MI-0006

Magnetic Design of the Main Injector Dipole

S. Snowdon

(coil off median plane w/racetrack ends-downsized version)

Contents

  1. References
  2. Performance Parameters
  3. Magnet Cross-Section Profile
  4. 2D Field Calculations
    1. Median Plane Field
    2. Field Harmonics
    3. Field Map of Magnet Cross-Section at 17.3kG
  5. 3D Field Calculations
    1. Central Field
    2. Integrated Field Harmonics
    3. Effective Field Length
  6. Figures
    1. First Quadrant Magnet Cross Section and Flux Plot
    2. Isometric View of Elements in Magnet End Block.
  7. Numerical Tables of Line Elements used in DANCAD3D

References

  1. 2D Field Code - POISSON/CERN. version w/Les Oleksiuk mods
    1. Median Plane Field and Harmonic Analysis
      I= 502A m=lOOOOO MIDIP-081889-l540
      I=270OA Armco B3 Steel B-H MIDIP-081889-1540
      1=4900A Armco B3 Steel B-H MIDIP-081889-1030
      I=7OOA Armco B3 Steel B-H MIDIP-081789-l545
      I=9417A Armco B3 Steel B-H MIDIP-081689-1130
    2. Field Map in Magnet Cross-Section
      I=9417A Armco B3 Steel B-H MIDIP-08 1789-1545
  2. 3D Field Code - GFUN3D/RAL code w/SCS mods(GFS)
      I=11OOOA Armco B3 Steel B-H MIEND-072889-1630
  3. 3D Pictorial Representation of Magnet End

    a. DANCAD3D/ver. i .30 registered with Daniel H. Hudgins

Performance Parameters

Central Field 17.30 kG
Central Integrated Field 4152.00 kG-in.
Central Radius of Curvature 954.80 ft
Magnet Length (effective see 3D Field Calculation) 240.00 in.
Sagitta 0.629 in.
Length of End Block (each end)
- iron length 5.875 in.
- magnetic length 5.800 in.
Arc Length of Magnet Body 228.40 in.
Gap Height ±l.OOO in.
Good Integrated Field Width -injection ±.750 in.
-transition ±1.125 in.
-150 GeV ±0.500 in.
Integrated Field Quality within Good Field Region
20.015%
Number of Conductor Turns 4/pole
Conductor Current 9417 A
Conductor Cross Section 1.000 in. by 4.000 in.
Conductor Hole Diameter 0.500 in.
Conductor Corner Radius 0.094 in.
Coil Resistance (series connected 0.000848W
Magnet Inductance 0.002003 H
Voltage Drop (linear ramp w/O.50 sec. rise time) 37.67 V
Voltage Drop (d.c.) 7.99 V
Power Consumed (d. c.)
 75.23 kW
Power Consumed (0.50 duty factor) 37.61 kW
Cooling Water Pressure Drop 65 psi
Number of Water Paths in Parallel 2
Water Flow 10.8 GPM
Temperature Rise (0.50 duty factor) 13.2 ºC
Magnet Weight:
- body laminations
 29311 lbs.
- end blocks (both ends) 1961 lbs.
Coil Weight (upper pole + lower pole) 5100 lbs.
Magnet Size(body) 29.5 in. by 20.5 in.
Magnet Size(ends) 32 in. by 23 in.

Profiles

Iron Iron Coil Package
x(in) y(in) x(in) y(in) x(in) y(in)
0.000 1.000 5.000 5.250 5.125 5.125
2.250 1.000 9.750 5.250 9.625 5.125
2.500 0.970 9.750 0.000 9.625 1.125
2.900 0.970 14.750 0.000 5.125 1.125
2.986 0.992 14.750 7.750 5.125 5.125
3.041 1.021 12.250 10.250
3.193 1.178 0.000 10.250
3.284 1.354 0.000 1.000

2D Field Calculation (x-y calculation)

Median Plane Field (DB/Bo - unit=.0001) - see p. 7 for plot.

