Continuous measurement of global difference coupling using a phase-locked-loop tune meter in the Relativistic Heavy Ion Collider

Abstract

We present a new technique to continuously measure and compensate the global difference coupling coefficient through the continuous measurements of eigenmode projection parameters, using a high resolution phase-locked-loop tune meter. First, four eigenmode projection parameters are defined as the observables for weak difference coupling. Then, their analytical expressions are obtained using the strict matrix treatment and the Hamiltonian perturbation theory of linear coupling. From these parameters, the complex global coupling coefficient can be fully determined and compensated. This method was successfully demonstrated in the Relativistic Heavy Ion Collider (RHIC) 2006 run.

Implementation of a coupled treatment of the one-turn mapping in the ray-tracing code Zgoubi

“…it is required by the equation 3.2. r is taken positive in [3,4,5,6] so one will keep this convention for the next analytical developments. In the following parts of this report the Edwards and Teng's parameters will refer to both the generalized Twiss' parameters and the coupling parameters r and C.…”

“…After some algebraic calculations made in [6] and [4] it has been proved that r > 1 corresponds to a case where the system is closer to a linear sum resonance than a linear dierence resonance. The case described by 0 < r < 1 is the opposite situation.…”

“…They only have a similar meaning in a transformed referential which is physically meaningless. 6 Floquet resonances: Resonances due to dipole and quadrupole imperfections. They correspond to integer and half-integer betatron tunes.…”

Simultaneous global coupling and vertical dispersion correction in RHIC

“…There is one skew quad for each triplet (total 12). Skew quads (total 48) between the arc and interaction region are for correcting linear difference global coupling [4], which are grouped as three families according to their coupling contribution's direction. There are 12 power supplies for these 48 skew quads, of which those in any given colored box form a single family with common setpoints to their respective power supplies.…”

High precision tune and coupling measurements and tune/coupling feedback in RHIC

“…The successful demonstration of simultaneous tune and coupling feedback in RHIC [1] during Run-6 was realized using direct-diode detection [2] for precision tune measurements (also referred to as BBQ, an acronym for base-band Q, or tune, measurements) and eigenmode projection [3][4][5] for direct measurement and hence control of the eigenmodes of the betatron oscillations. Since these very successful tests, routine use of tune and coupling feedback has been hampered by interferences from mains harmonics and complications with near-zero chromaticity [6], from rich spectral content at injection energy when accelerating ion beams [6,7], and from practicalities such as loss of lock of the phase lock loop used in determining the betatron frequencies [7,8].…”