Undulator radiation: Promises and problems

448

Nuclear Instruments and Methods in Physics Research A282 (1989) 448-454 North-Holland, Amsterdam

UNDULATOR RADIATION: PROMISES AND PROBLEMS W. PEATMAN and J. BAHRDT Berliner Elektronenspeicherring- Gesellschaft Ar Synchrotronstrahlung mbH, Lentzeallee 100, D-1000 Berlin 33, Germany

With the advent of undulators as sources of radiation when used on an electron storage ring, an increased brightness of the undulator source over a dipole source by a factor of Nz is often promised, N being the number of periods of the undulator. We discuss here factors which reduce thus enhancement, starting with the finite emittance of the storage ring and magnet errors and going through problems encountered m a typical beamlme. Illustrative examples are taken from the experiences at BESSY and elsewhere.

For much of the user community the published

values of brilliance or brightness for a particular storage ring and undulator promise enormous increases in ex-

perimental signal over what one has ever seen using the dipole radiation from the same or from a comparable

storage ring (fig. la) [1]. This impression can be somewhat overcome by publishing the flux curves for the

10 - :

a

same machine- undulator combination, whereby the actual photon intensity and energy distribution in space have been integrated out (fig. l b) . This takes care of the

fundamental differences in photon distribution between

a dipole source and an undulator source . With both sets of curves one can estimate the maximum gain over a dipole source on resolution, spot size and flux to be

U--3

x

C

10

10

10

i'

12

- BESSY

lo i

17

11

GeV

10 2

3

10

photon energy [eV]

Fig. 1 (a) Brilliance curves for BESSY 11 (100 mA, 1 .7 GeV) and BESSY 1 (300 mA, 0.8 GeV) . (b) Flux curves for BESSY Il and BESSY I as above. For complete details, see: "BESSY 11, eine optimierte Undulator/Wiggler- Speicherring Lichtquelle für den VUVund XUV-Spektralbereich." 0168-9002/89/$03 .50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

449

W. Peaiman, J. Bahrdt`/ Undulator radiation

expected, assuming that all other components of the system behave in the same manner for the two types of sources. Unfortunately they do not. Nonetheless, undulators do promise significant gains on the above quantities. What are the factors that tend to counteract these gains - the "problems" mentioned in the title . (1) Finite emittance of the ring? (2) Imperfections in the magnetic field of the undulator. (3) Imperfections in the geometry of optical components. (4) Heating of optical components by the undulator radiation. (5) Mundane effects, such as relative movements of the beamline, ring components, floor of the experimental hall, etc. (6) The "line" nature of the undulator spectrum coupled with the transmission of several orders of radiation by the monochromator. ty -

o.

X=255 .6

A.

Examples of these effects will be briefly presented and possible solutions mentioned. It is evident that many of the problems result from the fact that, to achieve high resolution and/or small spot size at the experiment, small slit widths must be employed . For example, at BESSY most of the monochromators for photon energies of 50-250 eV are presently operated with slit widths of 100 win or more. A resolution of ca . 500 (E/t1 E) is typical. In order to achieve a resolution of, say, 2000 on a suitably designed monochromator, slit widths of ca . 10 win must be used and everything must be and must remain perfectly adjusted and aligned during the experiment . Because of the necessarily large size of high-resolution monochromators, there are large lever arm effects and small errors (e.g . movements, figure errors of optical elements) tend to be magnified. Points 2-5 (above) are examples of such errors . It is not the intent of this work to discuss these individual problems in detail . Rather, the goal is to

I«nt . - l .5 x lOl4 Photons/mm2

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ou 00

02

01

06

08

10

12

Horizontal (mm)

b

a

ty = 5 x 10-9 m . rad. X=259 .5&

Icent. = 7.5 x lol3 Pholom/mm2

25

Ê

Ey

= 5 x 10-9 In

rad,

k = 132 3 À,

leent = 9 2 x 1012 Photons/mm 2

FF 1 5~-

Horizontal (mm)

Ilorlzontal (nun)

Fig 2. Calculated intensity cross section of the first and second harmonics as a function of distance from the central axis for the BESSY W/U (N=35, No = 7.0 cm). The cross section is taken 5.58 m from the nuddle of the W/U. Ring current =100 mA . (a) For the first harmonic with zero emittance and with e  = 5 x 10 -9 mrad . (b) For the second harmonic as above. Il . FELS AND UNDULATORS

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W Peatinan, J Bahrdt / Undulator radiation

â

0s

, .0 -

01

a 40

20

60

80

100

120

b

1~0

current (mA)

