Joint PSP/Taskforce minutes for 27 Aug 2020
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https://beamdocs.fnal.gov/AD-public/DocDB/ShowDocument?docid=8654

(a) Dave Capista gave an update on the 20 Hz test that will be coming
up before startup.
  (1)  Plan is to do the 20 Hz test on 16 Sep from 1100 to 1400 hours.
  (2)  Precautions: Power supplies should be turned off that pulse at
  15 Hz.
  (3) Linac is off. Booster RF should be off.

(b) John Johnstone gave a talk on 1/2 integer correction
  (1)   He gave an outline about how quad errors propagate with an
  exact derivation.
  	(i) Quad error propagation is described by transfer matrix.
	(ii) The transport matrices can be expanded in terms of
       submatrices with perturbing quad terms.
        (iii) Much more convenient to switch to normalized coordinate
       to make the transport matrices look like rotations.
       (iv) The effect of quads becomes more clear by using the trick
       by making transport the product of normalized matrices that
       project  from the origin.
       (v) Quad perturbations can be writeen out as phase advances.
       (vi) An exact derivation for thin lens for quads that include
       quad perturbations can be written exactly in this coordinate
       system.
   (2) It is hard to work with the product. Assume quad terms are
        small, kill off quadratic terms. First term is unperturbed
        transfer, 2nd term is tune shift. 3rd term is important for
        correcting intrinsic 1/2 integer stopband of a machine.
	   (a) The 3rd term is the beta wave that is twice the phase
           advance.
  (3) Correction using orthogonal quad families.
     (i) Any individual quad error can be decomposed into projections
  onto 2 orthogonal families.
    (ii) One way to determine the stop band is to ramp the two
  faimilies for max beam transmission.
    (iii) 2nd way is to measure measure the quadratic tune shift. and
    dtermine 1/2 integer strength. This is much more accurate.
   (4) An example in MI. The 2 families were scanned to find the minimum
       tune shift and that is where the families should be set for correcting the
       1/2 integer.
   (5) For Booster, 1/2 integer is exactly at 6.5, the phase advance per
     cell is 97.5 deg.
   (6)  Quads situated diametrically opposite the rings are separated
   by 90 deg (2 dpsi = 180 deg) for the first family.
   (7) Quads displaced by 6 cells are 45deg away (2 psi = 90 deg) form
  the second family.
  (8) Therefore, 2, 4, 8 6 8 quad families can be formed. John chose 8
  quad family to use in Booster lattice corrections.
  (9) 	 Families are orthogonal within their plane but have
  collateral impact on the other plane.
     (i)  At QS locations betax/betay =6 so horz corection will have
  small effect on vertical
     (ii) But betay/betax = 3 at QL location. 30%  will bleed into
  horz. Some iteration is needed for 1/2 integer correction.
  (10) Proof of principle studies show that the mimimum of the tune
  shift scans is approximately where the Booster best efficiency is
  located.
     (i) Yuri pointed out a puzzle that the minimum in the tune shift
  scan  should be a  maximum. John disagrees. Will discuss offline.
  (11) Lively discussion followed as to how to approach the
  corrections.
	(i) John suggest starting with zero corrector current and then
  do the 1/2 integer corretion on the dogleg error.
     (ii) Tan says that it is not possible to circulate beam with zero
  corrector currents.
     (iii) Jeff says that we can try it out if there is time. But is
  worried that it will take a long time to get to the optimum
  solution. Tan concurs.
     (iv) Tan says that the goal is to correct the HEP lattice of the
  1/2 integer with John's method to see if the tune space is larger
  and then use Jeff's local beta corrections to fix "known" problem locations.
     (v) This will be discussed at a lattice meeting to understand
  which is the best approach.