SLAC Magnetic Measurements
Date: 07-30-1996
Time: 13:52:59

Project: PEP2INJ
Magnet Type: QUAD
Magnet Name (Serial #): 2Q4W-08
Bar Code Number: QMR2-9410
Test Stand: MAGLAB #1
Measurement System: ROTATING COIL
Operator: pdr
Run Number: 1
Comment: BitBus (180 amps)

Standardization Currents
 6  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) 
--------+--------  --------+--------  --------+--------
   9.977    0.000   0.15738  0.00002   15.7738   0.0017
  30.019    0.000   0.45516  0.00002   15.1625   0.0006
  49.966    0.000   0.75538  0.00005   15.1179   0.0009
  60.101    0.000   0.90840  0.00004   15.1145   0.0007
  70.090    0.000   1.05927  0.00008   15.1130   0.0011
  80.053    0.000   1.20967  0.00012   15.1110   0.0014
  90.126    0.000   1.36143  0.00020   15.1059   0.0022
 100.068    0.000   1.51125  0.00009   15.1023   0.0009
 110.059    0.000   1.66164  0.00011   15.0977   0.0010
 120.164    0.001   1.81298  0.00011   15.0876   0.0009
 130.141    0.000   1.96215  0.00012   15.0771   0.0009
 140.104    0.000   2.11082  0.00005   15.0661   0.0003
 150.182    0.000   2.26058  0.00040   15.0522   0.0027
 159.782    0.001   2.40313  0.00031   15.0400   0.0020
 179.892    0.000   2.70063  0.00010   15.0125   0.0006
 150.181    0.003   2.27593  0.00017   15.1546   0.0011
 100.068    0.001   1.52774  0.00007   15.2671   0.0007
  49.966    0.000   0.77033  0.00002   15.4169   0.0004


           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)