report on the raytracing of a focussing mirror for a px station on the storage ring “siberia-2”

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Nuclear Instruments and Methods in Physics Research A308 (1991) 409-412 409 North-Holland Report on the raytracing of a focussing mirror for a PX station on the storage ring "SIBERIA-2" V.I . Raiko a and A.W . Thompson h Institute of Molecular Genetics, USSR Academy of Sciences, Moscow, USSR n SERC, Daresbury Laboratory, Warrington, England This report describes the use of the MAXRAY raytracing package [1,2] m assessing the design of a focussing mirror for the protein crystallography (PX) station due to be constructed on the storage ring "SIBERIA-2" in Moscow . Focussing optics are required for PX because of the large discrepancy m the size of the diverging synchrotron radiation beam and the protein crystal sample (typically 0 3 X 0 .3 X 0.3 mm3). The efficiency of X-ray collection is investigated as a function of grazing angle, magnification and misalignment error for both toroidal and ellmpsmodal mirror forms, and these results are used to recommend a flexible optical arrangement . 1. Introduction The storage ring "SIBERIA-2" is under construction at the Moscow Kurchatov Institute of Atomic Energy . Table 1 The biological experiments proposed for SIBERIA-2 ' Note that + and * represent shared stations. I _ -- -1- =--L -I - Fig. 1 Layout of the proposed biological stations on SIBERIA-2 . 0168-9002/91/$03 .50 © 1991 - Elsevier Science Publishers B .V . All rights reserved The main parameters of the storage ring are presented in ref. [3] . The Institute of Molecular Genetics (USSR Academy of Sciences) is planning several biological stations including PX - a full list of the planned work- VII. INSTRUMENTATION Beam line Station D24-1 + D24-2 + D24-3 Wl-1* WI-1* Source bending magnet bending magnet bending magnet wiggler wiggler Experiment isomorphous polychromatic MAD, EXAFS Laue time resolved replacement X-ray diffraction Laue Wavelength [A] 1 0 .5-3 .0 0.5-3 .0 0.2-3 .0 0.2-3 .0 8x/,\ 10 -3 10-2 -10-3 <10-4 10-, 10 -1 Expected focal spot size [mm X mm] 1 X 1 1 X 1 0.3 X0.3 unfocussed unfocussed Monochromator bent triangle bent triangle two crystal n/a n/a Mirror cylindrical cylindrical toroidal n/a n/a Detector MWPC film MWPC film film

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Page 1: Report on the raytracing of a focussing mirror for a PX station on the storage ring “SIBERIA-2”

Nuclear Instruments and Methods in Physics Research A308 (1991) 409-412

409North-Holland

Report on the raytracing of a focussing mirror for a PX stationon the storage ring "SIBERIA-2"V.I . Raiko a and A.W. Thompson

h

Institute of Molecular Genetics, USSR Academy of Sciences, Moscow, USSRn SERC, Daresbury Laboratory, Warrington, England

This report describes the use of the MAXRAY raytracing package [1,2] m assessing the design of a focussing mirror for theprotein crystallography (PX) station due to be constructed on the storage ring "SIBERIA-2" in Moscow . Focussing optics arerequired for PX because of the large discrepancy m the size of the diverging synchrotron radiation beam and the protein crystalsample (typically 0 3 X0.3 X 0.3 mm3 ). The efficiency of X-ray collection is investigated as a function of grazing angle, magnificationand misalignment error for both toroidal and ellmpsmodal mirror forms, and these results are used to recommend a flexible opticalarrangement.

1. Introduction

The storage ring "SIBERIA-2" is under constructionat the Moscow Kurchatov Institute of Atomic Energy .

Table 1The biological experiments proposed for SIBERIA-2

' Note that + and * represent shared stations.

I_ ---1-=--L -I -

Fig. 1 Layout of the proposed biological stations on SIBERIA-2.

0168-9002/91/$03 .50 © 1991 - Elsevier Science Publishers B.V . All rights reserved

The main parameters of the storage ring are presentedin ref. [3]. The Institute of Molecular Genetics (USSRAcademy of Sciences) is planning several biologicalstations including PX - a full list of the planned work-

VII. INSTRUMENTATION

Beam line Station

D24-1 + D24-2 + D24-3 Wl-1* WI-1*

Source bending magnet bending magnet bending magnet wiggler wigglerExperiment isomorphous polychromatic MAD, EXAFS Laue time resolved

replacement X-ray diffraction LaueWavelength [A] 1 0.5-3 .0 0.5-3 .0 0.2-3 .0 0.2-3 .08x/,\ 10 -3 10-2-10-3 <10-4 10-, 10 -1Expected focalspot size [mmXmm] 1 X1 1 X 1 0.3 X0.3 unfocussed unfocussed

