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Microwave applications of superconducting materials

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1977 J. Phys. E: Sci. Instrum. 10 1193

(http://iopscience.iop.org/0022-3735/10/12/001)

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REV I E W A RTI C LE

Microwave applications of superconducting mate r i al s

A Septiert and Nguyen Tuong \let$ tCNAM, 292, rue Saint-Martin,75141 Paris Cedex 03,France SInstitut d’Electronique Fondamentale, Laboratoire associe au CNRS, Universite Paris-XI, BBtiment 220, 91405 Orsay Cedex, France

as high as 70 MV m-1 have been obtained in resonators in the continuous-wave (cw) regime, the injected RF power being only a few watts. These facts suggest a wide domain of application not only in linear accelerator (or RF separator) technology, but also for RF energy storage.

The first survey paper of RF superconductivity given by

Abstract After recalling the characteristic properties of a superconductor, we present theoretical and experimental results concerning the microwave siirface resistance and upper-limit values of the radio frequency fields in a resonant cavity. Details are also given on technological processes used for the fabrication of resonators with high-quality metal surfaces.

important fieId of applications of superconducting resonators : the frequency stabilisation of microwave generators for metrological purposes, and the realisation of electron (or ion) continuous-wave linear accelerators.

Other applications also based upon a very low surface resistance are briefly reviewed. Microwave Josephson devices are not considered.

A great part of the paper is then devoted to the most

1 Introduction Superconductivity was observed for the first time in 1911, but it was only in 1957 that all fundamental features of the super- conducting state were explained satisfactorily in a theoretical paper by Bardeen et al.

The electrical resistance of a superconductor is zero for DC

currents. At finite frequencies, the surface resistance of super- conducting material is not zero, but it can be very much lower than the surface resistance of the best electrical conductors in the normal state, by six or seven orders of magnitude. As a direct consequence, radio frequency (RF) power losses in the walls of superconducting waveguides or resonators are lowered by the same factor; this makes possible new applica- tions of microwave resonant structures which were in the past precluded by the high losses in normal metals.

The figure of merit for resonators, the quality factor Q, given by the ratio of the stored RF energy to the energy dissi- pated each cycle in the cavity walls, may easily attain values in the range lO9-lOio, more exceptionally lolo-loll at low RF fields, the resonators being cooled to 1.5 K in a pumped liquid helium bath. These high Q values give to superconducting resonators a great potential for applications in a wide variety of devices, especially for the frequency stabilisation of micro- wave oscillators. It is also very important that high Q values can be maintained with high RF fields in the resonant cavity. RF magnetic fields greater than 0.1 T and electric field levels

Maxwell in 1964 contains a complete summary of the theoreti- cal and experimental work in this field prior to 1963. The theoretical and experimental situations have been reviewed more recently by Halbritter (1970), Turneaure (1971, 1972), Hartwig (1973) and Pierce (1974). Schwettmann et a1 (1965), Septier (1969), Wilson (1970) and Kuntze (1974) have con- sidered in detail the promise of RF superconductivity for linear accelerators. However, the recent progress made in the development of devices associated with superconducting resonators, and of accelerating structures for electrons and ions, seems a good reason to bring to the attention of workers in other fields the results obtained in a growing number of laboratories, the interest of RF superconductivity applications being now well demonstrated.

Another fundamental feature of the superconductivity state, namely the ability of the free electrons to condense in pairs in the same quantum state, thus having the same wave function, was investigated in 1962 by Josephson, who discovered the extraordinary properties of weakly coupled superconductors. Josephson (1962, 1964, 1965) found that when two super- conductors are separated by a very thin barrier made of insulator or normal metal (or by a narrow neck) a steady current of electron pairs is able to tunnel through the barrier with no voltage between the superconductors. Further, when this current, supplied by an external generator goes beyond a critical value, a voltage V appears across the barrier and there is an alternating current whose frequency v is given by h v = 2 eV(where h is Planck’s constant and e is the electron charge;

The two phenomena are now called the Josephson effects, and since 1962 all theoretical predictions made by Josephson have been verified. The first experimental evidence for the AC

Josephson effect was obtained by Shapiro in 1963, and from this date the properties of Josephson junctions have been extensively studied, giving rise through the last decade to many microwave devices such as detectors, mixers, frequency multipliers, amplifiers and bolometers, working from the microwave to the infrared radiation frequency region. All these superconducting devices, based on the quantum mech- anical properties of a junction between superconductors, are considered as being out of the scope in this paper. The reader will find in the literature a large number of recent review papers devoted to Josephson devices (Richards et a1 1973, Deaver and Vincent 1974, Kamper 1976).

V I V= 483 593 MHz pV-’).

2 1193

A Septiev and Nguyen Tuong Viet

2 The superconducting state The superconducting state is characterised by a DC zero electric resistance below a certain critical temperature T,, and perfect diamagnetism in a weak magnetic field (Meissner effect). If a superconductor is placed in a magnetic induction field and cooled downso that it becomes superconducting when T< Tc, the magnetic flux lines are completely expelled from the superconductor. In fact, the magnetic induction B does not go discontinuously to zero at the surface of the superconduct- ing metal, but decays exponentially with a characteristic length, called the penetration depth h:

B(x) = B(0) exp ( - x/X); h is of the order of a few nanometres for pure materials.

In type I superconducting materials, the superconducting state disappears suddenly when the applied field is higher than a critical value Be and the normal electric resistance is then restored. The value of Bc depends on both the material and the temperature, following approximately a law of the form

where Bc(0) is the critical field at absolute zero. All simple superconducting elements are of this kind, except niobium. Lead has the highest Bc(0): 80 mT.

Superconducting materials of type I1 act differently: there is a DC zero resistance and a perfect Meissner effect below a threshold value Bel. Above Bel and below a second critical induction Bc2 the resistance remains zero but partial flux penetration occurs in the form of normal filaments. This mixed state survives as more and more flux filaments are created with increasing B until Bcz is reached, whereupon the DC zero resistance is destroyed. Pure, annealed niobium has Bcl(0) 2 0.17 T and Bcz(0)z 0.4 T (Finnemore et al 1966). However, several alloys and compounds of niobium, such as Nb-Zr, Nb-Ti and NbsSn, can have much higher Bcz in the range up to a few tens of teslas. They are normally used to make high-field magnets. A new, interesting material with its highest known critical temperature Tc = 22 K is NbsGe (Gavaler et a1 1974) but it is still in a development state.

It has been known since 1940 (London) that at microwave frequencies the electric resistance of a superconductor is not zero but that it can be much less than the normal resistance. This resistance decreases rapidly with the temperature and increases with the frequency.

Until 1957, the year of publication of the microscopic theory of superconductivity developed by Bardeen et a1 (BCS theory), early attempts to describe the RF behaviour of superconduc- tivity were largely in terms of phenomenological theories (London 1940, Pippard 1947) based on the two-fluid model (Gorter and Casimir 1934). In the two-fluid model it is assumed that the conduction electrons are divided into two classes, superconducting and normal. The fraction of the superconducting electrons which flow without energy loss varies continuously from zero at the transition temperature to unity at zero temperature. When the temperature is slightly below Tc, there are very few superconducting electrons but, having zero resistance, they can completely shunt the normal electrons, resulting in zero DC resistance. At microwave frequencies, the inertial property of the superconducting electrons prevents the complete shorting and the normal electrons carry some current with consequent power absorp- tion.

