Showing papers on "Field (physics) published in 2007"

Classical Charged Particles

Abstract: Philosophy and Logic of Physical Theory A Short History of the Classical Theory of Charged Particles Foundations of Classical Mechanics The Maxwell-Lorentz Field Electromagnetic Radiation The Charged Particle Generalizations The Relations of the Classical Lorentz-Invariant Charged-Particle Theory to Other Levels of Theory The Theory's Structure and Place in Physics.

62.2: Invited Paper: Fast Electro‐Optical Switching in Polymer‐Stabilized Liquid Crystalline Blue Phases for Display Application

Abstract: Blue phases have two major advantages over commonly used nematic phases:1) the response is much faster, 2) the zero-electric field state is optically isotropic. We demonstrate the sufficiently large electric field-induced birefringence and the micro-second response of the polymer-stabilized blue phases and the induced-isotropic phases without any surface treatment.

Optomechanical entanglement between a movable mirror and a cavity field

Abstract: In this paper we propose an experimental scheme to create and probe optomechanical entanglement between a light field and a mechanical oscillator. This is achieved using a bright laser field that resonates inside a cavity and couples to the position and momentum of a moving (micro)mirror.

Near-field radiative heat transfer and noncontact friction

Abstract: All material bodies are surrounded by a fluctuating electromagnetic field because of the thermal and quantum fluctuations of the current density inside them. Close to the surface of planar sources (when the distance $d⪡{\ensuremath{\lambda}}_{T}=c\ensuremath{\hbar}∕{k}_{B}T$), thermal radiation can be spatially and temporally coherent if the surface can support surface modes like surface plasmon polaritons, surface phonon polaritons, or adsorbate vibrational modes. The fluctuating field is responsible for important phenomena such as radiative heat transfer, the van der Waals interaction, and the van der Waals friction between bodies. A general formalism for the calculation of the power spectral density for the fluctuating electromagnetic field is presented and applied to the radiative heat transfer and the van der Waals friction using both the semiclassical theory of the fluctuating electromagnetic field and quantum field theory. The radiative heat transfer and the van der Waals friction are greatly enhanced at short separations $(d⪡{\ensuremath{\lambda}}_{T})$ between the bodies due to the evanescent electromagnetic waves. Particularly strong enhancement occurs if the surface of the body can support localized surface modes like surface plasmons, surface polaritons, or adsorbate vibrational modes. An electromagnetic field outside a moving body can also be created by static charges which are always present on the surface of the body due to inhomogeneities, or due to a bias voltage. This electromagnetic field produces electrostatic friction which can be greatly enhanced if on the surface of the body there is a two-dimensional electron or hole system, or an incommensurate adsorbed layer of ions exhibiting acoustic vibrations. Applications of radiative heat transfer and noncontact friction to scanning probe spectroscopy are discussed. The theory gives a tentative explanation for the experimental noncontact friction data.

Air–Sea Exchange in Hurricanes: Synthesis of Observations from the Coupled Boundary Layer Air–Sea Transfer Experiment

Abstract: The Coupled Boundary Layer Air–Sea Transfer (CBLAST) field program, conducted from 2002 to 2004, has provided a wealth of new air–sea interaction observations in hurricanes. The wind speed range for which turbulent momentum and moisture exchange coefficients have been derived based upon direct flux measurements has been extended by 30% and 60%, respectively, from airborne observations in Hurricanes Fabian and Isabel in 2003. The drag coefficient (CD) values derived from CBLAST momentum flux measurements show CD becoming invariant with wind speed near a 23 m s−1 threshold rather than a hurricane-force threshold near 33 m s−1 . Values above 23 m s−1 are lower than previous open-ocean measurements. The Dalton number estimates (CE) derived from CBLAST moisture flux measurements are shown to be invariant with wind speeds up to 30 m s −1 which is in approximate agreement with previous measurements at lower winds. These observations imply a CE/CD ratio of approximately 0.7, suggesting that additional energy sour...

Generalized Nash Equilibrium Problems

Abstract: The Generalized Nash equilibrium problem is an important model that has its roots in the economic sciences but is being fruitfully used in many different fields. In this survey paper we aim at discussing its main properties and solution algorithms, pointing out what could be useful topics for future research in the field.

