SLAC Magnetic Measurements
Date: 04-10-1996
Time: 14:31:53

Project: QREFMAG
Magnet Type: QUAD
Magnet Name (Serial #): 04_10_96
Bar Code Number: 
Test Stand: MAGLAB #1
Measurement System: ROTATING COIL
Operator: pdr
Run Number: 3
Comment: repeatability runs

Test Currents
     0.0     0.0     0.0     0.0     0.0


           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)