The BCS theory gives a better understanding of the physical mechanism of superconductivity and predicts fundamental parameters. In a superconductor, below Tc the free electrons are condensed in pairs (Cooper pairs). The electrons of a pair

are bound together by an interaction involving the ion lattice vibrations (phonons). The binding energy of these pairs increases as the temperature decreases and reaches a maximum at T=O. The BCS theory gives to this energy the universal value

~ ( 0 ) = 2A(O) = 3.52 kTc

at T= 0. The existence of these pairs leads to the appearance of an energy gap ~ ( 0 ) near the Fermi level. The Fermi surface falls in the middle of the gap. This gap is temperature- dependent, varying from zero at Tc to ~ ( 0 ) at T=O.

One can associate a critical frequency vc to ~ ( 0 ) so that hvc= ~ ( 0 ) . For v > vc, the photons can directly break a pair and be absorbed, leading to finite dissipation even at T=O. For lead and niobium vc is of the order of 600 GHz. This phenomenon is totally negligible in the present-day microwave application range, except near Tc.

The pairs of electrons have a maximum length of inter- action & called the coherence length. For a pure super- conductor whose electron mean free path 1 is large. and at T=O, &=hv~/2&0), where L'F is the electron velocity at the Fermi energy.

Between 1957 and 1962, all theoretical works were devoted to the 'pseudoparticle' aspects of superconductivity in order to explain the experimental results, especially the RF conduc- tivity. Only since the work of Josephson (1962) showing that the phase and amplitude variations of the pair wave function can appear microscopically have experimenters taken an interest in the wave aspects of the phenomena to develop many Josephson effect devices.

varies with T and the material purity.

3 The surface impedance of supcrconductors 3.1 Theoretical value The complex surface impedance of a metal having finite conductivity is defined as the ratio of the tangential electric field to the tangential magnetic field at the surface:

Z, = Rs + iXs = ET/HT.

At room temperature Rs= Xs= ( p 0 w / 2 u ) ~ : ~ = p ~ w 8 ~ where 6,, the skin depth, is the effective penetration depth for the fields into the metal, and U is the DC conductivity.

Upon cooling, the electron mean free path 1 becomes greater than 6, and the classical Ohm's law is no longer valid. The theory of the anomalous skin effect (Reuter and Sond- heimer 1948) shows that R, decreases to a limit value RI as the temperature is lowered and XI= R12/3. The experimental gain on surface conductivity between room temperature and liquid helium temperature is about 6 for copper at 3 GHz (Biquard and Septier 1966).

For a superconductor, the penetration depth of the RF magnetic field is not related to U but varies with T as

X(0) is always greater than XL, the London penetration depth in the two-fluid theory, and this is confirmed by experiment: 1 < h ( O ) i h ~ < 5 (Bardeen and Schrieffer 1961). The surface reactance X s which is proportional to h(T) follows the same law. The surface resistance, equal to RI just above Tc, decreases suddenly at T= Tc and tends toward zero at T= 0 like the normal electron density, provided that the frequency is not too high (U< wc), If w > we, Rs is not zero at T=O (figure 1) . When w $ w e (infrared and visible regions), R,s RI.

The superconducting surface impedance has been calculated by Mattis and Bardeen (1958) and Abrikosov et a1 (1959) from the BCS theory. It is a function of the following parameters:

1194

Microwave auulications of superconducting materials

lo'ic ,,i.2 K

?educed t emperc iu re [ TIT-,)

Figure 1 Surface resistance of superconductor as a function of reduced temperature for various frequencies.

the temperature T, the critical temperature Tc, the frequency w12.?r, the reduced energy gap A.lkTC, the London penetration depth AL, the electron mean free path I , and the Fermi velocity U F or the coherence length &I =hvp/2h(O).

To a rough approximation, the surface resistance for frequencies w < w c and temperatures T<0.5 Tc is

R ~ K - W2 exp (-&I T

while more detailed calculations (Halbritter 1970) which take into account mean free path effects give slightly different frequency dependences.

The theoretical expression for the surface impedance has been evaluated using a numerical integration program based on the Mattis-Bardeen expressions (Turneaure 1967) or on the Green function formalism of Abrikosov et a1 (Halbritter 1969). The material parameters of lead and niobium used in the computation are given in the following table (Turneaure 1967, Turneaure and Weissman 1968).

Lead Niobium

TC 7.2 K 9.2 K AjkTc 2.05 1.85 hL 30.8 nm 31.5 nm 1 710 nm 1000 nm OF 6 x lo5 m s-l 2.9 x lo5 m s-l

Figure 2 is a graph of the surface resistance as a function of frequency for niobium and lead at 1.8 and 4.2 K (Turneaure 1972). The theoretical dependence of Rs upon material parameters has been studied in detail (Halbritter 1970, Lyneis 1974).

The relation of Rs shows that for applications using the low-loss feature of superconducting materials, it is advanta- geous to work at low frequencies at a reduced temperature T/Tc as low as possible, and to prefer large-energy-gap (high- Tc) material. Niobium (TC = 9.2 K) and lead (TC = 7.2 K) are the two superconductors which have been most intensively used for microwave applications. Because of its higher critical temperatures, a type I1 superconductor such as NbaSn ( TC = 18.2 K) might have several advantages compared to lead and niobium, especially at a working temperature of 4.2 K (T/Tc=O'23).

F r e q d e n i y (Hzl

Figure 2 Theoretical superconducting surface resistance of niobium and lead as a function of frequency at 1% and 4.2 K.

3.2 Experimental uahe of Rs A simple method to obtain Rs of a superconducting material is to measure the unloaded quality factor QO of a cavity made from that superconductor. QO is related to Rs by a geometrical constant A which depends

only on the shape of the cavity and the particular mode, according to Qo= A/Rs . Care must be taken to avoid loss in the coupling parts and loss due to current flowing across joints in the walls of the cavity. Necessary joints should be located where there is no surface current for the mode of interest. Electron-beam-welded joints prove to be satisfactory in all circumstances (Turneaure and Nguyen Tuong Viet 1970).

According to the BCS theory, the RF losses should vanish exponentially with temperature. Experimentally the losses in superconducting niobium cavities have been reduced to the theoretical value at all temperatures above 1.5 K (figure 3). At temperatures below 1.5 K a constant residual surface

, 1 3 - 5 \

2 6 8 T. i T

Figure 3 Variation of surface resistance of niobium with temperature at 3.6 GHz.

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A Septier and Ngiiyen Tuong Viet

resistance RO is obtained. Therefore, the measured surface resistance can be written as the sum of two terms:

Rs(meas) = Rs(th) + RO

where Rs(th) is the theoretical superconducting surface resistance.

A lot of work has been carried out to reduce Ro, and attempts have been made to identify and explain the loss mechanisms for a real superconductor surface. For the observed nearly temperature-independent term RO having a frequency dependence ranging from W O to U*, it is difficult to find a precise frequency variation law, and experimental results are often contradictory.

Among various possible mechanisms for residual loss, one well known type is that loss caused by trapped magnetic flux (Pierce 1973) when the surface is cooled in a non-zero magnetic field BO (earth’s magnetic field for example). This flux is concentrated in flux lines threading normal conductivity cores through the material. In the cores, the magnetic field is greater than or equal to the critical field and the normal spots on the surface where flux lines emerge give some residual losses. To a rough approximation these losses are proportion- al to Bo/Bc. They can be reduced to a negligible level if the cavity is placed inside a magnetic shielding in an ambient magnetic field of less than 10-7 T.

