SLAC Magnetic Measurements
Date: 07-16-1997
Time: 16:15:27

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: 3
Comment: measuring magnet after modifications for intallation into beam line.

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) 
--------+--------  --------+--------  --------+--------
   9.992    0.000   0.15594  0.00000   15.6054   0.0005
  30.009    0.000   0.44971  0.00001   14.9858   0.0004
  50.041    0.000   0.74746  0.00009   14.9370   0.0018
  60.051    0.000   0.89663  0.00005   14.9312   0.0008
  70.060    0.000   1.04608  0.00007   14.9312   0.0011
  80.067    0.000   1.19546  0.00008   14.9306   0.0010
  90.085    0.000   1.34466  0.00005   14.9266   0.0005
 100.095    0.000   1.49373  0.00015   14.9230   0.0015
 110.105    0.000   1.64256  0.00012   14.9182   0.0011
 120.122    0.000   1.79154  0.00025   14.9143   0.0021
 130.141    0.000   1.94003  0.00024   14.9071   0.0019
 140.151    0.000   2.08853  0.00018   14.9020   0.0013
 150.091    0.069   2.23724  0.00009   14.9059   0.0068
 160.122    0.000   2.38601  0.00022   14.9012   0.0014
 169.885    0.000   2.68055  0.00022   15.7786   0.0013
 150.091    0.068   2.25327  0.00012   15.0127   0.0068
 100.095    0.000   1.50939  0.00011   15.0795   0.0011
  50.042    0.000   0.76163  0.00006   15.2200   0.0012


           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)