Buschow K.H.J. (Ed.) Concise Encyclopedia of Magnetic and Superconducting Materials

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high performance cannot be achieved with any other

ﬁlter technology.

In addition, high quality ﬁlters based on microstrip

resonators have been developed for C-band satellite

transponders. Figure 7 shows a three channel IMUX

test module developed at Bosch SatCom GmbH in

Germany. This test module, which is considered to be

part of a space experiment, consists of three HTS

quasi-elliptic eight-pole channel ﬁlters, cryogenic cir-

culators, a cryogenic preampliﬁer, and a wide band

HTS input ﬁlter (Klauda et al. 2000).

Due to the nonlinear surface resistance of HTS

ﬁlms (see Sect. 1) power handling of HTS ﬁlters is

limited. In general, one can claim that planar HTS

ﬁlters with edge-parallel currents in their resonators

can handle power levels in the mW range without

significant intermodulation distortions. Applications

to transmit circuits with typical power levels of sev-

eral 10 W can only be handled by employing the

edge-current free disk resonator.

Figure 6

Measured characteristic of a HTS planar 17-pole elliptic

ﬁlter (from Kolesov et al. 2000).

Figure 5

Example of an HTS-planar ﬁlter with 8 poles and quasi-elliptic characteristic (from Hong et al. 1999).

Figure 7

Photograph of a three-channel IMUX module based on

HTS planar ﬁlters as part of a cryogenic C-band satellite

transponder. The HTS ﬁlters are indicated as large black

squares (from Klauda et al. 2000).

1160

Superconducting Microwave Applications: Filters

5.2 Subsystems

The most important ‘‘enabling technology’’ for appli-

cations of HTS in telecommunications is cryotechnol-

ogy. Cooling by liquid nitrogen is unacceptable,

because the amount of maintenance for each base sta-

tion should be as small as possible. The situation for

satellite communications is even more severe, because

the lifetime of a geostationary satellite is at least 10 yr.

The most convenient way of cooling is to use Stir-

ling-type closed-cycle refrigerators consisting of a

small stainless steel compressor with helium gas pres-

sure of a few bar and a cold ﬁnger with a displacer

inside, both connected by a thin stainless steel tube.

Typically, a compressor with an a.c. 50 Hz power

consumption of 100–200 W with the size of one or two

beer cans provides a cooling power of 3–10 W at 77 K,

which is the typical amount of cooling power needed

for a HTS subsystem, consisting of about three ﬁlters

and one cryogenic LNA (low-noise ampliﬁer). For the

sake of ﬁlter performance the base station subsystems

are operating between 60 K and 70 K, and the satellite

systems at 77 K because cooler efﬁciency is a crucial

parameter with respect to system mass reduction

(Klauda et al. 2000, Willemsen 2001).

Figure 8 shows a commercial system for potential

use in wireless base stations (Kolesov et al. 2000). The

ﬁlters are assembled inside a Dewar vacuum (left

side), the metal cylinder in the right part of the

assembly is the compressor of the Stirling-type

refrigerator.

In 2002, companies are focussing on improving

the coolers with respect to lifetime (currently about

3–5 yr for continuous operation) and cost reduction.

6. Tuneable and Switchable Filters

Tuneable and switchable ﬁlters are supposed to have a

strong potential for future receiver front-ends. First,

for military communications systems, most ﬂexible

interference suppression is an important issue. Second,

for future mobile communication systems beyond the

currently installed third-generation systems, most ﬂex-

ible allocation of bandwidth may require high-

performance reconﬁgurable ﬁlters (see also Sect. 7).

In general, the ﬁgure-of-merit (FOM) of a tuneable

resonator is given by

FOM ¼

Q ð8Þ

with Df/f being the relative frequency tuning range

and Q the unloaded quality factor of the resonator.

The most commonly investigated techniques which

can be used for HTS tuneable devices are based on

ferroelectrics and ferrites. For the future also micro-

mechanical switches (MEMS) are considered to be

relevant for planar HTS circuits (see, e.g., Rebeiz

et al. 2001).

6.1 Ferroelectric Varactors

These are very attractive for the integration with pas-

sive HTS microwave circuits because of the agile di-

electric materials which can be grown as epitaxial

heterostructures with YBCO. The current efforts are

concentrated on thin ﬁlms of SrTiO

(SrTiO

does not

exhibit a ferroelectric phase transition but the tem-

perature dependence of the permittivity exhibits a

Curie–Weiss law similar to ferroelectric above its

Curie temperature). Thin ﬁlms exhibit lower e

values

in comparison to the bulk single crystals, but a

stronger tuneability above about 60 K. Similarly, the

dielectric losses at microwave frequencies are in the

range of 10

2

(see, e.g., Petrov et al. 1998) in com-

parison to several 10

4

for bulk single crystals (Vendik

et al. 1998).

