SLAC Magnetic Measurements
Date: 09-30-1996
Time: 15:07:49

Project: PEP2HER
Magnet Type: SOLENOID
Magnet Name (Serial #): NEW
Bar Code Number: 
Test Stand: IR8
Measurement System: COIL
Operator: tss
Run Number: 3
Comment: solenoid at 600 amps, rotated 55 degrees about the horizontal axis with the top of the solenoid closest to the quad, both flux and round plate are on.

Test Currents
   600.0


                 Harmonics Measurements

Date: 09-30-1996
Time: 15:17:26
Magnet Name: NEW
Run Number: 3


                         FIELD HARMONICS

Magnet Current, Imag =  599.4282  +-  5.09746  A
Harmonics at Rcoil =  .0446722  m
Nmain =  1 

 n       BLn       sigBLn      THspole   sigTH    BLn/BLN sBLn/BLN
         (Tm)       (Tm)        (deg)    (deg)      (%)      (%)  
---   -----------+-----------  --------+--------  --------+--------
  1   0.00390723  0.00000331    -85.41     0.25  100.0000   0.1199
  2   0.00072977  0.00000386     42.90     0.78   18.6773   0.1001
  3   0.00002879  0.00001752     18.40    23.32    0.7369   0.4484
  4   0.00005392  0.00003865     10.58    30.99    1.3800   0.9893
  5   0.00003410  0.00001050      8.87    21.97    0.8728   0.2687
  6   0.00003990  0.00000121     12.32    13.50    1.0211   0.0309
  7   0.00008332  0.00001007      9.06    14.66    2.1324   0.2578
  8   0.00002440  0.00000499      7.50    12.81    0.6246   0.1276
  9   0.00001492  0.00000468      5.90    11.18    0.3820   0.1198
 10   0.00001187  0.00000879     -9.66     4.67    0.3039   0.2249
 11   0.00000859  0.00000176      3.07     8.32    0.2199   0.0449
 12   0.00000880  0.00000668     -2.20     4.20    0.2251   0.1710
 13   0.00000656  0.00000199      2.08     7.45    0.1679   0.0510
 14   0.00000509  0.00000179      1.50     8.31    0.1303   0.0459
 15   0.00000459  0.00000029      1.22     6.97    0.1174   0.0073


The magnetic center is at
X = %238413.3 +-  1280.0 microns
Y = %-19125.3 +-  1049.5 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:
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)