The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

電磁力を打ち消した超伝導磁石
和気正芳A)高エネルギー加速器研究機構 〒305-0801 茨城県つくば市大穂 1-1

Abstract
超伝導磁石は電力消費を低減するだけでも大きなメリットがあり、２T 以下でも使用する意味がある。
２T 以下ならば鉄の使用でより効率的な磁場の発生ができ、製作コストは下がるはずである。しかしながら、実際には超伝導ー鉄磁石が作られることは少なく、超伝導応用はほとんど高磁界に限られている。
これは巨大な電磁力を支えるため熱負荷が大きく冷凍が大掛かりになってしまうためである。導体に電磁力が働かない磁石を考え、超伝導導体だけを冷やすのであればたいした熱負荷ではありえない。本稿では電磁力を打ち消した超伝導磁石の設計が可能であることを示す。

INTRODUCTION
Beam line magnet has been an attractive application
area of superconducting magnet. High ramp rate thatgenerate transient loss of superconductor is not requiredin most of the beam lines. Power saving ofsuper-conducting magnets in DC operation is very large.
However, construction cost of superconducting magnets
and operation cost of cryogenic system has been
expensive enough to hesitate the use of superconducting
magnets unless the requirement of the bending field isvery high.
One of the solutions to use suprconducting magnet
efficiently at low field is the use of iron yoke.
Super-ferric magnet should be very economical because it
uses much less superconductor. The problem ofsuperferric magnet is the cryogenics. Cryostat containing
whole iron is costly and lossy. Warm iron design has aproblem of large electro-magnetic force between iron andconductors. Heavy-duty spacers to support coils in a
vacuum insulation easily give a very large heat load to thecryogenic system. Cost down merit of super-ferric magnet
is difficult to achieve in both case.

prevent quenches due to conductor motions. However, if
the direction of the field is opposite at both sides of aconductor, the total force working on the conductor could
be balanced out. This is automatically achieved in asymmetric structure having a single conductor in thecenter of the collider geometry. The pipetron magnet, ortransmission line magnet, in the VLHC phase I design, isbased on this principle [1]. Although it requires 100kA
class high current, 2T magnetic field in a 2 cm iron gap
was successfully achieved by a single conductor. Support
structure of the conductor of this magnet was very simple
and light with small heat load.
Two-aperture geometry of pipetron magnet requires
twice large current to generate field. Therefore, it is not
ideal to use such two-aperture magnet for a beam line,
which uses only one aperture. Because most of beam lines
require larger pole gap, typically 40mm, operation current
will become too large to operate. Although we have
solution for it, high current is the major disadvantage ofthis design. Since the electro-magnetic force on theconductor is generated by the leakage field comes fromthe pole gap, one gap which is not used for beam can besmaller than other gap if the conductor position is shiftedcloser to the smaller gap. The basic geometry of thismagnet is shown in Fig.1. Conductor is the only
cryogenic part of the magnet. It is supported in a vacuum
jacket covered by super-insulations and cooled by theliquid helium flow in the conductor. Other parts all stay atroom temperature. Therefore, the cold mass of the magnet
is very small.

The design presented in this paper balances out theelectro-magnetic field by two gaps of iron. Since support system
is very simple and light, cryogenic load is small andconstruction cost is very low. The principle of the force balanceis similar to the VLHC Pipetron magnet but the construction of
the magnet is made asymmetric so that it becomes suitable forsingle bore beam line magnets.

DESIGN PRINCIPLE
The electromagnetic force on the magnet conductor isthe vector product of field and current. For example, 20
turns of 5kA in 2T field results in 200,000N. It easily
becomes very large. This is the reason why we need todesign magnets with very rigid supporting structure toFigure 1: Asymmetric force balance structure.
1:Superonducting cable 2:Conductor support 3:Vacuum
tube for thermal insulation 4:Iron yoke 5:Iron supportstructures made of non-magnetic stainless steel. 6:Beamgap 7:Dummy gap to generate counter force

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

The conductor is made of superconducting braid
sandwiched between two invar pipes so that the thermal
contraction is avoided. The beam tube is placed in thelarge gap. The small gap works as the dummy gap togenerate the force balance field.

FORCE BALANCING
The problem of the asymmetric construction is thesaturation of iron. In a symmetric geometry, force balancecan be maintained no matter how iron is saturated but theforce balance can not be automatically maintained inasymmetric geometry when both side of iron saturate
differently. The calculation of magnetic field and theforce on the conductor has to be made using finite
element code with non-linear iron permeability. We used
ANSYS 6.2. The optimum design should be determinedby looking at the force as a function of the current.
Figure 2 is the plot of the force on the conductor as afunction of the central field of the beam space. Curves areplotted for different dummy gaps. Apparently, the force
balance changes with the current. Forces are notcompletely eliminated. However, the level of the force isin the order of several hundred Newton’s if the gap isadjusted to the optimum for the field of up to 1.5 Tesla.
This is not large and practically acceptable for a lightspacer system. Since conventional magnets are excitedoften to the saturation level, it is desired to go to higher
field to compete with conventional magnets in theconstruction of beam lines.
There is a way to control the saturation of iron to someextent. The force calculation result after saturation control
is shown in Fig.3. If the width of pole piece is wide, thesaturation starts at higher current. If a hole is made at theedge of the pole piece, local saturation of iron provide
counter electro-magnetic force at lower level ofexcitation.

