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Superconducting 499.8-MHz radio frequency (rf) cavities have been proposed for the High Energy Photon Source (HEPS), a 6-GeV diffraction-limited synchrotron light source currently under construction in Beijing. Being an active third-harmonic system, two cavities shall provide 3.5-MV rf voltage and 400 kW of beam power to enable a complex rf gymnastics required by a novel injection scheme. Adopting the veteran KEKB-type 500-MHz single-cell geometry, the cavity design has been focused on optimizing its mechanical properties. Various cavity wall thickness and external stiffening mechanisms were investigated to reinforce the cavity to ensure compliance to the pressure vessel codes under different working conditions from a bare cavity to a dressed cavity in the cryomodule. Small margins on operational pressure previously reported on this type of cavity have been largely improved with slightly reduced yet acceptable frequency tunability. Extensive design optimizations have been conducted aiming for lower stress, larger elastic buckling pressure, and higher frequencies of mechanical modes to cause microphonics, while the frequency tunability, pressure sensitivity, and Lorentz force detuning were being carefully monitored. In view of the HEPS’s lifetime, cavity fatigue was examined. This constitutes a comprehensive design optimization of the 499.8-MHz single-cell superconducting cavity with improved mechanical properties.

Superconducting β=1 quarter-wave geometry of 166.6 MHz has been proposed as main accelerating cavities for the high-energy photon source (HEPS) storage ring. HEPS is a 6-GeV kilometer-scale synchrotron light source promising ultralow emittance currently being constructed in Beijing. A proof-of-principle cavity has been previously in-house developed and vertical-tested achieving excellent cryogenic performances. A helium jacket was subsequently designed adopting a simple structure and an integrated magnetic field shielding. The mechanical properties of the dressed cavity were largely improved focusing on pressure sensitivity, stress, and Lorentz force detuning, while frequency tunability and microphonics were carefully monitored. Elastic buckling and fatigue were also examined. The helium jacket was later fabricated and welded directly with the niobium cavity. Mounted with an input power coupler and tuners, the dressed cavity was finally assembled in a modified cryomodule and tested at both 4.2 and 2.0 K. The favored low-pressure sensitivity and small Lorentz force detuning were confirmed. Microphonics spectrum was scanned and measured, presenting good consistencies with simulation predictions. Finally, the cavity was successfully tuned to the operating frequency of 166.6 MHz at cold and its frequency could be regulated within a ±3-Hz range. This article covers the mechanical aspects in the development and horizontal cryogenic tests of the first dressed 166.6-MHz superconducting cavity.

In almost all analyses of the least mean square (LMS) adaptive filter, it is assumed that the filter coefficients are statistically independent of the input data currently in filter memory, an assumption that is incorrect for shift-input data. We present a method for deriving a set of linear update equations that can be used to predict the exact statistical behavior of a finite-impulse-response (FIR) LMS adaptive filter operating upon finite-time correlated input data. Using our method, we can derive exact bounds upon the LMS step size to guarantee mean and mean-square convergence. Our equation-deriving procedure is recursive and algorithmic, and we describe a program written in the MAPLE symbolic-manipulation software package that automates the derivation for arbitrarily-long adaptive filters operating on input data with stationary statistics. Using our analysis, we present a search algorithm that determines the exact step size mean-square stability bound for a given filter length and input correlation statistics. Extensive computer simulations indicate that the exact analysis is more accurate than previous analyses in predicting adaptation behavior. Our results also indicate that the exact step size bound is much more stringent than the bound predicted by the independence assumption analysis for correlated input data.