Stochastic collective dynamics of charged--particle beams in the stability regime

We introduce a description of the collective transverse dynamics of charged (proton) beams in the stability regime by suitable classical stochastic fluctuations. In this scheme, the collective beam dynamics is described by time--reversal invariant diffusion processes deduced by stochastic variational principles (Nelson processes). By general arguments, we show that the diffusion coefficient, expressed in units of length, is given by $\lambda_c\sqrt{N}$, where $N$ is the number of particles in the beam and $\lambda_c$ the Compton wavelength of a single constituent. This diffusion coefficient represents an effective unit of beam emittance. The hydrodynamic equations of the stochastic dynamics can be easily recast in the form of a Schr\"odinger equation, with the unit of emittance replacing the Planck action constant. This fact provides a natural connection to the so--called ``quantum--like approaches'' to beam dynamics. The transition probabilities associated to Nelson processes can be exploited to model evolutions suitable to control the transverse beam dynamics. In particular we show how to control, in the quadrupole approximation to the beam--field interaction, both the focusing and the transverse oscillations of the beam, either together or independently.Comment: 15 pages, 9 figure

Beam Dynamics and Beam Losses - Circular Machines

A basic introduction to transverse and longitudinal beam dynamics as well as the most relevant beam loss mechanisms in circular machines will be presented in this lecture. This lecture is intended for physicists and engineers with little or no knowledge of this subject.Comment: 18 pages, contribution to the 2014 Joint International Accelerator School: Beam Loss and Accelerator Protection, Newport Beach, CA, USA , 5-14 Nov 201

Longitudinal Momentum Mining of Beam Particles in a Storage Ring

I describe a new scheme for selectively isolating high density low longitudinal emittance beam particles in a storage ring from the rest of the beam without emittance dilution. I discuss the general principle of the method, called longitudinal momentum mining, beam dynamics simulations and results of beam experiments. Multi-particle beam dynamics simulations applied to the Fermilab 8 GeV Recycler (a storage ring) convincingly validate the concepts and feasibility of the method, which I have demonstrated with beam experiments in the Recycler. The method presented here is the first of its kind.Comment: 11 pages, 3 figure

Beam halo dynamics and control with hollow electron beams

Experimental measurements of beam halo diffusion dynamics with collimator scans are reviewed. The concept of halo control with a hollow electron beam collimator, its demonstration at the Tevatron, and its possible applications at the LHC are discussed.Comment: 5 pages, 4 figures, in Proceedings of the 52nd ICFA Advanced Beam Dynamics Workshop on High-Intensity and High-Brightness Hadron Beams (HB2012), Beijing, China, 17-21 September 201