Our recent discoveries of magnetic fields in a small number of Herbig Ae/Be (HAeBe) stars, the evolutionary progenitors of main sequence A/B stars, raise new questions about the origin of magnetic fields in the intermediate mass stars. The favoured fossil field hypothesis suggests that a few percent of magnetic pre-main sequence A/B stars should exhibit similar magnetic strengths and topologies to the magnetic Ap/Bp stars. In this talk I will present the methods that we have used to characterise the magnetic fields of the Herbig Ae/Be stars, as well as our first conclusions on the origin of magnetism in intermediate-mass stars.
We present the results of our latest studies of the circumstellar magnetic fields in Herbig Ae stars and briefly discuss the cause of the failure of another recent study by our colleagues to confirm the Zeeman features in our spectra.
We present the results of a magnetic survey with FORS1 in polarimetric mode of a sample of B and Herbig Ae stars with previously undetected magnetic fields. For the first time a mean longitudinal magnetic field at a level higher than 3 sigma has been detected in one normal B star, two HgMn stars, one PGa star and four SPB stars. The observations of the three Herbig Ae stars (also known as Vega-like stars) reveal a definite longitudinal magnetic field in the star HD139614 at 4.8 sigma level: <B_z>=-450+-93 G. This is the largest magnetic field ever diagnosed for a Herbig Ae star. A hint of a ma…
Herbig Ae stars are young A-type stars in the pre-main sequence evolutionary phase with masses of ~1.5-3 M_o. They show rather intense surface activity (Dunkin et al. 1997) and infrared excess related to the presence of circumstellar disks. Because of their youth, primordial magnetic fields inherited from the parent molecular cloud may be expected, but no direct evidence for the presence of magnetic fields on their surface, except in one case (Donati et al. 1997), has been found until now. Here we report observations of optical circular polarization with FORS 1 at the VLT in the three Herbig A…
We have obtained accurate circular spectropolarimetric observations for a sample of Vega-like and Herbig Ae/Be stars with FORS1 at the VLT in an attempt to detect their magnetic fields. No magnetic field could be diagnosed in any Vega-like star. The most accurate determination of a magnetic field, at 2.6 sigma level, has been performed for the Vega-like star iota Cen for which we have measured <B_z> = -77+-30 G. In the prototype of Vega-like stars, the star beta Pictoris, which shows conspicuous signs of chromospheric activity, a longitudinal magnetic field is measured only at ~1.5 sigma level…
We intend to investigate separately the photospheric and circumstellar (CS) magnetic field components in seven Herbig Ae stars. The study is based on low-resolution (R ~ 2000 and 4000) spectropolarimetric data collected from 2003 to 2005 at the Very Large Telescope (ESO, Chile) with the multi-mode instrument FORS1. We show that the spectropolarimetric results strongly depend on the level of CS contribution to the stellar spectra. We have improved the determination accuracy of magnetic fields up to the 7 sigma level in the two Herbig Ae stars HD139614 and HD144432, observed in 2005 when these o…
The origin of the magnetic fields of the chemically peculiar main sequence Ap/Bp stars is still matter of intense debate. The recent discoveries of magnetic fields in Herbig Ae/Be stars using high resolution data obtained with the spectropolarimeter ESPaDOnS at CFHT provide a strong argument in favour of the fossil field hypothesis. Using a simple oblique rotator model of a centered dipole, we fit the Stokes V LSD profiles of two of these magnetic HAeBe stars, HD 200775 and V380 Ori, as well as their variations on timescales from days to months. We find that in both cases the dipole hypothesis…
Recently, strong, globally-ordered magnetic fields have been detected in some Herbig Ae and Be (HAeBe) stars, suggesting a possible evolutionary connection to main sequence magnetic chemically peculiar Ap and Bp stars. We have undertaken a detailed study of the binary system HD 72106, which contains a B9 magnetic primary and a HAeBe secondary, using the ESPaDOnS spectropolarimeter mounted on the CFHT. A careful analysis of the very young primary reveals that it has an approximately dipolar magnetic field geometry, strong chemical peculiarities, and strong surface chemical abundance inhomogenei…
Our recent discovery of magnetic fields in a small number of Herbig Ae/Be stars has required that we survey a much larger sample of stars. From our FORS1 and ESPaDOnS surveys, we have acquired about 125 observations of some 70 stars in which no magnetic fields are detected. Using a Monte Carlo approach, we have performed statistical comparisons of the observed longitudinal fields and LSD Stokes V profiles of these apparently non-magnetic stars with a variety of field models. This has allowed us to derive general upper limits on the presence of dipolar fields in the sample, and to place realist…
