LatticeBern Dynamics Working Group Summary Report * Mike Syphers BNL

Transcription

1 Workshop on Future Hadron Facilities in the U.S., Blooington, IN, 7 / / 9 4. BNL LatticeBern Dynaics Working Group Suary Report * Mike Syphers BNL Introduction The LatticeBern Dynaics Working Group was charged with reviewing and identifying technical issues and their potential solutions for (a) a 2x2 TeV h g h luinosity p-pbar collider, and (b) a 30x30 TeV high luinosity pp collider. Rather than attepting to solve very specific probles for these devices in the relatively short tie scale of a workshop, the group attepted to look at ore general questions to try to indicate in which directions future work in these areas should procede. The ephasis of the group tended toward lattice issues and general accelerator design issues for the above two cases, with ore specific questions being addressed as directed by the needs seen by the Workshop Synthesizers. Since this was a Workshop, foral presentations were kept to a iniu. A few, slightly ore "foral" Working Group presentations were ade during the workshop on topics such as a "Mobius Accelerator" (R. Talan), "Robinson Wigglers" ( S. Y. Lee), "Phase Trobones" (A. Garren) and the T E R N LHC Cobined Function Lattice" (R. Talan). Most of these were results of discussions which occured during the course of the workshop. 2 TeV x 2 TeV For the 2 TeV pbar-p collider, the lattice discussion consisted of a review of work perfored at Ferilab in on Tevatron upgrade lattices.[ 11 In this work, several alternatives were investigated, including: a) lengthening of the long straight sections in the Tevatron fro 53 to 73. This option required two different dipole agnets, with fields of 8 T and 9 T (for 1.8 TeV beas). The strong dipoles were used in the vicinity of the straight sections. b) lowering the ring dispersion function by using new quadrupole agnetdtris near the straight sections to atch the dispersion to the standard cells of the arcs. The dispersion peaks were reduced fro 6 to under 4. c) increasing the cell length in the arcs fro 30 to 40. The existing Tevatron arcs contain "issing dipole agnets" at the "17"and "48" locations; this new design has the sae aount of free space, but with the issing agnets arranged to better control the dispersion isatch. Dispersion suppressors are used at the ends of the arcs to ake zero dispersion straight sections. While the geoetry of this accelerator is slightly different than that of the existing Tevatron, the radial excursions within the tunnel were estiated to be typically 6-9 in., with a axiu of 13 in. *Work perfored under the auspices ids Crirbb i c u t \ STER

2 4-2 - Table 1 shows general paraeters of the above three cases. The general conclusion was that while a new Ferilab accelerator would be constrained by the Tevatron tunnel, it is possible to ake iproveents to the lattice design to provide longer straight sections, better atched lattice functions, and perhaps both. With the introduction of 90 cells, the dispersion function is lowered substantially, and this phase advance along with the saller bea size for coalesced bunches ay iprove the perforance of the separated beas accelerator. Table 1 Energy Radius Str.Sect. Length Cell phase adv. Cell Pax Global Pax Cell Dax Global D z D in str. sec. Magnet field Cell Quad Strength Cell Half-length TEV OPT1 OPT2 OFT3 1.o lo lo lo lo TeV deg rn T l/ Bea Intensity Issues Two bea intensity issues of the 2 TeV pbar-p collider were discussed. The first involved the ipedance thresholds for the paraeter sets provided by the Workshop Synthesizers. The longitudinal ipedance threshold for the icrowave instability was coputed to be on the order of Zil/n = 2 Ohs, and was not believed to pose any new technical challenges. The transverse ipedance of the accelerator needs to be less than about Z i / n = 800 kohs/, which also is not pushing any presently obtainable liits. The second intensity issue looked at for the pbar-p collider was the long-range bea-bea interaction. This collider will have 1-2 orders of agnitude ore long-range interactions than the present Tevatron collider. As an estiate of the agnitude of the effects, consider a head-on bea-bea tune shift of AVHO for each of two interaction points. Around the accelerator, there will be 2*ng long-range interactions, where n g is the nuber of bunches in each bea. Assuing the two beas are separated by several bea sigas (4-5, say) by the helical orbit separators, then a proton bunch will produce a long-range force on the antiproton bunch which is decreasing roughly as l/r = l/(d k x). (Here, d is the separation between the centers of the two bunches, and x is the displaceent of an antiproton fro the center of it's bunch.) The expansion of I/( 1 k d d ) generates all

3 DISCLAIMER Portions of this docuent ay be illegible in electronic iage products. Iages are produced fro the best available original docuent.