Other possible residual loss sources are: non-ideal surface (roughnesses, fissures, surface damage, oxides, contamination, impurities, grain size); dielectric and magnetic RF losses: electromagnetic generation of phonons (Halbritter 1971, Passow 1972); and the coupling of the electromagnetic fields to the microwave acoustic phonons (Kartheuser and Rod- riguez 1974). More details on the residual surface resistance can be found in the papers by Halbritter (1975), Pierce (1974) and Hartwig (1973).

The lowest values of residual resistance which have been achieved so far are Ro= 3 x Q in lead (Pierce 1973) and Ro z 0.5 - 2.0 x Cl in niobium (Turneaure and Nguyen Tuong Viet 1970, Allen et a1 1971, Kneisel et a1 1972, Benaroya et a1 1975). These are the best values and are difficult to reproduce regularly. In practice, they are higher by a factor of 2-10. Niobium is at present the material of choice compared to lead but its technology is difficult and more expensive.

Other type I1 superconductors have been tested for the past few years: NbN with T, z 15 K (Isagawa et a1 1974) and Nb3Sn with T, = 18.2 K (Hillenbrand and Martens 1976, Kneisel et a1 1976, Arnolds and Proch 1976). To date the residual surface resistance Ro= 1 . 6 ~ Cl, of the Nb3Sn surface is still higher than that of niobium or lead, but the surface resistance obtained at 4.2 K and 9.5 GHz by Hillenbrand et a1 (1976), Rs=2,9x a, is 70 times lower than the theoretical value for niobium (Rs=2x 10-5 Q) at the same temperature and frequency. Therefore, NbsSn is already superior to niobium for microwave applications at 4.2 K.

3,3 Superconductors in high RF fields For large RF magnetic fields the energy gap decreases and the penetration depth increases; thus an increase of the surface resistance Rs might be expected. With the use of Ginzburg- Landau theory (Ginzburg and Laudau 1950), the influence of magnetic field on Rs has been estimated in different papers (Schwettman et a1 1967, Halbritter 1968). It has been found that at T= 1.85 K, the ratio Rs(Bc)/Rs(0) is about 1.2, 1.8 and 3.3 respectively for tin, lead and niobium. In a cavity, the power dissipation per unit area equal to (1/2p02)RSB2 will cause a heating of the inner surface leading to a local tem- perature increase AT due to the low thermal conductance between the surface and the helium bath. This hT can be

eventually high enough to cause a transition to the normal state of the whole cavity.

In a TM cavity where there is a normal electric field at the surface, RE can be increased by electron loading (Halbritter 1972, Lyneis et al 1973), which is the result of field-emitted electrons accelerated by RF fields. These electrons when colliding with the cavity wall can produce x-radiation and secondary electrons.

If the RF field amplitude is increased, eventually a critical RF

magnetic field \ alue is obsened at which the superconducting state partially breaks down and a rapid increase of Rs is observed. This RF field is called the AC critical magnetic field BcAC. For type I superconductors (tin and lead), BegC may be as large as the DC thermodynamic critical field B, (Turn- eaure 1967, Bruynseraede et a1 1971). In type I1 materials, there exists a lower critical field Bc1 < Be, above Lthich flux is expected to penetrate into the metal: according to Halbritter (1972), for microwave frequencies, the RF field strength should be limited only by Bc which is equal to 190 mT for niobium and 535 mT for Nb3Sn. The highest reported Ialues of Bc*C are attained only in an X-band TEoll mode cavity: BcAC= 160 mT for niobium (Schnitzke et a1 1973) and BcAC= 106 mT for NbsSn (Hillenbrand et a1 1976). In a TMO,O mode cavity, Be can be as high as 149 mT (Hillenbrand et a1 1975) but only at X-band frequencies (9.5 GHz). Measured values of BcAC decrease considerably with decreasing frequencies from the X- to the S- and L-bands.

4 Technology of superconducting resonators Niobium and lead are the two pure superconducting metals which have been most intensively studied for resonator use. They have the highest critical temperatures and critical magnetic fields of all pure metals which are commercially available in reasonable purity. Because of its natural tendency to oxidation, which causes an important degradation of cavity performances, and the difficulty of polishing the surface of lead layers without contamination, lead is employed less and less now in microwave applications, especially for high-field devices. However, the major advantage of lead is that if one needs only moderate Q and field, lead-plated cavities can be realised with low-cost equipment.

In practice, lead layers 5-10 pm thick are deposited by an electroplating technique in a lead fluoborate bath on the inner surfaces of the OFHC copper resonator parts. Good RF proper- ties of a lead surface depend on a lot of parameters such as copper quality and surface treatment, bath and anode purity, nature and proportion of additives, current density and rinsing procedure. More details on these particular plating techniques can be found in the literature (Schwettman et a1 1967, Pierce 1973, Hahn et a1 1968, Carne et a1 1971, Septier and Salaiin 1969, Bruynseraede et all971). A lead surface has been also produced by ultrahigh-vacuum evaporation (Flecher 1969, Nguyen Tuong Viet and Biquard 1966), but the resulting surface has higher surface residual resistance than layers obtained by electroplating.

The technology of niobium cavities has been developed more recently. The method of cavity fabrication depends very much on the type of cavity. Small cavities are machined in one piece from solid reactor-grade niobium or in different pieces which are then assembled by electron-beam welding or by indium joints. Large cavities are made from niobium sheets by hydro- forming followed by electron-beam welding (Turneaure 1972, Ben Zvi et a1 1472). Helical cavities have been made by winding a niobium tube around a mandrel into the form of a helix and then mounting the helix in a superconducting can (Fricke et a1 1972, Benaroya et a1 1972). Niobium cavities have also been made by electroforming (Meyerhoff 1969).

1196

Microwave applications of superconducting materials

After manufacture, two methods of processing have initially been developed to obtain low residual loss and high critical field. (i) Ultrahigh-vacuum firing (1800-1900°C for a few hours in a vacuum of about 10-6-10-' Pa) followed by chemical polishing in a mixture of HN03-HF at O'C; then a second firing as the final step (Turneaure and Nguyen Tuong Viet 1970). (ii) Electropolishing with an oscillating electrolysis current in a solution of H2S04 -HF (Diepers et a1 1971) to remove about 100 ym; then anodising in an NH3 solution to produce a Nbp05 layer about 0.3 ym thick (Diepers and Martens 1972). Variations of the first method consist of eventually replacing chemical polishing by electropolishing and inserting an anodising or oxipolishing stage (oxipolishing means anodising the cavity and then dissolving the oxide layer) before the final firing (Kneisel et a1 1975). Variations of the second method consist of introducing an oxipolishing stage before the final anodising (Hillenbrand et a1 1974).

The problem of avoiding contamination of the cavities, particularly during the later stages of processing and during assembly, is very important. After the final UHV firing, the cavities must be assembled in a glove box to avoid contamina- tion of the cavity by the room atmosphere. After anodising or oxipolishing, the cavity has to be rinsed continuously during the installation by a jet of acetone or methanol. After assembly, cavities are evacuated with either UHV turbomolecular or sputter-ion pumps.

Cavities treated by the second method can have Q values as high as those treated by the first one, but they seem to be more sensitive to electron impact (Kneisel et al 1974a, b).

