Below are the concatenated e-mails from Kirk McDonald on Positron Spectrometer Updates 5,6,7,8, and 9. ------------------------------------------------------------------- From kirkmcd@Princeton.EDU Wed Apr 21 16:15:35 2004 Date: Wed, 21 Apr 2004 12:14:09 -0400 From: Kirk T McDonald To: E-166 List Subject: E-166 positron spectrometer design update no. 5 (Apr 14, 2004) Resent-Date: Wed, 21 Apr 2004 09:14:13 -0700 (PDT) During a visit yesterday with Alexander M at Cornell, I came to realize that the design of the E-166 positron transport was less than optimal -- in that there would still be considerable loss of particles that passed through the momentum slit. I eventually recalled that what we should be building is a "nondispersive, translating spectrometer". So old lore on this can be seen in the book of Steffen (DESY): http://puhep1.princeton.edu/~mcdonald/e166/steffen_nondispersive%20spectrometers.pdf One way to fix things up would be to put an inverting lens between the two dipole magnets. Since space is limited, a rather strong lens would be required. Maybe we could do this with a solenoid.... A sketch of the desirable patterns of rays is http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays.jpg Steffen shows another design, based on 3 60 deg bend magnets (and no quad or solenoid). This might also work for us. http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_3_magnets.jpg In this scheme, the central ray is bent by 180 deg.... The present state of my drawing is: http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer.dwg -------------------------------------------------------------------6 Date: Wed, 21 Apr 2004 12:31:17 -0400 From: Kirk T McDonald To: E-166 List Subject: E166 positron spectrometer update 6 (April 15, 2004) Resent-Date: Wed, 21 Apr 2004 09:31:23 -0700 (PDT) 0. This note expands upon my message earlier in the day, which remarked that while the present design of the E-166 positron spectrometer is decent, it does not yet achieve the kind of high standard set by past efforts in our community. However, time is quite short now, so we must be very efficient if we are to continue the design phase a while longer. 1. Our goals: Transmit as many positrons as possible in a +-5-10% momentum bite, with central momenta variable from ~3 to ~9 MeV/c, while minimizing backgrounds in the CsI detector due to lost electrons, positrons and gammas created by these lost particles. 2. Earlier GEANT studies by Ties Behnke indicated the merits of having all lost particle hit the walls upstream of the final bend in the spectrometer. To facilitate this, the geometry of the spectrometer should involve two 90 deg bends, such that the final positron beam line is parallel to the initial gamma line. Bend magnets in the form of sector magnets have the interesting property of providing a point-to-point focus in the bend plane, where the two focal points lie along a line that also contains the center of curvature of the central ray. Typically, in a system with two bend magnets, the output focal point of the first magnet serves as the input focal point of the second magnet. The intermediate focal point is dispersive, so one can place a set of jaws there to define the momentum bite, and to force the loss of off-momentum particles well upstream of the 2nd bend magnet. 3. A "natural" configuration of 2 90 deg bend magnets would have a symmetric arrangement of focal points along a diagonal line, as shown in the figure http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays.jpg However, this makes the central ray rather long, and so the acceptance is small. Therefore, Yuri Batygin and Ties Behnke considered a geometry in which the first focal point = the positron production target was moved close to the entrance of the first bend magnet. Now, another interesting fact about 90 deg bend magnets (in first order theory) is that when one focal point is placed at the edge of the magnet, the other focal point recedes to infinity. That is for point-to-parallel (or parallel-to-point) focusing with a 90 deg bend magnet, place the focal point at the entrance or exit of the magnet. This is also illustrated in the figure http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays.jpg by the 3 sets for rays: blue = on momentum, yellow = 10% high momentum, red = 10% low momentum. [These rays are drawn by ignoring fringe field effects....] We se that the rays or a given momentum are indeed roughly parallel at the exit of the first magnet, although the angle of the rays is a function of their momentum. Thus, the 2nd bend magnet has parallel bundles of rays presented to its entrance, and so brings them to a point focus at the exit of the magnet. To be consistent, we should place the positron reconversion target exactly at the exit of the 2nd bend magnet, it we adopt this scheme. Note that the design of the DESY/Efrimov iron-core solenoid places the positron reconversion target some 5 cm inside a reentrant cavity, and so the above condition could not be met. If the positron reconversion target is located downstream of the output focus of the spectrometer, then the off-momentum rays diverge before reaching the target, and hit the walls of the beampipe, etc. This is unfortunate, in that single scatters of these particles that are lost late in the beam transport can result in the deposition of (background!) energy in the CsI calorimeter. Furthermore, the acceptance of the double-bend spectrometer is considerably worse in the direction perpendicular to the bend plane, than in the bend plane itself. 