Monochromator bent triangle bent triangle two crystal n/a n/aMirror cylindrical cylindrical toroidal n/a n/aDetector MWPC film MWPC film film

Page 2: Report on the raytracing of a focussing mirror for a PX station on the storage ring “SIBERIA-2”

410

stations is given m table 1 . The schematic layout of thebiological beamline is given in fig . 1, and includes anexperiment at 29 .5 m from the tangent point of D24-3for PX, and one at 25 .5 m from the tangent point forsolid state physics (SSP) investigations . The raytracinginvestigation was required in order to determine whetherthese two stations could use the same focussing mirror,and to evaluate the aberrations associated with the twofocussing positions (1 .3 : 1 and 2 : 1) . The effect of mir-ror misalignments was also investigated in order tosimulate incorrect mirror mounting and positioning .

2. Raytracing

The MAXRAY package was developed at UppsalaUniversity, and has already been used at Daresbury mthe study of a mirror for a PX station [4] . Each opticalelement is represented by a subroutine, with rays from asimulated synchrotron source distribution being tracedthrough each element to the image plane. The output ofthe program therefore consists of a predicted two-di-mensional intensive distribution which can be in-tegrated over an area of interest (for example, the sizeof a typical X-ray collimator) in order to estimate theoverall efficiency of focussing . The drawback of theraytracing approach is that the images so producedrepresent those from a perfectly figured mirror unaf-fected by the heat load of the X-rays incident on it, andwith zero surface roughness. Prior to any raytracinganalysis it is important to take into account the aboveparameters and their likely impact on the quality offocus and reflectivity .

1 5E+12F-

-T-

0N

1E+12

5E+11

c

0

VI. Ranko, A. W. Thompson /Raytracnng ofa focussing mirror

100 cm mirror

3. Results

The following questions were addressed:(a) What is the optimum length of the mirror taking

into account collection efficiency, beam acceptanceand reflectivity, cost and difficulty of fabrication?

(b) Would it be more efficient to use a small ellipsoidthan a large toroid?

(c) It is possible to share a mirror between the twostations described above either by using a fixedfigure mirror and changing the grazing angle, or byrefocussing a toroidal mirror?

(d) What is the optimum magnification to use, and howquickly does aberration begin to dominate the imagewhen working away from this position?The flux from the storage ring at various energies

was calculated using the program due to Laundy [5] fora stored beam of 100 mA and integrated over severalvertical beam apertures corresponding to many possiblecombinations of mirror length and grazing angle. Thesefluxes were then multiplied by the calculated reflectivityof a Pt mirror with a typical (good!) surface roughnessof 10 Á rms. The results of these calculations are shownfor various mirror lengths and the preferred grazingangle of 3 mrad in fig . 2. It can be seen that there is adecreasing return in going for longer and longer mirrorswhen the escalating price and difficulty of fabrication istaken into account. It was therefore deemed unnec-cessary to increase the mirror length beyond 60-80 cm .

The 3 mrad grazing angle was selected as the largestpossible grazing angle (for a Pt coated nurror) to givethe required wavelength spread (0.5-1 .5 Á) for Lanecrystallography .

10

15

20

25

Energy (KeV)80 cm mirror

60 cm mirror

40 cm mirror

Fig . 2 . The calculated intensity times reflectivity for SIBERIA-2, with 100 mA of stored beam incident on various lengths of Ptcoated (plane) mirror and a 3 mrad graze angle.

Page 3: Report on the raytracing of a focussing mirror for a PX station on the storage ring “SIBERIA-2”

0

05

Efficiency (%)100

80

60

40

20

V I Raiko, A. W. Thompson / Rayiracing of afocussing mirror

01

0 3mm collimator

Fig. 3. The collection efficiency of a toroid vs changing magnification as calculated via raytracing

The efficiency of collection of rays from the mirrorwas calculated by summing the rays falling within auser selected box centred around the peak intensity. Thenumber of rays falling within this area is expressed as apercentage of the total number of rays striking themirror, and was calculated for square boxes with 0.3,0.5 and 0.7 mm edges. This forms a reproducible esti-mate only if a sufficiently large total number of rays aretraced (thus overcoming any non-randomness due tothe "seed" used to generate the starting point of the raym the computer code). This quantity is presented forvarious misalignments and magnifications (for thetoroidal mirror), with the more important results ex-pressed graphically in figs . 3 and 4.