The FOMs achieved at microwave frequencies for

single varactors or tuneable resonators are in the

range of about 100. Figure 9(a) shows an example of

a planar HTS resonator incorporating a ferroelectric

varactor based on a YBCO/SrTiO

multilayer struc-

ture. With such resonators a tuneability by about

10% was achieved (Marcilhac et al. 2001, B Mar-

cilhac, private communication). Such resonators

can be used to construct multipole bandpass ﬁlters

(Fig. 9(b)).

6.2 Ferrites

These represent a very common way of frequency

tuning utilizing the magnetic ﬁeld and magnetization

dependence of a permeability tensor. In general, the

microwave properties of a ferrite biased by a d.c.

magnetic ﬁeld H

in z-direction are deﬁned by the

Figure 8

Commercial HTS subsystem for potential use in base

stations. The ﬁlters and the LNA are inside a Dewar

vacuum (left side), the metal cylinder in the right part of

the assembly is the compressor of the Stirling-type

refrigerator (from Kolesov et al. 2000).

1161

Superconducting Microwave Applications: Filters

permeability tensor which is in the lossless case

(see, e.g., Pozar 1998)

m½¼

m ik 0

ikm 0

00m

with m ¼ m

1 þ

 o



and k ¼ m

 o

ð9Þ

The angular frequencies o

¼ m

and o

¼ m

are proportional to the external magnetic ﬁeld H

and the saturation magnetization M

with g ¼ 1:759

Ckg

1

being the gyromagnetic ratio. This pro-

portionality corresponds to a ratio of 2.8 MHz G

1

between the value of frequency f ¼ o=2p and mag-

netic ﬁeld.

Large tuning ranges can be achieved by exploiting

the ferrimagnetic resonance (o ¼ o

) in a YIG

sphere. However, the losses are quite high and there-

fore combinations with HTS are not worth consider-

ing. In addition, high magnetic ﬁelds applied during

operation may result in a significant degradation of

the surface resistance of the employed HTS ﬁlm. One

attractive possibility is to use latching devices, where

the magnetization of the ferrite can be switched be-

tween the remanent magnetization values M

and

þM

(usually slightly lower than M

) employing short

current pulses applied through a coil. This principle

has been employed successfully for the realization of

planar HTS phase shifters (Oates et al. 1997). Tune-

able resonators and simple Chebyshev ﬁlters with a

small number of poles have been demonstrated, the

FOM values are about several hundred.

However, there are several drawbacks associated

with ferrimagnetic tuning:

(i) The growth of HTS on ceramic YIG or other

ferrites is difﬁcult because no epitaxial growth can be

achieved; epitaxial growth of single crystal YIG

substrates has been achieved, but the substrates are

very expensive and only available in small dimen-

sions. Therefore, the working solutions rely on ﬂip-

chip assemblies.

(ii) The particular form of the m-tensor sets strong

limits on possible tuning and phase shifting topologies.

(iii) Experimentally, the losses below about 5 GHz

increase dramatically due to ferrimagnetic resonance

losses of partially magnetized segments of the ferrite

material in use (M

of YIG corresponds to 4.9 GHz).

As an alternative to YIG, Ga- or Al-doped YIG with

lower values of M

have been used (Yeo and Lan-

caster 2001). One of the challenges is the development

and optimization of ferrites with tailored properties

at cryogenic temperatures.

7. Impact of High-temperature Superconducting

Subsystems for Future Microwave Systems

The superior performance of HTS ﬁlters, namely high

selectivity combined with a very low passband inser-

tion loss can be used to enhance the performance of

receiver front ends with respect to both interference

resistivity as well as a reduced receiver noise ﬁgure.

Receiver front-ends are analogue subsystems,

placed in between the antenna ports and the ana-

logue-to-digital converters (ADCs). Their function

comprises pre-ampliﬁcation, down-conversion and

some ﬁlter functions. It is important to distinguish

between the different ﬁlter functions. Channel (car-

rier) selection and/or separation in principle can be

performed by analogue ﬁlters in the microwave or the

intermediate frequency (IF) section, or by software-

controlled digital ﬁlters in the digital part. In 2002,

analogue channel selection in the IF represents the

best choice. Future receivers are expected to utilize

Figure 9

Tuneable lumped element 2-pole bandpass ﬁlter based on a SrTiO

loaded interdigited capacitor (a) and experimental

result for measured ﬁlter response (b) (from Marcilhac et al. 2001).

1162

Superconducting Microwave Applications: Filters

more and more digital channel selection (‘‘software

deﬁned radio’’). Transparent transponders with sig-

nal processing exclusively in the microwave regime

represent an exception from this trend. In contrast to

channel selection, other ﬁlter functions need to be

performed in the microwave regime. These functions

are the suppression of image reception in superhet-

erodyne receivers and the rejection of strong out-of-

band interferers. The second function stems from the

necessity to prevent strong interfering signals from

entering the LNAs and mixers, where they would

cause saturation, desensitisation, and intermodula-

tion effects due to the nonlinear response of these

active devices.