Progressive field-state collapse and quantum non-demolition photon counting

Abstract: The irreversible evolution of a microscopic system under measurement is a central feature of quantum theory. From an initial state generally exhibiting quantum uncertainty in the measured observable, the system is projected into a state in which this observable becomes precisely known. Its value is random, with a probability determined by the initial system's state. The evolution induced by measurement (known as 'state collapse') can be progressive, accumulating the effects of elementary state changes. Here we report the observation of such a step-by-step collapse by non-destructively measuring the photon number of a field stored in a cavity. Atoms behaving as microscopic clocks cross the cavity successively. By measuring the light-induced alterations of the clock rate, information is progressively extracted, until the initially uncertain photon number converges to an integer. The suppression of the photon number spread is demonstrated by correlations between repeated measurements. The procedure illustrates all the postulates of quantum measurement (state collapse, statistical results and repeatability) and should facilitate studies of non-classical fields trapped in cavities.

New directions in single-molecule imaging and analysis

Abstract: Optical imaging and analysis of single molecules continue to unfold as powerful ways to study the individual behavior of biological systems, unobscured by ensemble averaging. Current expansion of interest in this field is great, as evidenced by new meetings, journal special issues, and the large number of new investigators. Selected recent advances in biomolecular analysis are described, and two new research directions are summarized: superresolution imaging using single-molecule fluorescence and trapping of single molecules in solution by direct suppression of Brownian motion.

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium.

Abstract: We report the observation of dynamo action in the von Karman sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R-m similar to 30. A mean magnetic field of the order of 40 G is observed 30\% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

NMR survey of reflected brownian motion

Abstract: Restricted diffusion is a common feature of many physicochemical, biological, and industrial processes. Nuclear magnetic resonance techniques are often used to survey the atomic or molecular motion in confining media by applying inhomogeneous magnetic fields to encode the trajectories of spin-bearing particles. The diversity and complexity of diffusive NMR phenomena, observed in experiments, result from the specific properties of reflected Brownian motion. Here the focus is on the mathematical aspects of this stochastic process, their physical interpretations, and their practical applications. The main achievements in this field, from Hahn’s discovery of spin echoes to present-day research, are presented in a unified mathematical language. A long-standing problem of restricted diffusion under arbitrary magnetic field is reformulated in terms of multiple correlation functions of the reflected Brownian motion. Many classical results are retrieved, extended, and critically discussed.

QuadCover - Surface Parameterization using Branched Coverings

Abstract: We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a branched covering of the 2-manifold and generates an integrable vector field by a Hodge decomposition on the covering space. Except for an optional smoothing and alignment of the initial frame field, the algorithm is fully automatic and generates high quality quadrilateral meshes.

Instability of the massive Klein-Gordon field on the Kerr spacetime

Abstract: We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued-fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l=1$, $m=1$ state, for $M\ensuremath{\mu}\ensuremath{\lesssim}0.5$. For a fast rotating hole ($a=0.99$) we find a maximum growth rate of ${\ensuremath{\tau}}^{\ensuremath{-}1}\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}(GM/{c}^{3}{)}^{\ensuremath{-}1}$, at $M\ensuremath{\mu}\ensuremath{\approx}0.42$. The physical implications are discussed.

A photon dominated region code comparison study

Abstract: Aims. We present a comparison between independent computer codes, modeling the physics and chemistry of interstellar photon dominated regions (PDRs). Our goal was to understand the mutual differences in the PDR codes and their effects on the physical and chemical structure of the model clouds, and to converge the output of different codes to a common solution. Methods. A number of benchmark models have been created, covering low and high gas densities n = 10 3 , 10 5.5 cm −3 and far ultraviolet intensities χ = 10, 10 5 in units of the Draine field (FUV: 6 < h ν< 13.6 eV). The benchmark models were computed in two ways: one set assuming constant temperatures, thus testing the consistency of the chemical network and photo-processes, and a second set determining the temperature self consistently by solving the thermal balance, thus testing the modeling of the heating and cooling mechanisms accounting for the detailed energy balance throughout the clouds. Results. We investigated the impact of PDR geometry and agreed on the comparison of results from spherical and plane-parallel PDR models. We identified a number of key processes governing the chemical network which have been treated differently in the various codes such as the effect of PAHs on the electron density or the temperature dependence of the dissociation of CO by cosmic ray induced secondary photons, and defined a proper common treatment. We established a comprehensive set of reference models for ongoing and future PDR model bench-marking and were able to increase the agreement in model predictions for all benchmark models significantly. Nevertheless, the remaining spread in the computed observables such as the atomic fine-structure line intensities serves as a warning that there is still a considerable uncertainty when interpreting astronomical data with our models.

Hall conductivity from dyonic black holes

Abstract: A class of strongly interacting $2+1$ dimensional conformal field theories in a transverse magnetic field can be studied using the AdS/CFT duality. We compute zero momentum hydrodynamic response functions of maximally supersymmetric $2+1$ dimensional $SU(N)$ Yang-Mills theory at the conformal fixed point, in the large $N$ limit. With background magnetic field $B$ and electric charge density $\ensuremath{\rho}$, the Hall conductivity is found to be $\ensuremath{\rho}/B$. The result, anticipated on kinematic grounds in field theory, is obtained from perturbations of a four-dimensional AdS black hole with both electric and magnetic charges.

