SLAC Magnetic Measurements
Date: 07-17-1997
Time: 10:52:31

Project: PEP2INJ
Magnet Type: QUAD
Magnet Name (Serial #): 2Q4W-11
Bar Code Number: QM31 9380
Test Stand: 1
Measurement System: DC100
Operator: tss
Run Number: 5
Comment: magnet poles were clamped tighter.  

Standardization Currents
 3  cycles, 0 to  180  to 0 A

Test Currents
    10.0    30.0    50.0    60.0    70.0    80.0    90.0
   100.0   110.0   120.0   130.0   140.0   150.0   160.0
   180.0   150.0   100.0    50.0



             INTEGRATED GRADIENT VS CURRENT

  Imag    sigImag     GL     sigGL      GL/I   sigGL/I 
  (A)       (A)       (T)     (T)      (T/kA)   (T/kA) 
--------+--------  --------+--------  --------+--------
   9.988    0.000   0.15706  0.00001   15.7251   0.0012
  30.005    0.000   0.45404  0.00003   15.1321   0.0011
  50.037    0.000   0.75502  0.00003   15.0892   0.0006
  60.046    0.001   0.90599  0.00003   15.0883   0.0006
  70.054    0.001   1.05699  0.00008   15.0882   0.0011
  80.062    0.001   1.20793  0.00006   15.0875   0.0008
  90.081    0.000   1.35884  0.00003   15.0846   0.0003
 100.090    0.001   1.50940  0.00008   15.0804   0.0009
 110.098    0.000   1.65964  0.00017   15.0741   0.0016
 120.117    0.001   1.80985  0.00017   15.0674   0.0014
 130.134    0.000   1.95958  0.00007   15.0582   0.0005
 140.144    0.001   2.10900  0.00020   15.0487   0.0014
 150.152    0.002   2.25811  0.00016   15.0388   0.0011
 160.171    0.004   2.40709  0.00009   15.0282   0.0007
 180.198    0.001   2.70304  0.00003   15.0003   0.0002
 150.155    0.001   2.27335  0.00032   15.1401   0.0021
 100.091    0.000   1.52511  0.00016   15.2372   0.0016
  50.036    0.000   0.76949  0.00008   15.3788   0.0016


           SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED


Calculation Of GL:
V2 = Nturns * velocity * B2 * L
   = Nturns * Rcoil * ang_freq * GL * Rcoil
   = Nturns * Rcoil^2 * ang_freq * GL
GL = V2 / (Nturns * Rcoil^2 * ang_freq)
For a double coil (for coil bowing correction),
GL = ( (1 / Nturns * Rcoil^2)1 + (1 / Nturns * Rcoil^2)2 ) * (V2 / ang_freq)
Let CoilConst = ( (1 / Nturns * Rcoil^2)1 + (1 / Nturns * Rcoil^2)2 )
GL = CoilConst * V2 / 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 / BL2 = Vn / V2

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 Magnetic Center:
In the quadrupole's frame, Bx' = G * y', By' = G * x'.
In the coil's frame (unprimed frame) the magnetic center is at (x0, y0).
In the coil's frame,
     Bx = G * (y - y0), By = G * (x - x0).
This gives the magnetic center in terms of the measured
dipole field.
     x0 = - By / G, y0 = - Bx / G
In terms of the measured integrated strengths,
     Xcenter = - (1/GL) * BL1 * sin(THspole1)
     Ycenter = - (1/GL) * BL1 * cos(THspole1)