Cryogenic units for base-transceiver stations (BTS)

of wireless communication networks became com-

mercially available in the late 1990s. These units

comprise HTS bandpass ﬁlters followed by cryogenic

LNAs, both integrated in an enclosed vacuum which

incorporates the cryocooler. In order to meet the

different requirements associated with frequency al-

location in a ﬁrst-generation analogue and second-

and third-generation digital systems, these systems

are available for different center frequencies and

bandwidths, as well as with multiple passbands and

with narrowband stopbands embedded in wider pass-

bands. The number of ﬁlter-LNA chains in one cry-

ogenic unit equals the number of antenna ports

(sector antennas and diversity antennas) implemented

in a one BTS.

For the evaluation of system beneﬁts offered by

cryogenic front-ends, the issue of a significantly im-

proved interference suppression due to steeper ﬁlter

skirts and the issue of an improved sensitivity due to

the reduced receiver noise ﬁgure should be clearly

distinguished. The ﬁrst feature becomes significant in

the case of wireless systems which have to operate in

areas with strongly interfering systems with unwanted

signals at frequencies closely spaced to the edge fre-

quencies of the desired signal. Here, the improved

selectivity is transformed into a lower intermodula-

tion noise level and hence into improving the quality

of service.

Alternatively, this advantage can be transformed

into reduced guard-band widths and hence in an en-

hanced spectral efﬁciency and capacity.

In case of spread-spectrum systems, like the third-

generation W-CDMA standard, HTS stopband ﬁlters

with extremely narrow bandwidths can be used to

reject narrowband interferers falling into the wide-

band operational frequency band.

The reduced receiver noise ﬁgure of cryogenic ﬁlter-

LNA conﬁgurations originates from three different

effects, namely the reduced noise temperature of the

cooled LNA, the reduced thermal noise of the ﬁlter

due to the lower physical temperature, and the reduced

contribution of the ampliﬁer noise due to the de-

creased passband insertion loss of the ﬁlter. Reduced

receiver noise becomes important in noise-limited

situations (e.g., rural areas), where it transforms into

a lower number of required BTSs or an improved

coverage for a ﬁxed number of BTSs. Typically, the

noise ﬁgure of a BTS with the cryogenic front end at

the ground (noise ﬁgure degeneration due to lossy ca-

ble between antenna and front-end) resembles the

noise ﬁgure of a conventional, but mast-mounted

front-end.

See also: High-temperature Superconductors: Thin

Films and Multilayers; Superconducting Radiation

Sensors

Bibliography

Alford N Mc N, Penn S J, Button T W 1997 High-temperature

superconducting thick ﬁlms. Supercond. Sci. Technol. 10,

169–85

Hein M 1999 High-temperature superconductor thin ﬁlms at

microwave frequencies. In: Tracts in Modern Physics. Spring-

er, New York, Vol. 155

Hieng T S, Huang F, Lancaster M J 2001 Highly miniature

HTS microwave ﬁlters. IEEE Trans. Appl. Supercond. 11,

349–52

Hong J-S, Lancaster M J, Greed R B, Voyce D, Jedamzik D,

Holland J A, Chaloupka H J, Mage J -C 1999 Thin ﬁlm HTS

passive microwave components for advanced communica-

tions systems. IEEE Trans. Appl. Supercond. 9, 3839–96

Klauda M, Kaesser T, Mayer B, Neumann Ch, Schnell F,

Aminov B, Baumfalk A, Chaloupka H, Kolesov S, Piel H,

Klein N, Schornstein S, Bareiss M 2000 Superconductors and

cryogenics for future communication systems. IEEE Trans.

Micro. Theory Tech. 48, 1227–39

Klein N 1997 Electrodynamic properties of oxide supercon-

ductors. Juelich report, July 3773, Post-doctoral thesis,

Juelich Research Centre, Germany

Kolesov S, Aminov B, Kaiser T, Kreiskott S, Piel H, Pupeter N,

Wagner R, Wehler D, Medelius H, Draganic Z, Chaloupka

H 2000 Cryogenic BTS receiver front end demonstrator Proc.

30th European Microwave Conf., Vol. 3, pp. 230–2

Kolesov S, Chaloupka H, Baumfalk A, Kaiser T 1997 Planar

HTS structures for high-power applications in communica-

tion systems. J. Supercond. 10, 179–87

Krupka J, Geyer R G, Kuhn M, Hinken J H 1994 Dielectric

properties of single crystals of Al

, LaAlO

, NdGaO

SrTiO

, and MgO at cryogenic temperatures. IEEE Trans.

Micro. Theory Tech. 42, 1886–90

Marcilhac B, Crete D G, Lemaitre Y, Mansart D, Mage J C,

Bouzehoua C, Jacquet E, Woodall P, Countur J P 2001 Fre-

quency agile microwave devices based on Y-Ba-Cu-O/Sr-

Ti-O/La-Al-O structures. IEEE Trans. Appl. Supercond. 11,

438–41

Matthaei G, Young L, Jones E M T 1980 Microwave Filters,

Impedance-matching Networks and Coupling Structures.

Artech House, Dedham

Oates D E, Dionne G F, Temme D H, Weiss J A 1997 Super-

conductor ferrite phase shifters and circulators. IEEE Trans.