Magnetic field amplification by shocks in turbulent fluids

Abstract: We consider the effect of preexisting, large-scale, broadband turbulent density fluctuations on propagating hydromagnetic shock waves. We present results from several numerical simulations that solve the two-dimensional magnetohydrodynamic equations. In our simulations, a plasma containing large-scale, low-amplitude density and magnetic field turbulence is forced to flow into a rigid wall, forming a shock wave. We find that the density fluctuations not only distort the shape of the shock front and lead to a turbulent postshock fluid, but they also produce a number of important changes in the postshock magnetic field. The average downstream magnetic field is increased significantly, and large fluctuations in the magnetic vector occur, with the maximum field strength reaching levels such that magnetic stresses are important in the postshock region. The downstream field enhancement can be understood in terms of the stretching and forcing together of the magnetic field entrained within the turbulent fluid of the postshock flow. We suggest that these effects of the density fluctuations on the magnetic field are observed in astrophysical shock waves such as supernova blast waves and the heliospheric termination shock.

Radio observational constraints on Galactic 3D-emission models

Abstract: (Abridged) We constrain simulated all-sky maps in total intensity, linear polarization, and rotation measure (RM) by observations. We test a number of large-scale magnetic field configurations and take the properties of the warm interstellar medium into account. From a comparison of simulated and observed maps we are able to constrain the regular large-scale Galactic magnetic field in the disk and the halo of the Galaxy. The local regular field is 2 microG and the average random field is about 3 microG. The known local excess of synchrotron emission originating either from enhanced CR electrons or random magnetic fields is able to explain the observed high-latitude synchrotron emission. The thermal electron model (NE2001) in conjunction with a proper filling factor accounts for the observed optically thin thermal emission and low frequency absorption by optically thick emission. A coupling factor between thermal electrons and the random magnetic field component is proposed, which in addition to the small filling factor of thermal electrons increases small-scale RM fluctuations and thus accounts for the observed depolarization at 1.4 GHz. We conclude that an axisymmetric magnetic disk field configuration with reversals inside the solar circle fits available observations best. Out of the plane a strong toroidal magnetic field with different signs above and below the plane is needed to account for the observed high-latitude RMs. Our preferred 3D-model fits the observations better than other models over a wide frequency range.

The XMM-Newton Wide-Field Survey in the COSMOS Field. I. Survey Description

Abstract: We present the first set of XMM-Newton EPIC observations in the 2 deg^2 COSMOS field The strength of the COSMOS project is the unprecedented combination of a large solid angle and sensitivity over the whole multiwavelength spectrum The XMM-Newton observations are very efficient in localizing and identifying active galactic nuclei (AGNs) and clusters, as well as groups of galaxies One of the primary goals of the XMM-Newton Cosmos survey is to study the coevolution of active galactic nuclei as a function of their environment in the cosmic web Here we present the log of observations, images, and a summary of first research highlights for the first pass of 25 XMM-Newton pointings across the field In the existing data set we have detected 1416 new X-ray sources in the 05-2, 2-45, and 45-10 keV bands to an equivalent 05-2 keV flux limit of 7 × 10^(-16) erg cm^(-2) s^(-1) The number of sources is expected to grow to almost 2000 in the final coverage of the survey From an X-ray color-color analysis we identify a population of heavily obscured, partially leaky or reflecting absorbers, most of which are likely to be nearby, Compton-thick AGNs

Direct Measurement of the Angular Dependence of Ionization for N 2 , O 2 , and CO 2 in Intense Laser Fields

Abstract: We experimentally measure the ionization probability as a function of alignment angle of three molecules in intense laser fields: nitrogen, oxygen, and carbon dioxide. Unlike atoms, molecules have a rotational degree of freedom. By controlling the alignment of the molecule relative to the laser field, molecules offer additional ways to understand strong-field ionization. The angular dependence of ionization directly maps to the orbital symmetry of each molecule. Carbon dioxide is seen to have a very sharp preference for ionization when aligned at 45 degrees to the laser field, in significant disagreement with current theories.

S-duality in N=2 supersymmetric gauge theories

Abstract: A solution to the infinite coupling problem for N = 2 conformal supersymmetric gauge theories in four dimensions is presented. The infinitely-coupled theories are argued to be interacting superconformal field theories (SCFTs) with weakly gauged flavor groups. Consistency checks of this proposal are found by examining some low-rank examples. As part of these checks, we show how to compute new exact quantities in these SCFTs: the central charges of their flavor current algebras. Also, the isolated rank 1 E6 and E7 SCFTs are found as limits of Lagrangian field theories.

