RECENT INVESTIGATIONS OF THE ORSAY GROUP ON RF PROPERTIESAND APPLICATIONS OF SUPERCONDUCTING CAVITIES

A. SEPTIER and NGUYEN TUONG VIETInstitut d'Electronique Fondamentale, Laboratoire associe au CNRS

Facult6 des Sciences, Batiment 220 - 91 - ORSAY (France)

ABSTRACT

After a large development of our experimental stu-dies on high stability oscillators, a theoretical workon different physical processes able to induce locali-zed transitions to the normal state at high field levelin superconducting cavities, is in progress. A theore-tical study of beam dynamics in low energy electron li-nacs (in the 1-5 MeV range) shows that a standing wavestructure have interesting focusing properties for shortbunches injected in the "unstable" rhase domain, andthat a single TMO10 cavity could be used to obtain e-lectrons of 2 MeV.

ELECTRON DYNAMICS IN LOW ENERGYSUPERCONDUCTING ACCELERATORS

Low energy superconducting C.W. linacs (2-5 Mev)with very narrow energy spectrum could be used in highvoltage electron microscopes, uiffractographs or X-raystubes.

Calculation of output energy dispersion and trajec-tories has been done for two types of accelerating sys-tems : a constant gradient iris waveguide with variablephase velocity vw (z) and a single TMoIo cavity. In afirst approximation, influence of space charge is ne-glected. Electrons will be injected in very short bun-ches, corresponding to a phase angle domain &YO* 20°,by using two travelling wave folded lines deflectors1.Injection energy WO is voluntarily chosen low (a fewtens of keV).

Iris waveguide

An analytical solution was given to the equationof motion for electrons moving in synchronism with theaccelerating wave, in a T.W. linac2'3 with no externalmagnetic focusing field, and working in S-band. Thissolution is used to determine the optimum injection pha-se 'to giving a minimum energy spread. The complete setof equations of motion has been solved numerically inboth cases : T.W. and S.W., for electrons moving alongthe axis, or at a short distance from the axis (para-xial rays). This study shows that for the same structu-re, working either in T.W. or in S.W. mode, the outputenergy difference is small in a very narrow phase domainaround Y' , but becomes important for particles injec-ted far from To(it is necessary to take into accountthis effect in normal linacs, in which &Sf > 9O0). InS.W. linacs, energy dispersion and phase spread aresmaller than in T.W. linacs. Taking into account elec-trons moving out of the axis, it is shown that an ener-gy spectrum width of 10-3, at Ws5 5 MeV, could be ob-tained, when Eo = 5 MV/m, WO = 80 keV, 'to= - 6o,4^%,15*,only if electrons are injected in a beam of diameter2 r0 $ 2 mm; in this case, space harmonics have practi-cally no influence on energy dispersion and phase spread.[Bunching factors AIf. /Afs > 10 are obtainedl

Concerning the radial motion, an important focusingeffect exists in a phase domain of about 250, in the so-called 'unstable" phase domain, due to the reflected wawve. In our case, the accelerating structure acts on thebeam like a converging HF lens. Approximate expressionsfor the focal distance of short HF lenses have been gi-ven3.

A study of the emittance shows no appreciable va-riation of this factor during acceleration. The emit-tance diagram corresponding to each value of forotatesin the (r',r) plane and the mean brightness of the beamhas to be calculated by taking into account this ef-fect3.

Short TMO10 cavity4

It seems now possible to obtain electric field va-lues at high as 40 MV/m on the axis of a cylindricalTMO10 niobium cavity. Taking into account the fringingfield in the entry and output channels, Loe have inves-tigated the ability of such a cavity to accelerate lowenergy electrons (WO = 35 keV) to energies of 1-2 MeV,with a small energy spread (A Ws/Ws < 10-2). Axial re-partition of Ez was measured in copper test cavities bya perturbation method, and Er and Bg fields repartitionwere calculated in a small region around the axis (ro <1 mm). Maximum of energy is attained only if the tran-sit time of the electrons is less than half a period.

There exists a domain of injection phase in whichelectrons may cross the cavity : for large negativephase angle, they are reflected at the entry and forlarge positive phase angle,retrodiffusion takes placein the output zone. An optimum phase value 'o existsfor which Ws is a maximum. Around the optimum phase, e-lectrons trajectories have been calculated for ro 41 mm,and r'e .10-2 rad. Beam emittance is a constant duringacceleration for o > - 1280, the cavity is equivalentto a converging lens. The bunching factor is weak (C1.3)

Selecting the following values of the parameters(Ez)max = 40 MV/m, L = 9 cm, (L is the distance betweencavity end-planes), fo = 1300 MHz, and taking the abscis-sae origine at a point of the axis where Ez = 0 in theentry tube, we find that Ws = 2.26 MeV, &Ws/Ws < 10-2for 64'o 4 200, around the optimum phase c.= - 1200.

