Accelerator Physics of PEP-1 Lecture #7 March 13,1998 Dr. John Seeman
Accelerator Physics of PEPJ John Seeman March 13,1998 1) What is PEP-? Lecture 1 2) 3) Beam parameters for an luminosity of 3~1~~/cm~/sec How to we get that luminosity? 4) Beam-beam interaction 5) Beam-beam tune shift limit 6) Low beta insertion 7) Beam separation 8) Multi-bunch operation
PEP4 &-Factory under construction at SLAC in PEP Tunnel by Stanford Linear Accelerator Center Lawrence Berkeley National Laboratory Lawrence Livermore National Laboratory Design Luminosity = 3 x W3 cm=* sed Beam Energy (e+le-) = 3.1 GeV 19. GeV
OX (pm at P) 155 OY (pm at P) 6.2 (Jz (cm) Lu m in o s i t Y v Tune shift 1. 1.15 3 x 133cm-2s-l.3 Beam aspect ratio (Y 1 h at P).4 Number of beam bunches 1658 Bunch spacing (m) 1.26 Beam crossing angle -- (head-on) --.DLT -A....-
U r' U W J L v) 8 P )r W.- S O c, O L
c
~ OPTONAL PEP-1 PARAMETERS (p;=l.scm both rings) Parameter Energy / particle Lorentz factor CM Energy Circumference Revolution frequency (time) Phase advance 1 cell Transverse emittances (natural) Momentum compaction Max beta functions Max dispersion (Arcs) Max dispersion (R) Betatron tunes Betatron frequencies Chromaticity (linear) Partition numbers JxJs chromaticity (linear) Damping times Turnsldamping time P beta functions P rms sizes P rms divergences Aspect ratio Optimum coupling Beam-beam tune shift RF frequency Harmonic number Bucket separation RF cavities RF voltage Longitudinal emittance (natural) Rel. (Abs.) energy spread Bunch length ($ = ) Synchrotron tune Synchrotron frequency 'urns/synch. period S.R. energy loss RF power (S.R. power) [on gap Colliding bunches Bunch separation Bunch population Bunch current Beam current Beam energy Beam power Luminosity/interaction Luminositv Symbol Units GeV GeV m khz (ps) nm.rad 1-3 m m m khz ms 13 m Pm pad MHz m (4 MV pmerad (MeV) mm (PS khz MeV/ turn MW % m (ns) lo'o/bunch ma/bunch A kj G W cm-* cm-2-1 S LER HER 3.19 / e+ 9. 1 e- 685 17613 1.58 2199.318 136.312 (7.336) 9oo/9 6O/6Oo 49.18 / 1.48 1.23 2.41 14.7 / 17. 522.4 / 433.5.67 1. 1.241 1. i1.222 1.12 1.814 /. 38.57 / 36.642 24.617 / 23.637 i7.698 / 87.512 84.15 / 86.831 -.7 /.12 -.76 /.58.974 1 2.26.995 1 2.5-24.77127.87-332.31334.3 63. 1 61.4 / 3.3 36.8 / 36.6 1 18.3 8.59 / 8.37 / 4.13 5.2 / 4.99 1 2.49.5 1.15 156.8 / 4.7 313.6 3% 3%.3 f.3 476. 3492.63 (2.1) 6 2 5.1 14. i.585 i.62.77 (2.39).61 (5.54) 9.87 (32.9) 11.5 (38.4).334.449 4.553 6.12 29.94 22.27.75 3.59 1.85 (1.62) 3.73 (2.7) 5 16.38 1.26 (4.2) 5.965 2.62 1.33.45 2.161.747 49.3 6.72 1.33 x 125 3 Y 1j3 (updated June 7. 199 ma~~,mo~tcx~pepp;rr~pcpp;r~~.~ex
1 c1 3 x z
k a, k 6 cn -e a,
f \ ' \' d \ 1 ru
t 1 f 1 o\ 1 cro m 1 :& E 1 m e- E &
NTRODUCTON 9.44 9.47 1. 1.3 1.33 1.37 1.53 1.62 Fig. 2-. The cross section for the production of hadrons in e+e- collisions in the center-of-mass energy region near O GeV. The data are characterized by a series of resonances, the T family, which herald the onset of the b quark threshold. The data in (a) are from the CUSB detector group; the data in (6) are from the CLEO detector group. (T) system; the first three prominent resonances are the lowest-lying S states of a bound b6 quark system. These states are analogous to the bound states in an atomic system (such as positronium); in this case, however, it is the strong (color) force that provides the binding 8
Table 2-1. Bottom, T, charm, and zyields ( yr = O7 s). B factory Channel World sample (April 1993) 2 = 3 x 133 (Per Yr> BB -2 x 16 3x 17 3.5 x 16 8.5 15 4.9 x 16 5 x 1s 2 x 18 1 x 1s DO D+ Ds ZfZ- - 6.9 17 3.3 17 2.3 17 2.8 17
*
i Displaced / Part ic e Force + 11-85 1 Beam\ e+ 5277A2 Fig. 2. A transversely displaced particle in a bunch sees a nonlinear beam-beam force. This force is nearly linear for small displacements.