Black Holes and Large N Species Solution to the Hierarchy Problem

Abstract: We provide the perturbative and non-perturbative arguments showing that theories with large number of species of the quantum fields, imply an inevitable hierarchy between the masses of the species and the Planck scale, shedding a different light on the hierarchy problem. In particular, using the black hole physics, we prove that any consistent theory that includes N number of the Z_2-conserved species of the quantum fields of mass \Lambda, puts a lower bound on the Planck mass, which in large N limit is given by N\Lambda^2. An useful byproduct of this proof is that any exactly conserved quantum charge, not associated with a long-range classical field, must be defined maximum modulo N, bounded by the the ratio of the Planck to the unit charge masses squared. For example, a continuous global U(1) `baryon number' symmetry, must be explicitly broken by gravity, at least down to a Z_N subgroup, with N bounded by the ratio of the Planck to baryon masses squared. The same constraint applies to any discrete gauge symmetry, as well as to other quantum-mechanically detectable black hole charges that are associated with the massive quantum hair of the black hole. We show that the gravitationally-coupled N-species sector that solves the gauge hirearchy problem, should be probed by LHC.

The First Direct Measurements of Surface Magnetic Fields on Very Low Mass Stars

Abstract: We present the first direct magnetic field measurements on M dwarfs cooler than spectral class M4.5. Utilizing a new method based on the FeH band near 1 μm, we categorize the integrated surface magnetic flux as low (well under 1 kG), intermediate (between 1 and about 2.5 kG), or strong (greater than about 3 kG) for a set of more than 20 stars ranging from M2 down to M9. Along with the field, we also measure the rotational broadening (v sin i) and Hα emission strength. Our goal is to advance the understanding of how dynamo field production varies with stellar parameters for very low mass stars, how the field and emission activity are related, and whether there is a connection between the rotation and magnetic flux. We find that fields are produced throughout the M dwarfs. In the mid-M stars, there is a clear connection between slow rotation and weak fields. In the late-M stars, rotation is always measurable, and the strongest fields are associated with with the most rapid rotators. Interestingly, these very cool rapid rotators appear to have the largest magnetic flux in the whole sample (greater than in the classical dMe stars). Hα emission is found to be a good proxy for magnetic fields, although the relation between the fractional emission and the magnetic flux varies with effective temperature. The drop-off in this fractional emission near the bottom of the main sequence is not accompanied by a drop-off in magnetic flux. It is clear that the methodology we have developed can be further applied to discover more about the behavior of magnetic dynamos and activity in cool and fully convective objects.

Non-linear force-free field modeling of a solar active region around the time of a major flare and coronal mass ejection

Abstract: Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of pre-existing atmospheric magnetic flux subject to surface plasma flows, or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA Active Region 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with 4 different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the ~10^32 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection.

Reformulation of the standard theory of Fowler–Nordheim tunnelling and cold field electron emission

Abstract: This paper presents a major reformulation of the standard theory of Fowler–Nordheim (FN) tunnelling and cold field electron emission (CFE). Mathematical analysis and physical interpretation become easier if the principal field emission elliptic function v is expressed as a function v(l 0 ) of the mathematical variable l 0 hy 2 , where y is the Nordheim parameter. For the Schottky–Nordheim (SN) barrier used in standard CFE theory, l 0 is equal to the ‘scaled barrier field’ f, which is the ratio of the electric field that defines a tunnelling barrier to the critical field needed to reduce barrier height to zero. The tunnelling exponent correction factor nZv( f ). This paper separates mathematical and physical descriptions of standard CFE theory, reformulates derivations to be in terms of l 0 and f, rather than y, and gives a fuller account of SN barrier mathematics. v(l 0 ) is found to satisfy the ordinary differential equation l 0 (1Kl 0 )d 2 v/dl 02 Z(3/16)v ;a n exact series solution, defined by recurrence formulae, is reported. Numerical approximation formulae, with absolute error j3j!8!10 K10 , are given for v and dv/dl 0 . The previously reported formula vz1Kl 0 C(1/6)l 0 ln l 0 is a good low-order approximation, with j3j!0.0025. With l 0 Zf, this has been used to create good approximate formulae for the other special CFE elliptic functions, and to investigate a more universal, ‘scaled’, form of FN plot. This yields additional insights and a clearer answer to the question: ‘what does linearity of an experimental FN plot mean?’ FN plot curvature is predicted by a new function w. The new formulation is designed so that it can easily be generalized; thus, our treatment of the SN barrier is a paradigm for other barrier shapes. We urge widespread consideration of this approach.

