Brightness enhancement optics for positron beams

Nuclear Instruments and Methods in Physics Research A313 (1992) 337` 339 North-Holland

RESEAR

Brightness enhancement optics for positron beams Antonio Zecca and Roberto S. Brusa

Dipartirnento di Fixicxt dell'Universita' di Trento. 38050 Poro, Trento (TN), ltul% Received 29 May 1991

Computer ray tracings were performed on four brightness enhancement configurations. Results for the area demagnification ratio of the four enhancement configurations are given . A very high area demagnification ratio is found for the spherical enhancer: a brightness gain of as much as 1(X00 could be achieved in a single stage with existing technologies .

l . Introduction

Slow positron beams arc produced by the use of the moderation process (sec ref. [1 ] and references therein). The brightness of beams from moderators is very low typically more than ten orders of magnitude smaller than the brightness of electron beams. This sets severe limits on the feasibility of a number of collision experiments both in the atomic and molecular physics and in the solid state physics fields. Mills [2] has proposed a technique to achieve "brightness enhancement" . A positron beam can be accelerated to an energy of a few keV. The Helmholtz-Lagrange law expresses the conservation of the brightness per volt : B I

V Af1V' where I, A, fl, V, are intensity, area, solid angle, and voltage at any section of the beam, respectively. Within the limits of this law it is possible to decrease the beam diameter by the use of demagnifying optics. It is relatively easy to achieve demagnification factors (DM = 1 /M from now on) of 10 to 20. If the beam is directed onto a second moderator, a fraction Y(E) of the positrons will be re-emitted. Y(E) is of the order of 20-30% for energies in the keV range. The re-emitted positrons escape from the second moderator with an energy typical of the moderating material but always near to 1 eV. Therefore the re-emitted positrons come from a source weaker than the original one but with a higher brightness. Supposing that the demagnifying optics achieves unity angular magnification, the brightness gain is of the order of 0.2 (DM)'. This enhancement process can be repeated by cascading two or more stages . Brightness enhancement has been implemented by several laboratories . Lynn [3] achieved a brightness

gain of more than 1(X0 with an area demagnification factor of about 100 per stage; Canter [4] reached an overall gain of 500 with an average area demagnification factor of about 100 per stage. In this paper we present a study of four different geometries intended to achieve brightness enhancement of the beam . The study was performed by computer ray tracing of the positron trajectories . Thcsc geometries had not been experimentally tested until now: they could be of interest in the future in connection with high brightness beams from reactors and accelerators . 2. Methodology Important parameters for the purpose of the present work are the emission characteristics of positrons from moderators and remoderators : average emission energy E, emission energy spread AE, emission half angle 0 (0 is measured from the normal to the moderator surface). As a basis of our work, we accepted the theory of positron moderation as presented in ref. [5]. Positrons are supposed to thermalize down to an energy of the order of kT in the moderator material . Positrons emitted from the surface gain an energy of eo, where 4~ is the negative positron work function typical of the moderator material and e the electron charge . Assuming isotropic motion of the positrons in the moderator, the half angle at the emitting surface can be calculated on the basis of energy conservation . The measured positron emission parameters do not allow until now to confirm this theory. Nevertheless, if we assume its validity, ray tracings performed with a given positron emission energy EO, and maximum half angle 0, can be scaled down to different values of these parameters . The ray tracings performed in this

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A. Zecca, R.S. Brusa / Brigittrte;ss enhancement optics for positron heatns

study, were obtained for positrons emitted with E = 1 cV and 8 = t 10° (0.17 rad). These figures are compatible with measured values for Ni and W moderators [6-K]. The positron optics performance of the studied apparatuses can be guessed for other moderator materials or different temperatures from our results. A poorer performance can be expected for higher emission energies and/or energy spreads, and/or higher temperatures . The ray tracing were performed with the SIMION PC/PS2 program written by Dahl and Delmore [9]. 3. Results The investigated geometries were designed to implement brightness enhancement by thin film transmission remoderators . Thin films were not reported to be used until now in brightness enhancement, but this looks more like a technological problem connected with the production of uniform, defect free films, with their handling and cleaning. On the opposite side, thin films promise a more simple optical and mechanical 400 V

design. A study of transmission remoderators can be found in ref. [10]. A brightness enhancement stage consists of an extraction optics plus a Icns or lens system intended to increase the positron energy to a few kcV and to reduce the spot size on the film remodcrator . High values of demagnification are desirable . In our tests we used a final energy of 4 kcV. We first investigated the successful version of the Soha gun as modified by Canter [it] by adding to it a single gridded accelerating lens in the form of two tubes of equal diameter D and lengths L t = 1 D and L, = 0.55D (fig la) . With an acceleration ratio of 10 (final energy = 4000 cV), the demagnification was DM = 30 (area demagnification factor = 900) with an active source diameter on the first moderator (diameter D t ) of 0.6D, . This configuration is reported as benchmark . The performance of configurations shown in figs. lb-Id can be compared with this standard. Fig. lb shows a geometry consisting of three electrodes . This configuration can be used with a thin film first moderator or with a backscattcring moderator. In the first instance, the radioactive source is situated

4000 V

D OV

10 mm (C)

4000 V

10 mm

Fig. 1 . Brightness enhancement geometries. Figures are to scale. (a) modified Soha gun with a single accelerating lens, (b) three electrodes geometry, (c) two electrodes geometry, (d) spherical accelerator .

