Nuclear Instruments and Methods in Physics Research A318 (1992) 789-793North-Holland

Progress with the slotted-tube pulsed microwigglerRoger WarrenLos Alamos National Laboratory, Los .-Ilantos, NM 87545, USA

1. Introduction

The gain of a free-electron laser depends stronglyon the K-value of its wiggler, where K=0.93 xperiod(cm) x field(T). A Kvalue near 1 is ideal formost uses, but higher K-values are needed to generateharmonics efficiently . The field of permanent magnetsis limited to about 1 T; therefore, a wiggler period ofabout 1 cm is the shortest that can be usefully builtwith permanent magnets. For practical reasons, a limit-ing period of about 3 cm is more common.A useful alternative to a permanent-magnet wiggler

is a pulsed electromagnetic one. Very high fields canbe obtained for short times with various configurationsof conductors . Ultimately, either heating of the con-ductors or the large stresses on them limit the field.Periods as short at 1 to 2 mm with a Kvalue of 1appear possible . A previous paper [1] reports our de-velopment of a pulsed wiggler based on a wounddouble-helix conductor configuration. A more recentpaper [2] reports calculations and initial constructionof a very different wiggler with a slotted-tube conduc-tor configuration . The slotted-tube conductor providesseveral advantages over the wound helix: it generatesplane-polarized rather than circularly polarized light, itdoes not need a support inside the winding, correctfields at the ends are easy to achieve, cooling is better,its inductance is less, and the electrical connections aresimpler to make. This paper relates the author's fur-ther experience with this slotted-tube design, in partic-

* Work supported by Los Alamos National Laboratory Di-rected Research and Development, under the auspices ofthe United States Department of Energy and the DOEOffice of Basic Energy Sciences, Division of AdvancedEnergy Projects.

2. Design concept

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NUCLEARINSTRUMENrs&METHODSIN PHYSICSRESEARCH

Section A

A pulsed microwiggler can produce a wiggler field of unusually short period and high strength . A period of a few millimetersand a field of 5 T appear possible . A satisfactory design is hard to realize . however, for many reasons: the high current, the currentnonuniformities caused by the skin effect, thermal stresses in the parts, the high precision, etc. In addition, measuring the field withadequate resolution in the time domain, as well as in all three spatial coordinates. is challenging, particularly inside the small boreof a microwiggler. This paper presents recent design modifications that illustrate new solutions to these problems and details of theconstruction, testing, and performance of wigglers already built.

ular, the engineering problems encountered, solutionsto them, the present status, and a view of the future ofthis wiggler type .

Fig. 1 simplifies the construction of the slotted-tubewiggler system. There are only four parts: an innercylinder (the wiggler), an outer cylinder (the currentreturn path), a plug connecting the cylinders at oneend, and connections from the cylinders to a powersupply at the other end. No field would be generatedinside the wiggler by the currents in these symmetriccoaxial conductors except for the periodic slots cut ontop and bottom of the wiggler . The slots divert thecurrent and generate strong transverse fields (horizon-tal in fig. 1) of the kind needed in a wiggler.

Various slot shapes have been investigated . Fig. 2shows four kinds cut in an - 3 mm (1/8 in.)-o.d.copper tube by spark machining techniques: 2-mil-wide

WIGGLER

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,

PERIODIC SLITSCOOLANT OUT

INSULATING SPACERS

THROUGH COPPER

Fig. 1 . Simplified diagram of a pulsed-wiggler system.

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straight slots, 12-mil-wide - S~ralght Slots, :'-slots, andcurved-T slots . Also shown are 2-mil-wide slots cut inan 1.5 mm tube. Each slot configuration has advan-tages. The simple slots are easy to make. The wideones allow the field to penetrate quickly from theoutside of the wiggler tube tQ its inside . The narrowslots _ generate smaller wake-fields as electrons pass .The T-slots reduce the current density and, therefore,excess heating at the tip of the slots. These effects, thatis, field penetration, wake-fields, heating and fieldstrength, dominate design considerations .

3. Engineering design

The distribution of current in the slotted tube andthe field that it produces is difficult to calculate, partic-ularly if three-dimensional, time-dependent factors areincluded. The static problem has been solved analyti-cally for a straight, thin slot in a thin tube [3] and on acomputer for more complex slots in a thin tube . Meas-urements of the fields produced by these arrangementsin enlarged models that use aluminum foil for theconductor and Hall-field probes agreed with the calcu-lation . Measurements of the field produced in realpulsed microwigglers also agreed with the calculation.

