SLAC Magnetic Measurements
Date: 07-02-1998
Time: 12:41:22

Project: PEP2LER
Magnet Type: SEXT
Magnet Name (Serial #): 153
Measurement System: 2895
Operator: zw
Run Number: 2
Comment: 60 A run

Standardization Currents
 3  cycles, 0 to  60  to 0 A

Test Currents
     5.0    10.0    15.0    20.0    25.0    30.0    35.0
    40.0    45.0    50.0    55.0    60.0



        INTEGRATED SEXTUPOLE STRENGTH VS CURRENT


  Imag    sigImag     SL     sigSL      SL/I   sigSL/I 
  (A)       (A)     (T/m)    (T/m)    (T/m/kA) (T/m/kA)
--------+--------  --------+--------  --------+--------
   4.206    0.001   1.15278  0.02960  274.0679   7.0382
   9.973    0.001   2.11748  0.00054  212.3121   0.0597
  14.982    0.000   3.09443  0.00101  206.5370   0.0680
  20.052    0.003   4.09247  0.00013  204.0921   0.0314
  25.013    0.001   5.07618  0.00019  202.9399   0.0133
  30.055    0.003   6.07955  0.00044  202.2813   0.0224
  34.946    0.003   7.05626  0.00041  201.9179   0.0205
  40.072    0.004   8.08231  0.00005  201.6926   0.0207
  45.075    0.003   9.08549  0.00010  201.5651   0.0125
  50.021    0.003  10.08107  0.00007  201.5350   0.0136
  55.031    0.003  11.08919  0.00083  201.5063   0.0179
  60.153    0.002  12.11978  0.00082  201.4811   0.0151


           SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED


Calculation Of SL:
V3 = Nturns * velocity * B3 * L
   = Nturns * Rcoil * ang_freq * 1/2 * SL * Rcoil^2
   = Nturns * Rcoil^3 * ang_freq * 1/2 * SL
SL = 2 * V3 / (Nturns * Rcoil^3 * ang_freq)
For a double coil (for coil bowing correction),
SL = ( (1 / Nturns * Rcoil^3)1 + (1 / Nturns * Rcoil^3)2 ) * (2 * V3 / ang_freq)
Let CoilConst = ( (1 / Nturns * Rcoil^3)1 + (1 / Nturns * Rcoil^3)2 )
SL = CoilConst * 2 * V3 / ang_freq


Calculation Of The Harmonics:
Magnitude, harmonic n:
Vn = Nturns * velocity * Bn * L
   = Nturns * Rcoil * ang_freq * (BLn)
BLn = Vn / (Nturns * Rcoil * ang_freq)
Rn = BLn / BL3 = Vn / V3

Phase, harmonic n:
At the coil radius, the radial field as a function of angle is,
BLn(th) = BLn * cos(n*(th - THspole))
The coil voltage Vn(th) = Nturns * velocity * BLn(th)
Vn(th) = Nturns * Rcoil * ang_freq * BLn * cos(n*(th - THspole))
The FFT gives Vn and PhiVn in the formula
Vn(i) = Vn * cos(n*2pi*i/N + PhiVn)
So, Nturns * Rcoil * ang_freq * BLn = Vn
    -n * THspole = PhiVn
Or, BLn = Vn / (Nturns * Rcoil * ang_freq)
    THspole = -PhiVn / n


Calculation Of The Sextupole Center:
In the sextupole's frame,
 Bx' = S * x' * y'
 By' = 1/2 * S * (x'^2 - y'^2).
In the coil's frame (unprimed frame) the magnetic center is at (x0, y0).
In the coil's frame,
 Bx = S * (x - x0) * (y - y0)
 By = 1/2 * S * [(x - x0)^2 - (y - y0)^2].
The magnetic center can be found in terms of the measured
quadrupole field.  Compare Br and Btheta on the x-axis to
 Bxquad = -S * (x0 * y + y0 * x)
 Byquad = -S * (x0 * x - y0 * y).
Evaluate at x = Rcoil, y = 0 and compare to
 Br(theta = 0) = Bx, Btheta(theta = 0) = By.
In terms of the measured integrated strengths, this gives
 Xcenter = x0 = - (1/(SL * Rcoil)) * BL2 * sin(2 * THspole2)
 Ycenter = y0 = - (1/(SL * Rcoil)) * BL2 * cos(2 * THspole2)