1. DESIGN OF A 7-CELLS, HOM DAMPED, SUPERCONDUCTING CAVITY FOR THE STRONG RF FOCUSING EXPERIMENT AT DANE David Alesini, Caterina Biscari, Roberto Boni, Alessandro Gallo, Fabio Marcellini, Mikhail Zobov (INFN/LNF, Frascati (Roma)); Carlo Pagani (INFN/LASA, Segrate (MI); DESY, Hamburg)

2. CAVITY DESIGN CRITERIA DAMPING OF HIGHER ORDER MODES CONTROL OF THE TM010-LIKE MODE FREQUENCIES COUPLED BUNCH LONGITUDINAL INSTABILITY CHOICE OF THE EXTERNAL Q INPUT COUPLING DESIGN

3. THE STRONG RF FOCUSING EXPERIMENT AT DANE HAS BEEN PROPOSED TO CREATE AND OBSERVE A BUNCH LENGTH MODULATION ALONG THE RING. THE STRONG FOCUSING REGIME REQUIRES A VERY LARGE RF GRADIENT THAT CAN BE ONLY REACHED BY A MULTI-CELL SUPERCONDUCTING CAVITY. TO DEMONSTRATE THE FEASIBILITY OF A HIGH LUMINOSITY COLLIDER BASED ON THIS PRINCIPLE, A TOTAL MULTIBUNCH CURRENT OF THE ORDER OF 1A HAS TO BE STORED UNDER STABLE CONDITIONS IN THIS REGIME. HIGH CURRENTS AND MULTIBUNCH STABILITY OPERATION INVOLVE PROBLEMS, SUCH AS THE CURE OF HOMS, THAT HAVE TO BE KEPT INTO ACCOUNT.

4. TESLA CAVITY For the experiment has been designed a 7-cells cavity based on the design of the TESLA cavity. Main modifications are: basic cell dimensions has been lightly changed to comply with the DANE revolution frequency. number of cells has been changed from 9 to 7 to reduce the number of the cavity HOMs beam tubes have been enlarged to let most of the HOMs propagate and be damped by room-temperature ferrite rings. CAVITY PROFILE AND DIMENSIONS Enlarged beam pipe CAVITY PARAMETERS RF frequency [MHz]1288.9 Max RF voltage [MV]8 R/Q geometric factor [  ]390 Quality factor (@ 1.8 K)1 · 10 10 Cavity wall power [W @ 1.8 K]8 Loaded quality factor (1  4) ·10 7 Cavity detuning for Beam Loading (@ 8MV, Ib=1A) [kHz] -60 RF generator power [kW]1 Cavity length [m]0.8

5. transmission coefficient between the two enlarged beam tubes for the 2 nd and 3 rd monopole bands. The highest quality factors are of the order of 10 3. DAMPING OF HIGH ORDER MODES

6. The modes of the first longitudinal band, which include the accelerating one, do not propagate in the beam tubes and remain undamped. Their resonant frequencies should not overlap the bunch revolution harmonics to avoid anomalous power exchange between the beam and the cavity. Modef [GHz] R/Q[] /7 1266.731. 10 -2 2 /7 1269.901.4. 10 -5 3 /7 1274.531. 10 -1 4 /7 1279.724. 10 -4 5 /7 1284.451.4 6 /7 1288.951.6. 10 -3 CONTROL OF THE TM 010 -LIKE MODE FREQUENCIES nominal resonant frequencies and R/Q of the non propagating modes of the 1st monopole band modes of the 1st monopole band

7. Frequency sensitivityElectric field sensitivity FREQUENCY SENSITIVITY OF EACH TM010 MODE AND FIELD FLATNESS OF THE -MODE AS A FUNCTION OF THE LONGITUDINAL DEFORMATION OF EACH CELL. The real frequency values of these modes will be displaced by few hundreds kHz respect to the nominal values, because of cell fabrication tolerances. A cavity tuning, by controlled plastic deformation of the cells, is then necessary to precisely position the frequency of the accelerating mode (-mode) and restore a good field flatness. In addition this procedure can be used for tuning the resonant frequency of the other 6 modes safely away from the DAFNE bunch revolution harmonics. CONTROL OF THE TM 010 -LIKE MODE FREQUENCIES

8. Example: assuming that a +200 kHz shift of a selected mode in the band is needed. Applying each of these sets of cell longitudinal deformations: frequency of the relative mode is shifted by +200kHz; frequency of pi-mode is unperturbed; field flatness degradation is minimized; frequency shifts of all the other modes of the band is minimized. independently of the selected mode, the required cell deformations are  0.3 mm, while the frequency shift of the other modes is  200 kHz. The accelerating mode R/Q reduction, due to the loss of field flatness, is only few percent. From previous results it is possible to calculate the cell deformations to implement in the final tuning procedure to shift the resonant frequency of one of the trapped modes by a given quantity.

9. COUPLED BUNCH LONGITUDINAL INSTABILITY It could rise from the coupling with the synchrotron sidebands. To reduce beam coupling impedance of 1st band monopoles the cavity has to be powered through an efficient direct RF loop. The use of a wideband, low group delay solid state amplifier is particularly suitable for this task. A comb filter tuned on the bunch revolution harmonics is necessary to avoid interaction with powerful spectral lines that may saturate the loop.

10. The cavity can be driven by combining 4, 250W each, solid state amplifiers. Three of them are already available at LNF, as spare for the DAFNE longitudinal feedback system.

11. OPTIMUM Q EXT AND MICROPHONIC NOISE The input coupling factor of the SC cavity is defined essentially by the amount of microphonic noise that shakes the SC cavity and continuosly displaces its resonant frequency. The optimum Q EXT value depends on the maximum tolerable frequency deviation of the accelerating mode. If this figure exceeds the 15 Hz value, the 1 kW RF power available from our solid state amplifier is no more sufficient to guarantee 8 MV of accelerating voltage. Depending on the amount of the microphonic noise the optimal Q ext of the input coupler ranges from 210 7 to 410 7.

12. INPUT COUPLING DESIGN Also the input coupler is of the same type of the TESLA one. Like in the TESLA cavity, coupling coefficient variations will be possible by regulations, through a bellows system, of the inner conductor penetration into the beam tube. d [mm]100 b [mm]57 p [mm]4554555861 Q1.225E69.439E67.428E61.298E71.922E7 Q LOADED SENSITIVITY TO THE COUPLER INSERTION DEPTH TARGET VALUE: Q L = 2E+7

13. TRANSMISSION FREQUENCY RESPONSE OF THE CAVITY. Q EXT HAS BEEN CALCULATED FROM 3dB BANDWIDTH. FIELD FLATNESS FOR A GEOMETRY WITH THE COUPLER INCLUDED. HFSS INPUT GEOMETRY

14. CONCLUSIONS A 7-cells SC cavity based on the TESLA design has been proposed for the bunch length modulation experiment to be made at DAFNE. The basic cell has been slightly modified to resonate on the 420th harmonics of the bunch revolution frequency. The high order modes, with the exception of modes of the 1st monopolar (TM010) band, propagate in enlarged beam tubes and are damped in room-temperature ferrite ring loads. The control strategy of the TM010 band, which includes the accelerating one, relies on detuning the modes from the bunch revolution harmonics and impedance reduction through the implementation of a direct RF feedback loop. The TESLA cavity input coupler allows adjusting the coupling coefficient, whose optimal value is defined by the amount of microphonic noise affecting the cavity accelerating mode.