Appl. Supercond. 7, 2347–50

Petrov P K, Carlsson E F, Larsson P, Friesel M, Ivanov Z G

1998 Improved SrTiO

multilayers for microwave applica-

tion: growth and properties. J. Appl. Phys. 84, 3134–40

Pozar D M 1998 Microwave Engineering. John Wiley, New

York

1163

Superconducting Microwave Applications: Filters

Rebeiz G M, Muldavin J B 2001 RF MEMS switches and

switch circuits. IEEE Microwave Magazine 59–71 and http://

www.eecs.umich.edu/rebeiz/Current

Research.html

Remilliard S K, Abdelmonem A, Radzikowski P O, Lazzaro N

D, Applegate D S 2001 Field deployable microwave ﬁlters

made from superconductive thick ﬁlms. J. Supercond. 14,

47–56

Vendik O G, Ter-Martirosyan L T, Zubko S P 1998 Microwave

losses in incipient ferroelectrics as functions of the temper-

ature and the biasing ﬁeld. J. Appl. Phys. 84, 993–8

Waldram J R 1996 Superconductivity of Metals and Cuprates.

Institute of Physics, Bristol

Willemsen B A 2001 HTS ﬁlter subsystems for wireless tele-

communications. IEEE Trans. Appl. Supercond. 11, 60–7

rdenweber R 1999 Growth of high-Tc thin ﬁlms. Supercond.

Sci. Technol. 12, R86–R102

Yeo K S K, Lancaster M J 2001 High-temperature supercon-

ducting ferrite phase shifter latching structures. IEEE Trans.

Appl. Supercond. 11, 430–3

Zuccaro C, Winter M, Klein N, Urban K 1997 Microwave

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Phys. 82, 5695–704

N. Klein

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H. Chaloupka

University of Wuppertal, Germany

Superconducting Permanent Magnets:

Potential Applications

When high-temperature superconductivity (HTS)

was discovered, it became possible to construct elec-

trical machines without high cryotechnic expenditure

which was necessary with classical superconductors.

Bulk superconductors (see Superconducting Perma-

nent Magnets: Principles and Results) could be used

for different types of electrical motors, e.g., hysteresis

motors, reluctance motors, and trapped ﬁeld motors

(Kovalev et al. 2000, Oswald et al. 1998, Barnes et al.

2000).

While the hysteresis motor is an asynchronous

motor type, the others are synchronous motors. For

those drives the rotors move synchronously with the

rotating ﬁeld. The superconductors arranged in the

rotors of synchronous motors are exposed to a d.c.

ﬁeld, if only the fundamental wave is considered.

However, the rotating ﬁeld has no pure sine-wave

form, it contains higher harmonics, causing hysteresis

losses and perhaps also eddy current losses in the

penetration depth of the magnetic ﬁeld.

With reluctance motors, the solid superconductor

is used as a diamagnet which has to exclude the

quadrature axis ﬁeld, if possible, totally. In case of

the trapped ﬁeld motor, the solid superconductor

works as a permanent magnet; here the strength of

the trapped ﬁeld is decisive and important for the

power density of the motor. These principal consid-

erations are not only true for rotating, but also for

linear, drives where there is a linear moving ﬁeld in-

stead of a rotating ﬁeld.

1. Theoretical Considerations

The intrinsic moment M

of a rotating ﬁeld machine

is normally dominated by the air gap ﬁeld B and the

ampere turns per meter A

in the stator. Additionally,

the phase angle e between the phasor of the main ﬁeld

and the ampere turns per length plays an important

role:

¼ CBA cos e ð1Þ

Here, C is a machine constant including the motor

geometry and the winding parameters. The phasor of

the main ﬁeld consists of the vector addition of the

rotor ﬁeld B

and the stator ﬁeld B

. For rotors with

permanent magnets B

is essentially larger than B

and eo201. Consequently:

BCB

ð2Þ

Therefore, high values for B

result in the case of

equivalent motor dimensions in relatively high tor-

ques. The advantage of trapped ﬁeld motors must

depend on improved values of the rotor ﬁeld accord-

ing to Eqn. (2).

2. Comparison with Conventional Motors

The possible advantages of superconductive perma-

nent magnets being used in electrical machines be-

come obvious in a comparison with conventional

motors. Here, especially the comparison with perma-

nent magnet motors with rare-earth elements has to

be discussed. Permanent magnets of the composition

Nd–Fe–B have remanence ﬁeld strengths of approx-

imately 1.2–1.5 T, coercive ﬁeld strengths of 800–

900 kAm

1

, and maximum energy densities of

400 kWsm

3

. In the air gap of such permanent mag-

net motors, we obtain mean operating ﬁeld strengths

of 0.7–0.8 T. The strength of the air gap ﬁeld deter-

mines according to Eqn. (2) the power density of a

motor.