9.P I mm I

Fig. 3 Disturbing effects of undulator operation on the ring : (a) vertical beam size blowup-, (b) reduction m beam lifetime [31 vs ring current for three W/U gaps . point out the problems and to illustrate them with real examples so that the expectations put on the new light sources may be more firmly based on the realities encountered . (1) Finite emittance of the ring . The most dramatic effect that the finite emittance of the electron beam has on the performance of the undulator is the reduction in on-axis flux and the shift in wavelength of the odd harmonics of the undulator spectrum together with a corresponding increase in on-axis flux of the even harmonics [2]. These effects result directly from the increase in beam size with emittance. The axial intensity of the first harmonic of the BESSY undulator is reduced by a factor of 2 by the 5 X 10 -x mrad emittance of the ring (fig . 2a). For BESSY 11 (e = 5 X 10 -9 m rad) a similar reduction is expected [2] . At the same time, the axial intensity of the second harmonic goes from 0 to about 10% of that of the first harmonic and from 0 to 80% of the third harmonic (fig . 2b). The absolute size of the electron beam also influences the characteristics of the optics necessary to yield high resolution and/or a small spot size . A typical vertical beam size for a third generation ring is a = 40

a

g m. Considering only the size and not the divergence for the moment, it is necessary to demagnify the source in order to get most of the light through the aforementioned 10 win entrance slit necessary for the resolution desired. If 68% (2a) of the light should get through, an 11 :1 demagnification of the source is required . This requires very high quality optical elements and good stability of them (see point 3, below) . (2) Imperfections to the magnetic field of the undulator .

These can be viewed from two standpoints : (a) degradation of the undulator spectrum, (b) undesired interactions of the undulator with storage ring operation. The first problem is unimportant for the general-purpose use of an undulator as a VUV or soft-X-ray light source . Since we have already had to accept the effect of the emittance on the undulator spectrum (point 1, above), magnet imperfections will cause only a small further degradation in this regard . Magnet errors (and emittance) place limits on the effectiveness of increasing the number of periods, N, or decreasing the period length, X o . This will not be further discussed here . The biggest problem resulting from magnet errors is

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200 250 300 hv (eV) Fig. 4. (a) Bessel functions for the axial intensity, F1, (K), of an undulator. IA (K) = 4 56 X 10 6N 2 y 2 1(A)FF (K) photons/[s(0.1% BW) mrad 2 ]. (b) Measured intensities with the W/U and TGM-5 for various values of K The gap in nun is also given. 100 niA ring current The acceptance is 0 h = 01 =125 g rad 1

K

4

100

f1J

150

W Peatinan, J Bahrdf / Undulator radiation that machine operation is adversely affected by undulator operation (fig. 3) [3] . As is seen in the figure, changes in the magnetic field of the undulator (BESSY 1) produce a change in electron beam size and lifetime . Changes in beam position and/or emission angle of the SR are less problematic and have been reduced at BESSY to the 10 1im and 10 wrad range by a dynamic feedback system [3] . Better reductions will be necessary in the future but are possible with present technology. Thus, mainly lifetime and profile changes appear to be problematic in the long run . They increase dramatically at higher values of the undulator magnetic field strength and can be referred to as wiggler crosstalk or "WC" effects . The profile and lifetime effects result evidently from skew quadrupole and octupole behaviour as shown m machine studies [4] . The former cannot be reduced or eliminated to the present case and will remain a characteristic of Plus particular W/U . There are three ways of minimizing such WC effects : (1) make the magnetic field of the undulator as perfect as possible ; (2) use low betatron functions in the undulator straight section ; and (3) operate the undulator at low field strengths (axial field strength B[T] = K/0 .9 X 0 [cm], where X 0 is the length of the undulator period) . Regarding this last point, it can be seen from the Bessel functions for the axial intensity of an undulator that with K-values <_ 2, at least 50% of the peak intensity is achieved for all harmonics up to K = 11 (fig . 4a) . Measured spectra from the BESSY W/U show that this effect is not just theoretical (fig. 4b). Thus, the advantage in obtaining higher intensities by going to higher field strengths is more than outweighed by the problems wrought by the increasingly strong WC effects . Only at the low end of the undulator spectrum do higher Kvalues bring a qualitative change : the first harmonic is driven to lower energies. This, however, can also be achieved by employing a multi-undulator with various period lengths, as has already been done at SSRL and Photon Factory [5,6] . One last point on this item is worth mentioning. In order to exploit the advantages brought about by the development of undulators, the users must be able to scan the undulators at will (vary K) and without restrictions except for the maximum K-value allowed . The nature of the undulator spectrum makes any other mode of operation impractical for many experiments . (3) Imperfections in the geometry of optical elements . For the spatial and energy resolution desired, optical components with smaller tangent errors (< 1 artsec) must be employed. In the past, only plane and spherical geometries have been available which fulfill this requirement . Recently, there has been some progress made in the manufacture of aspheric elements [7] but the fact remains that it is easier and therefore less expensive to produce plane and spherical elements with both (a) figure errors less than 1 artsec and (b) surface rough-