Studies of stellar magnetism at the pre-main sequence phase can provide important new insights into the detailed physics of the late stages of star formation, and into the observed properties of main sequence stars. This is especially true at intermediate stellar masses, where magnetic fields are strong and globally organised, and therefore most amenable to direct study. This paper reviews recent high-precision spectropolarimetric observations of pre-main sequence Herbig Ae/Be stars, which are yielding qualitatively new information about intermediate-mass stars: the origin and evolution of the…
We are investigating the magnetic characteristics of pre-main sequence Herbig Ae/Be stars, with the aim of (1) understanding the origin and evolution of magnetism in intermediate-mass stars, and (2) exploring the influence of magnetic fields on accretion, rotation and mass-loss at the early stages of evolution of A, B and O stars. We have begun by conducting 2 large surveys of Herbig Ae/Be stars, searching for direct evidence of photospheric magnetic fields via the longitudinal Zeeman effect. From observations obtained using FORS1 at the ESO-VLT and ESPaDOnS at the Canada-France-Hawaii Telesco…
The general context of this paper is the study of magnetic fields in the pre-main sequence intermediate mass Herbig Ae/Be stars. Magnetic fields are likely to play an important role in pre-main sequence evolution at these masses, in particular in controlling the gains and losses of stellar angular momentum. The particular aim of this paper is to announce the detection of a structured magnetic field in the Herbig Ae star HD 190073, and to discuss various scenarii for the geometry of the star, its environment and its magnetic field. We have used the ESPaDOnS spectropolarimeter at CFHT in 2005 an…
We present a statistical study of the X-Ray emission toward 22 Herbig AeBe stars using the Chandra archive. We probe the origin of the X-Rays toward Herbig stars: are they intrinsic? This question is addressed by correlations between the physical stellar properties and the X-Ray emission. There is a weak correlation between the continuum radio emission at lambda = 3.6cm and Lx, which suggests that the X-Ray emission depends upon the source. On the other hand, no correlation was found with the stellar rotational period, but that only excludes solar-like magnetic activity as the origin of the X-…
Among the A/B stars, about 5% host large-scale organised magnetic fields. These magnetic stars show also abundance anomalies in their spectra, and are therefore called the magnetic Ap/Bp stars. Most of these stars are also slow rotators compared to the normal A and B stars. Today, one of the greatest challenges concerning the Ap/Bp stars is to understand the origin of their slow rotation and their magnetic fields. The favoured hypothesis for the latter is that the fields are fosils, which implies that the magnetic fields subsist throughout the different evolutionary phases, and in particular d…
Studies of stellar magnetism at the pre-main sequence phase can provide important new insights into the detailed physics of the late stages of star formation, and into the observed properties of main sequence stars. This is especially true at intermediate stellar masses, where magnetic fields are strong and globally organised, and therefore most amenable to direct study. This talk reviews recent high-precision ESPaDOnS observations of pre-main sequence Herbig Ae-Be stars, which are yielding qualitatively new information about intermediate-mass stars: the origin and evolution of their magnetic …
We present linear spectropolarimetric data for eight Herbig Be and four Herbig Ae stars at H alpha, H beta and H gamma. Changes in the linear polarisation are detected across all Balmer lines for a large fraction of the observed objects, confirming that the small-scale regions surrounding these objects are flattened (i.e. disk-like). Furthermore, all objects with detections show similar characteristics at the three spectral lines, despite differences in transition probability and optical depth going from H alpha to H gamma. A large fraction of early Herbig Be stars (B0-B3) observed show line d…
The origin of magnetic fields in intermediate-mass and high-mass stars is fundamentally a mystery. Clues toward solving this basic astrophysical problem can likely be found at the pre-main sequence (PMS) evolutionary stage. With this work, we perform the largest and most sensitive search for magnetic fields in pre-main sequence Herbig Ae/Be (HAeBe) stars. Sixty-eight observations of 50 HAeBe stars have been obtained in circularly polarised light using the FORS1 spectropolarimeter at the ESO VLT. An analysis of both Balmer and metallic lines reveals the possible presence of weak longitudinal ma…
We report the XMM-Newton observation of a large X-ray flare from the Herbig Ae star V892 Tau. The apparent low mass companion of V892 Tau, V892 Tau NE, is unresolved by XMM-Newton. Nevertheless there is compelling evidence from combined XMM-Newton and Chandra data that the origin of the flare is the Herbig Ae star V892 Tau. During the flare the X-ray luminosity of V892 Tau increases by a factor of ~15, while the temperature of the plasma increases from kT ~ 1.5 keV to kT ~ 8 keV. From the scaling of the flare event, based on hydrodynamic modeling, we conclude that a 500 G magnetic field is nee…
