Nuclear Instruments and Methods 188 (1981) 669-670 North-Holland Publishing Company
LETTERS TO THE EDITOR FIRST RESULTS ON ELLIPTICALLY SHAPED CAVITIES
P. KNEISEL, R. VINCON and J. HALBRITTER Kernforschung~zentrum Karlsruhe, 11£11, Postfach 3640, D-7500 Karlsruh'e, FR G Received 25 May 1981
First theoretical and experimental results on elliptically shaped Nb rf cavities important for storage ring applications are presented.
In wide gap accelerator cavities multipacting and field emission loading have been the major problems at low frequencies for many years [1,2]. Recently, due to the development of square corner and spherical-shaped cavities, the problem of multipacting has been overcome - as summarized in ref. I. An elliptical-shaped cavity with tilted end-plates-proposed at the workshop  - should have the potential of further improvements. This type of cavity (see fig. 1) has several features important for superconducting Nb cavities :
~'~- ~ 47
Fig. 1. Elliptically shaped TMol o cavity resonating at 1.5 GHz. For measuring this single cavity two beam tubes of 90 mm length have been TIG welded yielding Ep/Eac c = 1.6;
Hp/Eac c = 4.48 mT/(MV/m);
GH = 253 s2. Eac c is the effective accelerating field including transit time
factor. 0029-554X/81/0000-0000/$02.50 © 1981 North-Holland
a) The smooth, continuous change in curvature is very well suited for spinning or deep drawing techniques and yields a very high mechanical stability. b) The continuous curvature and tilting  of the endplates allow good access for surface treatments resulting in a reduction of etching and chemical residues, which often enhance the losses and the electron emission . c) By an optimized design , the ratio of peak electric surface field Ep to accelerating field Eacc, is with 1.6 about 10% lower  than for spherical cavities with the same cell-to-cell coupling factor. d) No multipacting has been found by trajectory calculations . e) Electron trajectory calculations have shown  that in field emission loading most electrons drift out through the beam hole, so that the electron impact onto regions with high peak Hp is reduced compared to parallel plate cavities [5,7]. f) The elliptical shape yields a reduced magnetic geometry factor G H  and enhanced electric geometry factor GE . Thus the residual losses  1/Qres=RresE/Gg+Rresg/Gn, which at low frequencies are dominated by RresE [5,8], are lowered, in addition to the effects mentioned in (c). g) Preliminary calculations have indicated  that in the elliptical cavity (fig. 1) the cell-to-cell coupling factor of TMo~n-modes is increasing with n, potentially easing the damping of higher modes. In this Letter we present first experimental results which qualitatively support the ideas presented above. The cavity shown in fig. 1 was formed by spinning  out of 2.5 mm Nb sheet in 2 steps with a stress annealing at 1000°C before the final shaping was done. Prior to the TIG welding both cavity halves
P. Kneisel et al. / Elliptically shaped cavities
0°2 15 ;
d) Up to Eacc = 1 1 . 5 MV/m the field could be raised immediately. After some time of running at high fields the cavity degraded to Qres = 101° and Eacc ~ 9 MV/m (Hp 40 mT). We attribute this to surface damage  caused by impinging electrons. Electropolishing and heat treatments should reduce the electron loading and the susceptibility to surface damage .
Fig. 2. Qo at 1.8K vs Eac c. Above Eac c ~ 6 M V / m field emitted electrons degrade the Qo, which fits  Lx(1/Q)/ Ep1.5 ~ exp[-c/(/3Ep)] with/3 = 860.
have been machined on a copying lathe to final dimensions by the removal of about 0.2 m m from the surface. A slight chemical polish (<~20/~m) in a HNO3/HF solution at 20°C was given to the surface prior to the measurements. The experimental results are: a) Af/z~p = 125 Hz/Torr shows the good mechanical stability of the design. b) Qres > 101° is quite high for the applied treatments. c) In the test reported here the field was limited by magnetic breakdown at Hp = 51.5 mT or Eac c = 11.5 MV/m (see fig. 2).
References [ 1 ] C.M. Lyneis, KfK-report 3019 (Kernforschungszentrum, Karlsruhe, 1980)p. 119.  J. Halbritter, ibid., p. 190.  P. Kneisel and J. Halbritter, to be published.  E.g., J.P. Turneaure, H.A. Schwettman, H.D. Schwarz and M.S. Mc Ashan, Appl. Phys. Lett. 25 (1974) 247.  Ph. Bernard, G. Cavallari, E. Chiaveri, E. Haebel, H. Heinrichs, H. Lengeler, E. Picasso, V. Piciarelli, J. T~ickmantel and H. Piel, Nucl. Instr. and Meth. (1981) to be published.  P. Fernandes and R. Parodi, Alta Frequenza (1981) and private communications.  Sh. Noguchi, Y. Kojima and J. Halbritter, Nucl. Instr. and Meth. 179 (1981) 205.  J. Halbritter, Z. Physik B31 (1978) 19; IEEE Trans. MAG-17 (1981) 943 and to be published in Proc. of LT16.  Fa. Gebriider Schmidt, Erlangen, West Germany.  C.M. Lyneis, P. Kneisel, O. Stoltz and J. Halbritter, IEEE Trans. MAG-11 (1975) 417.