451

E 300

Tangent error( a arc sec) 0 o sphere plane ellipse 0 ellipse 2,5 plane " plane ellipse 5,0

n

3 `" 200

ô

awé

it

ô

3 a

100

0

9

12,5 7.5 10 Demagnification of Source Size

a

15

Fig . 5 . Image size from a vertically focussing premirror with an undulator source . Source characteristics : ax = 0 .4 mm, ay = 0.3 mm, L =1400 mm, a,= 0 .5 mrad, a,, = 0 .4 mrad . The image size for a perfect sphere with a reduced vertical acceptance (a,'. = 0 .25 mrad) is shown as " X ".

ness less than 8 Â rms. Both are required for X-ray optics but are to some extent mutually exclusive in manufacturing practice to date. The effect of tangent error on focussing ability of a premirror for an undulator beamline is shown m fig . 5 . Here we have compared a perfect spherical premirror with an elliptical nurror with 0, 2 .1 and 5 .0 artsec tangent error (only vertical focussing is considered) by means of ray trace calculations . Several points are readily apparent : (a) the ability of the sphere to demagnify the undulator source is limited (by coma), (b) this limitation can be significantly reduced by limiting the vertical acceptance ("X" points), (c) a perfect ellipse focusses a long undulator source very well, (d) a manufacturable but expensive ellipse can also be better than a perfect sphere but a price comparison should be made, (e) a "usual" ellipse (5 artsec) is still more expensive than a sphere, offers more uniform illumination of the entrance slit than the latter but is similarly limited in demagnification . The same considerations apply to the optics within the monochromator, but there the resolution is directly involved as well . (4) Heating of optical components by the undulator radiation . Local heating of the optical elements produces geometry changes in the surface. Such changes are qualitatively similar to figure errors and produce similar problems (see 3, above) (fig . 6) [8] . The four main solutions to this sort of heat problem are (a) to use materials with small coefficients of expansion and high thermal conductivity, (b) to minimize the heat density by using grazing angles of incidence and long distances, (c) to cool the substrate just under the heated surface and (d) to lower the amount of heat impinging on the surface (low K-values, see above) . Much attention is being paid to thus problem [9] . Deformations are par1I . FELS AND UNDULATORS

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W. Petitman, J. Bahrdt / Undulator radiation

ticularly severe where the undulator radiation is focussed : i .e . on slits and especially slit-mirror combinations . The use of small slits for high resolution exacerbates the problem. The cooling system for mirrors is also critical : the temperature fluctuations of a +0 .5'C cooling system on a premirror at BESSY were directly reflected on the light intensity passing through the 20 ltm entrance slit (fig. 7) . The problem was eliminated by nuxing the water in a tank before the mirror, thereby reducing the short term AT to less than 0.01 a C. The effect of a ca.

Quartz

Fig. 6. Deformation of a nurror surface from synchrotron radiation (heat) [8].

1a°C Il 1

6.5

RROR

MIN .

IEIIPERATURE

281 C~_ 1 PHOTON

--T-

INTENSITY (1 . U .1

0.5

RING CURRENT RIA)

0

165

S

7

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b

('IIN)

18°C

MIRROR TEMPERATURE

PHOTON INTENSITY (A . U .)

RING CURRENT

(11) 0 0

33

56

99

TIME

132

165

(MIN)

Fig. 7 The variation m intensity through a 20 I_tm slit compared with the temperature of the focussing mirror used to illuminate it . Cooling water regulated to (a) ±0 .5 a C and (b) < ±0 05 a C, respectively .