Hard X-ray emissions from a Herbig Be star MWC297 were discovered in three separate observations spanning 5 days in April 1994 with the Advanced Satellite for Cosmology and Astrophysics (ASCA). An X-ray flare was found at the beginning of the second observation with a maximum luminosity of 4.9E32 ergs/s, which is five times larger than that of the quiescent phase (the first observation). It then declined with an e-folding time of ~5.6E4 sec to the pre-flare level in the third observation. The X-ray spectra are explained by absorbed thin-thermal plasma models. The temperature in the quiescent p…
H_alpha spectropolarimetry on Herbig Ae/Be stars shows that the innermost regions of intermediate mass (2 -- 15 M_sun) Pre-Main Sequence stars are flattened. This may be the best evidence to date that the higher mass Herbig Be stars are embedded in circumstellar discs. A second outcome of our study is that the spectropolarimetric signatures for the lower mass Herbig Ae stars differ from those of the higher mass Herbig Be stars. Depolarisations across H_alpha are observed in the Herbig Be group, whereas line polarisations are common amongst the Herbig Ae stars in our sample. These line polarisa…
Among the main sequence intermediate mass A and B stars, around 5% host large-scale organized magnetic fields. Most of these stars are very slow rotators compared to their non-magnetic counterparts, and show photospheric abundance anomalies. They are referred to as the Ap/Bp stars. One of the greatest challenges, today is to understand the origin of their magnetic field and their slow rotation. The favoured hypothesis is a fossil origin of the magnetic field, in which the magnetic fields of Ap/Bp stars are relics of those which existed in the parental molecular clouds during the formation. Thi…
We present evidence of magnetically-mediated disk accretion in Herbig Ae/Be stars. Magnetospheric accretion models of Balmer and sodium profiles calculated with appropriate stellar and rotational parameters are in qualitative agreement with the observed profiles of the Herbig Ae star UX Ori, and yield a mass accretion rate of ~ 10^{-8} Msun/yr. If more recent indications of an extremely large rotation rate for this object are correct, the magnetic field geometry must deviate from that of a standard dipole in order to produce line emission consistent with observed flux levels. Models of the ass…
We present new X-ray observations of the nearby Herbig Ae star HD 104237 (= DX Cha) with XMM-Newton, whose objective is to clarify the origin of the emission. Several X-ray emission lines are clearly visible in the CCD spectra, including the high-temperature Fe K-alpha complex. The emission can be accurately modeled as a multi-temperature thermal plasma with cool (kT < 1 keV) and hot (kT > 3 keV) components. The presence of a hot component is compelling evidence that the X-rays originate in magnetically confined plasma, either in the Herbig star itself or in the corona of an as yet unseen late…
Chandra X-ray imaging spectroscopy of the nearby Herbig Ae star HD 163296 at 100 AU angular resolution is reported. A point-like, soft (kT~0.5 keV), emission-line source is detected at the location of the star with an X-ray luminosity of 4.0e29 erg/s. In addition, faint emission along the direction of a previously-detected Ly-alpha-emitting jet and Herbig-Haro outflow may be present. The relatively low luminosity, lack of a hard spectral component, and absence of strong X-ray variability in HD 163296 can be explained as originating from optically-thin shock-heated gas accreting onto the stella…
We present Halpha spectropolarimetry observations of a sample of 23 Herbig Ae/Be stars. A change in the linear polarisation across Halpha is detected in a large fraction of the objects, which indicates that the regions around Herbig stars are flattened (disc-like) on small scales. A second outcome of our study is that the spectropolarimetric signatures for the Ae stars differ from those of the Herbig Be stars, with characteristics changing from depolarisation across Halpha in the Herbig Be stars, to line polarisations in the Ae group. The frequency of depolarisations detected in the Herbig Be …
After our recent discovery of four magnetic Herbig stars, we have decided to study in detail one of them, HD 200775, to determine if its magnetic topology is similar to that of the main sequence magnetic stars. With this aim, we monitored this star in Stokes I and V over more than two years, using the new spectropolarimeters ESPaDOnS at CFHT, and Narval at TBL. Using our data, we find that HD 200775 is a double-lined spectroscopic binary system, whose secondary seems similar, in temperature, to the primary. We determine the luminosity ratio of the system, and using the luminosity of the system…
