Brief
summary of discussion on crab cavity, 27.07.2006
Participating:
Rama Calaga, Joachim Tuckmantel, Rogelio Tomas, Frank Zimmermann
Frank
raised three points: turn-to-turn noise requirement 0.002 ps (achievable?),
size of crab cavities compared with beam-beam distance, and goals for the optics
design (maximum luminosity, residual effects, possibility of flat-beam solution
with doublet).
Crab
cavity tolerance is essentially left-right jitter tolerance, and to some extent
also left-left, right-right tolerance (in order that the beams do not collider
off-center.
Beam
loading and mechanical vibration may be different for the different cavities
and could cause left-right etc. jitter.
In
the rf sections the beams are separated by 42 cm - the largest separation in
the LHC. The standard separation between the two beams in the rest of the
machine seems to be 19.4 cm.
How
well need the beam be centered in the crab cavity in regard to beam loading?
Rama
had proposed 2-in-1 crab cavity for LHC using fundamental mode, but there are
some issues with this proposal, e.g., beam loading and wake fields.
Can
we allow the beam to propagate tilted around the machine (probably, yes, to be
verified in simulations and possibly experiments.
The
detuning with amplitude is specified to be smaller than 2e-3 at 6 sigma, and 36
times smaller at 1 sigma.
See
page 14 of
"Field
Quality Specification for the LHC Main Dipole Magnets", Brüning, Olivier
Sim; Fartoukh, Stéphane; LHC-Project-Report-501; CERN-LHC-Project-Report-501 http://doc.cern.ch/archive/electronic/cern/preprints/lhc/lhc-project-report-501.pdf
Multicell
cavities could be problematic in terms of feedback on two modes, feedback gain
and frequency split to be achieved.
The
minimum crossing angle for independent low-beta quadrupoles is 2 mrad or less
according to:
"Performance Limits and IR Design of a Possible LHC Luminosity Upgrade
Based on
A.
Devred (DSM, DAPNIA, Saclay) , O.S. Bruning, R. Ostojic, L. Rossi, F. Ruggiero,
W. Scandale, T.M. Taylor (CERN).
EPAC-2004-MOPLT030,
Jul 2004. 3pp.
Presented
at the 9th European Particle Accelerator Conference (EPAC 2004),
http://accelconf.web.cern.ch/AccelConf/e04/PAPERS/MOPLT030.PDF
Rogelio
showed a draft optics with 5.4 mrad crossing angle,
and new position of D2, inverted bending angles for D1 and D2, new quadrupoles
for dispersion matching. There is more han 60 m free space longitudinally,
the transverse separation is 30-35 cm.
Left-right
and left-IP transfer matrices can be obtianed from this optics.
Frank
asked how the dispersion is matched in the nominal IP.
Rogelio
mentioned that according to Nikolai Mokhov a shorter bunch length implies
enhanced energy deposition (correct? and why?).
If
squashed cell cavities are used the large dimension is in the plane of the
crabbing, which is unfortunate.
We
need a different approach to crab cavity design for solving the space issue.
Frequency
higher than 400 MHz appears excluded. See Eqs. (21) and (23), plus Fig. 43 in
Frank's Arcidosso paper.
-
Typo in Eq. 20 has been corrected; (21) does not change.
From
email by Rama Calaga on 28.07.2006
You
are right about 800 MHz, the wave with the right slope
will accommodate 2.5 sigma of the bunch. For some reason, I thought that the
bunch length was smaller than 7.5cm (initially I thought 7.5cm to be 3sigma).
It might be interesting to calculate how many bunch lengths would one ideally
require in a bucket (is 3sigma or 10 sigma) ?? But I
guess you have a formula that estimates luminosity reduction as a function of this...
but didn't seem like it too much (20% or so compared to 200 MHz cavity??). How about a moderate bunch shortening scheme + crab crossing.
Since,
400 MHz in the IR with conventional elliptical cavities are not practical, we
could think of something like a spoke cavity. I am a novice when it comes to
these beasts but the transverse dimensions are approx 1/2 the size of the
regular pillbox/elliptical cavity. So, an 400 MHz
cavity is ~ the size of 800 MHz elliptical cavity (TM010 mode).
However,
these spoke cavities are used for low beta applications. I remember from a talk
from SRF conference that gradients suffer badly when you approach beta=1. And
this is just for TM010 kind of mode. Not sure how deflecting modes behave here.
I
guess the more questions than answers... have a nice weekend and vacation.
-Ram
From
email by Joachim Tuckmantel on 28.07.2006
As
long as you have only one (or very few) cells or gaps, the synchronous
condition is much less stringent. Example: with one gap (provided the gap is
shorter than a half free wavelength) you can accelerate any beta-particles.
With a single spoke (see picture) you have 2 gaps, between the spoke and the
two endplates each ....
But
a spoke is for longitudinal acceleration, one had to invent a transverse-spoke ...
Cheers Joachim