A. Zcccu, R.S. Brusu / llrightnexc cvdiurnecwient crntics for /wasiiron bruntx upstream of the first moderator . The demagnification of this stage was DM = 22 when using an active source diameter on the first moderator up to 0 .75D,, This is a situation readily obtainable with a thin film first moderator. In the second instance, the use of a ring source [121 is hypothesized . With the geometry of fig . lb the inability to extract positrons from the entire moderator surface can reduce the performance of ring sources by at least 40"l with respect to the figures published in ref. [121. In spite of this the ring source plus backscattcring moderator geometry should deliver a brightness higher by a factor of 7 to K than the thin film transmission first moderator . The third brightness enhancement configuration consists of two electrodes only (fig. lc). The first electrode contains the first moderator. As in fig . lb, this can be a thin film coupled with a planar source upstream of it, or a backscattering moderator coupled with a ring source . The second moderator is a thin film located in the second electrode . Here a grid was inscrtcd to obtain a griddcd lens action. With an active area of less than 0.3D, on the first moderator, this geometry could achieve DM = 30. Our calculation show a DM = 15 when the active diameter is about 0.7D, ; aberrations reduce the achievable demagnification and displace the minimum confusion position slightly towards the grid. This geometry has the advantage of being very compact ; but this could turn out to be a drawback with respect to first and second moderator in situ cleaning and heating. Since only one accelerating voltage is used, it is not possible here to make an electrical tuning of the optics . This can be a disadvantage in some cases or an advantage in future industrial grade beams. The last studied configuration is a spherical symmetry accelerator (fig. Id). The internal face of the outer sphere is supposed to act as a first moderator . An internal concentric sphere with a radius ratio R in /Ro = 0.25 is constructed as a grid. The mesh of the grid simulating the internal sphere was -Rin in order to ensure an adequate field uniformity in the proximity of the grid itself. The internal sphere is continued by a cylinder electrode in the direction in which beam extraction is desired . The ratio Ri /Rout = 0.25 is not compulsory and was chosen on the basis of practicability of a future mechanical design only. The remoderator film is supposed to be somewhat downstream with respect to the geometrical center of the spheres (see later) . We studied the behaviour of this accelerator as a function of the maximum ~ angle subtended by the first moderator spherical bowl (see fig . 1d). The ray tracings show that the system has useable focusing properties up to 0 = ± 60°. Due to the nonpcrfcct sphericity of the equipotential surfaces inside this accelerator, the point of minimum confusion is not ex-

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actly in the geometrical centre of the sphere . From our ray tracings. it was found to be at downstream of` the centre . It is not possible for the spherical accelerator to dcf ;ne the linear demagnification (13M). We used the area demagnification factor i .e. the ratio of the first moderator area to the beam spot area at the point of minimum confusion . The area demagnification for it 0 = ± 60® moderator was found to be of the order of f`r(KX) . If a second remoderator efficiency of 0.2 is assumed, this figuec implies that it brightness cnhaneemcnt higher than 1tß)0 can be achieved in ,s single step with the spherical accelerator . We note that the quoted demagnification is independent of the size of the apparatus : rather the actual performance of it real spherical enhancer can be limited by the machining tolerances . The spherical enhanccr could be most useful in accelerator and reactor-based beams, where large source areas and/or self moderating source areas can be obtained. Strong requirements on machining tolerances render this configuratation less suitable for laboratory beams (equipped with small sources). Acknowledgements This work was supported by Ministero dclla Ricerca Scientifica e Tecnologica (Italy) and by Consorzio Interuniversitario Nazionale per la Fisica dclla Materia . References [11 P.J . Schultz and K.G . Lynn, Rev. Mod . Phys . 60 (1988) 701 . [2] A.P. Mills, J . Appl . Phys . 23 (1980) 189. [3] W.E . Frieze, D.W . Gidley and K.G . Lynn, Phys. Rev . B31 (185) 5628 . [4] K.F. Canter, P.H. Lippel, W.S . Crane and A.P . Mills, Jr.. in: Positron Studies of Solids, Surfaces and Atoms eds. A.P. Mills, Jr., W.S . Crane and K.F . Canter (World Scientific, 1986) p. 102. [5] D.A. Fischer, K.G . Lynn and D.W . Gidley, Phys . Rev . B33 (1986) 4479 . [6j B.L. Brown, W.S . Crane and A.P . Mills, Jr ., Appl . Phys . Lett . 48 (1986) 739. [7] P.J . Schultz, E.M . Gullikson and A.P . Mills, Jr.. Phys . Rev. B34 (1986) 442. [8] N. Zafar, J. Chevallier . G. Laricchia and M. Charlton, J. Phvs . D22 (1989) 868. [9] D.A . Dahl and J.E . Delmore, EGG-CS-7233 Rev. 2, April 1988, Informal Report version 4.0, Idaho National Engineering Laboratory . [10] F.M . Jacobsen, M . Charlton, J. Chevallier, B.I . Deutch, G. Laricchia and M.R. Poulsen, J. Appl . Phys . 67 (1990) 575. [I 1 ] Ref. [4] p. 199 . [12] R.S . Brusa, R. Grisenti, S. Oss, A. Zecca and A. Dupasquier. Rev . Sci. Instr. 56 (1985) 1531 .