We present Halpha spectropolarimetry observations of a sample of 10 bright T Tauri stars, supplemented with new Herbig Ae/Be star data. A change in the linear polarisation across Halpha is detected in most of the T Tauri (9/10) and Herbig Ae (9/11) objects, which we interpret in terms of a compact source of line photons that is scattered off a rotating accretion disk. We find consistency between the position angle (PA) of the polarisation and those of imaged disk PAs from infrared and millimetre imaging and interferometry studies, probing much larger scales. For the Herbig Ae stars AB Aur, MWC…
Context: Recent spectropolarimetric observations of Herbig Ae/Be stars have yielded new arguments in favour of a fossil origin for the magnetic fields of intermediate mass stars. Aims: To study the evolution of these magnetic fields, and their impact on the evolution of the angular momentum of these stars during the pre-main sequence phase, we observed Herbig Ae/Be members of young open clusters of various ages. Methods: We obtained high-resolution spectropolarimetric observations of Herbig Ae/Be stars belonging to the young open clusters NGC 6611 (< 6 Myr), NGC 2244 (~1.9 Myr), and NGC 2264 (…
We present the V band polarization of 81 Herbig Ae/Be (HAeBe) candidates from the Pico dos Dias Survey (PDS). A good estimate of the foreground polarization was possible for most stars. A large number of objects shows intrinsic polarization, which indicates that their circumstellar envelopes have some kind of non-spherical symmetry. In this work, however, we study these data focusing on their relation with the interstellar medium. Our data seem to indicate a correlation between the position angle of the HAeBe star polarization and that of the corresponding field stars. This may be an evidence …
The interpretation of X-ray detections from Herbig Ae/Be stars is disputed as it is not clear if these intermediate-mass pre-main sequence stars are able to drive a dynamo and ensuing phenomena of magnetic activity. Alternative X-ray production mechanisms, related to stellar winds, star-disk magnetospheres, or unresolved late-type T Tauri star companions have been proposed. In a series of papers we have been investigating high-resolution X-ray Chandra images of Herbig Ae/Be and main-sequence B-type stars to test the T Tauri hypothesis by spatially resolving known visual companions from the pri…
We present the ASCA results of intermediate-mass pre-main-sequence stars (PMSs), or Herbig Ae/Be stars (HAeBes). Among the 35 ASCA pointed-sources, we detect 11 plausible X-ray counterparts. X-ray luminosities of the detected sources in the 0.5-10 keV band are in the range of log LX ~30-32 ergs s-1, which is systematically higher than those of low-mass PMSs. This fact suggests that the contribution of a possible low-mass companion is not large. Most of the bright sources show significant time variation, particularly, two HAeBes - MWC 297 and TY CrA - exhibit flare-like events with long decay t…
We present the first high-resolution X-ray spectrum of a prototypical Herbig star (AB Aurigae), measure and interpret various spectral features, and compare our results with model predictions. We use X-ray spectroscopy data from XMM-Newton. The spectra are interpreted using thermal, optically thin emission models with variable element abundances and a photoelectric absorption component. We interpret line flux ratios in He-like triplet of O VII as a function of electron density and the UV radiation field. We use the nearby co-eval classical T Tauri star SU Aur as a comparison. AB Aurigae reveal…
Today, one of the greatest challenges concerning the Ap/Bp stars is to understand the origin of their slow rotation and their magnetic fields. The favoured hypothesis for the latter is the fossil field, which implies that the magnetic fields subsist throughout the different evolutionary phases, and in particular during the pre-main sequence phase. The existence of magnetic fields at the pre-main sequence phase is also required to explain the slow rotation of Ap/Bp stars. However, until recently, essentially no information was available about the magnetic properties of intermediate-mass pre-mai…
The origin of the strong magnetic fields observed in chemically peculiar Ap and Bp stars stars has long been debated. The recent discovery of magnetic fields in the intermediate mass pre-main sequence Herbig Ae and Be stars links them to Ap and Bp stars, providing vital clues about Ap and Bp stars and the origin and evolution of magnetic fields in intermediate and high mass stars. A detailed study of one young magnetic B star, HD 72106A, is presented. This star appears to be in a binary system with an apparently normal Herbig Ae star. A maximum longitudinal magnetic field strength of +391 +/- …
We report the discovery, using FORS1 at the ESO-VLT and ESPaDOnS at the CFHT, of magnetic fields in the young A-type stars HD 101412, V380 Ori and HD 72106A. Two of these stars (HD 101412 and V380 Ori) are pre-main sequence Herbig Ae/Be (HAeBe) stars, while one (HD 72106A) is physically associated with a HAeBe star. Remarkably, evidence of surface abundance spots is detected in the spectra of HD 72106A. The magnetic fields of these objects display intensities of order 1 kG at the photospheric level, are ordered on global scales, and appear in approximately 10% of the stars studied. Based on th…