As considerable progress is expected from the use of high-T. superconductors at microwave frequencies, many laboratories have started to study Nb&n cavities (Hillenbrand et a1 1975, Kneisel et a1 1976, Arnolds and Proch 1976, Padamsee et a1 1976). Superficial layers of Nb3Sn are prepared by exposing niobium to a saturated tin vapour at about 1050°C for several hours in an evacuated fused-quartz ampoule or niobium can. The surface properties may be improved by oxipolishing (Hillebrand et a1 1976).

5 Main applications of superconducting resonators The two main applications, superconducting-cavity-stabilised oscillators and superconducting particle accelerators (or separators) in which practical realisations are currently being made, are emphasised. Other applications, still at the labora- tory development stage, will be discussed briefly in the next section.

5.1 Superconducting-cauity-stabilised oscillators (SCSO)

5.1.1 Microvt'am cavities Microwave cavities in a variety of shapes and modes are suitable for stable oscillators, but the two types which have been used to date are the T E m and the m o l 0 mode cavities (figure 4). Such cavities are realised to study the superconducting surface itself and are in general available for oscillator applications. In the TEoii mode cavity, since no currents flow from the cylinder wall to the short- circuit planes, the lead-plated or niobium cavity can be made in two parts (a niobium pot-shaped cup and a flat end-p1ate)which are then assembled by an indium joint. Coupling to the outside circuit is done through a small iris bored in the end-plate. TivOlO mode niobium cavities are usually fabricated in two parts which are then welded together by electron-beam welding. Coupling is done with an electric probe on the cavity axis through a small, circular cut-off waveguide. The cavity wall is thick enough to reduce the sensitivity of the cavity resonant frequency to external pressure or radiation pressure.

Niobium and lead-plated cavities for oscillator applications

i,,, ncde TV.. _ _ mode

Figure 4 Microwave superconducting cavities.

have been realised in S- and X-band frequencies. The Q values achieved at 1.3 K range from 109 to lolo; best values some- times reach 101l (Turneaure and Nguyen Tuong Viet 1970, Allen et a1 1971, Kneisel et a1 1974a, b).

5.1.2 Simple superconducting-cacitjl oscillators (sco) For a decade, the Orsay group has been building various low-cost and simple stabilised oscillators? using a high-Q superconduct- ing cavity with the main purpose of illustrating feasibility (Jiminez et a1 1973). However, the attained stability, defined as the standard deviation of the fractional frequency fluctua- tion u,(.T), where T is the measuring time, ranges from to 10-12 for .T= 10 s compared to 10-5-10-7 for unstabilised oscillators.

The S-band sco realised by Nguyen Tuong Viet (1964,1967) used a tunable, lead-plated, ~ ~ 0 1 1 mode cavity placed in the external feedback loop of a low-noise travelling-wave tube (TWT) amplifier (figure 5). When the amplifier gain exceeds the

Figure 5 Block diagram of superconducting TWT oscillator.

losses and the total phase shift around the loop is a multiple of 2n, oscillation can occur. The measured stability was about 6 x 10-11 for T = 1 s, limited essentially by phase fluctuations in the loop and by the variation of the helix voltage. This

The cost of a klystron oscillator locked by injection to a superconducting cavity is about $15 000-20 000 (including the cryostat) compared to the cost of a hydrogen maser ($150 000) or of a commercial caesium clock ($25 000-30 000). Prices of the maser and clock are given in a review paper by Audoin and Vanier (1976).

1197

A Septier and Nguyen Tuong Viet

type of sco was first developed by Khaikin (1961) in the X-band with a stability of about 10-9 for times of about 1 h. The spectral density of the phase fluctuations was measured by Kukushkin and Nasonov (1969) in a 7.5 GHz TWT sco to be - 96 dB Hz-l at 300 Hz from the carrier, while Blomfield and Pointon(l973)found - 120 dB Hz-1 at 1 kHz from the carrier in an L-band TWT oscillator.

A direct method of making an oscillator was developed by Biquard et al (1967). This is a monotron-type oscillator (figure 6) using a superconducting S-band, lead-plated, TM010

Lers

9.8 GHz niobium ~ ~ 0 1 0 mode cavity (ee= 109) was 3 x 10-l2 for an averaging time T of 10 s (BCnard et a1 1972). When a Gunn diode oscillator was used with an 8.6GHz niobium cavity (Qe=2.5 x log), the short-term stability was 7 x for T = 10 s and the long-term stability was excellent: k 5 x

for almost 3 h (Jimenez-Lidon and Benard 1973, Jimenez-Lidon and Septier 1973).

The disadvantage of using a room-temperature oscillator is the line length between the oscillator and the superconducting cavity. In the tunnel-diode scso (Jimenez-Lidon and Septier 1973, Jimenez-Lidon and Benard 1973) the coupling line is very short as a cooled, free-running tunnel-diode oscillator is coupled very closely to a tunable 3 GHz, m o l l mode, lead- plated cavity via a variable, superconducting coupling loop through a cylindrical cut-off waveguide on the end-plate. The useful power is extracted through a second loop and the cavity acts as a stabilising and filtering system (figure 8). The measured stability was 2 x 10-11 for ~ = 0 . 3 s although the cavity Q was only 2 x 108.

SJpercwduct rg TM,,, c3ti1tj: -L

Figure 6 Superconducting-cavity monotron. Stub

I c l l tpu t

mode cavity (Q= lo7 at 4.2 K). An electron beam is acceler- ated along the axis of the cavity. If the transit time of the electrons is well chosen, power can be delivered to the electro- magnetic field and an oscillation can arise in the cavity. The stability of the output signal (150 mW) was 2 x 10-lo for ~ = 0 . 1 s, with 7-112 behaviour for shorter times and stability independent of T for 7 as long as several minutes (Biquard 1970). Short-term stability was probably limited in this experiment by noise due to electron field emission from the cavity walls, the macroscopic electric field being greater than 2 MVm-1. Benard (1973) found a slightly better result, ~ ( ~ ) = 1 0 - ~ 0 f o r ~ = 3 0 0 m s w i t h a n i o b i u m c a v i t y ( Q = 1 * 7 ~ lo7 at 4.2 K) at a useful power level greater than 100 mW.

Better stability was obtained by coupling directly a high- Q cavity to a klystron or a Gunn diode oscillator (figure 7). This

K l y s t r 3 r 3r Gun, o s c i ' l m r

Phase

S u p e r c c r t x t n g c@"-Y

U

Figure 7 Block diagram of stabilised oscillator.

type of sco was discussed in detail by Sudraud (1971) and Jimenez-Lidon (1 974). The oscillator is injection-locked by the power reflected from the superconducting cavity. The stabili- sation factor, which is the ratio of the free-running oscillator frequency fluctuation to the cavity-stabilised oscillator fre- quency fluctuation, is approximately equal to the ratio of the external Q (Qe) of the superconducting cavity to the external Q of the free-running oscillator. The measured stability of a 2K25 reflex klystron (Qe=200) stabilised by a

1 I Figure 8 Cooled tunnel-diode superconducting-cavity- stabilised oscillator.

5.1.3 Electronic-stabilised (Pound-type) oscillators To achieve the ultimate frequency stability, electronic stabilisation with its higher feedback loop gain has to be preferred to direct stabilisation. This approach has been followed by Stein and Turneaure at Stanford University since 1972 to develop a state-of-the-art scso (Stein and Turneaure 1972, 1973, 1975, Stein 1974) with a short-term stability as low as u(T)= 6 x

Figure 9 is the simplified block diagram of the scso. It represents in fact an ameliorated version of the Pound system (Pound 1947). The method of modulation has been changed to decrease the effect of variations in the length of the wave- guide; the modulation frequency was chosen to be 1 MHz instead of the more normal 30 MHz to reduce the phase changes between the carrier and the sidebands due to dis- persion. The microwave source is a 50 mW voltage-controlled Gunn effect oscillator operating at a nominal frequency of 8.6 GHz. A portion of its output is phase-modulated (PM) at

for 7 = 100 s.

