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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 s orbit change at triplet)

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Transfer Function for Separation Dipoles

Frank Zimmermann

LHCCWG 12.07.2006

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

The problem
the problem

D1-D2 transfer function errors can have a significant effect on closed orbit during squeeze (10 units → 3s 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]

IR1 layout







common BPMs



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

Original procedure
original procedure

  • triplet alignment optics with low-b 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
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

“refined” procedure (?)

  • 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?

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


  • low-b 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 mrad (?), 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.


  • 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?

I propose following procedure

  • 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