The LHC RF system, which must handle high intensity (0.5 A d.c.) beams, makes use of superconducting singlecell cavities, best suited to minimizing the effects of periodic transient beam loading. There will be eight cavities per beam, each capable of delivering 2 MV (5 MV/m accelerating field) at 400 MHz. The cavities themselves are now being manufactured by industry, using niobium-on-copper technology which gives full satisfaction at LEP. A cavity unit includes a helium tank (4.5 K operating temperature) built around a cavity cell, RF and HOM couplers and a mechanical tuner, all housed in a modular cryostat. Four-unit modules are ultimately foreseen for the LHC (two per beam), while at present a prototype version with two complete units is being extensively tested. In addition to a detailed description of the cavity and its ancillary equipment, the first test results of the prototype will be reported.
where C(S) satisfies (16). Equation (17) is our general smoothing formula for (1 ).The formula in (17) along with ItG's chain rule [SI can be used to obtain the fixed-point and fixed-lag smoothed estimates of x(Z). These were obtained in [9] via a longer argument.In practise the "correction term" [lo] for the state-dependent noise may be important. This is easily included in our results on using results from [lo]. In fact, in the results above, one_ need only replace A by ; i and F by r' where A^ is defined in [5l and F is defined in an analogous manner.
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