Permanent magnet motors have also a high power

factor compared with other motor types, e.g., asyn-

chronous motors, and principally no losses in the

ﬁeld-generating part. Both advantages allow a small

motor size and an appropriately high dynamic of the

motors. Superconductive permanent magnet motors

certainly become interesting when their power density

is significantly higher than that of normal permanent

magnet motors. If it is possible to trap very high ﬁelds

in the superconductors, motors could be designed

1164

Superconducting Permanent Magnets: Potential Applications

without magnetic yoke in the stator and, therefore,

avoid hysteresis and eddy current losses in the iron.

Consequently the size and the weight of the motor

could be reduced significantly.

If superconductive permanent magnets are used,

the ﬁeld geometry which results from the local current

density in the form of a Bean cone (see Supercon-

ducting Permanent Magnets: Principles and Results)

differs from the rectangular ﬁeld shape of conven-

tional permanent magnets. Comparing these different

motor types, this difference must be taken into

account and yields a possible disadvantage of super-

conductive permanent magnets.

3. Further Developments

The present developments on bulk superconductors

concentrate on the improvement of the current den-

sities at possibly high operating temperatures, and on

the manufacturing of large single domain structures.

Large geometries are absolutely necessary for the con-

struction of medium- and large-size motors. Super-

conductive connections across grain boundaries

can perhaps become useful with a view to larger

structures.

The current density in the superconductor and its

geometry determine the achievable magnetic induc-

tion. The current density can be increased in bulk

superconductors by decreasing the operating temper-

ature. But, consequently the effort for the cooling

system will increase significantly. Trapped ﬁeld mo-

tors need a magnetizing facility that has to be inte-

grated in the motor. Superconductive permanent

magnets must be recharged in the superconductive

state, i.e., at a low temperature after every period of

heating up. This certainly creates a technical problem

that requires an appropriate effort.

4. Possible Fields of Application

4.1 Motors

Electrical machines with superconductive permanent

magnets are certainly of advantage if they offer a

higher power density and simultaneously a high de-

gree of efﬁciency in comparison with conventional

solutions. Here all those applications are of special

interest where the volume of the motor and its weight

play a decisive role, e.g., in case of high-accelerated

vehicles or in airplanes and rockets. Apart from that,

ﬁelds of application exist where the cryotechnique is

already available, e.g., in case of liquid gas pumps.

The power density is also important with linear mo-

tors as servo drives, because the rotor mass directly

inﬂuences the power need of these drives. This is

particularly true for positioning drives, the moving

cycle of which is essentially composed of only quick

positive and negative accelerations.

At the present level of technique, the necessary

cryotechnique is certainly still a serious obstacle for

many possible applications. In future, however, the

advantages of superconductive drives will lead step-

by-step to industrial applications.

4.2 Magnetic Bearings; Fly Wheels; and Maglevs

The combination of HTS and permanent magnets,

e.g., rare-earth magnets, can be used in magnet bear-

ings, ﬂy wheels, and magnetically levitated transport

systems (Maglevs, Proceedings of ASC 1998, Pro-

ceedings of EUCAS 1999). The forces achieved de-

pend on the superconducting currents and the ﬁeld of

the permanent magnet as discussed before. The higher

the current density in the superconductor the higher

are the levitating forces for ﬂy wheels and for Maglev,

and the restoring force in the case of bearings. For

ideal conditions, i.e., an inﬁnite current density in the

superconductor, the area of which is large compared

to the area of the permanent magnet, the force density

is given by

ð3Þ

where B

is the ﬁeld produced by the permanent mag-

net on the surface of the superconductor.

In the case of B

¼0.5 T the force density is about

10 Ncm

2

Superconductive magnetic bearings are advanta-

geous for very high rotating speeds, as they are nearly

absolutely friction-free. However, the stiffness of

such bearings, measured as force per deﬂection, must

still be distinctly improved before their application in

electric drives.

As Eqn. (3) shows, much higher force densities can

be achieved using superconducting permanent mag-

nets with trapped ﬁelds significantly higher than 1 T.

See also: Magnetic Levitation: Materials and Pro-

cesses; Magnetic Levitation: Superconducting Bear-

ings; Superconducting Machines: Energy Storage

Bibliography

Barnes G J, McCulloch M D, Dew-Hughes D 2000 Computer

modelling of electric motors containing bulk type II super-

conducting materials in the rotor. In: Obradors X, Sand-

iumenge F, Fontcuberta J (eds.) Applied Superconductivity

1999. Institute of Physics Conference Series. IOP Publishing,

Bristol, UK, pp. 1075–8

Kovalev L K, Ilushin K V, Penkin V T, Koneev S M A, Pol-

tavets V N, Larionoff A E, Modestov K A, Larionoff S A,

Gawalek W, Habisreuther T, Oswald B, Best K J, Strasser T

2000 Hysteresis and reluctance electric machines with bulk

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Obradors X, Sandiumenge F, Fontcuberta J (eds.) Applied

1165

Superconducting Permanent Magnets: Potential Applications

Superconductivity 1999. Institute of Physics Conference

Series. IOP Publishing, Bristol, UK, pp. 1037–42

Oswald B, Krone M, So

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Gawalek W, Kovalev L 1998 Superconducting reluctance

