Aordingly, the U. S. Government retains a nonexlusive, royaltyfree liense to publish Effets of Vertial Aperture on Beam Lifetime at the Advaned Photon Soure ( A P S ) Storage Ring* Hana M. Bizek Advaned Photon Soure, Argonne National Laboratory 97 South Cass Avenue, Argonne, llinois 39 USA Abstrat When a positron s energy deviation E/E exeeds the rf aeptane, or when it reeives an angular kik for the betatron motion that exeeds some limiting admittane, the positron will be lost. The main ontributions to the total beam lifetime ome from single Coulomb and Toushek sattering. n this report we investigate the dependene of the residual gas pressure and the vertial aperture of the Advaned Photon Soure storage ring on the total beam lifetime. We present results of alulating the total beam lifetime as a funtion of vertial aperture for varying average ring pressure, beam urrent, and oupling oeffiient. where P is the assumed pressure in ntorr. The singlecoulomb sattering lifetime and Toushek lifetime are inserted into the following equation = total l + gas Toushek in order to obtain the total beam lifetime. The Toushek lifetime is alulated for the APS storage ring, by use of the ode ZAP [3]. For the SPEAR saling alulations, one needs to find the ms value of the lenghtened bunh, o,,and its orrespondingrms momentum spread,. One these numbers are obtained from Option of the ZAP ode, they are input into the Toushek sattering routine of. NTRODUCTON ZAP. The results are used in the present work. n eah ase, the alulated rms minimum bunh length The vertial aperture and pressure enter the lifetime aluor is. m and the orresponding rms momentum spread lation through the single Coulomb sattering. n partiular, the variation in vertial aperture is due to elasti sattering on a, is.9~3. n the ase of SPEAR saling, and nuleii. The Toushek lifetime numbers do not vary with vertial aperture and are read from the table in Ref. [l]. The total beam lifetime is alulated and ploaed as a funtion of the vertial aperture. The soalled SPEAR saling alulation is also inluded. Experimental observations [] at the SPEAR storage ring seem to suggest that, for short bunhes with rms bunh length, smaller than the beam pipe radius b, the effetive longitudinal broadband impedane seen by the beam at frequenies beyond a, = /b ( being the speed of light) is saled down by a fa. tor of (l/b)l.* This phenomenologial power law is referred to as the SPEAR saling law. T. METHOD OF CALCULATON The single Coulomb sattering lifetime for a pressure of ntorr, T, is alulated for a range of vertial apertures. nluded are elasti and inelasti sattering on nuleii and eletrons. The vertial aperture is taken from mm to mm, in lmm inrements. The highest value of the vertial aperture orresponds to the aperture in the insertion straight setions. inrease, respetively, to.9 m and.xp3 for. ma urrent, and, respetively, to. m and.oxw3 for. ma urrent. m. ANmSS OF RESULTS Eah plot shows the total beam lifetime, as a funtion of vertial aperture, for pressures of, ntorr,, and nton; for urrents of ma,. ma, and. ma, and for % and % oupling. The total beam lifetime for.ma urrent and % oupling is not shown. n this ase, the urrent is too high and the oupling too low to obtain interesting results. The buket height is assumed to be _+ %..C\s may be seen in Figs. through, the beam lifetime dereases with inreasing urrent and dereasing oupling. n the ase of SPEAR saling, holding the oupling fixed and inreasing the urrent wil not appreiably hange the lifetime. This may be seen by omparing Fig. with Fig. and Fig. 7 with Fig. 9. Eah of these graphs also shows a vertial bar, at the total beam lifetime of hours. This is the minimum allowed life The vertial aperture values and the orresponding singlecou time for optimum APS storagering operation. Clearly, lifelomb sattering lifetime values are used to obtain the single times below hours for given vertial apertures are too low. Coulomb sattering lifetime as a funtion of the assumed pressure from the formula Suh vertial apertures are to be avoided. Therefore, this method may predit what kinds of bunhes may be sustained at what apertures by estimating the a p e m e for whih a given T bunh will operate at exatly hours. For the A P S storage gas = ring we onsider three phases []: the ommissioning phase, for whih the vertial aperture is.7 mm, Phase, for whih * Work supported by the U.S.Department of Energy, Offie of Basi the vertial aperture is mm, and Phase,for whih the vertial aperture is mm. Aording to the A P S list of parameenergy Sienes, under Contrat No. W39ENG3. DSTRBUTON OF THS DOCUMENT S UNLMTED$V
3 DSCLAMER This report was prepared as an aount of work sponsored by an ageny of the United States Government. Neither the United States Government nor any ageny thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the auray, ompleteness, or usefulness of any information, apparatus, produt, or proess dislosed, or represents that its use would not infringe privately owned rights. Referene herein to any speifi ommerial produt, proess, or servie by trade name, trademark, manufaturer, or otherwise does not neessarily onstitute or imply its endorsement, reommendation, or favoring by the United States Government or any ageny thereof. The views and opinions of authors expressed herein do not neessarily state or reflet those of the United States Government or any ageny thereof.,
DSCLAMER Portions of this doument may be illegible in eletroni image produts. mages are produed from the best available original doument.