4. For these reasons, we have been considered possible improvements in the positron spectrometer for some time now. Our main effort has been to increase the acceptance in the "vertical" plane -- by adding a solenoid lens upstream of the first bend magnet. The basic scheme for this is shown in figure http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays2.jpg [This figure is representative of the PRESENT design of the spectrometer.] The solenoid lens provides a point-to-parallel focus at its output face, with a fairly short focal length. The horizontal and vertical acceptances of the solenoid are equal, and large. The goal of the rest of the beam transports is now to preserve the acceptance of particles as they emerge from the solenoid -- while provided a dispersive focus where a momentum slit can be placed. We see that the parallel beam is focused (in the horizontal plane only) by the first bend magnet to a point at the downstream edge of the first magnet. The momentum slit should be placed up against the downstream edge of the first bend magnet in this scheme. Up to now, we have been considering a configuration in which there is a substantial gap between the first and 2nd bend magnets. This has the effect that the focus downstream of the 2nd magnet is still rather close to that magnet -- and the angles of the rays are a strong function of momentum there. Hence, unless the momentum slit is very narrow, particles will still hit the beam pipe just upstream of the positron reconversion target, leading to backgrounds in the CsI detector. Despite these shortcomings, a spectrometer configured as in http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays2.jpg has about 5 times the acceptance of the spectrometer http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays.jpg 5. However, it would be desirable to reduce the number of particle lost into the beam pipe downstream of the 2nd bend magnet. This requires are particles of all momenta be essentially parallel to the optic axis there. That is, we desire a NONDISPERSIVE parallel-to-parallel beam transport from the output of the solenoid magnet to the positron reconversion target. Of course, we desire an intermediate focus that is dispersive, so that we can place a momentum slit there. One scheme that accomplishes this was developed by K. Brown and W.Panofksy in the late '50's: http://puhep1.princeton.edu/~mcdonald/e166/alwarez_rsi_31_556_60.pdf This scheme actually involves a 220 deg bend in the central ray, and has rather limited acceptance transverse to the bend plane. But it was accomplished using only 2, well-designed bend magnets! Some other schemes for nondispersive parallel-to-parallel transports are shown in the book of Steffen: http://puhep1.princeton.edu/~mcdonald/e166/steffen_nondispersive%20spectrometers.pdf These schemes all involve an additional focusing lens besides the 2 bend magnets. The additional lens adds an additional focus in the transports, which provides an inverted image of the output of the first bend magnet that becomes the object for the 2nd bend magnet. This cancels the momentum dependence of the angles of the rays out of the 2nd magnet -- which is what we want. Because almost no particles are lost after the momentum slit (as is highly desirable to reduce backgrounds), the acceptance of the spectrometer is increased over the previous schemes. 6. Because we have decreed that the positron beam transport involve two parallel lines offset by 45 cm = 18", space is very limited between the two 90 deg bend magnets to implement the inversion. I believe that it would be barely possible to effect the desirable inversion with a solenoid magnet of about 1 T that fills the entire gap between the two bend magnets. This possibility is illustrated schematically in http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays3.jpg Note that the new solenoid is not actually shown. Rather, an idealized inversion of all rays is performed exactly half way between the first and second magnets. Such a transformation "obviously" has the desired effect. Since a solenoid lens would invert in both the horizontal and vertical planes, the vertical acceptance would also be well behaved (i.e., large). But, could we implement this scheme in the space and time that remain for E-166? 7. Steffen shows another kinds of nondispersive spectrometer, involving 3 60 deg bend magnets, which bend the positrons by 180 and send them back in a direction opposite to the input gamma line. http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays4.jpg If R = bend radius of the central ray in each magnet, the total offset of the beamline is 6R. Since we desire an 18" offset, we would need R = 3" => rather small magnets! Nonetheless, the simple ray tracing suggests that we could maintain nearly +_10% momentum acceptance with this scheme. Can/should we make a study of this scheme using Maxwellian fields? I think so! An important question is whether the triple bend magnet scheme could maintain good acceptance in the "vertical" direction" 8. Another option that is a less drastic change from the present spectrometer design would be to use only 2 bend magnets (+ the initial solenoid), and increase the bending radius until the coils of one magnet touch those of the other. http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays5.jpg The cuts down the transverse dispersion of the ray between the two bend magnets, and improves things somewhat over the present design. But this solution is still considerably less elegant than that of a nondispersive spectrometer. -------------------------------------------------------------------7 Date: Wed, 21 Apr 2004 12:32:01 -0400 From: Kirk T McDonald To: E-166 List Subject: Positron spectrometer update 7 (also