Luminosity of PEP 1 The luminosity in PEP 1 is given by when the beam sizes in each plane are equal at the interaction poifit and the beam-beam tune shifts are equal (tx- = Ex+ = cy- = 5 Y+ = 5) and where 6 is the maximum beam-beam tune shift r E is the beam size aspect ratio at the P ( = flat and 1 = round) is the beam energy (GeV) is the beam current (A) i p*y is the vertical betatron function at the P (cm)
How to Maximize the Luminosity -------- > Raise E, r, 5, and and lower p*y. Constraints : E r 5 P*Y <L> is restricted by the required Ecm = 1.5 GeV and the needed asymmetric energies. is limited to small values (<.1) from detector background considerations. may be raised if beam-beam effects are understood and ameliorated. Studies are converging on detailed understanding. A conservative approach is to assume 6 =.3. PEP achieved at least this tune shift in this energy range years ago. Parasitic Crossings (PC) are in a regime where calculations just start to show small effects. More studies of PCs are under way. (if raised) provides challenges for several systems: High power RF, Coupled bunch feedback, and Vacuum technology (when lowered) requires careful study of the beam dynamics of the high chromaticity interaction region and detailed layout of the focusing and separation of the two beams with different energies. to be high requires good beam lifetimes and good injection efficiency.
n E Y v)
B 3 1 1 r P & P QF7 B4 64 4.1 Lattice Design 25 2.5 4 8 12 16 2 Fig. 4-O. Lattice functions for the right-hand half of the collision sextant of the HER. The B4 magnets that steer the orbit into the arcs are shown here. beam (at the expense of some horizontal defocusing). Quadrupole QF2 (see Section 5.1.3.4) is a septum quadrupole, affecting the low-energy beam only; the high-energy beam passes through a field-free region. Upon entering QF2, the low-energy beam is fully separated from the high-energy beam and the HER optical elements are independent of those for the LER. Beyond QF2 is a small permanent-magnet dipole BHl and the main HER focusing elements QD4 and QF5. Although BH1 has a negligible effect on the optics of the high-energy beam, it serves to deflect the beam orbit sufficiently that the synchrotron radiation from QD4 and QF5 is not pointing directly at the P, thereby avoiding this potential source of background. As Fig. 4-11 shows, QD4 and QF5 serve to turn over the beta functions coming from the R and reduce the slope of the dispersion function to near zero. The dispersion function produced by the bending in the R should be corrected before matching the R into the arc region. (Strictly speaking, this is not necessary, but to keep the design modular, it is advantageous to insist on it.) Figure 4-12 shows the 6 m from the P to the start of the arc (that is, to the entrance of the dispersion suppressor). The dispersion function and its slope are brought to zero by the dipole combination B2 and B3. These are very weak dipoles, each made up of four of the PEP low-field bends. The bending is purposely kept very weak to avoid problems with synchrotron radiation shining into the R. The dipoles B2 and B3 are followed by a pair of matching quadrupoles QD6 and QF7 that, in conjunction with QD4 and QF5, match the beta functions into the dispersion suppressor.
77. - 66. -; 55. -: 44. -1 33. -; 22. : 1 1 2-L LER LATTCE FUNCTONS FOR BETA*.5m/l.5cm(ler,vl.39.mad) RS6 - AX version 8.15/2 1 1 /3/96 1.1.48 n 11. E P 99. L 11. -. ' n 1 1 e 1 11 1 1 1 t 1 1 1 1 1 1 1 1 1 1 6&oc =. Toble nome = TWlSS
.7.65.55 i 1.5.5.55.6.65.7 Horizontal tune Fig. 4-95. Beam footprint of the LEB, including the effect of the parasitic crossings. The large-amplitude distortion of the footprint produced by the longrange collision is apparent (see Fig. 4-92 for a comparison). The lines in the footprint correspond to particles with constant amplitude (vertical and horizontal) ato,,2,3,4,5,6,8andoa.
OdoONa3Md*O NNONdNNNMrn rl M M N b a3 N a3 d, Lo N O*" N m e H U c H H
L1 a3-3 CD a - E \ h a E v LD c\j R Lo - - a3 U, W
b u d! N E f