# A comparison of calculations and measurements of the magnetic characteristics of the SSC (Superconducting Super Collider) design D dipole Page: 2 of 4

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also be made. This correction is estimated to be 1.0027. The

Nitronic 40 collar, with a permeability of 1.0025, increases the

transfer function by a factor of 1.00078 and 62 is decreased

by 0.68. The 3 corrections multiplied are 1.0053. With this

correction, the transfer function calculated by MDP is 1.0373

at 2.0 kA, by POISSON is 1.0388 at 2.36 kA, and the measured

value is 1.0358 : .0007 T/kA at 1.8 kA.

There may be an additional correction, the magnitude of

which is known for only one magnet; this arises from the dis-

tortion of the coil during curing and collaring. Magnet no. 11

was sectioned, photographed and the conductor locations de-

termined by an x,y, measuring deviceal. It was found to have

an oblateness (increase of the radius at the midplane and de-

crease of the vertical radius) of about 10 mil. An ellipse is an

approximation to the observed distortion. Calculations using

this amount of ellipticity indicate it would increase the transfer

function by a factor of 1.00045. There was considerable varia-

tion in curing and assembly pressures in the remaining magnets

and it is not known if this amount of distortion is typical. There

is some indication from b2 measurements that the distortions

in Magnets 8 and 9 are smaller.

By both MDP and POISSON calculations, the pole and

midplane notches introduce a low field value of b2 of about

1.1 units compared to smooth circular iron. Figure 3 shows

the variation of b2 with current, both calculated and measured;

no corrections for shims have been made to the calculations.

Harmonics are measured with a rotating tangential coill.1O.

The two programs agree on a low field value of b2 = +1.1, and

Magnets 8 and 9 have 0.0 and -1.0 at 2 T, reap. The shims in

Magnets 8 and 9 increase b2 over the value calculated by 3.1.

With this correction, and the one for the Nitronic 40 collar, the

calculated value is 3.5, for differences from measurement of -3.5

and -4.5, resp. If these differences are attributed entirely to

elliptical coil distortion, at Ab2 = 0.64 per mil of distortionl"J,

this would indicate Magnet 8 had 5.5 mil and Magnet 9 had

7.0 mil of oblateness. Magnet 11, with an oblateness of 10

mil and a 62 increase of 2.0 in the calculated value due to

shims, has a 62 = -3.8 by measurement, for a difference of -6.2,

compared with -6.4 that one would calculate from the measured

oblateness.

The measurements of both magnets show a shift in 62 from

the 2 T value to the peak value of 2.05 units. The shift com-

puted by both POISSON and MDP is 2.0. The same iron

permeability table was used in both programs, based on mea-

surements and an assumed packing factor of 97.5%; the actual

packing factor was 97.34%.

The measurements in Figure 3 show a slight droop in b

at low field. The measurements are the average of data for

up and down current ramps in order to eliminate the effects of

superconductor magnetisation. The droop is thought to be due

to an asymmetry in the magnetisation at these low fields.

The notches in the iron aperture change 64 very little from

the value for a smooth circular aperture; MDP predicts a low

field b4 offset of -.07 and POISSON an offset of -.03. At 2 kA,

the values of 64 by MDP and POISSON are -0.07 and +0.18,

respectively. Recall that the POISSON model has an error

in the coil of 6. = +0.24, so the 2 kA value should be -.06,

about the same as MDP. The correction for shims is -.47, for

a total of about -.53. Coil ellipticity, if present in the amount

previously calculated from the 62 measurements, would increase

this to about -.47. The measurements in Magnets 8 and 9 are

-.2 and -.45, resp. The lack of agreement in Magnet 8 and asimilar discrepancy in Magnet 11 suggest that coil distortions

other than elliptical are responsible for 64 errors. The change

in decapole with excitation is less than 0.1 by both calculation

and measurement. Both MDP and POISSON show A84 = -.03

from 2 to 6 kA, and the measurements of the two magnets are

-0.05 and -0.10. Both calculation and measurement indicate a

rise back to or above the low field value above 7 kA.

Discussion and Summary

Measurements and calculations of the low field transfer

function are in agreement to +0.14% by MDP and 0.29% by

POISSON, neglecting coil distortion, which may increase these

errors by .05%. POISSON tracks the change in transfer func-

tion with excitation to within 0.1% up to 7 kA, and 0.3% at 7.2

kA. MDP tracks to within 0.5% up to 7 kA, but is only 0.3%

high at 7.2 kA.

The measured sextupole at 2 kA differs from that calcu-

lated by A62 = -3.5 and -4.5 unit in the two magnets, after

corrections. The difference is probably due to elliptical coil dis-

tortion during fabrication. At higher fields, the calculations

track the changes in 62 due to iron saturation to within about

0.3 unit.

The measured decapole at low field differs from that calcu-

lated by about 0.2 unit. An elliptical model of the coil distortion

does not predict the 64 errors very well. Changes in b4 due to

saturation are accurately tracked by both programs.

The shift in'b of 2 units because of iron saturation was

found during the present study to be largely due to the notches

at the poles, whereas the notches at the midplane reduce it.

A redesigned, smaller pole notch will be used in new magnets.

With other minor changes in the iron, the new design is pre-

dicted to have a 82 shift of about 0.4 units at the peak.

References

[1] P.Dahl et al, "Performance of Three 4.5 m Dipoles for

SSC Reference Design D', Proc. 9th Int. Conf. Magnet

Technology, Zurich, 1985, p. 80.

121 S.Caspi, W.Gilbert,M.Helm,L.J.Laslett,C.Taylor, 'De-

velopment of a 40 mm Bore Magnet Cross Section With

High Field Uniformity for the 6.6 T SSC Dipole', 1986

Appl. Superconductivity Conf., Baltimore, 10/86, LBL-

21297.

13] C.W.'lowbridge, 'Progress in Magnet Design by Com-

puter", Proc. 4th Int. Conf. Magnet Technology, Brook-

haven, N.Y., 9/72 (RHEL Rpt. RPP/A92).

[4] S.Caspi, M.Hebm,L.J. Laslett, 'Numerical Solution of

Boundary Condition to Poisson's Equation and its In-

corporation into the Program POISSON', IEEE Trans

Nucl. Sci., Vol. NS32 no. 5, 10/85.

[5] R.C.Gupta, 'Improved Mesh Generator for the POISSON

Group Codas', Paper D16, this conference.

[6] G.H.Morgan, 'Use of an Elliptical Aperture to Control

Saturation in Closely Coupled, Cold Iron, Superconduct-

ing Dipoles', IEEE Trans. Nucl. Sci., Vol. NS32, no. 5,

10/85.

[7] P.Wanderer, 'B/I: Calculation vs Measurement for SLN008-

SLN015', BNL Magnet Div. Note 191-11 (SSC-MD-142),

8/29/85, unpubl.

]8] S.Kahn, 'Conductor Placement From Magnet Cross Sec-

tion Measurements', BNL Magnet Div. Note 189-1 (SSC-

MD-141), 7/28/86, unpubl.

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Gupta, R.C.; Morgan, G.H. & Wanderer, P. A comparison of calculations and measurements of the magnetic characteristics of the SSC (Superconducting Super Collider) design D dipole, article, January 1, 1987; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc1212388/m1/2/: accessed April 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.