MI-0005

A Magnetic Design for a Dipole with Copper on the Medial Plane

S. Snowdon

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= 90A m=1000 MIDIPA=080189-1545
      I= 470A Armco B3 Steel B-H MIDIPA=080289-1300
      I= 850A Armco B3 Steel B-H MIDIPA=080389-1545
      I= 1230A Armco B3 Steel B-H MIDIPA=080489-1630
      I= 1645A Armco B3 Steel B-H MIDIPA=080489-1630
    2. Field Map in Magnet Cross-Section
      I= 1645 Armco B3 Steel B-H MIDIPA=072889-1630
  2. 3D Field Code - GFUN3D/RAL code w/SCS mods(GFS)
    I= 1915A Armco B3 Steel B-H MIENDA=101389-0830
  3. 3D Pictorial Representation of Magnet End

    a) DANCAD3D/ver. 1.30 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 5.625 in.
- magnetic length 6.110 in.
Arc Length of Magnet Body 227.78 in.
Gap Height ±1.000 in.
Good Integrated Field Width -injection ±1.750 in.
-transition ±1.750 in.
-150 GeV ±0.875 in.
Integrated Field Quality within Good Field Region 0.015%
Number of Conductor Turns 23/pole 
Conductor Current 1645 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 0.03188W
Magnet Inductance 0.06466  H
Voltage Drop (linear ramp w/O.50 sec. rise time) 212.74 V
Voltage Drop (d.c.) 52.45 V
Power Consumed (d. c.) 86.28 kW
Power Consumed (0.50 duty factor) 43.14 kW
Cooling Water Pressure Drop 85 psi
Number of Water Paths in Parallel 4
Water Flow 10.3 GPM
Temperature Rise (0.50 duty factor) 15.9 ºC
Magnet Weight:
- body laminations 26194 lbs.
- end blocks (both ends) 1260 lbs.
Coil Weight (upper pole + lower pole) 4538 lbs.
Magnet Size(body) 29.5 in. by 17.5 in.
Magnet Size(ends) 29.5 in. by 17.5 in.

Profiles

Iron Iron Coil Package
x(in) y(in) x(in) y(in) x(in) y(in)
0.000 1.000 4.875 2.000 2.250 0.062
2.000 1.000 4.875 3.875 4.987 0.062
2.125 0.995 9.750 3.875 4.987 0.937
3.250 0.995 9.750 0.000 2.250 0.937
3.375 1.063 14.750 0.000 5.043 0.062
3.500 1.250 14.750 6.500 9.642 0.062
3.750 1.875 12.625 8.625 9.642 3.786
4.750 1.875 0.000 8.625 5.043 3.786


2D Field Calculation

Median Plane Field (AB/Bo - unit=.0001) - see p. 7 for plot.
x(in)\B o(kG) 1.024 5.313 9.604 13.819 17.326
0.000 0.00 0.00 0.00 0.00 0.00
0.125 0.00 0.01 0.01 -0.01 -0.05
0.250 0.01 0.02 0.02 -0.01 -0.14
0.375 0.03 0.05 0.04 -0.02 -0.30
0.500 0.06 0.09 0.08 -0.03 -0.52
0.625 0.11 0.15 0.13 -0.04 -0.81
0.750 0.18 0.23 0.20 -0.04 -1.17
0.875 0.26 0.34 0.30 -0.04 -1.60
1.000 0.40 0.49 0.43 -0.01 -2.13
1.125 0.56 0.68 0.60 0.02 -2.76
1.250 0.75 0.89 0.79 0.05 -3.53
1.375 0.85 1.10 0.98 0.04 -4.50
1.500 1.00 1.19 1.04 0.13 -5.85
1.625 0.71 0.94 0.75 -0.69 -7.84
1.750 -0.40 -0.15 -0.37 -2.16 -11.02
1.875 -3.24 -2.97 -3.23 -5.43 -16.40
2.000 -9.46 -9.18 -9.48 -12.19 -25.7
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.0   I=2700A    Ampfac=l.0064
N BN(kG) RN BN(kG) RN
1 1.023933 1 .0000000 5.313290 1.0000000
2 -0.000000 -0.000000 -0.0000000 -0.000000000
3 0.000022 0.0000215 0.000166 0.0000313
4 -0.000000 -0.0000000 -0.000000 -0.0000000
5 0.000016 0.0000161 0.000082 0.0000155
6 -0.000000 -0.0000000 -0.000000 -0.0000000
7 0.000004 0.0000035 0.000019 0.0000035

 

I-4900A Ampfac=1.0077 I=7100A Ampfac=l.O144
N BN(kG) RN BN(kG) RN
1 9.604501 1 .0000000 13.818493 1.0000000
2 -0.000000 -0.0000000 -0.000000 -0.0000000
3 0.000246 0.0000256 -0.000185 -0.0000134
4 -0.000000 -0.0000000 -0.000000 -0.0000000
5 0.000l45 0.0000151 0.000153 0.0000111
6 -0.000000 -0.0000000 -0.000000 -0.0000000
7 0.000034 0.0000035 0.000040 0.0000029

 

1=9417A Ampfac=l.0770
N BN(kG) RN
1 17.326024 1.0000000
2 -0.000000 -0.0000000
3 -0.003406 -0.0001966
4 -0.000000 -0.0000000
5 -0.000218 -0.0000126
6 -0.000000 -0.0000000
7 -0.000000 -0.0000000


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

Central Field (BO in midsection):    15.316484 kG
Integrated Field Harmonics at 1.00 in. radius
1 93.563980 1.000000
3 0.027368 0.000293
5 0.000440 0.000005
7 0.001312 0.000014

Effective Length of End Block

93.56398 / 15.31648 = 6.11 in.

Thus the body section (29.5" by 17.25") terminates 6.11 in. in from the effective entrance plane and 6.11 in. in from the effective exit plane; the distance between the planes being 20 ft.

Iron Length of End Block: 4.000 + 1.625 = 5.625in.

Hence the effective field termination planes are outside the iron termination planes by: 6.110 - 5.625 = 0.485in. at each end.


Arc Length of Magnet Body:

The desired effective magnetic length is 20 ft or 240.00 in.  Subtracting 6.11 in. from each end gives:

240.00 - 2*6.11 = 227.78

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.