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Microwave applications of superconducting materials

- Vo I t ag e - - Superconduct ing control led Phose cov i t y

~ f r eqJency microwave + modulator osc i I l a to r 6 isc r im ina tor

control led Phose microwave modulator

cov i t y f reqJency

t-l A C error s igro l

D C error s ignal Figure 9 Simplified block diagram of the superconducting-cavity-stabilised oscillator.

1 MHz and this PM signal is transmitted to the cavity. Upon reflection of the carrier and the phase modulation sidebands from the cavity, part of the power is converted into a 1 MHz amplitude modulation (AM) signal whose magnitude is propor- tional to the frequency offset and whose sign depends on whether the deviation is above or below the resonant fre- quency. The 1 MHz AM signal component is detected, ampli- fied and finally demodulated with a 1 MHz reference. After DC amplification and filtering, this DC error signal is fed back to a varactor tuning element in the Gunn effect oscillator to control its frequency. The effective DC open-loop frequency gain is about 220 dB.

Three independent scso systems have been realised and the short-term frequency stability was studied by comparing each oscillator with the other two. The measured time domain stability U(.) for a single superconducting oscillator in a 10 Hz bandwidth decreases with T approximately as 1 x lO-I4 7-l

for 0.1 < T < 10 s, reaching a noise floor of 6 x 10-16 at 7% 100 s. The long-term stability was measured via a comparison with a group of caesium frequency standards. A linear frequency drift rate of about 1 x 10-14 d-1 was observed for the best scso system (Turneaure and Stein 1975).

The stability of the scso is compared with those of the caesium clock (a standard which is used for the definition of the second) and hydrogen maser in figure 10. Such good stability of the scso can be attained only by identifying and eliminating various sources of instability.

Figure 10 Measured stabilities of caesium clock, hydrogen maser and scso. Data used for maser and clock are taken from Hellwig (1975).

5.1.4 Sources of instability in an scso (Stein and Turneaure 1974, Jimenez-Lidon and Septier 1973) The sources of frequency instability can be divided into two categories : instability due to fluctuation of the superconducting cavity resonant frequency, and instability introduced by the rest of the scso system. The superconducting cavity is the essential element of an scso. Its fabrication must be executed with care to obtain a Q factor higher than l o 9 and to reduce as far as possible variations of the resonant frequency. The super- conducting cavity resonant frequency depends on a number of factors, any one of which can lead to frequency noise and drift. (a) Vibrations can introduce frequency modulation of the resonant frequency. Qualitative measurements indicate that vibrational noise is the principal limiting factor for a short averaging time T < 10 s. The helium Dewar has to be located on a vibration isolation pad and the floor of the room must have a relatively low vibrational level. (b) A static frequency shift of the cality resonant frequency is produced by the electromagnetic radiation pressure or by a nonlinear surface reactance. This frequency shift is approxi- mately proportional to the power incident on the cavity. The incident power has to be regulated and kept as small as possible. (c) Small pressure changes exterior to the cavity can shift the resonant frequency, especially when the cavity is directly in the helium bath, the level of which decreases with time causing a decrease of the external pressure on the cavity walls. This effect can be reduced by placing the cavity in a constant- pressure can filled with helium gas at about 10-2-1 Pa. Cooling of the cavity is accomplished by conduction through the input waveguide and by convection through the gas. ( d ) Temperature changes of the cavity produce a resonant frequency shift due to the temperature dependence of the surface reactance and to the thermal expansion. This effect is quite small if the working temperature is below 1.5 K; however, good temperature control (k 10-5 K) has to be used for long-term stability. (e) Instability introduced by the rest of the scso system depends on noise and drifts of the free-running oscillator and on the dependence of the oscillator frequency upon the path length of the feedback loops. Low-noise active elements such as parametric amplifiers or cooled MESFET amplifiers placed in a controlled temperature environment with well regulated power supplies and short transmission lines have to be used.

At the National Bureau of Standards work is in progress on a superconducting parametric oscillator (Stein 1975). Two resonators whose frequencies are w1 and W P are coupled by a varying capacitance modulated by a pump frequency w3=

W I + ~ 2 . Figure 11 represents the equivalent circuit of the

1199

A Septier and Akciyen Tuong Viet

K o r m a l n . 1 Superconduct ing resonator t rans former resonator

Figure 11 parametric oscillator.

The equivalent circuit of a superconducting

parametric oscillator. A portion of the pump power is trans- ferred to the electromagnetic fields in the cavities. When this power is larger than the cavity losses, the system will oscillate. To reduce the influence of the frequency fluctuations of the pump source upon the final stability of the oscillator, only one of the two resonators is made superconducting. If Q z % Ql,

but the pump power threshold leading to oscillation is quite high and the problem of evacuating heat into the helium bath has to be solved. A cooled MESFET amplifier associated with a superconducting cavity is under consideration at Orsay.

5.1.5 Applications of the scso The scso is remarkable for its spectral purity and stability and considered as a secondary frequency standard. It has already been used by Turneaure and Stein (1975) to set an upper limit on the time variation of the fine-structure constant. When operating at X-band, it appears to be an excellent source for frequency multiplication to and synthesis at infrared frequencies. It will replace the klystron in the new laser frequency chains which are under construction a t the National Bureau of Standards (USA) and at the Bureau National de Metrologie (France).

The scso can also be of interest in certain physics experi- ments, such as very-long-baseline interferometry or measure- ments related to the fundamental constants.

5.2 Linear accelerators A linear accelerator consists of a slow-wave structure in which particles travel in synchronism with an accelerating RE wave having an axial electric field E. For electrons, the velocity approaches the velocity of light c at relatively low energy (2 MeV) and the structure is a circular iris-loaded waveguide (figure 12) working in general at 3 GHz. For ions which are heavy particles the velocities of which approach c only at energies higher than 109 eV, special structures such as the Alvarez structure (figure 12) in which the wave velocity can be slowed down t o u6 x 10-2 c, or multiple cavities with gaps and drift tubes have to be used.

At room temperature, losses in the copper walls of the structure are considerable (14 MW m-1). Since it is impossible to produce such high cw power between 1 and 10 GHz, conventional accelerators have to work in short pulses (1-2 p s for electrons, 100-500 ms for ions) at low repetition rates. The particle beam must be injected in even shorter pulses, so the average accelerated current is low. In addition to this fact, the pulsed operation limits the energy resolution of the accelerated particle beam, due to transient phenomena. The duty cycle and the energy resolution can be improved by the use of superconducting resonant structures. As their losses can be reduced by a factor of 10j-106, the superconducting accelerators can operate continuously with a quite good energy resolution of one part in lo4, which is highly desirable in many nuclear experiments, especially in coincidence experiments where the signal-to-noise ratio can be greatly increased by a continuous beam.

