Ergodicity criteria for non-expanding transformations of 2-adic spheres

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems $$ on 2-adic spheres $\mathbf S_{2^{-r}}(a)$ of radius $2^{-r}$, $r\ge 1$, centered at some point $a$ from the ultrametric space of 2-adic integers $\mathbb Z_2$. The map $f\colon\mathbb Z_2\to\mathbb Z_2$ is assumed to be non-expanding and measure-preserving; that is, $f$ satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and $f$ preserves a natural probability measure on $\mathbb Z_2$, the Haar measure $\mu_2$ on $\mathbb Z_2$ which is normalized so that $\mu_2(\mathbb Z_2)=1$

Production of (τ+τ−)b(\tau^+\tau^-)_b in electron positron collisions

$(\tau^+\tau^-)_b$ is an atom of simple hydrogenlike structure similar to positronium $(e^+e^-)_b$ and $(\mu^+\mu^-)_b$. In this paper energy levels and decay widths of different decay channels of $(\tau^+\tau^-)_b$ are given. Cross section of production of this atomic system in $e^+e^-$ annihilation taking into account radiative corrections is calculated. According to our estimates 886 $(\tau^+\tau^-)_b$ atoms may be produced at BEPCII and 29 $(\tau^+\tau^-)_b$ atoms are produced at VEPP-4M under the present experimental conditions.Comment: 5 pages, submitted to Int. Jour. Mod. Phys.

A hydrogen ion beam method of molecular density measurement inside a 4.2-K beam tube

In our first experiments on synchrotron radiation-induced photodesorption in a 4.2-K beam tube, the moleculm density was measured by room temperature ion gauges and RGAs outside the beam tube. The molecular density inside the 4.2-K beam tube was therefore unknown, since the mean molecular speed of photodesorbed molecules had not been measured. To determine the density inside the 4.2-K beam tube we have developed a direct method of measurement utilizing the neutralization of H{sup +} beams, which are proportional to gas density. The hydrogen ion beams (up to 20 keV, {approximately}1 {mu}A) are extracted from an rf ion source and guided into the cold beam tube by a bending magnet. The H{sup 0} and H{sup {minus}} produced in the beam tube are magnetically separated from H{sup {minus}} and detected with secondary electron multipliers (SEMs). Small superconducting dipole magnets located near the center of the beam tube allow a {approximately}20-cm segment of the injected ion beam to be offset a few mm from the injection axis; detection of H{sup 0} and H{sup {minus}} produced along this offset segment provides a localized density measurement. If necessary, detector background due to synchrotron radiation photons can be discriminated against by gating the detector on between the bursts of synchrotron radiation. The experimental setup and initial data will be presented

Reflection of photons and azimuthal distribution of photoelectrons in a cylindrical beam pipe

In a cryogenic proton accelerator, such as the LHC, the creation of an electron cloud and generated heat loads resulting from electron bombardment are strongly dependent on the azimuthal distribution of created photoelectrons. In this context, photon reflection and photoelectron yield measurements have been performed using a beam line on the VEPP-2M storage ring. Six electrodes, covering the complete vacuum chamber perimeter, were mounted such that they could be suitably biased, and while one electrode was irradiated with synchrotron radiation the resulting electron current of all others could be measured. A detailed description of the experimental apparatus and the results of the measurements of photon reflection and the azimuthal distribution of generated photoelectrons are presented