arXiv subjects

J. A. Ellison

Publications and source records attributed to J. A. Ellison.

3 recordsLinked to original sources

arXiv2006

A New Model for the Collective Beam-Beam Interaction

The Collective Beam-Beam interaction is studied in the framework of maps with a ``kick-lattice'' model in the 4-D phase space of the transverse motion. A novel approach to the classical method of averaging is used to derive an approximate map which is equivalent to a flow within the averaging approximation. The flow equation is a continuous-time Vlasov equation which we call the averaged Vlasov equation, the new model of this paper. The power of this approach is evidenced by the fact that the averaged Vlasov equation has exact equilibria and the associated linearized equations have uncoupled azimuthal Fourier modes. The equation for the Fourier modes leads to a Fredholm integral equation of the third kind and the setting is ready-made for the development of a weakly nonlinear theory to study the coupling of the pi and sigma modes. The pi and sigma eigenmodes are calculated from the third kind integral equation. These results are compared with the kick-lattice model using our weighted macroparticle tracking code and a newly developed, density tracking, parallel, Perron-Frobenius code.

physics.acc-ph↗

arXiv2004

Quasiperiodic spin-orbit motion and spin tunes in storage rings

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.

physics.acc-ph↗

arXiv1999

Beam extraction studies at 900 GeV using a channeling crystal

Luminosity-driven channeling extraction has been observed for the first time in a 900 GeV study at the Fermilab Tevatron. This experiment, Fermilab E853, demonstrated that useful TeV level beams can be extracted from a superconducting accelerator during high luminosity collider operations without unduly affecting the background at the collider detectors. Multi-turn extraction was found to increase significantly the efficiency of the process. The beam extraction efficiency was about 25%. Studies of time dependent effects found that the turn-to-turn structure was governed mainly by accelerator beam dynamics. An investigation of a pre-scatterer using the accelerator flying wire system showed that a fiber could produce a significant extracted flux, consistent with expectations. Based on these results, it is feasible to construct a parasitic 5-10 MHz proton beam from the Tevatron collider.

physics.acc-ph↗