5.2.1 Electron superconducting accelerators (ESCA) In 1967, based on early feasibility studies, the High Energy Physics Laboratory (HEPE) at Stanford University began develop- ment of the first superconducting accelerator (SCA). At that time the primary objective was a 2 GeVilOO pA machine with an energy resolution of 0.01 7; and working continuously at 1.3 GHz (Chambers 1970). The chosen frequency was a compromise between the theoretical advantage gained by low- frequency operation (shunt impedance proportional to 1 /U) and the increasing dimensions required. Eecause the design accelerating energy gradient of 13 MeV m-1 could not be reached in the iris-loaded waveguide section and because recirculation of the beam many times through a linear SCA

was considered an economical method of increasing the beam energy it was decided to build a superconducting 700 MeVilOO p A ‘recyclotron’ (or microtron) (McAshan et a1 1974) instead of the projected 2 GeV linear machine. A general layout of the

I r i s - l o a d e d s t r u c L r e A l v a r e z s t ruc tu re Figure 12 Accelerating structures.

r i I Superconddct ing : inear accelerator

P:e - accele:ator

1 Figure 13 Layout of a recyclotron.

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Microwave applications of superconducting materials

recyclotron is shown in figure 13. The beam emerging from the linear SCA section is recirculated many times through the SCA

after 180’ successive deviations in two independent magnets. Tests on two 6 m sections of the SCA showed that, although

only modest energy gradient (2-4 MeV m-l) was attained, the other important objectives like high duty factor, high mean intensity, excellent beam quality and beam stability were achieved. Published beam parameters (McAshan et a1 1974) are: maximum energy 37 MeV, maximum peak current 500 PA, energy resolution AE/E< 5 x This energy has been increased slightly and doubled to 80 MeV by recirculating once (J P Turneaure 1977, private communication). The superconducting linear accelerator developed at Stanford University has been operated up to 25 MeV for 15 months in a series of experiments to demonstrate the feasibility of a free- electron laser (McAshan et a1 1974).

At the University of Illinois (Axel et a1 1975) a 3 MeV, L-band superconducting structure has been used in a six-pass microtron. For two years electron beams with energies up to 19 MeV have been provided reliably on demand for resonance fluorescence experiments and tagged-photon experiments. A larger microtron using a 3 MeV Van de Graaff as an injector and a 6 m superconducting acceleration section is under construction; an energy of 60 MeV is expected.

At Cornell University (Kirchgessner et a1 1975) an S-band, 2.4 MeV superconducting ‘mufin-tin’ niobium structure (figure 14), installed in the electron synchrotron, has been used for two months to accelerate the synchrotron beam to 4 GeV.

Beam direct

Figure 14 ‘Muffin-tin’ structure.

The accelerating structure for the linear SCA is in general a loaded iris-type structure. The one shown in figure 15 is used in the Stanford SCA. This structure represents a compromise in achieving acceptable fabrication costs and good accelerating characteristics while providing unexcited cells so that low-loss indium joints between demountable substructures can be tolerated. It is fabricated from reactor-grade niobium in the form of circular discs about 5 mm thick. Half-cells are made from these plates by hydroforming and after machining to the final dimensions they are electron-beam-welded together to form a substructure which is subsequently processed by the method described before. Seven of these substructures are then

joined by indium seals to form a 6 m structure. Tests in this standing-wave accelerator structure gave unloaded Q as high as 6.9 x lo9 measured at a field level of 3 MV m-1 and a temperature of 1.9 K ; the maximum cw energy gradient was limited to 3.8 MeV m-l, probably by localised heating due to surface imperfections (Turneaure et a1 1974). At energy gradients somewhat above this level, electron-loading Dhen- omena become important in 1.3 GHz structures and the electron-loading problem would have to be solved to improve the energy gradient further. One solution is to work at a higher frequency.

Studies on an S-band iris, niobium structure at Stanford (Kneisel et a1 1975) have shown that an average energy gradient of 6.5 MeV m-l (&e& = 35 mT) with Qo at this field level of 4.6 x lo9 can be attained. A superconducting X-band acceler- ating iris structure was also studied at Wuppertal (Arnolds et a1 1976). An effective accelerating field of 8 MV m-1 corresponding to a peak magnetic field of 59 mT has been reached.

In an SCA another problem called ‘beam break-up’ occurs when the beam current increases. Under certain conditions electrons circulating out of the axis can excite deflecting modes of the structure. When the power delivered from the beam into the deflecting field exceeds the power losses of the mode in the walls of the structure, the deflecting field amplitude increases dramatically and the beam is deviated toward the wall. The threshold beam current for beam break-up is frequently called the starting current Is . Since Is is inversely proportional to the loaded Q of the deflecting modes which, in an SCA, are inherently very high, Is is much lower in an SCA than in a conventional linear accelerator. To increase I s , one way is to load down the Q of all the deflecting modes without decreasing the Q of the accelerating mode. This method is used in the Stanford SCA (Mittag et a1 1973) and it was demonstrated that the starting mean current for beam break-up in an SCA can be increased to 500 PA. 5.2.2 Superconducting ion linear accelerators The iris structure used in electron acceleration is no longer suitable for the acceleration of particles having very low velocities c’ compared to the velocity of light. Since 1945, the most widely used structure in proton accelerators has been the so called ‘Alvarez structure’ (see, for example, Carne 1970) consisting of a series of drift tubes located along the axis of a cylindrical cavity resonating on the TMOlO mode at relatively low frequency (200 MHz). Particle acceleration takes place through the gaps between the tubes; the transit time of the particles between two successive gaps being equal to the RF period, the energy increments are cumulative. This structure is well adapted to particle velocities in the range 0.04 < r /c < 0.5, corresponding to an energy range 0.75 <E< 150 MeV for protons. Unfortu- nately, at a frequency foz 200 MHz, the outer diameter of the tank is greater than 1 m.

From an economic point of view, the diameter of a super- conducting structure has to be limited to about 30 cm, and it

RF coupling port

L Elec t ron - b e a m - w e l d e d Figure 15 Electron-beam-welded niobium structure.

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A Septier and higuyen Tuong Viet

has been necessary to study again a number of slow-wave structures known for a long time, but never used in accelerator technology, or to discover new structures, in order to fulfil several imperative requirements : a small diameter, even for low RF frequencies (0.05 to 1 GHz); simple cooling of the regions of walls where the currents have their maximum value; and peak fields on the walls to be as low as possible for a given value of the axial accelerating field. To date, several types of structures - each being well adapted to an energy (or velocity) range - have been proposed, and some prototypes have already demonstrated their ability to accelerate protons or heavy-ion beams.

A great deal of work in this field was devoted to helix waveguides (figure 16) - a structure used in travelling-wave

k Figure 16 Helix-loaded structure.

tubes. The structure is essentially made of niobium tubing (or of lead-plated copper tube) in helical shape and internally cooled by liquid helium. This conductor is located around the axis of a cylindrical superconducting shield. The RF wave propagates along the tube at a velocity nearly equal to c, but the apparent axial velocity of the E field is considerably reduced, depending on the values of helix radius and pitch. The helix may be self-supported by welding the extremities of the tube on the lateral wall. Such a cavity resonates when the helix length is close to fh. Adjusting properly the dimen- sions of the helix conductor allowed the reduction of the ratio Es:Ea between the peak electric field and the axial accelerating field to about 7-8. The energy gain in safe working conditions will be of the order of 2-2.5 MeV m-1 corresponding to Es z 15 MV m-1 on the helix conductor. Such cavities working at 90 MHz ha\e been extensikely studied at Karlsruhe(Mittag e t all970, Piosczyk et a1 1975, Citron et all976) and Argonne (Benaroya et a1 1972, 1975), as prototypes for the first section of high energy accelerators.

