Brief
summary of discussion on crab cavity, 19.09.2006
Participating:
Joachim
pointed out that the beam is sentivie to noise at the
betatron harmonic of about 3 kHz. Rama
commented that this is higher than typical mechanical vibration frequencies.
Joachim emphasized that second order terms of any kind could prove important
over 1e8 turns.
Rogelio
showed a new optics design for crab cavities, now with a larger crossing angle
of 8 mrad. This leaves sufficient space for the Q1 quadrupoles, unlike the 4.5 mrad
optics, and it would even allow for further reduction of beta* below 0.25m .
There are three dipoles per side of the IP, and the beta functions are less
regular due to the effect of the dispersion match. At Q1 the interbeam distance is 200 mm and at the crab cavity
location the spacing between the beam lines is 60 cm. The nominal full aperture
at Q1 is 9 sigma including the effect of beta mismatch,
dispersion mismatch and closed orbit errors. The dipoles have a field of 8 T. If higher
field magnets become available their length could be shortened gaining
additional space for the crab cavities. A remaining challenge may be that the
axes of two beam lines are not parallel in the Q1 magnet. The crab cavity
proposed by Rama has a half aperture of 53 cm and
would thus fit in the region with 60 cm separation. A total 400-MHz crab
voltage of 111 MV is needed, so that 4-5 MV/m would be adequate. The total
longitudinal space available for crabbing rf is 25
per beam.
Joachim
remarked that the high field of the crab cavity could be a problem. The other constraints is the aperture of Q.
Rama discussed other problems to
be addressed. He presented a baseline design consisting of double-squashed-cell
units. As always the B field providing the crab kick.
The length of the two cells is 0.75 m. Leaving another 0.75 space for damping, 46 cells with 2,.5
MV kick voltage per cell would fit on 35 m. The half apertures of the squashed
cell are 37.5 cm and 53 cm, respectively. For the aspect ration of 0.75, the
frequency separation between the TM110,Y (unwanted)
and TM110,X (crabbing) mode is 50 MHz. An aspect ratio closer to 1 with reduced
separation might be feasible. Rama argued that a
2-cell design is not as bad in terms of mode damping as a higher multi-cell
cavity. Joachim suggested to watch out for the sigma
and pi modes, quoting experience with lepton
Joachim
suggested a sausage type cavity geometry which would allow for larger
transverse extent without overlapping the second beam line. MAFIA calculation are needed to verify such a design. Space needs
to be reserved for superinsulation and vacuum tank. Rama mentioned that the geometry could be slightly reduced
by means of capacitive leading. Joachim replied that this is difficult for
Rogelio
asked which simulation codes can simulate luminosity for protons. Frank did not
know an immediate answer. Presumably the codes of Andreas Kabel
and Tanaji Sen are able to
predict luminosity. Reliability is another question.
Rama then showed the orbit and tune shift in the
case of two crab cavity sections in IP2 and 8 only, as a function of the
crossing angle. At a 4 mrad angle, the peak orbit at
the bunch head or tail (1 sigma) changes by 6-7 mm, and the tune by 5e-3, which is not considered acceptable. This option might work
for 500 microrad crossing angle, and is a cheaper?
alternative to reducing longitudinal emittance and
adding higher-harmonic rf for bunch shortening. Rogelo commented that Tanaji Sen’s optics with Ti3Sn could be used for such scheme.
Frank noticed that the tune shift with crossing angle could probably be reduced
by optimizing the sextupole strengths and the arc
optics.
It
was noticed that LEP rf noise data could be of
interest as example. There seems to be no promising R&D on