Magnetostrictive behaviour of thin superconducting disks

Flux-pinning-induced stress and strain distributions in a thin disk superconductor in a perpendicular magnetic field is analyzed. We calculate the body forces, solve the magneto-elastic problem and derive formulas for all stress and strain components, including the magnetostriction $\Delta R/R$. The flux and current density profiles in the disk are assumed to follow the Bean model. During a cycle of the applied field the maximum tensile stress is found to occur approximately midway between the maximum field and the remanent state. An effective relationship between this overall maximum stress and the peak field is found.Comment: 8 pages, 6 figures, submitted to Supercond. Sci. Technol., Proceed. of MEM03 in Kyot

Dust Evolution and the Formation of Planetesimals

The solid content of circumstellar disks is inherited from the interstellar medium: dust particles of at most a micrometer in size. Protoplanetary disks are the environment where these dust grains need to grow at least 13 orders of magnitude in size. Our understanding of this growth process is far from complete, with different physics seemingly posing obstacles to this growth at various stages. Yet, the ubiquity of planets in our galaxy suggests that planet formation is a robust mechanism. This chapter focuses on the earliest stages of planet formation, the growth of small dust grains towards the gravitationally bound "planetesimals", the building blocks of planets. We will introduce some of the key physics involved in the growth processes and discuss how they are expected to shape the global behavior of the solid content of disks. We will consider possible pathways towards the formation of larger bodies and conclude by reviewing some of the recent observational advances in the field.Comment: 43 pages, 6 figures. Chapter in International Space Science Institute (ISSI) Book on "The Disk in Relation to the Formation of Planets and their Proto-atmospheres", published in Space Science Reviews by Springe

Large N limit of orbifold field theories

We consider certain orbifoldization of the ${\cal N}=4$ field theories that leads to ${\cal N}=2,1,0$ field theories in 4 dimensions. These theories were recently analyzed using the string theory perturbation technique. It was found that in the large $N$ limit all correlation functions of the orbifold theories coincide with those of ${\cal N}=4$, modulo the rescaling of the gauge coupling constant. In this paper we repeat the same analysis using the field theoretical language.Comment: 12 pages, 3 figures, harvmac. Minor change

The Saturation Limit of the Magnetorotational Instability

Simulations of the magnetorotational instability (MRI) in a homogeneous shearing box have shown that the asymptotic strength of the magnetic field declines steeply with increasing resolution. Here I model the MRI driven dynamo as a large scale dynamo driven by the vertical magnetic helicity flux. This growth is balanced by large scale mixing driven by a secondary instability. The saturated magnetic energy density depends almost linearly on the vertical height of the typical eddies. The MRI can drive eddies with arbitrarily large vertical wavenumber, so the eddy thickness is either set by diffusive effects, by the magnetic tension of a large scale vertical field component, or by magnetic buoyancy effects. In homogeneous, zero magnetic flux, simulations only the first effect applies and the saturated limit of the dynamo is determined by explicit or numerical diffusion. The exact result depends on the numerical details, but is consistent with previous work, including the claim that the saturated field energy scales as the gas pressure to the one quarter power (which we interpret as an artifact of numerical dissipation). The magnetic energy density in a homogeneous shearing box will tend to zero as the resolution of the simulation increases, but this has no consequences for the dynamo or for angular momentum transport in real accretion disks. The claim that the saturated state depends on the magnetic Prandtl number may also be an artifact of simulations in which microphysical transport coefficients set the MRI eddy thickness. Finally, the efficiency of the MRI dynamo is a function of the ratio of the Alfv\'en velocity to the product of the pressure scale height and the local shear. As this approaches unity from below the dynamo reaches maximum efficiency.Comment: Accepted by The Astrophysical Journa

Oscillatory regimes of the thermomagnetic instability in superconducting films

The stability of superconducting films with respect to oscillatory precursor modes for thermomag- netic avalanches is investigated theoretically. The results for the onset threshold show that previous treatments of non-oscillatory modes have predicted much higher thresholds. Thus, in film supercon- ductors, oscillatory modes are far more likely to cause thermomagnetic breakdown. This explains the experimental fact that flux avalanches in film superconductors can occur even at very small ramping rates of the applied magnetic field. Closed expressions for the threshold magnetic field and temperature, as well oscillation frequency, are derived for different regimes of the oscillatory thermomagnetic instability.Comment: 5 pages, 5 figure

Dendritic flux avalanches in rectangular superconducting films -- numerical simulations

Dendritic flux avalanches is a frequently encountered instability in the vortex matter of type II superconducting films at low temperatures. Previously, linear stability analysis has shown that such avalanches should be nucleated where the flux penetration is deepest. To check this prediction we do numerical simulations on a superconducting rectangle. We find that at low substrate temperature the first avalanches appear exactly in the middle of the long edges, in agreement with the predictions. At higher substrate temperature, where there are no clear predictions from the theory, we find that the location of the first avalanche is decided by fluctuations due to the randomly distributed disorder.Comment: 3 pages, 2 figure

Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration

We present simulations of the non-linear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian time-scale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random walk, depends strongly on their stopping time and on the solids-to-gas ratio of the background state, but diffusion is generally modest, particularly for tightly coupled solids. Angular momentum transport is too weak and of the wrong sign to influence stellar accretion. Self-gravity and collisions will be needed to determine the relevance of particle overdensities for planetesimal formation.Comment: Accepted for publication in ApJ (17 pages). Movies of the simulations can be downloaded at http://www.mpia.de/~johansen/research_en.ph