For obtaining high energy gains, either several short helices may be placed close together along the axis of a common cylindrical shield, or several short independent cavities may be used. In the latter case, difficulties were encountered in operating more than one resonator: all cavities have to work at the same frequency and at a fixed relative phase. The band- width of the cavities is very small, and frequency modulation induced by 'i ibrations of the internal conductor may often exceed the bandwidth. To solve this problem it has been necessary to make the helix out of a thicker tubing with short stems and to develop a special electronic fast tuner and fast feedback RF control systems which compensate the electrical effects of vibrations (Schulze et a1 1972, Hochschild et a1 1973).

It was recently demonstrated that these cavities are able to accelerate low-energy protons (Brandelik et a1 1972, Aron et a1 1973) or sulphur ions delivered by a DC electrostatic accelerator (Piosczyk et a l 1975, Vetter et a1 1976). Energy gains were in good agreement with the values of the axial

accelerating field E, given by previous experiments on cavities. For an ion velocity greater than 0.1 c, Alvarez structures

working at relatively high frequencies (700-800 MHz) may be used (Citron 1974, Citron et a1 1976), the energy gain being in the range 2-2'5 MeV m-1. Figure 17 shows a structure tested

Figure 17 Niobium Alvarez test section.

at Karlsruhe. To ensure good cooling, the tubes are hollow and the stem supporting each tube is made out of a niobium tube welded on the outer tank.

To reduce the transverse dimensions of the cavity, the stems may also be bent in a short helix shape (figure 18), the new

/

Figure 18 Inductively loaded slow-wave structure.

structure proposed by Dick and Shepard (1974). A 1Ocm structure of this type called 'split-ring structure' with an outer diameter of only 26 cm at 238 MHz, cooled to 2 . 6 4 2 K and placed at the output of a Van de Graaff accelerator, recently accelerated heavy ions in a velocity range 0.04< /3<0.09

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Microwave applications of superconducting materials

/ Focusing lens

u,w Becm stop

Figure 19 Two-cavity RF separator (U, unwanted particles; w, wanted

\ particles).

(Dick et a1 1976) with a net energy gain of 2-2.75 MeV m-l. The RF energy needed to supply the cavity was only a few watts. This structure, in which the ratio EJEa is small (5-6), will be used in a heavy-ion linear accelerator under construc- tion at Argonne (Bollinger et a1 1976, Citron et a1 1976a).

In the high-velocity region (0.5 < vic < 1, corresponding to protons of energy greater than 200 MeV) at least three struc- tures have been proposed. (i) A series of independent re-entrant cavities, individually supplied with RF energy (Ceperley et all975, 1976), working at around 430 MHz; a peak electric field of 22 MV m-1 has been measured on the axis. (ii) An iris-loaded waveguide, derived from the electron- accelerating structure (Bauer and Mittag 1975). (iii) The ‘muffin-tin’ structure developed at Cornel1 for electrons, and now studied at Orsay (Boussoukaya et al 1976) and Karlsruhe (Bauer and Mittag 1975).

5.3 Superconducting RF particle separators Superconducting RF separators for use with proton synchro- trons have been developing at Rutherford Laboratory (Carne et a1 1971, 1974) and at Karlsruhe (Bauer er a1 1971, Citron et a1 1976b).

The Karlsruhe separator is composed of two iris-loaded waveguides (figure 19) where a deflecting mode - having transverse electric field - is excited. All the injected particles, preliminarily deflected by a magnet, have the same momentum but different masses and velocities. The first cavity imposes on the particles a deviation depending on their velocity. After crossing a focusing lens, the particles are injected in the second deflecting cai ity. A beam stop placed at the output eliminates the unwanted particles. Particle separators, which are largely used around high-energy accelerators, work in a short-pulse regime. As the particle beam is composed of long pulses, a cw superconducting deflector will be advantageous.

The waveguide built at Karlsruhe is similar to an iris accelerating structure, but at the same working frequency (about 3 GHz) its outer diameter is about 1.5 times larger. The guide, 3 m in length, is made in five sections of individual cells machined from bulk niobium and assembled by electron- beam welding. To ensure good mechanical rigidity, three solid bars of niobium are welded at the periphery, parallel to the axis. After electropolishing, each section is oxipolished, oxidised and then annealed in UHV at 1850°C; the five sections are assembled together by special RF contact.

In a first measurement with the full deflector, Qo= lo9 and a deflecting field EO= 1.2 MV m-1 have been reached (Citron er a1 1976). The separator will be installed in a particle beam for counter experiments at the CERN laboratory in Geneva, with an intercavity distance of 30 m allowing separation of kaons and antiprotons in the momentum range 10-40 GeV:c.

The RF separator developed at the Rutherford Laboratory was planned to provide separated kaon beams in the 2-45 GeV/c momentum range. The operating frequency is 1.3 GHz and the superconductor chosen is lead, electrodeposited on to an OFHC copper iris structure. The superconducting separator

has been also considered at Brookhaven National Laboratory (Hahn and Halama 1967). Niobium S-band and X-band deflectors were built and tested (Aggus et aZl973).

6 Miscellaneous applications of superconducting resonators and waveguides We make now a rapid survey of various applications in the microwave domain, which have essentially been studied or proposed in several laboratories but not yet - t o our know- ledge - developed for use in practical applications. No attempt is made to give a complete listing of all applications.

6.1 Transmission and delay lines Coaxial lines may be used as delay lines, a voltage pulse propagating in the line at a velocity equal to the light velocity in the dielectric material. However, losses in the copper (and in the dielectric) are responsible for a large attenuation: this attenuation increases when the line diameter decreases, and is greater for the high frequencies of the spectrum of a pulse than for the low frequencies, leading to a distortion of the pulse shape.

Superconducting delay lines are able to improve the trans- mission of a signal over very long distances, due to the fact that the losses in the metal are greatly reduced and the loss angle of a dielectric such as Teflon or polyethylene is greatly improved by cooling to values in the 10-5-10-6 range at 4.2 K.

A dispersion-free superconducting coaxial line, 30 m in length, has been used (Nahman 1973) for the transmission of nanosecond or high-voltage pulses (1 5 kV) with nanosecond rise times (Cummings and Wilson 1966). Attenuations as low as 0.7 dB km-1 were measured in lead-plated copper coaxial lines of 1.6 mm diameter (Nobuyuki et a1 1973).

In microstrip lines (figure 20), the wave propagation

Superconductor 1

I Dielectric I :hickness d I I

Scpercorcuctor 2

Figure 20 Diagram of superconducting microstrip line.

velocity is reduced by the penetration depth in both super- conducting films (vacuum-evaporated lead) covering the faces of a dielectric ribbon. vd is given by (Swihart 1961)

where cd represents the light velocity in the dielectric of thick- ness d ( C R = C / Z / E ) ; and hi, hz are the penetration depths of the electromagnetic field h depending on the coherence length and

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A Septier and Nguyen Tuong Viet

the electron mean free path in the superconducting material. V $ can be reduced - without increasing the losses - by using impure superconductor or superconducting alloys (Mason and Gould 1969, Sass and Friedlander 1964).

