Search Results (7 total)

The Tevatron in Collider Run II (2001–present) is operating with 6 times more bunches, many times higher beam intensities and luminosities than in Run I (1992–1995). Electromagnetic long-range and head-on interactions of high intensity proton and antiproton beams have been significant sources of beam loss and lifetime limitations. We present observations of the beam-beam phenomena in the Tevatron and results of relevant beam studies. We analyze the data and various methods employed in operations, predict the performance for planned luminosity upgrades, and discuss ways to improve it.

The Tevatron in Run II is operating with three trains of 12 bunches each. Long-range beam-beam interactions have been significant sources of beam loss and lifetime limitations of antiprotons. The dynamics due to the long-range beam-beam interactions depends on several beam parameters such as tunes, coupling, chromaticities, beam separations, intensities, and emittances. We have developed analytical tools to calculate, for example, amplitude dependent tune shifts and chromaticities, beam-beam induced coupling, and resonance driving terms. We report on these calculations and estimates of dynamic aperture and diffusion coefficients with long-term tracking. These theoretical results are compared with observations and used to predict performance at design values of beam parameters.

The Very Large Hadron Collider design is converging on a program where a 233 km circumference tunnel would first be occupied by a low field dipole system producing 40 TeV in the center of mass, followed by a higher field magnet system producing nearly 200 TeV in the center of mass. We consider the possibility of first using the tunnel for a large e⁺e^- collider. We assume that the total radiated synchrotron power will be limited to 100 MW. We describe the design strategy, the luminosity and energy reach, the factors that limit the machine performance, the scaling laws that apply to its design, and the technology that would be required for its implementation.

We develop the method of weighted macroparticle tracking (WMPT) for simulating the time evolution of the moments of the phase space densities of two beams which are coupled via the collective (strong-strong) beam-beam interaction in the absence of diffusion and damping. As an initial test we apply this method to study the π mode and the σ mode in three different 1D limits of the beam-beam interaction. The three limits are flat beams and transverse motion in the direction of the small width, round beams, and flat beams and motion in the direction of the large width. We have written a code (BBDeMo1D) based on WMPT, which allows testing of all three limits and is suited for extension to 2 degrees of freedom.

Random fluctuations in the tune, beam offsets, and beam size in the presence of the beam-beam interaction are shown to lead to significant particle diffusion and emittance growth in hadron colliders. We find that far from resonances high frequency noise causes the most diffusion while near resonances low frequency noise is responsible for the large emittance growth observed. Comparison of different fluctuations shows that offset fluctuations between the beams cause the largest diffusion for particles in the beam core.

We consider the geometrical phases arising in the state vector of two-level atoms due to their interaction with a self-consistently generated classical electrical field propagating without loss through the atomic medium. Three conservation laws are shown to exist generally and are used to solve for the individual quantum amplitudes, phases, and the electric field. We calculate the geometrical phases in two situations: (a) where the atoms are initially in the ground state and (b) where the initial state is a coherent superposition of the ground and excited states. In both cases the geometrical phase is the Aharonov-Anandan phase resulting from the atomic state vector tracing out a closed curve on the projective Hilbert space–here the Bloch sphere. We show that geometric quantities associated with the curve on the Bloch sphere are directly related to physical observables. The solid angle subtended by the closed curve (shown to equal twice the geometric phase) is a measure of the maximum atomic inversion, while the speed with which the curve is traced is related to the energy uncertainty in the state. An experimental method to observe the total phase change in a two-level subsystem is outlined, using photon echoes in a three-level medium.

A perturbative method, using Lie transforms, is given for calculating the Hannay angle for slow, cyclic evolutions of a classical system, taking into account the finite rate of change of the Hamiltonian. The method is applied to the generalized harmonic oscillator. The classical Aharonov-Anandan angle is also calculated. The interpretational ambiguity in the definitions of geometrical angles is discussed.