------------------------------------------------------------------ LHC High Gradient Quadrupole (HGQ) Expected Harmonics at COLLISION ------------------------------------------------------------------ Version 1.2 August 10, 1998 *************************************************************************** Quoted harmonic values are given in "units" of 10^-4 of the main quadrupole field at 17 mm reference radius. These harmonics are AFTER tuning shim correction has been applied. European convention: b2 is quadrupole! Body values are the same as in Version 1.1. Lead end values for integrated harmonics have been reduced from Version 1.1. Injection and collision BODY harmonics differ only in n = 3 and 6. Magnetic length of the straight section: Q1/Q3: L = 6.3 [m] - L(lead end) - L(return end) Q2a/Q2b: L = 5.5 [m] - L(lead end) - L(return end) where L(lead end) = 0.323 [m], and L(return end) = 0.177 [m] Notation: bn/an: Mean of normal/skew harmonics d(bn)/d(an): Uncertainty of mean normal/skew harmonics sig(bn)/sig(an): Standard deviation of normal/skew harmonics Bn/An: Integrated harmonics (at lead ends) coil id 70 mm ref. radius R 17 mm BODY (unit) -------------------------------------------------------------------------- n bn d(bn) sig(bn) an d(an) sig(an) -------------------------------------------------------------------------- 3 .0 .34 .85 .0 .34 .85 4 .0 .26 .87 .0 .26 .87 5 .0 .20 .34 .0 .20 .34 6 .0 .17 .25 .0 .17 .25 7 .0 .14 .11 .0 .14 .11 8 .0 .10 .07 .0 .10 .07 9 .0 .08 .07 .0 .08 .07 10 .0 .06 .03 .0 .06 .03 -------------------------------------------------------------------------- LEAD END (unit-m) -------------------------------------------------------------------------- n Bn d(Bn) sig(Bn) An d(An) sig(An) -------------------------------------------------------------------------- 2 17.4 6 .34 -.34 10 -.04 -.06 -------------------------------------------------------------------------- RETURN END (unit-m) -------------------------------------------------------------------------- n Bn d(Bn) sig(Bn) An d(An) sig(An) -------------------------------------------------------------------------- 6 .02 10 -.06 --------------------------------------------------------------------------