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Proceedings of ASC, Palm Springs 1998 IEEE Trans. Applied

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of Physics Conference Series. IOP Publishing, Bristol, UK,

B. Oswald

Oswald Elektromotorenbau GmbH

Miltenberg, Germany

Superconducting Permanent Magnets:

Principles and Results

Bulk type II superconductors are able to trap magnetic

ﬁelds and to act as permanent magnets. The trapped

ﬁelds are generated by superconducting persistent

currents circulating macroscopically within the super-

conductor. The main feature of the resulting ﬁeld

distribution is a maximum trapped ﬁeld B

in the cen-

ter of the superconducting domain. High trapped

ﬁelds B

in bulk superconductors require a high crit-

ical current density of the supercurrents and large

superconducting domains. Several melt-processing

techniques were developed in the last years of the

twentieth century to produce superconducting perma-

nent magnets from bulk high temperature supercon-

ductors (HTS) as YBa

7x

(YBCO), SmBa

7x

(Sm-123), and GdBa

7x

(Gd-123).

Trapped ﬁelds B

up to 2.1 T can be obtained at

the temperature of liquid nitrogen on the surface of

HTS disks several centimeters in diameter. Higher

trapped ﬁelds were observed at lower temperatures

due to the increasing critical current density. How-

ever, the trapped ﬁeld is limited by the mechanical

properties of the material, because Lorentz forces

cause considerable tensile stresses during the mag-

netization procedure and can cause cracking of the

material. To avoid cracking, HTS disks can be rein-

forced by steel tubes which produce a compressive

stress on the superconductor after cooling from

300 K to the measuring temperature. Mechanical

properties are also improved by the addition of silver.

Very high trapped ﬁelds beyond 10 T have been

achieved in this way in bulk YBCO material at tem-

peratures between about 20 and 40 K.

The inﬂuence of ﬂux creep on the properties of su-

perconducting permanent magnets will be discussed.

Furthermore, levitation forces between superconduc-

tors and permanent magnets will be considered.

1. Type II Superconductors and Trapped Fields

1.1 Field Proﬁle

The magnetization vs. ﬁeld dependence of a type II

superconductor is shown in Fig. 1. In the Meissner

state (B

with B

as the lower critical ﬁeld), a

superconducting surface current screens off the ex-

ternal magnetic ﬁeld B

so that the magnetic induc-

tion B in the bulk superconductor vanishes. In the

mixed state between B

and the upper critical ﬁeld

, magnetic ﬂux penetrates the superconductor in

the form of ﬂux lines, each containing one quantum

of magnetic ﬂux f

¼2.1 10

15

. A ﬂux line is

composed of a normal conducting core of radius x

(coherence length) and a surrounding circulating su-

percurrent region where the magnetic ﬁeld and the

supercurrents fall off within a distance l (London

penetration depth). In the absence of defects, the ﬂux

lines form a triangular lattice. As the external ﬁeld B

increases towards B

, the size of the superconducting

region between the cores of the ﬂux lines shrinks to

zero, and the sample shows a continuous transition to

the normal state. The M(B

) dependence of a defect-

free type II superconductor is reversible and after

switching off the external ﬁeld no magnetic ﬂux is

trapped within the superconductor.

The M(B

) dependence becomes highly irreversible

if the superconductor contains defects like disloca-

tions, precipitates, etc., which interact with the ﬂux

lines. The interaction force between the defects in the

material and the ﬂux line lattice, the volume pinning

force F

, balances the driving force F

¼j

B ¼

1/m

(rot B B) acting on the ﬂux lines due to the

density gradient of ﬂux lines. According to the con-

cept of the critical state (Bean 1962), the gradient of

the magnetic ﬁeld has its maximum value 1/m

dB/

dr ¼j

within regions of the superconductor pene-

trated by the ﬁeld, or dB/dr ¼0 for those regions that

never felt the magnetic ﬁeld.

The resulting ﬁeld distribution for increasing ex-

ternal ﬁeld is shown in the lower inset of Fig. 1. Ne-

glecting the ﬁeld dependence of the critical current

density, the ﬁeld within the superconductor decreases

linearly with increasing distance from the sample

edge. As the external ﬁeld is reduced, the gradient of

the local ﬁeld near to the sample edge changes its

sign, but has the same absolute value as before. The

resulting ﬁeld proﬁle for decreasing external ﬁeld is

shown in the upper inset of Fig. 1. The magnetization

becomes positive because a ﬁeld is trapped in the su-

perconductor by the pinning effect.

