SLAC Magnetic Measurements
Date: 01-16-1997
Time: 07:03:43

Project: SLC
Magnet Type: QUAD
Magnet Name (Serial #): 314
Bar Code Number: 
Test Stand: 1
Measurement System: STRETCHED WIRE
Operator: tss
Run Number: 5
Comment: 2 button run to 160 amps.

Standardization Currents
 4  cycles, 2 to  140  to 2 A

Test Currents
   140.0   150.0   160.0   150.0   140.0



             INTEGRATED GRADIENT VS CURRENT

  Imag    sigImag     GL     sigGL      GL/I   sigGL/I 
  (A)       (A)       (T)     (T)      (T/kA)   (T/kA) 
--------+--------  --------+--------  --------+--------
 140.183    0.000   3.03275  0.00010   21.6343   0.0007
 150.192    0.000   3.24398  0.00020   21.5989   0.0013
 160.210    0.000   3.45439  0.00018   21.5616   0.0011
 150.192    0.000   3.25546  0.00028   21.6753   0.0019
 140.184    0.000   3.04966  0.00029   21.7547   0.0020


           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 = ( (Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2 )^-1 * (V2 / ang_freq)
Let CoilConst = ( (Nturns * Rcoil^2)1 + (Nturns * Rcoil^2)2 )^-1
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)