SLAC Magnetic Measurements
Date: 01-25-1997
Time: 11:02:48

Project: SLC
Magnet Type: QUAD
Magnet Name (Serial #): QE_LINAC
Bar Code Number: 
Test Stand: 1
Measurement System: DC34
Operator: TSS
Run Number: 1
Comment: Gl vs I 200 amp run.

Standardization Currents
 3  cycles, 20 to  200  to 20 A

Test Currents
    20.0    40.0    60.0    80.0   100.0   120.0   140.0
   160.0   180.0   200.0   200.0   180.0   160.0   140.0
   120.0   100.0    80.0    60.0    40.0    20.0



             INTEGRATED GRADIENT VS CURRENT

  Imag    sigImag     GL     sigGL      GL/I   sigGL/I 
  (A)       (A)       (T)     (T)      (T/kA)   (T/kA) 
--------+--------  --------+--------  --------+--------
  20.048    0.000   1.16211  0.00005   57.9657   0.0024
  40.068    0.000   2.29651  0.00017   57.3150   0.0043
  60.094    0.000   3.44211  0.00031   57.2788   0.0051
  80.108    0.000   4.58644  0.00066   57.2535   0.0082
 100.133    0.000   5.72475  0.00050   57.1714   0.0050
 120.158    0.000   6.84686  0.00034   56.9821   0.0028
 140.182    0.000   7.91099  0.00115   56.4336   0.0082
 160.209    0.000   8.82989  0.00082   55.1148   0.0051
 180.233    0.000   9.60382  0.00104   53.2855   0.0058
 200.255    0.001  10.21556  0.00105   51.0127   0.0052
 200.251    0.004  10.21545  0.00038   51.0133   0.0021
 180.231    0.001   9.62001  0.00090   53.3759   0.0050
 160.207    0.001   8.84925  0.00099   55.2364   0.0062
 140.180    0.001   7.93320  0.00045   56.5930   0.0032
 120.155    0.000   6.86733  0.00017   57.1539   0.0015
 100.130    0.000   5.74267  0.00033   57.3523   0.0033
  80.103    0.000   4.60271  0.00055   57.4598   0.0069
  60.089    0.000   3.45770  0.00013   57.5432   0.0021
  40.063    0.000   2.30873  0.00031   57.6276   0.0077
  20.042    0.000   1.16084  0.00007   57.9196   0.0035


           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)