SLAC Magnetic Measurements
Date: 02-06-1995
Time: 10:07:07

Magnet Name: 2Q4-22
Project: PEP II Injection Line
Test Stand: Rotating Coil Stand 2
Measurement Coil: DC100
Operator: Wendy Sibbring
Run Number: 4
Comment: Revers Pol (fixed stdz & parameter)

Standardization Currents (A):
    18.0     1.0    18.0     1.0    18.0     1.0

Test Currents (A):
     9.0    12.0


                      HARMONICS MEASUREMENTS

Date: 02-06-1995
Time: 10:20:32
Magnet Name: 2Q4-22
Project: PEP II Injection Line
Run Number: 4


                          FIELD HARMONICS

Magnet Current, Imag =  9.002306  +-  2.871336E-05  A
Coil Radius, Rcoil =  .0189973  m
Coil # Turns, Nturns =  30 
Average, # Rotations/Measurement =  10 , # Measurements =  4 

 N   BLn    sigBLn  THspole  sigTH  BLn/BL2 sBLn/BL2
     (Gm)    (Gm)    (deg)   (deg)    (%)     (%)   
--- -------+------- -------+------- -------+------- 
  1   0.166   0.001   25.25    0.21   0.651   0.003
  2  25.527   0.007   47.66    0.07 100.000   0.000
  3   0.086   0.004   51.77    0.78   0.337   0.015
  4   0.016   0.003   27.90    2.26   0.061   0.013
  5   0.004   0.001  -15.43    5.04   0.016   0.005
  6   0.052   0.003   -9.58    0.26   0.204   0.013
  7   0.019   0.003  -12.61    1.27   0.075   0.013
  8   0.038   0.007   11.02    1.01   0.151   0.026
  9   0.021   0.004    6.15    2.34   0.082   0.014
 10   0.041   0.002   -5.62    0.31   0.159   0.009
 11   0.003   0.001   -1.68    2.02   0.010   0.003
 12   0.002   0.001    1.93    1.83   0.007   0.002
 13   0.002   0.000   -4.66    0.86   0.006   0.001
 14   0.007   0.000   -3.77    0.31   0.029   0.001
 15   0.001   0.001    5.43    4.98   0.003   0.002
 16   0.001   0.000   -0.99    5.00   0.003   0.001


The magnetic center is at
X =   -52.7 +-     0.5 microns
Y =  -111.8 +-     0.5 microns

The magnetic center is measured relative to the coil axis
effectively at the longitudinal center of the magnet.
Pitch and yaw are not seen by the coil.

View from the non-lead end of the magnet:

           y          
           ^          
           |          
        N     S       

                --> x 

        S     N       


           SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED


Calculation of GL using a double coil (assumed flat):
V2 = (Nturns * velocity * B2 * L)_1 + (Nturns * velocity * B2 * L)_2
   = (Nturns1 * Rcoil1 * ang_freq * GL * Rcoil1)
          + (Nturns2 * Rcoil2 * ang_freq * GL * Rcoil2)
   = (Nturns1 * Rcoil1^2 + Nturns2 * Rcoil2^2) * ang_freq * GL
If Nturns1 = Nturns2 == Nturns12, then
V2 = Nturns12 * (Rcoil1^2 + Rcoil2^2) * ang_freq * GL
Let Reff^2 = Rcoil1^2 + Rcoil2^2, then
V2 = Nturns12 * Reff^2 * ang_freq * GL
Or,
GL = V2 / (Nturns12 * Reff^2 * ang_freq)


Calculation of the harmonics:
The integrated radial field for the n'th harmonic at the
coil radius is given by
BLn(th) = BLn * cos(n*(th - THspole))
The coil voltage is V = Nturns * v_theta * B_r * L
Vn(th) = Nturns * velocity * BLn(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)
Then,
Vn = Nturns * Rcoil * ang_freq * BLn
PhiVn = - n * THspole
Or,
BLn = Vn / (Nturns * Rcoil * ang_freq)
THspole = - PhiVn / n


Calculation of the magnetic center:
Xcenter = - (1/GL) * BL1 * sin(THspole1)
Ycenter = - (1/GL) * BL1 * cos(THspole1)