This paper presents results of experimental and theoretical investigations of transverse beam stability at injection to Fermilab Booster and discusses a novel scheme for transition crossing allowing to avoid the longitudinal emittance growth related to the transition. At reduced chromaticity a multibunch high order head-tail mode develops with growth time of 12 turns at fractional part of tune close to zero. An estimate of the growth rate based on known sources of impedance results in significantly smaller value and cannot explain observed instability growth rate.

The Fermilab Booster - built more than 40 years ago - operates well above the design proton beam intensity of 4 · 1012 ppp. Still, the Fermilab neutrino experiments call for even higher intensity exceeding 5.5 · 1012 ppp. A multitude of intensity related effects must be overcome in order to meet this goal including suppression of coherent dipole instabilities of transverse oscillations which manifest themselves as a sudden drop in the beam current. In this report we present the results of observation of these instabilities at different tune, coupling and chromaticity settings and discuss possible cures.

This study is motivated by the proposed upgrades of a whole sequence of Fermilab's accelerators; Linac, Booster, Main Ring or Main Injector and the Tevatron. Two leading high-luminosity collider upgrade scenarios involve larger numbers of colliding bunches of higher intensity. This obviously raises a question of coherent instabilities, which was already quite vital in the present fixed target and collider scenarios. Furthermore, multi-bunch instability limitations due to the resistive wall impedance are studied for the fixed target mode. The same question of coupled bunch instabilities is also addressed for new collider schemes involving large number of colliding bunches (up to 100 on 100 bunches), where the inter-bunch communication may become important. 4 refs.

This book provides a comprehensive treatment of intensity dependent particle beam instabilities in accelerating rings. Written for researchers, the material is also suitable for use as a textbook in an advanced graduate course for students studying accelerator physics. The presentation starts with a brief review of the basic concept of wake potentials and coupling impedances in the vacuum chamber followed by a discussion on static and dynamic solutions of their effects on the particle beams. Special emphasis is placed separately on proton and electron machines. Other special topics of interest covered include Landau damping, BalakinOCoNovokhatskyOCoSmirnov damping, Sacherer''s integral equations, Landau cavity, saw-tooth instability, Robinson stability criteria, beam loading, transition crossing, two-stream instabilities, and collective instability issues of isochronous rings. After the formulation of an instability, readers are provided a thorough description of one or more experimental observations together with a discussion of the cures for the instability. Although the book is theory oriented, the use of mathematics has been minimized. The presentation is intended to be rigorous and self-contained with nearly all the formulas and equations derived."

Based around recent lectures given at the prestigious Ritsumeikan conference, the tutorial and expository articles contained in this volume are an essential guide for practitioners and graduates alike who use stochastic calculus in finance.Among the eminent contributors are Paul Malliavin and Shinzo Watanabe, pioneers of Malliavin Calculus. The coverage also includes a valuable review of current research on credit risks in a mathematically sophisticated way contrasting with existing economics-oriented articles.