In order to share a mirror between the SSP and PXmodes of beamline D-24 (distances 9 and 13 m from themirror position), the curvatures of two types of mirror(toroid and ellipsoid) were optimised for a point inbetween the two stations (11 m) and the two systems

0 5mm collimator

0 7mm collimator

Magnification

traced at various grazing angles . In the case of thetoroid it is possible to re-bend the mirror in order tofocus at the new position, however this necessitates asuitable mirror tilt and bending mechanism. For there-bent case, however, the collection efficiency becomesalmost as good as at the optimal focus. The calculationsdiscussed above were for fixed figure mirrors, and theresults are presented in table 2. These figures for ef-ficiency should be compared to those (also presented intable 2) for the optimised efficiency of the two mirrors.

4. Discussion

02

03Yaw Angle (mrad)

The raytracing for the ellipsoidal mirror shows theexpected very high quality of focus. These mirrors,however, are extremely difficult to fabricate, particu-larly if a large (60-80 cm) mirror is required . From thegraph in fig. 2 it is apparent that this is the optimum

04

05

0 3 mm collimator

0 5 mm collimator

0 7mm collimator

Fig. 4. The variation collection efficiency with yaw angle for a toroidal mirror .

VII. INSTRUMENTATION

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412

V. I. Raiko, A W

Table 2The efficiency (as a percentage of total number of rays traced)of a simulated toroid and ellipsoid are given for image collec-tion at 9 m (SSP station) and 13 m (PX station) from themirror for beam line D-24 . The figure of the two mirrors isoptinused for a focus between the two stations i.e . at 11 mfrom the mirror . The grazing angle of the two mirrors isadjusted to achieve better focussing, but the curvatures of thesurfaces remain fixed The optimum focus (at 11 m) of the twomirrors is also given.

length (taking into account ease of manufacture andexpected cost) for the mirror .

The efficiency of the focus of the real mirror will becritically dependent on the figure accuracy of the mir-ror, and (in particular) on the slope error. This is the"flatness' of the surface in the long direction of themirror, and effectively makes the mirror appear asseveral mirrors at slightly different grazing angles . When

Thompson / Raytracing ofa focussing mirror

this slope error is 5 arc sec, the vertical increase inimage size is approximately equal to the expected size ofthe image. It is very important to reduce this figure tothe smallest possible value.

Fig. 4 shows the variation of yaw angle with ef-ficiency for a toroid . The changing yaw angle presentsthe source with a different effective meridional curva-ture, and consequently the focus degrades quickly. Fora mirror with variable meridional curvature, adjustmentcan be made, but since the source is now off axis thiswill improve the vertical focus but cannot restore opti-mum conditions . It is critical, therefore, to have a veryfine adjustment (better than 0.05 mrad over the lengthof the mirror) at both ends of the mirror . It is useful todesign into your mirror system a method of defining theaxis of the mirror.

The improved efficiency of the ellipsoid would allowthe mirror to be half the length for the same number ofphotons in the focal spot (see table 2 and fig. 2) . Thearguments about slope error, figure and off axis source,however, still apply i.e . there are still the same difficul-ties in aligning the mirror . The opportunity of refocus-sing the mirror for different image distances is also lost .

References

[1] S. Svensson and R. Nyholm, Uppsala University Instituteof Physics Report UUIP-1139 (1985) .

[2] RC. Brammer, Raytracing with MAXRAY and the designof PX station 9.5, Daresbury Lab. Technical MemorandumDL/SCI/TM56E (1987) .

[3] S.D . Fanchenko, Synchrotron Radiation News 3 (1990) 6.[4] R.C . Brammer, JR. Helliwell, W. Lamb, A. Li11as, P.R .

Moore, A.W . Thompson and K.A . Rathbone, Nucl . Instr.and Meth . A271 (1988) 678.

[5] D. Laundy et al., DL/SCI/P683E .

Grazeangle[mrad]

Efficiency [%]

0.3 mm 0.5 mmcolli- colli-mator mator

0.7 mmcolli-mator

Distance[m]

Toroid 2.6 6.5 12 .8 19 .6 132.7 16 .8 35 .2 48 .5 132.8 9.6 267 50 .1 133.3 10 .6 25 .9 441 93 .4 22 .8 43 .2 67 .4 93 .5 9.9 20.7 33 .2 9

Optimum 3 .0 44 58 .2 69 .3 11

Ellipsoid 2.6 5.1 11 .1 18 .8 132.7 24 .6 49 .1 68 132.8 9 3 15 25 .7 133.3 14 .3 27 .2 48 .5 93.4 35 .3 62 .4 90 .4 93.5 8.7 21 36 .3 9

Optimum 3.0 88 .9 99 .5 100 11