Fig. 3 shows the value of K produced by a thin tubewiggler with different values of S, the ratio of circum-ference to period, with simple slots of ideal depth andwith a current of 25 kA flowing through it . More

R. Warren / Slotted-tube pulse microwiggler

rnmFig. 2. Various slotted tubes used .

complex slots produce fields that can exceed those offig. 3, but only by about 25%. The ideal depth isdiscussed below. For several reasons, we usually choosea value for S near 1. The value of K is then near unity.Thus, for a wiggler of any period, the current neededfor K= 1 and S = 1 is about 25 kA. If the diameter ofthe wiggler tube were increased without changing theperiod, for example, to provide room for another tubewithin it, the value of S would increase and the currentneeded to produce K= 1 would increase rapidly.

This extra tube appears to be essential to provide avacuum enclosure for the electron beam and to excludethe water used for cooling. However, the large reduc-tion in field and complexity in design that the extra

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1

2

3CIRCUMFERENCE/PERIOD

Fig . 3. K vs S for a simple slot .

tube introduces, prompted the decision to eliminate itand to solve the vacuum and cooling problems inanother way. Various glasses, enamels, and epoxy gluesbond well to copper and can be used to fill the slots.Then the copper conductor will act as its own vacuumenclosure .

4. Supplying the current

The resistance R and inductance L of a typicalwiggler system are 1 m11 and 50 nl I. These impedancevalues present two problems : the internal impedanceof the pulsed-power supply, and the impedance of theconnecting cables exceed greatly 1 mil, making opera-tion inefficient. In addition, the time constant, L/R,which determines the rise time of the current in thewiggler is too long, - 50 Ws, for many uses . Connectinga transformer between the wiggler and the power sup-ply corrects the impedance problem. Fig. 4 illustratesthe compact arrangement [4] used with the transformerto reduce the system's inductance . The size of thetransformer core is chosen to generate a 100 p.s pulse.The single-turn secondary is composed of the wiggler,the return tube, and the close-fitting sheet-metal coversurrounding the core . The transformer has two primarywindings of ten turns each . One of the primary wind-ings is connected to a pulse-forming network (PFN) of0.1 S2, internal impedance delivering the 2 to 3 kAcurrent pulse. The other is connected through an in-ductor to a 2 A current supply to prebias the uncutcore and thus allow the maximum pulse length beforecore saturation occurs.

Lowering the circuit's inductance can reduce theL/R time constant of the wiggler system . This alter-ation is most easily made by shrinking the outerreturn-path cylinder around the inner wiggler tube.The plan is to cool both cylinders by flowing water in

R. Warren / Slotted-tube pulse microwiggler

the gap between them, so there is a conflict betweeninductance reduction and water flow restriction . A gapof 0.5 mm will give an inductance of - 10 nH. Increas-ing R can further reduce the time constant. An exter-nal series-connected resistance will accomplish thisgoal, but at the expense of increased demand on thepower supply.

5. Other critical time constants

Fig. 4. Diagram illustrating transformer use.

If one were able to supply a perfectly square cur-rent pulse to the wiggler, its field would not be con-stant during the pulse. There are at least three differ-ent reasons for this result: For very early times in thepulse, the field is confined to the space between thewiggler and the return tube. The slots act as tinycapacitors, passing unattenuated the high-frequencycomponents of the pulse. To develop a field on the axisof the wiggler, the field must penetrate from the out-side of the wiggler tube to the inside through the slots.This penetration takes 1 to 10 Ws, depending on thewidth, shape, and orientation of the slots .

When the field is established inside the wiggler,current flows on both the inside and outside surfacesof the wiggler tube and on the sides of the slots. Ittakes from 5 to 20 ws, depending on the thickness ofthe tube and the material of its construction, for thecurrent distribution in the wiggler to smooth out andfill the conductor's volume . During this time, the fieldintensity and shape will shift moderately .

Toward the end of the pulse, conductor heatingbecomes important. It shows up first where the currentdensity is the greatest, at the tip of the slot. Thetemperature can be lowered considerably by using a"softer" slot like the curved-T slot. The major conse-quence of this kind of localized heating is an increasein resistance at the tip of the slot that shifts thf-- current

CorePrimaryWinding

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792

away from the slot . The shift introduces a quadrupolemoment to the field that exerts a focusing or defocus-ing force on the electron beam . The length of the slotwas initially carefully chosen and carefully cut to havethe ideal length for which no quadrupole field is gener-ated . Upsetting this delicate balance can have seriouseffects on the electron beam.

