Transfer Function for Separation Dipoles

Frank Zimmermann

LHCCWG 12.07.2006

Discussions with O. Bruning, S. Fartoukh, M. Giovannozzi

the problem

D1-D2 transfer function errors can have a significant effect on closed orbit during squeeze (10 units → 3 orbit change at triplet)

local correction requires careful analysis and distinction between

• D1/D2 transfer function errors• Triplet alignment errors• Triplet gradient errors with crossing-angle bump

offsets

[O. Bruning, Chamonix XII]

D2 D2D1 D1

common BPMsseparate BPM

separate BPM

BPM distances to IP: 21.35, 31.53, 58.32, 151.14 m

IR1 layout

original procedure

• triplet alignment optics with low- quads off to define straight line with 6 or 8 BPMs;

• k-modulation of individual Q1, Q2 or Q3 magnets to find offsets w.r.t. to reference line from BPMs

• differences in the lines for beam1 and beam2 indicates D1/D2 transfer line error

• after correcting D1/D2 powering error obtain reference line for triplet alignment

[O. Bruning, Chamonix XII]

LHC triplet alignment optics

[A. Verdier, LHC PN 325, 2003]requires about half the nominal emittance for aperture reasons;x&y tunes lower by 1 unit, if IR1 & 5 both use this optics

•correct incoming beam upstream of D2 for zero offset and angle

•adjust D1 on one side to steer beam on 0-slope trajectory through the IP

•then look at other side

•and/or adjust D1 and D2 together to get both beams on the same orbit?

“refined” procedure (?)

S. Fartoukh, M. Giovannozzi, F.Z.

problems

• low- quads: misalignment of mechanical & magnetic axes 0.1-0.2 mm in x, 0.5 mm in y; beam needs to be steered through the mechanical center!

• BPM offsets may cause error of up to 5 rad (?), compared with total deflection angle of 1.5 mrad; this is larger than desired precision of 3x10-4

• BPMs might have different offsets for beam1 and beam2 (?)

S. Fartoukh, M. Giovannozzi, F.Z.

questions

• in which aspect is the D1/D2 transfer function effect any different from other closed-orbit errors of the two beams, and why does it need to be treated differently?

• do we want to measure transfer functions with beam at 450 GeV and at 7 TeV?

• do we want to use alignment optics?; if yes, with which beam and which BPM resolution?

• alignment optics at injection to define straight reference line for both beams (BPM readings)

• K-modulation to measure quad misalignments and align where necessary

• apply 2-beam orbit correction across IR region; include D1 and D2 as additional correctors

I propose following procedure