ters [S, the maximum irulating urrent for a single bunh is ma. From Figs. 9 it is immediately seen that a.m bunh will not be sustained under nton pressure at all,and a.m, ma bunh annot be sustained under a pressure of 3 nton either (Figs. 3 and ). For SPEAR saling, both.9m and.m bunhes having % oupling an be sustained under 3nTon pressure in the insertion straight setions (Figs. and ), while the.9m bunh with % oupling an also be sustained under this pressure in Phase (Fig. ). For the pressures of and ntorr and % oupling, the.m bunhes, as well as the SPEARsaled.9m and,mbunhes, are sustained for vertial apertures of. un bunh length. ma urrent. oupllno ntorr ol e all three phases, Moreover, for the lowest pressure (), only the.m bunhes with ma urrent and %oupling are not sustained (Fig. ). As an be expeted, the.m bunhes with the best lifetimes are those with ma urrent and % oupling. As Fig. shows, they an be sustained in the ring environment of, and 3nTorr pressure for all three phases. Figure shows that the ma urrent bunhes with %oupling also do well; however, at 3 nton they annot be sustained in Phase. On the other hand, the.m, ma bunhes do rather poorly, From Fig. it is seen that only bunhes having % oupling are sustained at nton pressure. Longer bunhes stand a better hane under these onditions. Toushek lifetlme.7 hours Figure m bunh length. ma urrent, h s V. ACKNOWLEDGEMENT nton x We would B e to aknowledge Drs. Edwin A. Crosbie amd Glenn Deker for ontinued assistane in this work. Drs. Mihael Borland and Louis Emery provided assistane with ZAP. VREFERENm [l] Bizek, Hana M., private ommuniation. [] Chao, A. W., Coherent nstabilities of a Relativisti Vertial oprture (mm) Toushak lifetime Bunhed Beam, Physis of High Energy Partile Aelerators, SLAC Summer Shool 9, AP Conf. ROC. No.,93, p. 33. [3] Zisman, M. S., Chattopadhya, S., Bisognano, J. J., ZAP User s Manual, LBL7, Deember 9. [] 7GeV Advaned Photon Soure Coneptual Design Report, ANL7, April 97. S [] bid,appendix A. hours Figure. m bunh length,. ma urrent, 7: oupllng ntorr B E n Vertial aperture Toushek nfetlme (mm) 9. hours Figure 3
. m bunh length, % ma urrent. X oupling.9 rn bunh length,. ma urrent oupling O ntorr? f B 3 P v )t F Vertial operture (mm) Toushek llfetlme =. hours ~. m bunh length,. ma urrent. OX oupllng f n :._ Figure7 Figure C?. ' r. r vertrol aperture (mm) Toushek lifetime 7.9 hours (SPEAR sdlng).. m bunh length,. ma urrent. 7: oupling e * ntorr ntorr a Vertiol operture (mm) Toushek llfetlme =. houra B P L Figure Figure.9 om bunh length.. ma urrent, 7: oupling Vertlol aperture fmm) Toushek lifetime. hours (SPEAR sollng). m bunh length,. ma urrent, 7: wupllng x" E F nton Vertiol aperture (mm) Toushek llfetlme 9.99 hours (SPEAR soling) Figure ntorr Verliol aperture (mm) Toushk lifetime =.97 hours (SPEAR soling) Figure 9