6. Manufacturing tolerances

The major tolerance issues are control of the wallthickness of the wiggler tube and control over theshape and position of the slots. Many of our wigglersare made from common 3 mm (1/8 in.) tubing. Be-cause it is made in large quantities, we can easily selectsamples with relatively uniform walls. Without selec-tion, the thickness can vary by 10% from one side ofthe wiggler to the other. Fig. 5 shows a measurementof the (integral of the) field on the axis of a wigglermade with such a tube . Its slope is caused by wallnonuniformitv. The nonuniform wall has caused thecurrent to flow more strongly on one side of the tubethan on the other and to generate a uniform transversefield that would deflect electrons with an ever-increas-ing angle.

The slots are cut with a spark-erosion technique ona numerically controlled machine. If the wiggler tube isperfectly straight, the slots will be positioned perfectlywith a constant depth. If, however, the tube is bent,their depth will vary with position . This variation cre-ates transverse fields that bend the electron beamseriously. Currently, special tubes are being obtainedthat are very straight and that have better wall uni-formitv.

Fig . 5. Field measurement of a wiggler with nonuniform walls.

. Warren / Slotted-tune pulse nricrowiggler

7. Performance of tested models

Testing the performance of microwigglers is not atrivial pursuit. The field probe must be small enough tofit into the bore of the wiggler and to have adequatetime res(lution to provide information about the rela-tive field strengths during the various time-dependentevents previously described. The pulsed-wire tech-nique, described in these Proceedings and elsewhere[5,6], was used . We were easily able to monitor theL/R time constant, the time constant governing thepenetration of the fields through the slots, and theheating time constant . Aberrations in the field causedby imperfectly made wigglers were measured and thencorrected by drilling small holes in the return tube tomodify its current distribution . We also measured thequadrupole fields in such a wiggler by displacing thewire used in the measuring technique various distancesfrom the wiggler's axis. Using the transformer to multi-p!y the current available from the PFN, we havereached a current of 20 kA with the short-period (3mm) simple-slit wiggler system. This current produceda peak field of 2 T, a peak K value of 0.5, and an rmsK value of 0.4 . A higher current and field were notreached because of the combined effects of a poorlychosen S value, insufficient core area in the trans-former, and excessive inductance of the wiggler. Modi-fications that should easily allow attainment of an rmsK value of 1 are being made to all three. The averagetemperature rise in the wiggler for the 20 kA currentwas less than 10 K for a 100-ps-long pulse. We havenot yet devised a good way to measure the local tem-perature rise near a slot and have not installed coolingprovisions on this wiggler. We have, therefore, nottried to exceed this field or to achieve a high repetitionrate .

8. Conclusions

We have investigated the physics and engineeringissues posed by microwiggler systems, chosen an ac-ceptable geometry for the current conductors, solvedmost of the engineering problems encountered, builtseveral prototype systems, and have measured the fieldsproduced. We have achieved a K value of - 0.5 with awiggler period as short as 3 mm for a 100 p,s pulse.This combination of short period and high K value isabout a factor of 10 better than that achieved withpermanent magnet wigglers . We intend to achieve Kvalues greater than 1 with this wiggler, to extend thislevel of operation to high repetition rates, and toachieve even higher K values and shorter periods byreducing the pulse length to 10 to 20 Ws .

References[1] R.W. Warren, D.W . Feldman and D. Preston, Nucl . Instr.

and Meth . A296 (1990) 558.[2] R.W. Warren, Nucl . Instr. and Meth . A304 (1991) 765.[3] R.L. Gluckstern, Phys. Rev. A15 (1991) 3889 .[4] Transformer built by Stangenes Industries, Inc., 1052 East

Meadow Circle, Palo Alto, CA 94303, USA.

R. Warren / Slotted-tube pulse microwiggler 793

[5) R.W. Warren and C.J . Elliott, in : Undulator Magnets forSynchrotron Radiation and Free Electron Lasers, eds. R.Bonifacio, L. Fonda and C. Pellegrini (World Science.1988) p. 28.

[6] R.W . Warren, Nucl . Instr. and Meth. A272 (1988) 257.

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