Abstract
Linear dynamics in a storage ring can be described by the one-turn map matrix. In the case of a resonance where two of the eigenvalues of this matrix are degenerate, a coupling perturbation causes a mixing of the uncoupled eigenvectors. A perturbation formalism is developed to find eigenvalues and eigenvectors of the one-turn map near such a linear resonance. Damping and diffusion due to synchrotron radiation can be obtained by integrating their effects over one turn, and the coupled eigenvectors can be used to find the coupled damping and diffusion coefficients. Expressions for the coupled equilibrium emittances and beam distribution moments are then derived. In addition to the conventional instabilities at the sum, integer, and half-integer resonances, it is found that the coupling can cause an instability through antidamping near a sum resonance even when the symplectic dynamics are stable. As one application of this formalism, the case of linear synchrobetatron coupling is analyzed where the coupling is caused by dispersion in the rf cavity, or by a crab cavity. Explicit closed-form expressions for the sum/difference resonances are given along with the integer/half-integer resonances. The integer and half-integer resonances caused by coupling require particular care. We find an example of this with the case of a crab cavity for the integer resonance of the synchrotron tune. Whether or not there is an instability is determined by the value of the horizontal betatron tune, a unique feature of these coupling-caused integer or half-integer resonances. Finally, the coupled damping and diffusion coefficients along with the equilibrium invariants and projected emittances are plotted as a function of the betatron and synchrotron tunes for an example storage ring based on PEP-II.
Highlights
The design of an electron storage ring typically uses a lattice of bending and focusing magnets to steer and focus the beam along with rf cavities to replenish energy to the beam lost to radiation
We give general expressions for instability widths, including many of the results of Hoffstaetter and Chao for synchrobetatron coupling, but we address the question on beam distribution
II, we summarize and give definitions regarding the computation of the invariants and their equilibrium values starting from a general one-turn map and the local damping and diffusion from synchrotron radiation
Summary
The design of an electron storage ring typically uses a lattice of bending and focusing magnets to steer and focus the beam along with rf cavities to replenish energy to the beam lost to radiation. In the general case including coupling, an algorithm was given in [9] to numerically compute the equilibrium distribution moments given the linear lattice of the storage ring. This is efficient for precise where x;y;z are the unperturbed damping decrements (percentage reduction of the x, y, and z amplitudes per turn) and is a dimensionless coupling constant to be defined later.. We use the parameters for the PEP-II LER as an example storage ring to plot the coupled damping and diffusion coefficients and equilibrium emittances as a function of the betatron and synchrotron tunes near each of the resonances. Once the basic approach is understood, the information contained in these tables would give the main results needed to apply the approach to a new type of perturbation or a new set of parameters
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physical Review Special Topics - Accelerators and Beams
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