The ﬁeld proﬁle after switching off the external ﬁeld

is shown in Fig. 2. The trapped ﬁeld decreases linearly

from its maximum value B

at the center of the sample

to zero at the edge of the sample. The gradient of this

ﬁeld proﬁle is determined by the pinning force of the

defects acting on the ﬂux lines. Therefore, the maxi-

mum trapped ﬁeld B

of a superconducting permanent

1166

Superconducting Permanent Magnets: Principles and Results

magnet depends on the critical current density j

the supercurrents and the radius R of the current

loops. For a cylindrical sample of inﬁnite length, B

given by

¼ j

R ð1Þ

Using j

¼10

Acm

2

and R ¼1 cm, Eqn. (1) gives a

maximum trapped ﬁeld B

¼12.6 T within the super-

conductor or in the gap between two long supercon-

ducting samples. The trapped ﬁeld on the surface of a

long superconducting sample is half as large as this

value, hence B

¼6.3 T. It should be noted that the

results obtained from Eqn. (1) overestimate the

trapped ﬁeld, because a ﬁeld-independent critical cur-

rent density is assumed, whereas in real superconduc-

tors, the critical current density decreases with

increasing magnetic ﬁeld. Nevertheless, this approxi-

mation gives an idea about the relation between the

critical current density and the trapped ﬁeld in super-

conducting permanent magnets.

The ﬁeld proﬁle of a YBCO disk (Fig. 3) is shown

in Fig. 4. The curved shape of the distribution of the

trapped ﬁeld in bulk YBCO superconductors can be

calculated taking into account the ﬁeld dependence of

the critical current density of the supercurrents as was

demonstrated by Klupsch et al. (1997).

1.2 Trapped Fields in Low- and High-temperature

Superconductors

Trapped ﬁelds in low-temperature superconductors

have been investigated at the temperature of liquid

helium. In a niobium hollow cylinder, magnetic ﬁelds

up to 0.26 T have been trapped (Garwin et al. 1973).

Higher magnetic ﬁelds up to 2.2 T were permanently

trapped at 4.2 K in a hollow cylinder consisting of

copper-clad Nb

Sn ribbons (Rabinowitz et al. 1977).

However, the trapped ﬁeld in bulk superconductors

at low temperatures was found to be strongly limited

by thermomagnetic instabilities resulting in ﬂux

jumps. An initial thermal disturbance in the critical

state caused, for example, by the motion of magnetic

ﬂux during increasing external ﬁeld, reduces the crit-

ical current. The released magnetic energy changes

unstably into thermal energy as the external ﬁeld

Figure 1

Magnetization vs. applied magnetic ﬁeld of a type II superconductor. In the two insets the typical ﬁeld distribution

within the superconductor (radius R) is shown for increasing (lower inset) and decreasing (upper inset) magnetic ﬁeld

assuming a ﬁeld-independent critical current density.

1167

Superconducting Permanent Magnets: Principles and Results

exceeds a certain value B

which depends on the spe-

cific heat of the superconductor. The low specific heat

of superconductors at helium temperatures reduces

their instability ﬁeld B

to very low values, limiting

the trappable ﬁeld in the bulk superconductor.

The discovery of high-temperature superconduc-

tors (HTS) stimulated new activities in the ﬁeld of

superconducting permanent magnets in bulk materi-

al. Because of the large specific heat of HTS at liquid

nitrogen temperature, the instability ﬁeld B

becomes

much larger than at 4.2 K. A second advantage of

HTS is that the use of liquid nitrogen instead of he-

lium as coolant of the superconductor makes the

handling of superconducting permanent magnets

much easier. However, HTS have several peculiari-

ties that make the preparation of bulk material

with high critical current densities rather difﬁcult.

The primary problems with these materials are their

extremely small coherence length, their large aniso-

tropy, and their brittleness.

A key parameter for the performance of supercon-

ductors for applications is the coherence length which

determines the size of the normally conducting core

of the ﬂux lines. In order to control the motion of ﬂux

lines one needs a microstructure with defects as small

as the coherence length. The extremely small coher-

ence length of HTS, which for YBCO is only 1.8 nm,

is the reason that defects as grain boundaries—which

are very beneﬁcial in low temperature superconduc-

tors because they act as pinning defects—serve now

as weak links and limit the critical current, especially

in the presence of an external magnetic ﬁeld.

The crystal structure of HTS is highly anisotropic,

which has implications for both the physical and me-

chanical properties. The electrical conductivity is

highly anisotropic with much higher conductivity

Figure 3

Melt-textured YBCO disk with a Sm-123 seed crystal in

the centre of the disk.

Figure 2

Field proﬁle of a type II superconductor for a constant

critical current density after switching of the external

magnetic ﬁeld and schematic view showing the

circulating supercurrent (current density j) and pinned

ﬂux lines within the superconductor.

Figure 4

Typical ﬁeld proﬁle of a YBCO disk measured at 77 K

(after Fuchs et al. 2000).

1168

Superconducting Permanent Magnets: Principles and Results

within the CuO

planes than perpendicular to the

planes. Therefore, supercurrents can ﬂow only within

the CuO

planes, i.e., the trapped ﬁeld generated by

these supercurrents is directed along the c-axis.

The brittleness of HTS is mainly caused by the an-

isotropy of the mechanical properties. For YBCO in

particular, the anisotropic expansion coefﬁcient re-

sults in large stresses causing microcracking because,

by cooling from the crystal formation temperature to

the superconducting transition temperature, the lat-

tice contracts far more along the a, b planes than

perpendicular to the planes. Microcracking is a cen-

tral issue to be solved for any application of YBCO

and especially for superconducting permanent mag-

nets in which large Lorentz forces arise by the inter-

action between magnetic ﬁelds and supercurrents.