4 ultipoles, giving rise to steering errors, tune shift errors, chroaticity, and tune spread. For siplicity, if we assue a siple 1-D odel, then these errors can be written in ters of AVHO as: 47~AVHO / (d/o) = a) (AXco/o)ax b) Av = 2 AVHO / (d/o)2 = C) A t = 4 AVHO (D/o) (d/oi3 = 3.2 c- (D is the dispersion function = 4, say, and take o = 0.4 at j3 = 100 ) d) Avax = 9 AVHO / (for particles at a = 2.4 o) = where these expressions are for a single long-range encounter. The nuerical results are for AVHO = 0.01, and d/o = 5. One can see that the effects of hundreds of such encounters (1500, for one paraeters list considered) will give rise to substantial operational probles for this accelerator. The ost recent paraeters list for the 2 TeV accelerator reduces the nuber of long-range interactions 10216, which akes soe of the nubers ore tolerable, though the issues reain, especially for chroaticity copensation. The analysis should be carried through further, looking at the details of the 2-D long-range interactions along the helical orbit. In addition, the effects of uneven bunch spacing (which is surely to be the case for scenarios with several hundred bunches) need to be investigated -- in particular, the Pacan effect due to average corrections of the longrange bea-bea interactions. 30 TeV x 30 TeV For the 30 TeV x 30 TeV Collider, ost of the discussion was centered around optiization of the lattice. Drawing upon the lessons fro the SSC, the group felt that siplification of the lattice -- fro a hardware standpoint -- was absolutely necessary. This entailed developing a workable lattice in which the nuber of different types of coponents are iniized, long cable runs for correctors are avoided and the nuber of power leads are iniized. This philosophy led to a design with "sparse/luped" correctors, and assuptions about having power and vacuu hardware physically attached to the sae cryostat containing the ain quadrupole agnets, thus avoiding the need for separate "spool pieces" in every half-cell. The group also held discussions on agnet aperture and field quality, and instabilities thresholds. Ipedance issues were not seen to be an iediate issue which could be addressed by this group in this workshop. The proinent ipedance issue will be the bea tube liner, and so will depend very strongly on the agnet and cryogenic/vacuu design.

5 - 4 - One of the ore exciting aspects of the new accelerator was the possibility of reducing the transverse eittance daping tie due to synchrotron radiation by a factor of 2 or 3. The Working Group also spent tie on the design of a standard cell to perfor this function. Lattice Issue It was realized by the Working Group that the lattice of a new, large, high energy collider could be siplified in such a way that ay have a signficant ipact on the cost of the accelerator. The ephasis on uch of the discussion was how to avoid the need for "spool pieces," which are devices used in present superconducting accelerators to interface the accelerator to power and vacuu systes, bea instruentation systes, and which typically contain accelerator correction agnets. In the SSC, each 90 half cell of the Collider ring contained a 5 spool piece, at least half of which was used for correction agnets -- dipoles, quadrupoles, and sextupoles in particular, with occasional other correctors such as skew quadrupoles. There were a variety of spool pieces, soe of which contained recooling apparatus, soe having power and vacuu interfaces, different ones with different corrector packages, etc. The Working Group envisioned a scenario as follows. The "arcs" of the accelerator are ade up of 90 FODO cells. Each FODO cell is coposed of a quadrupole and 5 dipole agnets. As a working exaple, the Working Group copared these concepts to the general lay-out of the SSC arcs. In the SSC, roughly every 24 cells there was an interface point to the power and cryogenics systes. In the new schee, the lattice would contain a section of 4 cells which would have free space generated by leaving out a sequence of dipole agnets (10, in our exaple) as a "dispersion-atched insertion." These "free spaces" would contain "epty cryostats," which could then be converted to function as spool pieces as required. That is, there would be devices which are of the sae length and outer diaeter as standard dipole cryostats, but which ay contain correctors, power feeds, cry0 feeds, etc. as needed. An exaple of such an insertion is shown in Fig. 1. Fig. 1 To avoid having spool pieces in each half cell, standard systes hardware, which occurs every cell, would be designed into the quadrupole assebly resulting in a single piece of hardware, It was assued that the quadrupole stands would be reotely oveable with stepping otors to perfor orbit adjustents throughout each arc. In regions such as the IRs and utility straight sections (not discussed by this Working Group), steering correction agnets could be ipleented (as well as in the free-space

6 - 5 - insertions discussed above, as necessary) to perfor injection bups, etc.. However, in the arcs, where such distortions generally are not necessary, the quadrupole alignent could be set and left alone. To ake a 5 orbit bup in the ring, one would need only about f l oveent of a standard quadrupole. Such reotely controllable agnet stands could also allow one to relax the alignent requireents of the accelerator upon installation. It was pointed out, however, that if this accelerator incorporates a 2-in- 1 agnet design, siultaneous alignent of both beas using oveable agnets ay be ore difficult operationally. The adjustent of the global tunes of the accelerator will be perfored by Phase Trobones -- one at each end of each arc. These consist of 5 "standard" cells with 5 independently controlled quadrupole circuits, allowing one to tune the phase advance across the Trobone in each plane, while keeping the section atched to the rest of the ring. If it is found that such sections cannot eet the required tuning range (roughly 1-2 units), then other easures would need to be considered, the ost straightforward being the placeent of tri quadrupoles in the "free-space" insertions. Chroaticity adjustents will be ade using sextupoles in the free-space insertions. In our exaple, each insertion contains four straight sections by F quads, four next to D quads, each the length of a standard dipole. It was felt that this would be plenty of space to encorporate the sextupoles necessary for chroaticity correction. Naturally, the effects on dynaic aperture of such a luped schee will have to be studied carefully. In addition, the free-space insertions contain "issing agnets" in the iddle of half cells, which can contain skew quadrupoles to perfor decoupling. A scheatic layout of one arc of the accelerator is shown in Fig. 2 free space insertions Phase Trobone Disp. Suppressor I.R./UT Fig. 2