To obtain longer delay times in short lines, slow-wave lines are used at room temperature, The most popular are the helix line and the meander line, in which the wave propagates along the conductor at a velocity close to c, but the apparent velocity between output and input is very low. Flat meander lines are well adapted to a superconducting realisation (Gandolfo et a1 1968, Passow et a1 1972). Figure 21 represents such a line

Figure 21 important dimensions ; (b) dispersion curve (ug, group velocity; LX, velocity of a TEM wave in the dielectric medium surrounding the line).

Meander line: (a) arrangement showing

folded in a thin meander ribbon made of lead vaporised through a mask on the surface of a Teflon (PTFE) sheet. A second Teflon sheet separates the lead from the upper super- conducting shield and a second superconducting shield placed below the central conductor closes the line, avoiding losses by radiation. When the spaces between the parallel parts of the meander, about X/4 in length, are too small, coupling between them leads to dispersive properties of the line. The energy \elocity then depends on the frequency, and the line can be used as a pulse compressor, the low and high frequen- cies of the spectrum propagating with a higher velocity than that of medium frequencies. Dispersion-free meander lines are obtained when the coupling between adjacent straight parts of the centrzl conductor is made negligible. In all super- conducting lines, co is a function of A, and may be varied by changing the working temperature, the effect being greater near T,.

Superconducting delay lines have many advantages com- pared to acoustic delay lines: the insertion losses are lower, and methods of fabrication - using thin-film and mask tech- niques - are simpler. Performances per volume unit are superior, even taking into account the Dewar. Finally, they can be directly coupled to cryogenic systems.

6.2 Sliperconducting antennas Performances of a loop antenna of small dimensions are essentially limited by the losses due to RF currents in the loop and in the coupling system. With a superconductor, these losses are negligible: all the injected power can radiate, and it is then possible to reduce considerably the dimensions of the antenna. As an example, figure 22 represents such an antenna working at 400 MHz proposed by Walker and Haden (1969). The lead-plated loop, having an area as small as 1 cm2, is placed in a lead-plated resonator. The Q factor is about 36 500 at 4.2 K (at room temperature, the Q factor of an equivalent system is only 360). For a given input RF power the superconductor solution increases the radiated power by a

Ground p lane ‘Aptenno

Figure 22 Superconducting antenna.

l ine

factor of 500. By grouping in parallel a great number of small- sized superconducting antennas, high-directivity antennas could be realised.

6.3 Superconducting filters Thc high Q of a superconducting resonator could be exploited in a microwave filter. Performances and interests of super- conducting filters in the I O MHz-1 GHz range have been summarised by Stone and Hartwig (1968). Lumped-parameter circuits, a helical resonator and a quarter-wave re-entrant cavity were considered. Superconducting miniature microstrip resonators which can be used as a filter have been studied in several laboratories (Di Nardo et all971, Jimenez-Lidon 1973, Combet 1972). Recently the interest of a superconducting filter has been emphasised for use in frequency metrology. Walls and De Marchi (1975) demonstrate that the use of such a filter with a bandwidth of 6 Hz at 9.2 GHz would in principle make it possible to multiply the present state-of-the-art, commercial, 5 MHz crystal-controlled oscillators to 100 THz n ithout the need for intermediate oscillators.

6.4 Superconducting resonators used f o r matevial characterisa- tion (Hinds and Hartwig 1971, Hartwig 1973) If a small dielectric sample is introduced in a cavity, the resonant frequency f o and the QO factor are modified. If E = E ’ - , ~ E ’ ’ is the relative permittivity of the material and if E ” < E’ , the relative frequency shift Afo/j’i only depends on E’

and the sample volume. Otherwise, measurement of AQoiQo allows the calculation of the loss tangent, tan S = E “ / E ‘ .

At room temperature, the QO values of copper resonators are always less than a few7 times lo4. The use of superconduct- ing resonators increases by several orders of magnitude the sensitivity of the method and then permits tan6 in the range IO-8-10-9 to be attained.

Using this technique, Hartwig and Grissom (I 964) have measured the loss tangents of silica (1.5 x 10-4 at 98 MHz), Teflon (1.2 x at 118 MHz) and liquid helium (less than lo-$ at 158 MHz) at temperatures below 7.2 K, while Mittag et a1 (1970) found 4 x at 230 MHz and 4 x at 30-180 MHz, respectively, for sapphire, alumina and Teflon at temperatures below 4.2 K.

Another application, concerning semiconductors, has been proposed by Hartwig and Hinds (1969). Illumination by light pulses of a small sample located in the region of a high-E field in a re-entrant resonator increases the density of free carriers in the material, thus providing knowledge, with good pre- cision, of the carrier density and relaxation time; of the

at 130 MHz, 5 x

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Microwave applications of superconducting materials

density of traps and the positions in the forbidden band of energy levels corresponding to these traps; and of the Fermi level, capture cross section of the traps and numerous other characteristic parameters of the material (Arndt et a1 1968). No ohmic contacts are needed, as in the other methods of study of semiconductor material.

6.5 Other applications Superconducting resonators may be used as gravitational wave detectors (Braginskii and Menskii 1971), for the measurement of very weak mechanical displacements in the range 10-9-10-10 nm (Dick and Yen 19721, and also as a means of increasing the energy of RF photons by sudden mechanical compression of a cavity filled by low-energy photons (Delayen et a1 1975, Dick 1975).

Re-entrant-type superconducting cavities have been recently proposed for the correction of the spherical aberration of round lenses in a superconducting electron microscope (Dietrich et al 1975), each cavity playing the role of a weak lens with time-dependent focal length for very short electron bunches (Passow 1976).

7 Conclusion The improvements realised during the last 10 years on super- conducting resonator technology allows us to obtain Q factors frequently greater than 109 at normalised working tempera- tures TITc less than or equal to 0.2, even with complex-shape structures needing many weldings. The physical origins of residual surface resistance are not yet sufficiently well under- stood and an important piece of work still to be done is to obtain reproducibly RF field amplitudes close to the limits imposed by the existence of the thermodynamic critical magnetic field Bc.

A new compound, NbsSn, v,ith a high critical temperature ( T c z 18 K), is being intensively studied in many laboratories. Although its measured residual surface resistance is still higher than that of niobium, it is low enough at T=4,2 K ( T I T , 2 0.25) for RF applications at this temperature, which presents a real economic interest. On the other hand, the high value of Be (Be 0.5 T) lets one hope for an important increase of the RF electromagnetic stored energy densities in super- conducting resonators.

The results obtained on electron and ion accelerator proto- types recently built at Stanford, Urbana and Karlsruhe demonstrate clearly the interest of superconducting material in the realisation of accelerators able to work in a continuous regime.

Another high-field application seems possible now: that is the storage of RF energy in superconducting resonators to produce high-energy short pulses.

The most spectacular result obtained to date with super- conducting resonators is in frequency and time metrology : superconducting-cavity-stabilised oscillators have attained frequency stabilities better than that of the best atomic clock known so far. the hydrogen maser. Such oscillators will be adopted as secondary frequency standards, especially in infrared frequency synthesis chains.

The realisations and use of high-quality, small resonators are now within the capabilities of every laboratory. They find their applications in several areas of experimental physics for high-precision measurements.

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