2. Trapped Fields in Bulk HTS at T ¼77 K

YBCO has a superconducting transition temperature

of about 91 K. The critical current density of bulk,

polycrystalline YBCO material with randomly orient-

ed grains is strongly limited by its pronounced weak

link behavior. Only very small currents are able to

ﬂow across the grain boundaries, especially if a mag-

netic ﬁeld is applied. Weak links can be avoided by

growing large grains using melt-processing techniques.

Several techniques have been found to be suitable for

the growth of large single-domain YBCO material

without high-angle grain boundaries (Murakami 1993,

McGuinn 1995, Krabbes et al. 1997).

In most cases, seed crystals (Sm-123 or MgO) are

used in order to orientate the c-axis of the YBCO

sample perpendicular to the plane surface of the

sample. Large superconducting domains with a c-axis

texture can be produced in this way. A single-domain

YBCO sample 35 mm in diameter with a Sm-123

crystal on top of the sample is shown in Fig. 3. In the

present state of the art, the upper limit of bulk, single-

domain YBCO samples is about 10 cm in diameter.

The simplest way to control the grain structure is

to investigate the distribution of the trapped ﬁeld at

77 K. By applying a magnetic ﬁeld in the c-direction,

ﬂux lines penetrate the material and supercurrents are

induced in the a, b plane of the YBCO sample which

is cooled by liquid nitrogen. After switching off

the applied ﬁeld, the distribution of the trapped ﬁeld

in the superconductor is scanned by means of a Hall

sensor with a small active area. An example for

the ﬁeld proﬁle obtained for a single-domain YBCO

sample is shown in Fig. 4.

It was mentioned above that the main problem in

obtaining high critical current densities in YBCO is to

create a deﬁned microstructure with defects as small

as the coherence length. But also the identiﬁcation

of the relevant defects in bulk YBCO which are re-

sponsible for pinning is difﬁcult. Usually, different

kinds of pinning defects of different size as normal

conducting Y

BaCuO

(Y-211) precipitates, arrays of

stacking faults, dislocations and twin boundaries are

present in the material.

The role of the different defects for the pinning

effect in melt-texured YBCO material has been in-

vestigated very extensively and several review articles

of the subject are available (Murakami 1992, McGu-

inn 1995). The Y-211 precipitates which can be ob-

served by light microscopy have rather large

extensions between about 0.5 and 20 mm compared

with the diameter 2x ¼3.6 nm of ﬂux lines in YBCO

at 77 K. However, pinning at the interface between

the superconducting matrix and the large Y-123 pre-

cipitates due to the abrupt change of the order para-

meter over a short distance can explain many j

results found for melt-textured YBCO, as was point-

ed out by Murakami (1992).

Flux pinning can be improved by radiation-induced

columnar defects using heavy ions of high energy.

However, these defects are limited to a relatively thin

layer of a few tens of microns near to the surface of the

sample. In order to introduce strong pinning defects

into bulk superconductors,

235

U-doped YBCO mate-

rial was irradiated with thermal neutrons (Weinstein

et al. 1994). Columnar defects were produced by ﬁs-

sion in the bulk material and these defects were almost

of optimum size with a diameter of about 5 nm. High

critical current densities up to 8.5 10

Acm

2

and

trapped ﬁelds up to 2.1 T were obtained on the surface

of a single YBCO sample 20 mm in diameter at 77 K

(Weinstein et al. 1996). For comparison, the best

trapped ﬁeld results at 77 K for nonirradiated bulk

YBCO are in the range slightly above 1 T (Walter et al.

2000, Krabbes et al. 2000). Very promising results

have recently been reported for bulk Nd-123 and Sm-

123 material. Trapped ﬁelds up to 2.1 T (Ikuta et al.

1999) were achieved at 77 K for Sm-123 disks.

3. Relaxation Effects in Bulk YBCO

As was mentioned in Sect. 1.1, a large gradient of the

ﬁeld proﬁle in superconductors requires pinned ﬂux

lines. However, pinned ﬂux lines can also be ther-

mally activated at a ﬁnite temperature and hop from

one pinning defect to the other driven by the Lorentz

force. Thermally activated ﬂux motion or ﬂux creep

tends to reduce the ﬁeld gradient and, therefore, the

maximum trapped ﬁeld B

in the superconductor.

Flux creep effects are small at low temperatures

and for high pinning energies. For HTS, ﬂux creep

becomes extremely large at 77 K, since kT is about 20

times larger than at 4.2 K. Therefore, in HTS the ﬂux

lattice is much more mobile than in low-temperature

superconductors and there are large portions of the

H–T plane where extremely large ﬂux creep effects

are observed.

For 77 K, typical relaxation rates of d(B/B

d(ln t/t

)E0.05 were reported for melt-textured

1169

Superconducting Permanent Magnets: Principles and Results