x(in)\B o(kG) .9932 5.304 9.621 13.848 17.300
0.000 0.00 0.00 0.00 0.00 0.00
0.125 0.01 0.00 0.00 -0.03 -0.20
0.250 0.02 0.01 0.00 -0.09 -0.60
0.375 0.03 0.03 0.01 -0.20 -0.60
0.500 0.06 0.05 0.02 -0.35 -1.27
0.625 0.11 0.09 0.04 -0.56 -0.233
0.750 O.17 0.14 0.07 -0.81 -5.18
0.875 0.26 0.22 0.14 -1.13 -7.27
1.000 0.38 0.33 0.20 -1.51 -9.88
1.125 0.54 0.47 0.31 -1.99 -13.13
1.250 0.73 0.64 0.43 -2.59 -17.18
1.375 0.91 0.78 0.53 -3.39 -22.31
1.500 0.96 0.80 0.49 -4.55 -28.87
1.625 0.61 0.41 0.03 -6.39 -37.47
1.750 -0.74 -0.98 -1.44 -9.56 -49.05
1.875 -4.30 -4.60 -5.14 -15.32 -65.17
2.000 -12.33 -12.68 -13.32 -25.95 -88.32

Field Map in Magnet Cross Section at Bo =17.3kG - see p.8

Field Harmonics at 1.00 in. radius. Armco B3 Steel except as noted

I=502A m Ampfac=l.O I=2700A Ampfac=l.0072

N BN(kG) RN BN(kG) RN
1 0.993241 1.0000000 5.303914 1.0000000
2 -0.000000 -0.0000000 -0.000000 -0.0000000
3 0.000020 0.0000204 0.000083 0.0000157
4 -0.000000 -0.0000000 -0.000000 -0.0000000
5 0.000016 0.0000156 0.000078 0.0000147
6 -0.000000 -0.0000000 -0.000000 -0.0000000
7 0.000004 0.0000036 0.000019 0.0000035

I-4900A Ampfac=1.0077 I=7100A Ampfac=l.O144

N BN(kG) RN BN(kG) RN
1 9.621290 1.0000000 13.848178 1.0000000
2 -0.000000 -0.0000000 -0.000000 -0.0000000
3 0.000037 0.0000038 -0.001865 -0.0001346
4 -0.000000 -0.0000000 -0.000000 -0.0000000
5 0.000134 0.0000139 -0.000186 -0.0000134
6 -0.000000 -0.0000000 -0.000000 -0.0000000
7 0.000033 0.0000034 -0.000013 -0.0000009

1=9417A Ampfac=l.0770

N BN(kG) RN
1 17.299926 1.0000000
2 -0.000000 -0.0000000
3 -0.014346 -0.0008292
4 -0.000000 -0.0000000
5 -0.002167 -0.0001253
6 -0.000000 -0.0000000
7 -0.000396 -0.0000229

3D Field End Simulation (x-y-z calculation w/Armco B3 steel B-H)

Central Field (BO in midsection) : 16.508687 kG

Integrated Field Harmonics at 1.OO in. radius

N GN (kG-in.) RN
1 95.77896 1 .000000
3 0.090973 0.000950
5 -0.055411 -0.000579
7 0.011131 0.000116

Effective Length of End Block

95.77896/16.50869=5.80 in.

Thus the body section(293" by 203") terminates 5.80 in. in from the effective entrance plane and 5.80 in. in from the effective exit plane; the distance between the planes being 20 ft.

Iron Length of End Block: 4.000 + 1.875 = 587Sin.

Hence the effective field termination planes are inside the iron termination planes by: 5.875 - 5.800 = 0.075in. at each end.

Arc Length of Magnet Body:

The desired effective magnetic length is 20 ft or 240.00 in. Subtracting 5.80 in. from each end gives:

240.00 - 2*5.80 = 228.40

Isometric View of Elements in End Block - see p. 9

Numerical Tables of Line Elements of End Block - see p. 10

Underlined points 1,2,3,·········,10 represent end shim bump.