Apr 15, 2004) Resent-Date: Wed, 21 Apr 2004 09:32:12 -0700 (PDT) The concerns raised in my previous updates about the fate of lost particles in the positron spectrometer should in principle be addressed by detailed simulations -- a time consuming process. The suggestions for alleviating the problem by increased complexity of the spectrometer are probably inappropriate, given the limited time available to construct and commission the spectrometer. Here, I consider whether a simplification of the spectrometer might address enough of the concerns to be worth acting on. In the figure http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_ray6.jpg I propose to replace the 2 90 deg bends with a single 180 deg bend magnet. As is well known, such a system is focusing, but dispersive. It does have the merit that rays that enter perpendicular to the entrance face of the magnet leave it perpendicular to the exit face => parallel to parallel transport. => very little loss of particles into the beam pipe after the magnet. However, some of the off-momentum particles that pass through a momentum slit (in the middle of the magnet, as shown in the figure) will be bent outside the exit aperture and become "lost". The momentum spectrum the emerges from the exit aperture will be roughly triangular, with a large (20%) full width, assuming a 2" diameter pipe. This is acceptable, I believe. The particles that are lost after the momentum slit can "all" be intercepted by an aluminum absorber at the exit face of the magnet. This absorbed could be backed up by lead to a ttenuate the gammas that are created as the "lost" positrons range out.... Classic 180 deg bend magnets have had rather small acceptance. Here, we use the input solenoid to permit decent transport with a wide (2") gap of the 180 deg magnet. Still, some care will be required in the details of the pole tip design to insure that the actual transport is close to the idealized first-order transport sketched in my figure. This will require additional help from Alexander Mikhailichenko, who is quite busy now preparing the undulator. I believe that this scenario is both cleaner and simpler that the present baseline design, although the new scenario is not perfect. Of the possible revisions that I have thought of, this is the one that has the most overall appeal to me. If any of you have additional suggestions, it would be timely to discuss them soon. --Kirk -------------------------------------------------------------------8 Date: Wed, 21 Apr 2004 12:34:17 -0400 From: Kirk T McDonald To: E-166 List Subject: E-166 spectrometer update 8 (Apr 16, 2004) Resent-Date: Wed, 21 Apr 2004 09:34:21 -0700 (PDT) How should we proceed on the issues of the positron spectrometer design? 1. While I remain rather uncomfortable with the issue of positrons lost late in the transport, the present design with the improved acceptance due to the solenoid, http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays2.jpg is, I believe, of very similar quality in this respect to the older design of Batygin/Behnke, http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays.jpg If there is clear consensus that the old design was "good enough", then I believe the present design is also "good enough" in the same sense, and we could/should simply proceed to implement the new design (rays2). 2. If however, we feel that the issue of particles lost late is important enough to deserve a response, then we face the task of evaluating a new design -- to a higher standard than has been applied thus far. We may not have time to embark on the extensive simulations that could clarify the merits of a broad class of options. We may have to proceed on the basis of "intuition". In my case, "intuition" is largely guided by the naive ray tracing diagrams that I have posted in the last days. If the scheme of http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays3.jpg is in fact implementable with the addition of a small solenoid, this is perhaps not too great a perturbation on our plans, and would provide a near optimal resolution of the lost particle issue. If we feel that we cannot add the construction of an additional magnet to our plans at this late date, then the scheme of http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_ray6.jpg now appeals to me more than either the old scheme (rays) or the present scheme (rays2). Of course, there may be other schemes worth considering as well.... -------------------------------------------------------------------9 Date: Wed, 21 Apr 2004 12:35:21 -0400 From: Kirk T McDonald To: E-166 List Subject: e-166 spectrometer update 9 (also Apr 16, 2004) Resent-Date: Wed, 21 Apr 2004 09:36:09 -0700 (PDT) http://puhep1.princeton.edu/~mcdonald/e166/e166_positron_spectrometer_rays7.jpg shows a variant of the original Batygin/Behnke scheme that in principle is a slight improvement. Namely, from the ray tracing that I have been doing, I thought it might be better to place the positron production target so the its image from the first bend magnet was at the entrance of the 2nd bend magnet => the 2nd bend magnet would then provide a point-to parallel transport, which might improve the acceptance. Well, the figure shows that this idea sort of works -- but the dispersion of final angles vs momentum is so large that there remains a considerable problem from particles lost into the output beam pipe..... I guess this just reinforces that I'd like to move away from the problematic aspects of the original design -- many of which remain in the present baseline design with a solenoid. --Kirk -------------------------------------------------------------------End