Magnetic energy cascade in spherical geometry: I. The stellar convective dynamo case

We present a method to characterize the spectral transfers of magnetic energy between scales in simulations of stellar convective dynamos. The full triadic transfer functions are computed thanks to analytical coupling relations of spherical harmonics based on the Clebsch-Gordan coefficients. The method is applied to mean field $\alpha\Omega$ dynamo models as benchmark tests. From the physical standpoint, the decomposition of the dynamo field into primary and secondary dynamo families proves very instructive in the $\alpha\Omega$ case. The same method is then applied to a fully turbulent dynamo in a solar convection zone, modeled with the 3D MHD ASH code. The initial growth of the magnetic energy spectrum is shown to be non-local. It mainly reproduces the kinetic energy spectrum of convection at intermediate scales. During the saturation phase, two kinds of direct magnetic energy cascades are observed in regions encompassing the smallest scales involved in the simulation. The first cascade is obtained through the shearing of magnetic field by the large scale differential rotation that effectively cascades magnetic energy. The second is a generalized cascade that involves a range of local magnetic and velocity scales. Non-local transfers appear to be significant, such that the net transfers cannot be reduced to the dynamics of a small set of modes. The saturation of the large scale axisymmetric dipole and quadrupole are detailed. In particular, the dipole is saturated by a non-local interaction involving the most energetic scale of the magnetic energy spectrum, which points out the importance of the magnetic Prandtl number for large-scale dynamos.Comment: 21 pages, 14 figures, 1 table, accepted for publication in the Astrophysical Journa

Hard X-ray Quiescent Emission in Magnetars via Resonant Compton Upscattering

Non-thermal quiescent X-ray emission extending between 10 keV and around 150 keV has been seen in about 10 magnetars by RXTE, INTEGRAL, Suzaku, NuSTAR and Fermi-GBM. For inner magnetospheric models of such hard X-ray signals, inverse Compton scattering is anticipated to be the most efficient process for generating the continuum radiation, because the scattering cross section is resonant at the cyclotron frequency. We present hard X-ray upscattering spectra for uncooled monoenergetic relativistic electrons injected in inner regions of pulsar magnetospheres. These model spectra are integrated over bundles of closed field lines and obtained for different observing perspectives. The spectral turnover energies are critically dependent on the observer viewing angles and electron Lorentz factor. We find that electrons with energies less than around 15 MeV will emit most of their radiation below 250 keV, consistent with the turnovers inferred in magnetar hard X-ray tails. Electrons of higher energy still emit most of the radiation below around 1 MeV, except for quasi-equatorial emission locales for select pulse phases. Our spectral computations use a new state-of-the-art, spin-dependent formalism for the QED Compton scattering cross section in strong magnetic fields.Comment: 5 pages, 2 figures, to appear in Proc. "Physics of Neutron Stars - 2017," Journal of Physics: Conference Series, eds. G. G. Pavlov, et al., held in Saint Petersburg, Russia, 10-14 July, 201

Peeling Bifurcations of Toroidal Chaotic Attractors

Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review

On the structure and stability of magnetic tower jets

Modern theoretical models of astrophysical jets combine accretion, rotation, and magnetic fields to launch and collimate supersonic flows from a central source. Near the source, magnetic field strengths must be large enough to collimate the jet requiring that the Poynting flux exceeds the kinetic-energy flux. The extent to which the Poynting flux dominates kinetic energy flux at large distances from the engine distinguishes two classes of models. In magneto-centrifugal launch (MCL) models, magnetic fields dominate only at scales $\lesssim 100$ engine radii, after which the jets become hydrodynamically dominated (HD). By contrast, in Poynting flux dominated (PFD) magnetic tower models, the field dominates even out to much larger scales. To compare the large distance propagation differences of these two paradigms, we perform 3-D ideal MHD AMR simulations of both HD and PFD stellar jets formed via the same energy flux. We also compare how thermal energy losses and rotation of the jet base affects the stability in these jets. For the conditions described, we show that PFD and HD exhibit observationally distinguishable features: PFD jets are lighter, slower, and less stable than HD jets. Unlike HD jets, PFD jets develop current-driven instabilities that are exacerbated as cooling and rotation increase, resulting in jets that are clumpier than those in the HD limit. Our PFD jet simulations also resemble the magnetic towers that have been recently created in laboratory astrophysical jet experiments.Comment: 16 pages, 11 figures, published in ApJ: ApJ, 757, 6

Nonlinear Dynamics of Particles Excited by an Electric Curtain

The use of the electric curtain (EC) has been proposed for manipulation and control of particles in various applications. The EC studied in this paper is called the 2-phase EC, which consists of a series of long parallel electrodes embedded in a thin dielectric surface. The EC is driven by an oscillating electric potential of a sinusoidal form where the phase difference of the electric potential between neighboring electrodes is 180 degrees. We investigate the one- and two-dimensional nonlinear dynamics of a particle in an EC field. The form of the dimensionless equations of motion is codimension two, where the dimensionless control parameters are the interaction amplitude ($A$) and damping coefficient ($\beta$). Our focus on the one-dimensional EC is primarily on a case of fixed $\beta$ and relatively small $A$, which is characteristic of typical experimental conditions. We study the nonlinear behaviors of the one-dimensional EC through the analysis of bifurcations of fixed points. We analyze these bifurcations by using Floquet theory to determine the stability of the limit cycles associated with the fixed points in the Poincar\'e sections. Some of the bifurcations lead to chaotic trajectories where we then determine the strength of chaos in phase space by calculating the largest Lyapunov exponent. In the study of the two-dimensional EC we independently look at bifurcation diagrams of variations in $A$ with fixed $\beta$ and variations in $\beta$ with fixed $A$. Under certain values of $\beta$ and $A$, we find that no stable trajectories above the surface exists; such chaotic trajectories are described by a chaotic attractor, for which the the largest Lyapunov exponent is found. We show the well-known stable oscillations between two electrodes come into existence for variations in $A$ and the transitions between several distinct regimes of stable motion for variations in $\beta$

Symmetry-surfing the moduli space of Kummer K3s.

A maximal subgroup of the Mathieu group M24 arises as the combined holomorphic symplectic automorphism group of all Kummer surfaces whose Kaehler class is induced from the underlying complex torus. As a subgroup of M24, this group is the stabilizer group of an octad in the Golay code. To meaningfully combine the symmetry groups of distinct Kummer surfaces, we introduce the concepts of Niemeier markings and overarching maps between pairs of Kummer surfaces. The latter induce a prescription for symmetry-surfing the moduli space, while the former can be seen as a first step towards constructing a vertex algebra that governs the elliptic genus of K3 in an M24-compatible fashion. We thus argue that a geometric approach from K3 to Mathieu Moonshine may bear fruit.Comment: 20 pages; minor changes; accepted for publication in the Proceedings Volume of String-Math 201