Controllable optical bistability in a four-subband semiconductor quantum well system

Abstract: We study optical bistability (OB) behavior based on intersubband transitions in asymmetric double quantum wells (QWs) where tunneling-induced quantum inference can be observed. The system interacts with a probe-laser field and a control laser field by means of a unidirectional ring cavity. We show that OB can be controlled efficiently by tuning the coupling strength of the tunneling, the Fano-type interference, and the intensity of the control field. The influence of the frequency detuning of the probe and control fields on the electronic OB behavior is also discussed. This investigation can be used for the optimal design of semiconductor QW systems to achieve fast and low-threshold all-optical switches, which is much more practical than that in an atomic system because of its flexible design and the controllable interference strength.

Domain wall mobility, stability and Walker breakdown in magnetic nanowires

Abstract: We present an analytical calculation of the velocity of a single 180° domain wall in a magnetic structure with reduced thickness and/or lateral dimension under the combined action of an external applied magnetic field and an electrical current. As for the case of field-induced domain wall propagation in thick films, two motion regimes with different mobilities are obtained, below and far above the so-called Walker field. Additionally, for the case of current induced motion, a Walker-like current density threshold is defined. The threshold field and current density, stating the wall's internal structure stability, differ from those in thick films; both are reduced by the same geometrical demagnetising factor which accounts for the confinement. This points out the fact that the velocity dependence over an extended field/current range and the knowledge of the Walker breakdown are mandatory to draw conclusions about the phenomenological Gilbert damping parameter tuning the magnetisation dynamics.

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and \beta-carotene

Abstract: In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with near-exact accuracy the optimised complete \pi-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.

Modeling Magnetic Torque and Force for Controlled Manipulation of Soft-Magnetic Bodies

Abstract: We calculate the torque and force generated by an arbitrary magnetic field on an axially symmetric soft-magnetic body. We consider the magnetization of the body as a function of the applied field, using a continuous model that unifies two disparate magnetic models. The continuous torque and force follow. The model is verified experimentally, and captures the often neglected region between weak and saturating fields, where interesting behavior is observed. We provide the field direction to maximize torque for a given field magnitude. We also find an absolute maximum torque, for a given body geometry and material, which can be generated with relatively weak applied fields. This paper is aimed at those interested in systems-level analysis, simulation, and real-time control of soft-magnetic bodies.

Weak magnetic fields in Ap/Bp stars : Evidence for a dipole field lower limit and a tentative interpretation of the magnetic dichotomy

Abstract: Aims. We investigated a sample of 28 well-known spectroscopically-identified magnetic Ap/Bp stars, with weak, poorly-determined or previously undetected magnetic fields. The aim of this study is to explore the weak part of the magnetic field distribution of Ap/Bp stars. Methods. Using the MuSiCoS and NARVAL spectropolarimeters at Telescope Bernard Lyot (Observatoire du Pic du Midi, France) and the cross-correlation technique Least Squares Deconvolution (LSD), we obtained 282 LSD Stokes V signatures of our 28 sample stars, in order to detect the magnetic field and to infer its longitudinal component with high precision (median σ = 40 G). Results. For the 28 studied stars, we obtained 27 detections of StokesV Zeeman signatures from the MuSiCoS observations. Detection of the Stokes V signature of the 28th star (HD 32650) was obtained during science demonstration time of the new NARVAL spectropolarimeter at Pic du Midi. This result clearly shows that when observed with sufficient precision, all firmly classified Ap/Bp stars show detectable surface magnetic fields. Furthermore, all detected magnetic fields correspond to longitudinal fields which are significantly greater than some tens of G. To better characterise the surface magnetic field intensities and geometries of the sample, we phased the longitudinal field measurements of each star using new and previously-published rotational periods, and modeled them to infer the dipolar field intensity (Bd, measured at the magnetic pole) and the magnetic obliquity (β). The distribution of derived dipole strengths for these stars exhibits a plateau at about 1 kG, falling off to larger and smaller field strengths. Remarkably, in this sample of stars selected for their presumably weak magnetic fields, we find only 2 stars for which the derived dipole strength is weaker than 300 G. We interpret this “magnetic threshold” as a critical value necessary for the stability of large-scale magnetic fields, and develop a simple quantitative model that is able to approximately reproduce the observed threshold characteristics. This scenario leads to a natural explanation of the small fraction of intermediate-mass magnetic stars. It may also explain the near-absence of magnetic fields in more massive B and O-type stars.