7 - 6 - Dapiny Tie Enhanceent The daping rates, or daping partition nubers, of the collider are constrained to add up according to Robinson's Theore[2]: Jx + Jy + Js = 4, where Jx = 1-0, Jy = 1, and JS = 2+D. Here, D is given by D=c (D/p2)(l/p + (2B'/B)> / <l/$> where the averages are taken over the entire ring. For a pure FODO lattice, where B'=O when B is not zero, and vice versa, then JX= Jy = 1, and JS = 2. To take advantage of the synchrotron radiation daping inherent in a 30 TeV proton collider, schees were investigated to enhance the daping rate. A design of a cobined function lattice for the LHC[3] was reviewed by the group, and a cobined function lattice was briefly discussed for the 30 TeV ring. This was initially discussed in the spirit of siplifying the coponets of the standard cell. But, it was quickly realized that the pure cobined function lattice would lead to anti-daping in the horizontal plane. Next, two lattices consisting of defocusing bending agnets were envisioned. The first lattice used cells containing a single focusing quadrupole and defocusing bending agnets elsewhere. Analytical expressions for this siple syste were developed. Though the hardware layout is siple (one quadrupole type, and one bending agnet type), to obtain increased daping one needs a gradient of about 3 T/ in a 10 T agnet. (D = 2<DB'/B> = -1, which for B=lOT, and <D> = 1.5 leads to B'=-3 T/.) This leads to rather long cells (if we deand 900 phase advance in both planes) and unacceptable aplitude functions. The second lattice used defocusing bending agnets, but retained both F and D quadrupoles in the standard FODO-type structure. In this case, the two quadrupoles are of different strengths (lengths), and so one gives up the siplicity one was after. Another, sipler schee involves isaligning the quadrupoles by roughly 5. If the otherwise standard quadrupole agnets are all oved radially outward by this aount, then the quadrupoles will steer the bea and hence generate radiation. For this Case, D = - (8 6 1(L ob) ) (Lb/Lq) = - (8 6 / ((90 )(7.5 rad)) ) (80 )/(5 ) = > 6 = 5.5, for SSC-type cell paraeters. The 5.5 shift would thus double the transverse daping rate. On the other hand, it ay be ore econoical or sipler to design a quadrupole agnet with a sall central bend field of order 1.2 T to perfor the sae task. And, if the quadrupole positions are reotely tunable, as we have previously assued, then one could conteplate "tuning" the daping rate.

8 - 7 - One afternoon's discussion focused on agnet aperture issues. It was the concensus of the Working Group that a 50 agnet design was acceptable for a 2 TeV x 2 TeV pbar-p collider. For the 30 TeV x 30 TeV collider, the group held the assuptions that this accelerator would use a 2 TeV injector, and would have a fill tie of under 30 inutes. For this case it was felt, priarily fro SSC experience, that f5 were required for a "good field region," and +lo of physical aperture was required to perfor injection and bea abort procedures. It was felt that the field quality generated by present 50 agnets was satisfactory. Because the nonlinear field quality suffers in a inor way by going through the agnet off-axis, one could consider having the 20 bea pipe off-center through the (presued) 50 agnet bore, if this siplified any engineering efforts of the vacuu/liner designs. It was later noted that if full advantage of synchrotron radiation daping enhanceents can be realized in this collider -- by appropriate choice of lattice, or quadrupole offsets, for exaple -- then the field quality at injection could perhaps be relaxed. In this scenario, a saller agnet bore, or lower injection field ight be tolerable. Bibliography [ 11 A. A. Garren and M. J. Syphers, "1.8 TeV Tevatron Upgrade Lattices," proc Part.Accel. Conf., IEEE K. W. Robinson, "Radiation Effects in Circular Electron Accelerators," Phys. Rev. [2] 111, No. 2 (1958). F. Meot and T. Tortschanoff, "Cobined Function Focusing, Cobined Function [3] Superconducting Dipole for the LHC," CERN SL/94-20(AP),CERN, DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Governent. Neither the United States Governent nor any agency thereof, nor any of their eployees, akes any warranty, express or iplied, or assues any legal liability or responsibility for the accuracy, copleteness, or usefulness of any inforation, apparatus, product, or process disclosed, or represents that its use. would not infringe privately owned rights. Reference. herein to any specific coercial product, process, or service by trade nae, tradeark, anufacturer, or otherwise does not necessarily constitute or iply its endorseent, recoendation, or favoring by the United States Governent or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Governent or any agency thereof.