Validation of frequency and mode extraction calculations from time-domain simulations of accelerator cavities

The recently developed frequency extraction algorithm [G.R. Werner and J.R. Cary, J. Comp. Phys. 227, 5200 (2008)] that enables a simple FDTD algorithm to be transformed into an efficient eigenmode solver is applied to a realistic accelerator cavity modeled with embedded boundaries and Richardson extrapolation. Previously, the frequency extraction method was shown to be capable of distinguishing M degenerate modes by running M different simulations and to permit mode extraction with minimal post-processing effort that only requires solving a small eigenvalue problem. Realistic calculations for an accelerator cavity are presented in this work to establish the validity of the method for realistic modeling scenarios and to illustrate the complexities of the computational validation process. The method is found to be able to extract the frequencies with error that is less than a part in 10^5. The corrected experimental and computed values differ by about one parts in 10^$, which is accounted for (in largest part) by machining errors. The extraction of frequencies and modes from accelerator cavities provides engineers and physicists an understanding of potential cavity performance as it depends on shape without incurring manufacture and measurement costs

Crab cavities for linear colliders

Crab cavities have been proposed for a wide number of accelerators and interest in crab cavities has recently increased after the successful operation of a pair of crab cavities in KEK-B. In particular crab cavities are required for both the ILC and CLIC linear colliders for bunch alignment. Consideration of bunch structure and size constraints favour a 3.9 GHz superconducting, multi-cell cavity as the solution for ILC, whilst bunch structure and beam-loading considerations suggest an X-band copper travelling wave structure for CLIC. These two cavity solutions are very different in design but share complex design issues. Phase stabilisation, beam loading, wakefields and mode damping are fundamental issues for these crab cavities. Requirements and potential design solutions will be discussed for both colliders.Comment: 3 pages. To be published in proceedings of LINAC 2008, Victoria, Canad

Design of the ILC Crab Cavity System

Abstract The International Linear Collider (ILC

Wake fields and beam dynamics simulations for the 3.9-ghz cavities of the ILC

Crab cavities are used for the ILC in order to increase the luminosity of the colliding beams at the interaction point. These cavities operate at the 3rd harmonic of the accelerating frequency. 1.3GHz. We study the LOM (Lower Order Modes) and HOM (Higher Order Modes) excited by the beam. The corresponding wake field is calculated and simulations are conducted on the beam dynamics of the interaction of the wake field with the multi-bunch beam train

Analysis of Wakefields in the ILC crab cavity.

The large crossing angle schemes of the ILC need a correction of bunch orientation at the interaction point (IP) in order to recover a luminosity loss of up to 80%. The orientation of bunches can be changed using a set of transverse deflecting cavities. The location of these crab cavities would be close to the final focus, and small deflections caused by wake fields in the cavities could cause misalignments of the bunches at the IP. Wake fields in the 3.9GHz deflecting cavities under development at FNAL have been analysed and their effects studied in view of use as the ILC crab cavity. Numerical simulations have been performed to determine the long-range wake potentials of up to quadrupole order modes in this cavity and their effect upon bunches passing through this cavity. Trapped modes within the CKM cavity have been investigated. Short-range wakes have also been a topic of study. The effect of the final focus quadrupole magnets on the deflection given to the bunch have also been calculated and used to calculate luminosity loss due to wake fields

Power coupler for the ILC crab cavity

The ILC crab cavity will require the design of an appropriate power coupler. The beam-loading in dipolemode cavities is considerably more variable than accelerating cavities, hence simulations have been performed to establish the required external Q. Simulations of a suitable coupler were then performed and were verified using a normal conducting prototype with variable coupler tips

Copper prototype measurements of the HOM, LOM and SOM couplers for the ILC crab cavity

The ILC Crab Cavity is positioned close to the IP and delivered luminosity is very sensitive to the wakefields induced in it by the beam. A set of couplers were designed to couple to and damp the spurious modes of the crab cavity. As the crab cavity operates using a dipole mode, it has different damping requirements from an accelerating cavity. A separate coupler is required for the monopole modes below the operating frequency of 3.9 GHz (known as the LOMs), the opposite polarization of the operating mode (the SOM), and the modes above the operating frequency (the HOMs). Prototypes of each of these couplers have been manufactured out of copper and measured attached to an aluminum nine cell prototype of the cavity and their external Q factors were measured. The results were found to agree well with numerical simulations