POSSIBLE ORIGINS FOR A LIMITATION OF RF FIELDS

Local enhancement of the RF magnetic field by surfacemicrodefects3

Neglecting the penetration depth, a pure supercon-ductor in a RF field is equivalent to a perfect diama-gnetic material (C/= 0). Magnetostatic equations can beused to calculate the magnetic field around microprotru-sions existing on polished surfaces (whisker-likepoints, grain boundariesl In a TMO10 cavity, each micro-scopic surface defect may be considered as immersed ina homogeneous macroscopic field Ho parallel to the wallsurface. Rigorous calculations have been done for twotypes of protrusions: semi-ellipsoidal points, ridges ofsemi-ellipsoidal cross-section and infinite length in adirection normal to Ho. Numerical relaxation methodswere used to find the field along the edge of a rightangle ridge (dihedral or step). For points, the maximumenhancement factor f3 (such as (3 = H local/HO) is al-ways less than 2, but for a ridge with a prolate ellip-soidel cross-section, one has f3 >_ 2. At the surface ofa dihedral having a curvature radius of a few mm, (I3Fattains values greater than 4. In cavities realized bywelding two machined parts, such surface irregularities

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are present, and H may locally attain the Hc value.Normal zones appear, and if cooling is not sufficient"magnetic breakdown" of the whole cavity could be ob-served. Variations of (PH max) from cavity to cavitymay explain the observed dispersion in the experimentalvalues of (Ho max) recently obtained in niobium cavi-ties.

Heating of micropoints by Nottingham effect6

If sharp wisker-like points exist on a surface,electron field emission takes place, due to a large lo-cal enhancement of the electric field at the top of thepoint (E local = PE.Eo). Each electron leaving thepoint at very low temperature is replaced by an elec-tron coming from the metal lattice and a mean energy<AW>tO0.1-0.2 eV is given to the small emitting surface;the temperature of the point top increases and a tho-rough study of this energy exchange (Nottingham effect)has been done in order to evaluate the temperature dif-ference A T between top and base of the point (supposedin good thermal contact with the plane surface which isat the He-bath temperature TO). Measurements show thatPE w 200-300 for unpolished lead surfaces and PEE100for well polished Nb surfaces. For Pb surfaces, AT >60if Eo > 25-30 MV/m, and for Nb, transition would occuronly at fields Eo a 100-150 MV/m.

ULTRASTABLE OSCILLATORS USING HIGH QSUPERCONDUCTING CAVITY

In the drive system of a superconducting accelera-tor, the frequency stability requirement is about 10-10or better. This degree of stability can be achieved inoscillators using a high Q superconducting cavity eitheras an active part or as external stabilizing element.Four such oscillators have been sudied : TWT oscillator,monotron, tunnel-diode oscillator and frequency stabili-zed klystron.

7In the S-band TWT oscillator , the superconducting

cavity is introduced in the external feedback loop of aTWT amplifier. Power output as high as 1 Watt and fre-quency stability of 10-10 over several minutes havebeen obtained.

In the S-band monotron oscillator , a continuouselectron beam exchanges power with the rf field of aTMO10 mode superconducting cavity. If the transit timeof electrons is well chosen, energy can be transferredto the rf field and if this energy is greater than walllosses, oscillation can take place in the system. Witha Q of 107 at 4.20K, the frequency stability was

6 [4<>t] /ZIA+ = z xIO

for C = 10 s (output power = 150 mW).

A low noise tunnel-diode oscillator working athelium temperatures was realized and inserted into onecoupling hole of a S-band TEj11 mode superconductingcavity. The frequency of the oscillator and the couplingbetween the oscillator and the cavity were adjustable.The frequency stability was :

-II

In the X-band frequency stabilized klystron10, thesuperconducting cavity was placed between a 2K 25 klys-tron and the load, in one branch of an E-plane T - junc-tion. By adjusting the phase between cavity and klystronthe best operating point can be found. With a TMO10 modeNb cavity having QO = 3.6x109 at 1.4°K the stabilityobtained was :

6 [ c>t,tl /2X4 -=t x I

for ' = Jos and output power = 10 mW(2x10-12 when frequency shift is removed).

Our studies show that these oscillators can beused as a pilote oscillator for superconducting acce-lerators, the long term frequency shift, due to pressu-re variations on the cavity walls being eliminated by apressure stabilization device.

PROJECTS

Our work with Nb cavities is only at the beginningAn U.H.V. furnace for high temperature treatment of so-lid Nb will be delivered by Varian next October. We in-tend to study electron beam welded cavities of diffe-rent types and acceleration by a single cavity at1300 MHz. Our work on stable oscillators is going on,and an experimental work on heating of superconductingpoints will start in a few months.

ACKNOWLEDGMENTS

The authors are grateful to all members of thegroup for their fruitful work : J. Benard, H.Bergeret,F. Biquard, M. Boussoukaya, J. Jimenez and P. Sudraud.

REFERENCES

1. H. BERGERET, J. MARCOU, A. PAPIERNIK and L.WARTSKI -C.R. Ac. Sc. Paris 268 B, 1969, p.733.

2. M. BOUSSOUKAYA and A. SEPTIERNucl. instr. Meth. 80, 1970, p.109.

3. A. SEPTIER and M. BOUSSOUKAYA - Nucl. instr. Meth. 87,1970, p.273.

4. A. SEPTIER and M. BOUSSOUKAYA - Submitted to ParticleAccelerators.

5. M. BERGERET and A. SEPTIER - C.R. Ac. Sc. Paris271 B, 1970, p.1048.

6. A. SEPTIER and H. BERGERET - to be published inRev. Gen. Electricite, 1971,

7. NGUYEN TUONG VIET - Ann. Phys. (France) 2, 1967,p.225

8. F. BIQUARD - Rev. Phys. Appliquee 5, 1970, p.705.

9. J. JIMENEZ, F. BIQUARD and A. SEPTIER - to be publi-shed in Electronics Letters, 1971.

10.J. JIMENEZ, P. SUDRAUD and A. SEPTIER - Submitted toElectronics Letters.

for TC= 1 s and output power = 10AW(2x10-11 when the slow frequency shift is removed).

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,S [ 44>t,-,] /z-nf = 5 x 10