We present in this paper the first results of a spectropolarimetric analysis of a small sample (~ 20) of active stars ranging from spectral type M0 to M8, which are either fully-convective or possess a very small radiative core. This study aims at providing new constraints on dynamo processes in fully-convective stars. The present paper focuses on 5 stars of spectral type ~M4, i.e. with masses close to the full convection threshold (~ 0.35 Msun), and with short rotational periods. Tomographic imaging techniques allow us to reconstruct the surface magnetic topologies from the rotationally modul…
We present here the first results of a spectropolarimetric analysis of a small sample (about 20) of active stars ranging from spectral type M0 to M8, which are either fully-convective or possess a very small radiative core. This study aims at providing new constraints on dynamo processes in fully-convective stars. Results for stars with spectral types M0-M4 -- i.e. with masses above or just below the full convection threshold (about 0.35Msun) -- are presented. Tomographic imaging techniques allow us to reconstruct the surface magnetic topologies from the rotationally modulated time-series of c…
Stellar magnetic fields can be investigated using several, very complementary approaches. While conventional spectroscopy is capable of estimating the average magnetic strength of potentially complex field configurations thanks to its low sensitivity to the vector properties of the field, spectropolarimetry can be used to map the medium- and large-scale structure of magnetic topologies. In particular, the latter approach allows one to retrieve information about the poloidal and toroidal components of the large-scale dynamo fields in low-mass stars, and thus to investigate the physical processe…
White-light observations of the solar corona show that there are two characteristic types of Coronal Mass Ejections (CMEs) in terms of speed-height profiles: so-called fast CMEs that attain high speeds low in the corona and slow CMEs that gradually accelerate from low initial speeds. Low and Zhang (2002) have recently proposed that fast and slow CMEs result from initial states with magnetic configurations characterized by normal prominences (NPs) and inverse prominences (IPs), respectively. To test their theory, we employed a two-dimensional, time-dependent, resistive magnetohydrodynamic code …
We present here additional results of a spectropolarimetric survey of a small sample of stars ranging from spectral type M0 to M8 aimed at investigating observationally how dynamo processes operate in stars on both sides of the full convection threshold (spectral type M4). The present paper focuses on early M stars (M0--M3), i.e. above the full convection threshold. Applying tomographic imaging techniques to time series of rotationally modulated circularly polarised profiles collected with the NARVAL spectropolarimeter, we determine the rotation period and reconstruct the large-scale magnetic …
The recently discovered magnetic Herbig Ae and Be stars may provide qualitatively new information about the formation and evolution of magnetic Ap and Bp stars. We have performed a detailed investigation of one particularly interesting binary system with a Herbig Ae secondary and a late B-type primary possessing a strong, globally ordered magnetic field. Twenty high-resolution Stokes V spectra of the system were obtained with the ESPaDOnS instrument mounted on the CFHT. In these observations we see clear evidence for a magnetic field in the primary, but no evidence for a magnetic field in the …
To properly understand the physics of upper main sequence stars it is particularly important to identify the origin of their magnetic fields. Recently, we confirmed that magnetic fields appear in Ap stars of mass below 3 M_sun only if they have already completed at least approximately 30% of their main-sequence lifetime. The absence of stars with strong magnetic fields close to the ZAMS might be seen as an argument against the fossil field theories. Here we present the results of our recent magnetic survey with FORS1 at the VLT in polarimetric mode of a sample of A, B and Herbig Ae stars with …
We have started a systematic study of the field topologies of magnetic single and accreting white dwarfs using Zeeman tomography. Here we report on our analysis of phase-resolved flux and circular polarization spectra of the magnetic cataclysmic variables BL Hyi and MR Ser obtained with FORS1 at the ESO VLT. For both systems we find that the field topologies are more complex than a dipole or an offset dipole and require at least multipole expansions up to order l = 3 to adequately describe the observed Zeeman features and their variations with rotational phase. Overall our model fits are in ex…
We report the "5+1" dynamical classification of the most frequently observed topologies of the magnetic field in sunspot groups associated with powerful flares.
