.&lt;/sec&gt;&lt;sec&gt;As for the initial dipole magnetic fields of magnetars, we mainly refer to the rersearch by Viganò et al. (Viganò D, Rea N, Pons J A, Perna R, Aguilera D N, Miralles J A 2013 &lt;i&gt;Mon. Not. R. Astron. Soc.&lt;/i&gt; &lt;b&gt;434&lt;/b&gt; 123), because they first proposed the up-dated neutron star magneto-thermal evolution model, which can successfully explain the X-ray radiation and cooling mechanism of young pulsars including magnetars and high-magnetic field pulsars. Objectively speaking, as to the decay of toroidal magnetic fields, there are some differences between our theoretical calculations of magnetic energy release rates and the actual situation of magnetic field decay in magnetars, this is because the estimate of initial dipolar magnetic field, true age and the thickness of inner crust of a magnetar are somewhat uncertain. In addition, due to the interstellar-medium’s absorptions to soft X-ray and the uncertainties of distance estimations, the observed soft X-ray luminosities of magnetars have certain deviations. With the continuous improvement of observation, equipment and methods, as well as the in-depth development of theoretical research, our model will be further improved, and the theoretical results are better accordant with the high-energy observation of magnetars.&lt;/sec&gt;&lt;sec&gt;We also discuss other possible anisotropy origins of soft X-ray fluxes of magnetars, such as the formation of magnetic spots and thermoplastic flow wave heating in the polar cap. Although anisotropic heating mechanisms are different from Ohmic decay, all of them require that there exist strong toroidal magnetic fields inside a magnetar. However, the anisotropic heating mechanisms require higher toroidal multipole fields inside a magnetar (such as magnetic octupole field) and are related to complex Hall drift: these may be our research subjects in the future.&lt;/sec&gt;