SLAC Magnetic Measurements
Date: 07-17-1997
Time: 09:15:03

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: 4
Comment: measuring magnet after modifications for installation into beam line.  Repeat of run 3 do to current.

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) 
--------+--------  --------+--------  --------+--------
   9.997    0.000   0.15605  0.00001   15.6087   0.0007
  30.013    0.000   0.44980  0.00003   14.9871   0.0011
  50.046    0.000   0.74752  0.00007   14.9368   0.0014
  60.055    0.000   0.89677  0.00007   14.9326   0.0012
  70.063    0.000   1.04615  0.00009   14.9315   0.0013
  80.070    0.000   1.19546  0.00008   14.9302   0.0010
  90.088    0.000   1.34474  0.00004   14.9269   0.0005
 100.097    0.000   1.49390  0.00022   14.9245   0.0022
 110.106    0.000   1.64278  0.00015   14.9201   0.0013
 120.123    0.000   1.79159  0.00013   14.9146   0.0011
 130.141    0.000   1.94015  0.00022   14.9081   0.0017
 140.149    0.000   2.08855  0.00011   14.9023   0.0008
 150.158    0.000   2.23718  0.00019   14.8989   0.0013
 160.177    0.000   2.38604  0.00033   14.8962   0.0021
 180.204    0.000   2.68033  0.00032   14.8739   0.0018
 150.158    0.000   2.25352  0.00002   15.0076   0.0002
 100.098    0.000   1.50942  0.00015   15.0795   0.0015
  50.044    0.000   0.76160  0.00010   15.2185   0.0021


           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)