The dynamical effects of magnetic fields in models of radiative, Herbig-Haro (HH) jets have been studied in a number of papers. For example, magnetized, radiative jets from variable sources have been studied with axisymmetric and 3D numerical simulations. In this paper, we present an analytic model describing the effect of a toroidal magnetic field on the internal working surfaces that result from a variability in the ejection velocity. We find that for parameters appropriate for HH jets the forces associated with the magnetic field dominate over the gas pressure force within the working surfa…
The heating of the solar corona is likely to be due to reconnection of the highly complex magnetic field that threads throughout its volume. We have run a numerical experiment of an elementary interaction between the magnetic field of two photospheric sources in an overlying field that represents a fundamental building block of the coronal heating process. The key to explaining where, how and how much energy is released during such an interaction is to calculate the resulting evolution of the magnetic skeleton. A skeleton is essentially the web of magnetic flux surfaces (called separatrix surf…
New observational techniques and sophisticated modelling methods has led to dramatic breakthroughs in our understanding of the interplay between the surface magnetism, atomic diffusion and atmospheric dynamics in chemically peculiar stars. Magnetic Doppler images, constructed using spectropolarimetric observations of Ap stars in all four Stokes parameters, reveal the presence of small-scale field topologies. Abundance Doppler mapping has been perfected to the level where distributions of many different chemical elements can be deduced self-consistently for one star. The inferred chemical spot …
We present optical linear polarimetry in the line of sight to HH135/HH136. The polarimetry of the field stars reveals two populations: one corresponds to a foreground interstellar component; the other originates in the interstellar medium in the vicinity of the Herbig-Haro pair and, therefore, can be used to study the magnetic field in the star forming region. Its direction is aligned with the jet of HH135/HH136, which could be an indication that the interstellar magnetic field is important in the outflow collimation. The interstellar magnetic field magnitude was estimated to be of order 90 uG…
This paper reports on an analysis of two Chandra X-ray observations of the young magnetic B star rho Ophiuchus S1. X-ray emission from the star was detected in both observations. The average flux was almost the same in both, but during each observation the flux showed significant time variations by a factor of two on timescales of 20-40 ks. Each spectrum could be fit by either an absorbed power-law model with a photon index of ~3 or a thin-thermal plasma model with a temperature of ~2 keV and an extremely low metal abundance (<~0.1 solar). The spectrum of the first observation has a weak-line …
The MHD instabilities can generate complex field topologies even if the initial field configuration is a very simple one. We consider the stability properties of magnetic configurations containing a toroidal and an axial field. In this paper, we concentrate mainly on the behavior of non-axisymmetric perturbations in axisymmetric magnetic configurations. The stability is treated by a linear analysis of ideal MHD equations.In the presence of an axial field, it is shown that the instability can occur for a wide range of the azimuthal wavenumber $m$, and its growth rate increases with increasing $…
A description is given of the algorithms implemented in the AstroBEAR adaptive mesh refinement code for ideal magnetohydrodynamics. The code provides several high resolution, shock capturing schemes which are constructed to maintain conserved quantities of the flow in a finite volume sense. Divergence free magnetic field topologies are maintained to machine precision by collating the components of the magnetic field on a cell-interface staggered grid and utilizing the constrained transport approach for integrating the induction equations. The maintenance of magnetic field topologies on adaptiv…
