DESIGN CONSIDERATION ON SUPERC9NDUCTING MAGNETS WITH HIGH
CURRENT DENSITIES
H.Hirabayashi, K.Hosoyama, T.Mlto, S.Mitsunobu, T.Shintomi,T.Tominaka, K. Tsuchiya and A.Yamamoto
KEKNational Laboratory for High Energy Physics
Oho-Machi, Tsukuba-Gun, Ibaraki-Ken, 300-32, Japan
Abstract
Two important parameters of superconducting magnets, overall
current density and electromagnetic force are discussed from a vie~
point of economical magnet design. The overall current density iscrucial in small magnet and the electromagnetic force is decisive inlarge magnet.
l. Introduction
Among the parameters of superconducting magnets, overall current
density J in the coil and electromagnetic force F to the conductor
are seemed to be essentially important.
In the following, the overall current density J means the average current density in the coilincluding superconducting wire, insulator, reinforcement and coolingchannel except winding bobbin and supporting structure. The overall
current density is a dominant design parameter in the magnet. The
higher current density gives the higher performance of magnet.
The electromagnetic force is also decisive parameter in large
magnet. The wire can not stand without reinforcement. The reinforcement reduces the overall current density in the coil, therefore, theproblem of making a high performance magnet is complicated. We wantto consider the problem in the following parag~aphs.
2. Our Experience
In order to make use of supercondpcting magnets for high energy
accelerators and experimental faciliti~s, we have designed and constructed various types of magnets.
Some of them are listed in theTable l.
As is shown in the Table, e~ch magnet has the coil of highcurrent density. All coils have been o/ound with the partially stabilized, fine-multi,twisted solid wire or compacted strands of NbTi
superconductors. No reinforcement in the coil is used. The ratio ofsuperconductor/copper is in the range of l/8 to l/1.8.
Table l .
Type ofMagnet

Examples of Superconducting Magnets in KEK

5T
Solenoid

SD430
Dipole8SPQ310
Quadrupole

3SD324
DipoleTRISTAN
Test Dipole

Current

lOOOA

3500A

730A

2200A

4400A

Field
OverallCurrent
DensityStoredEnergy

5T

4T

2T

4.5T

l5T/m828l. 9xl0 A/m 2.0xl0 8A/m 2 l. 7xl0 A/m 2 2.5xl0 8A/m 2 3.lxl0 8A/m 225kJ

620kJ

80kJ

50kJ

220kJ

We had no difficulty with the 5T solenoid. The quench current ofthe solenoid is l040A at 5.2T and 4.3°K and the value is seemed to benear to the critical current at the field and temperature.

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3. Solenoid
As is well known, the central field of a solenoid is given in
the following equation.
F ( c< , ;3 )Where U is permeability, J is overall current density, a 1 is inner
radius' of solenoid and F ( ''\,03) is shape factor dpending on II\ and{3. The
ratio of outer radius to inner radius is ~ and the one of a half
length to inner radius is 8 .
In small or medium size solenoids, the overall current density
often reaches the maximum value which is expected from the criticalcurrent of the wire as is shown in the previous paragraph. The maximum field point of solenoid is always in the center of inner column.
The field enhancement at the point changes depending on 0(, {3 and J.
The shorter and thinner solenoid has the larger field enhancement. The
overall current density is limited with the critical current at theenhanced field.
Small or medium size solenoid can stand alone without any reinforcement or supporting structure and keep a considerable. current
density. Many excellent solenoids have been manufactured here andthere.
On the other hand, large solenoid in which the electromagnetic
force on the wire is superior to its mechanical strength, requires
reinforcement. The electromagnetic force is roughly proportional tothe product of magnetic field and radius. Combination of superconductor and reinforcement or supporting structure and selection of theoverall current density are important design problems.
4. Dipole and Quadrupole
There is a quite different aspect in the dipole or quadrupole
magnets.
Superconducting wires in the dipole or quadrupole scarcely
survive without supporting structure under the strong electromagnetic
force, therefore, self-supporting coils of dipole or quadrupole could
not be designed. Furthermore an accurate control of wire position isrequired to generate high quality magnetic field.
The electromagnetic bursting force of typical accelerator dipole
reaches the value larger than SOOtonjm.
Main design problems of the dipole or quadrupole are how to support the electromagnetic force and how to fix the wire in right position. High current density is required to induce a high field withsmall amount of wire material.
5. Stabilization and Quench Protection
One of the most important problems in operation.of high current
density magnets, is to install a quench protection;system suitable tothe stablization condition of the coil. The minimum requirement forthe system is to prevent burn out of the coil.
6. Conclusion
Two important parameters, overall current density and electromagnetic force, are governing the magnet performance. The excellent
superconducting magnets should be studied and constructed to savematerial required for the magnets.

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