Transcript Nonlinear Field Quality Checks

Nonlinear Field Quality Checks
Frank Zimmermann
LHCCWG 12.07.2006
Based on presentation in Chamonix 2003 including
references therein (O. Bruning, S. Fartoukh, M. Hayes,
B. Jeanneret, J.-P. Koutchouk, R. Ostojic, Q. Qin, F.
Schmidt, S. Weisz, and others)
LHC optics in a nutshell
8 arcs with 27 FODO cells each
(23 regular cells, 2x2 cells for dispersion
suppressor)
phase advance/cell ~ 90 degrees
8 straight sections,
4 of which low-b insertions
3 types of corrector circuits
• spool pieces at dipole ends for b3, b4 and
b5; powered differently per arc and per
beam; total number of circuits 48
• lattice correctors for a2, b2, a3, b3, and
b4; total number of circuits 168
• correction coils for triplet field errors a3,
b3, a4, b4, & b6; total number 40
total # of independent correction circuits: 256!
#arc correction circuits &
#elements/circuit
type
spool piece b3
spool piece b4
spool piece b5
lattice corr b2
lattice corr a2
lattice corr b3d
lattice corr b3f
lattice corr a3
lattice corr b4
# circuits
16
16
16
32
24
32
32
16
32
elements/circuit
154
77
77
8
4 or 2
11 or 12
10 or 9
4
8 or 13
nonlinear optics tolerances
observable
target
dynamic aperture
12 s
tune spread
0.0
linear chrom. Q’x,y
>0
2nd o. chrom. Q’’x,y
0
3rd o. chrom. Q’’’x,y
0
geom. det. dQx,y/de
0
chr.-g. det. d2Qx,y/de/dd
0
tolerance
0.5-1 s
7x10-3
0<Q’<2
-103<Q’’<103
-5x105<Q’’<3x106
+/-7x103 m-1
+/-7x106 m-1
numbers include considerations on dynamic aperture,
tune footprint, and off-momentum measurements
[O. Bruning, S. Fartoukh, LHC PR 501]
general nonlinear measurement scheme
measure change on phase advance or tune resulting from
an off-center orbit in a nonlinear field; orbit can be shifted
either by closed-orbit bumps or using dispersion
[study by Jean-Pierre Koutchouk for RHIC low-b insertions]
xcon  2
n  1 B0
Q 
bbn n 1 ds

4 B
Rref
orbit bump yields:
b
n/2
dispersion bump yields:
bn ds  0
n2
b
D
 x bn ds  0
MAD design:
 b ds  0
n
differences are of the order of 10%!
10% variation in b3 or b5 corrector strengths can change
dynamic aperture by >1s [Q. Qin, S. Weisz, LHC PN 42, 1996]
normal sextupole b3
Local correction (arc by arc) to within 50% needed
[M. Hayes, LHC PR 522]
Proposed procedure:
• pre-set spool pieces to values determined from
magnet measurements
• adjust Q’ to ~2 units with 2 (pairs of) families of
lattice sextupoles
• check local correction with local dispersion
bumps or groups of 7 bumps across individual
arcs, octant by octant
• complementarily or additionally, measure offmomentum (chromatic) phase advance
local b3 correction: bumps across one arc
scheme by M. Hayes [LHC PR 522] & O. Bruning [LHC PR 473]
orbit with 7 bump across one arc;
peak value of 3 mm
tune difference vs.
quality of correction
Q~0.01 for 20% mispowering of b3 spool pieces;
→ we can adjust b3 to within 10% (much better than 50% target)
local b3 correction: chromatic phase advance
[Chamonix03]
simulated f for 1s kick for dp/p=10-3 and dp/p=0;
3 cases: (1) no spool piece mispowered,
(2) sextupole circuit KCS45 missing (BPMs 194 to 257),
(3) decapole circuit KCD45 missing
we can detect missing b3 circuits, but not missing b5!
example: chromatic phase-advance measurement
in the SPS at 26 GeV
measured f in the SPS from averaging over four 5-10 mm
(2-4 s) kicks for p/p=5x10-3 and p/p=0 [R Tomas];
large discrepancies remain –
at the level of the expected missing b3 signature for LHC
skew sextupole a3
J.-P. Koutchouk [LHC PN 113]: generation of 2nd o. chromaticity
1 c
Q 
2 
   Qx  Qy , c ~  1 ds b b D K exp i    

x y
x 2,s
x
y
2 
,  a3U , c~,arc,rms  22200  s a
c~,arc,U  63500
3
''
I , II
where
and
~ 2

tolerance on
this effect
Q' '  200  c~ ~ 3.5
Proposed procedure: likely no correction needed;
check with off-momentum closest tune approach
  d   QI d   QII d     c
2

tolerance to meet:
~ 2

d2
  d   0.007 for d  2  103
normal octupole b4
global correction to within 30% needed
[M. Hayes, LHC PR 522]
Proposed procedure:
• leave lattice octupoles switched off
• separate tunes (to reduce contribution from a3)
& minimize Q’’
• verify detuning with amplitude
If Qy’’ and dQx/dey are zeroed, dQx/dex, dQy/dey and
Qx’’ are corrected to about 10%
uncor.: Q~10-3 at 3s, cor.: Q<10-4 at 3s
normal decapole b5
Local correction (arc by arc) to within 50% needed
[M. Hayes, LHC PR 522]
Proposed procedure:
• first minimize Q’’’ (global)
• measure off-momentum detuning with
amplitude; without any correction expect
Q~10-3 at 3s and d=10-3 (8x smaller for single
arc)
• complementarily, measure chromatic phase
advance (effect could be difficult to detect)
• measure resonant driving terms (option)
• varying kicks to obtain “frequency map’’ (option)
nonlinear chromaticity
simulated nonlinear chromaticities in the LHC;
optics with all correctors active, and with missing
b3 or b5 spool piece circuit
though fitted 3rd order coefficient changes, also here
identification of missing b5 circuit looks challenging!
SPS as testbed for
off-momentum studies?
observabl SPS
LHC
e
(meas.
(simul.
06/20/2002 example)
LHC
tolerance
|Q’’|
Q’’’
<1000
>5x105
600
-1.8x106
1500
-3x105
SPS at 26 GeV as nonlinear as the LHC
(3.5 times LHC tolerance in Q’’’)
conclusions
• huge number of LHC corrector circuits;
only spool pieces considered
• if effect of corrector important, we can
adjust it with beam-based methods
• several alternative diagnostics schemes
available for each type of error
• methods function well in simulations
including BPM noise (except b5)
• reality may be different (SPS example)
• verify as many procedures as possible in
the SPS (or PS,…)