W. Peatmari, J. Bahidt / Undulator radiation 1 ° C change in the temperature of the 1 .2 m high stand for the mirror is probably responsible for the longer-term fall-off shown. This sort of heat problem is fundamentally different from the first one described above and is better included in the next group, "mundane effects" . (5) Mundane effects . Relative movements of the floor of the hall, expansions of frames for ring and beamline components, vibrations, etc., have all been shown to be present at SR facilities . Because of the extended nature of storage rings and beamlines, it is difficult to maintain everything at the same or even at constant temperature . Seasonal and diurnal variations in ring performance have been reported [10]. One of the most difficult and potentially expensive areas is in the design of the floor for the ring and for the experiments . The sources of difficulty lie in the following areas : (a) Long-term settling of foundations . (b) Short-term or seasonal movements of foundations. (c) Vibrations (power supplies, compressors, injector, cooling systems, cranes, fork lifts, wind, street traffic, etc .) . There did not appear to be general agreement on how to eliminate or minimize these problems, money playing a significant role in the decisions made at the individual sites . Sunlight, as welcome as it is to make the lab more humane, is a varying source of heat . Certainly, direct sunlight should be avoided at all costs. Heat-reflecting coatings on overhead windows at BESSY have reduced but not eliminated the effects of direct sunlight . The extent to which cooling (water) systems have to be regulated has been mentioned above and depends on the component to be cooled . The temperature dependence of magnet iron, for example, is well known. The cooling of magnets should be accordingly dimensioned. At the same time, vibrations produced by pumping the water must be avoided . (6) The "line" nature of the undulator spectrum . The final point to be mentioned here is a more or less new problem brought about by the quasi-line-nature of undulator spectra together with the transmission of different orders of radiation by most monochromators . The resulting spectrum can be quite complicated (fig . 8) [111 . Although there are several ways of dealing with this problem, the method employing two rotatable but parallel mirrors with various coatings is the most effective [12,13] . Used directly behind the exit slit of a monochromator, it is possible to suppress higher orders, for example, by 50 : 1 while at the same time reducing the desired intensity by only a factor of 2. The resolution of the monochromator is not affected by this arrangement and the users can tune the extent of suppression desired at will, or remove the mirrors from the beam altogether .

453 GAP 40mm K =1718 38 mA

20

10

1,2

0

GAP 50 mm K =1089 46 mA

30 N C

ä

20 -

10 0

x

b)

I GAP 75 mm K =0347 41 mA

5

z

c)

ô a0 Without Undulator 39mA

0

50 PHOTON

100 ENERGY

d)

, 1eV1

,-150

Fig. 8 . Undulator spectra showing the presence of both higher harmonics (Roman numerals) and higher orders (Arabic numerals) [111. "Without Undulator" is for a gap of 200 mm where the photon flux comes from the neighbouring dipole magnets . It is hoped that these comments will be of use in the design of new storage rings for synchrotron radiation, especially those optimized for use with undulators . Undulators will not make life easier . They will make new experiments possible if sufficient effort and thought is employed in ring and beamline design so that the possible advantages do not go down the drain of the realities encountered . Acknowledgement The results shown here were largely provided by the BESSY staff and users who are to be thanked for their efforts and their patience .

References [1] A . Gaupp, BESSY 11 calculations . [21 W . Peatman and J . Bahrdt, to be published . Calculations employ the "SMUT" computer code of C . Jacobsen and H . Rarback, SPIE 582 (1985) 201 . 11 . FELS AND UNDULATORS

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W. Peatman, J. Bahidt / Undulator radiation

[3] W. Peatman, C. Carbone, W. Gudat, W. Heinen, P Kuske, J. Pflüger, F. Schäfers and T. Schroeter, SRI-88, Rev. Sci. Instr., m press. [4] P. Kuske et al ., to be published. [5] R.Z Bachrach, R.D. Bnngans, B.B . Pate and R.G. Carr, SPIE 582 (1985) 251 [6] G. Isoyama, S. Yamamoto, T. Sluoya, H. Ohkuma, S. Sasaki, T. Mitsukoslu, T. Yamakawa and H. Kitamura, SRI-88, Rev. Sci. Instr., in press. [7] C. Zeiss GmbH has recently produced aspheric optics for the Rosat project and for the BESSY SX 700 with tangent errors of < 1 arcsec over 80% of the useful surface

[8] T. Ohta and T. Fujikawa, KEK 81-10 (1981) fig. 10 . [9] See, for example, Nucl . Instr. and Meth. A266 (1988) 491-530. [10] See, for example, K. Huke, SRI-88, Rev. Sci. Instr., m press. [111 J. Pflüger et al ., Nucl . Instr. and Meth A266 (1988) 120, fig. 6. [12] E.S. Gluskin and E. Trachtenberg, Nucl . Instr. and Meth. 152 (1978) 133. [13] R.J . Bartlett, D.R Kania, R.H . Day and E. Kâllne, Nucl . Instr. and Meth . 222 (1984) 95 .