maximum force –200 N. Combining such techniques, one
can design a no-force magnet for a single aperture beamline magnet. Figure 4 is the cross section of the design
example. Flux line pattern in the optimised geometry is
also shown in the figure. It is shown that the force balanceis well maintained even after a severe saturation of ironstarted at 1.5T. Essentially there is no force up to 1.7T.
The vertical force is zero if the conductor is in the verticalcenter but this is an unstable balance. De-centering forceof 2kN/mm works on the conductor. Therefore, verticalalignment of less than 0.1 mm is required to stay within
200N, although the field quality is not much affected by
the position of the conductor. The conductor support canachieve this accuracy [1]. The beam gap of the magnet in
Fig.4 is 140mm x 40mm. Operation current is 129.2 kA at
1.7T. Most of beam line requirement is satisfied by thisdesign. For example, a beam line of 50GeV proton withbending radius 110m needs 1.514 T in the average. If
magnetic field of 1.7T is provided in the magnet, 20cm
spaces are available between every magnet of length 2m.
Monitors and other instrumentation can be installed inthese spaces. One side of beam tube is opened andaccessible in this magnet and the necessary spaces inbetween magnets are not as much as H shape magnets.
Since the field of this magnet is generated bysingle-conductor cable, quadrupole magnet of this type isnot possible. Alternate gradient configuration is necessary
to make magnet combined with the focusing capability.

OTHER ADVANTAGES
By moving the conductor from the center to theasymmetric position, the space for the structure toconnect top and bottom iron became available.

Fig.3 Electro-magnetic force in adjusted construction
Fig.2 Electro-magnetic force in asymmetric construction
Forces for different dummy gaps are plotted. Half gap
15.3 mm provides optimum force balance up to 1.5T with

Pole width 200mm and half gap 13.2mm with 5mm
diameter hole in the dummy pole piece gave optimum.

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

With the combination with the spacer in the dummygap, both iron yokes can be firmly connected. Since thefield quality of this magnet is dependent on the iron shape,
and the force between two irons is very large, such
structure is helpful to achieve the field quality.
It is important to reduce unnecessary field in producedby the current at the spaces in between magnets. If we use
symmetric two gap magnet, it is difficult to shield thebeam tube from the field coming from the conductor.
Beam tube is too close to the conductor. In this design,
the distance between the beam tube and the current
provide the space for shielding. Even just rotating the ironstructure by 90 degree would provide a nice magnetic
shield with no-force on the conductor.
The connecting structure of iron also works as theradiation shield. Since conductors are exposed to thebeam space in usual magnet design, beam induced
quenches are serious problems for superconducting
magnets. Magnets are often designed with extra large
aperture to avoid beam induced quenches and this causes
high cost of production and operation. But this magnet
hide superconductor behind the thick stainless steel blockand there is no problem of beam induced quenches.

OPERATIONAL
To operate this magnet in a beam line, we need to set
up the vacuum insulated conductor along the beam line
just like a power transmission line. Iron yokes covering
this transmission line will simply make the magnet strings.
The return current bus has to be made separately. Thereis a possibility to use return current but the contributionof the return current to the single aperture magnet is very
little [2]. Very simple structure of the magnet makes theconstruction cost very reasonable.

However, the operation of this magnet requires a verylarge current. At low field, 100kA is not a very large
current for superconductor. The current carrying capacityof superconductor increases very much at low field. A testof conductor operation for pipetron was successfully
made including joints at Fermilab [1]. In case of very
long beam line, Nb3Sn can be used to run the system withelevated temperature [3].
Thermal contraction in thick straight line is difficult tohandle but the transmission line conductor uses invar
pipes both for liquid helium channel and the pressure pipeso the contraction effect is minimized to the level thatmechanical stresses resulting from contraction/expansion
can be well controlled. A 100kA power supply istechnically not difficult but costly if it is done inconventional way. We have introduced a special powersupply system. Even the current is high, the voltage
required to excite this magnet is very low. Recent
development of IGBT chopper and shotky diode enables
us to build low voltage high current power supply. A
100kA power supply was already built at Fermilab. KEK
demonstrated feasibility of such a power supply using asmaller version [4]. Current leads to supply 100kA into
the conductor have been fabricated at Fermilab and will
be tested soon. The cryogenic heat load of the current
lead is about 1kw including the helium flow in the leads
and this is the main part of the heat load. Still total heatload is not as much as the usual superconducting magnet
if the length of the beam line is sufficiently long.

CONCLUSION
The force free design of superferric beam line magnet
was successfully performed. A test operation of thismagnet is being prepared using the VLHC test bench atFermilab. Detailed force balance characteristics will be
studied in the test operation. If this design is applied insome of the accelerator beam line, it becomes a good
performance proof of the VLHC phase I superconducting
magnet system for the operation economy and long termreliability.

REFERENCES

Fig.3 No-force cross-section.
1:Superonducting cable 2:Conductor support 3:Vacuum
tube for thermal insulation 4:Iron yoke 5:Iron support
structures made of non-magnetic stainless steel. 6:Beamgap 7:Dummy gap to generate counter force 8:Holes inthe dummy pole piece to control the saturation of iron[1] ”Design Study for a Staged Very Large Hadron
Collider”, Fermilab-TM-2149, 2001.
[2] M.Wake and R.Yamada, “New Types ofSuper-conducting Magnet Designs for High Energy
Collider”, Proc. MT-15 p.47-50, Science Press,Beijin, 1998.
[3] E.Barzi, G.W.Foster, E.Malamud, P.O.Mazur,
H.Piekarz, M.Wake, K.Hayashi, M.Koganeya,“Nb3Al Prototype Conductor for the Transmission
Line Magnet”, proc.1999 Particle Accelerator Conf.
3330-3332,1999.
[4] M.Wake, H.Sato, K.Suda, “A Battery-Powered
High-Current Power Supply for superconductors (inJapanese)” Teion-kogaku, 37 783-786,2002.