Profiles of inflated surfaces

We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves which we describe explicitly as the solutions of a certain differential equation.Comment: 13 pages, 2 figure

Ultimate parameters of the photon collider at the ILC

At linear colliders, the e+e- luminosity is limited by beam-collision effects, which determine the required emittances of beams in damping rings (DRs). While in gamma-gamma collisions at the photon collider, these effects are absent, and so smaller emittances are desirable. In present damping rings designs, nominal DR parameters correspond to those required for e+e- collisions. In this note, I would like to stress once again that as soon as we plan the photon-collider mode of ILC operation, the damping-ring emittances are dictated by the photon-collider requirements--namely, they should be as small as possible. This can be achieved by adding more wigglers to the DRs; the incremental cost is easily justified by a considerable potential improvement of the gamma-gamma luminosity. No expert analysis exists as of yet, but it seems realistic to obtain a factor five increase of the gamma-gamma luminosity compared to the ``nominal'' DR design.Comment: Talk at LCWS06, Bangalore, India, March 2006, to be published in Indian Journal of Physics, 5 pp, Latex, 1 .eps figur

Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: I. Turbulence Statistics

Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256^3 and 512^3 simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li, McKee, & Klein (2006). Our calculations are based on the assumption that the number of ions is conserved, but we show that these results approximately apply to the case of time-dependent ionization in molecular clouds as well. Convergence studies allow us to determine the optimal value of the ionization mass fraction when using the heavy-ion approximation for low Mach number, sub-Alfvenic turbulent systems. We find that ambipolar diffusion steepens the velocity and magnetic power spectra compared to the ideal MHD case. Changes in the density PDF, total magnetic energy, and ionization fraction are determined as a function of the AD Reynolds number. The power spectra for the neutral gas properties of a strongly magnetized medium with a low AD Reynolds number are similar to those for a weakly magnetized medium; in particular, the power spectrum of the neutral velocity is close to that for Burgers turbulence.Comment: 37 pages, 11 figures, 4 table