Implementation of Round Colliding Beams Concept at VEPP-2000 Dmitry - PowerPoint PPT Presentation

Implementation of Round Colliding Beams Concept at VEPP-2000 Dmitry Shwartz BINP, Novosibirsk Oct 28, 2016 JAI, Oxford

Introduction Beam-Beam Effects 2

Circular colliders e  e  Different schemes: Single ring / two rings Multibunch beams Number of IPs Interaction Points (IP) Head-on / crossing angle Low-beta insertion (Interaction Region − IR) 3

Colliders in operation: 1 × 10 34 cm -2 s -1 , 1 × 10 27 cm -2 s -1 LHC pp, PbPb 7 TeV, 2.8 TeV/n 1 × 10 32 cm -2 s -1 , 1.5 × 10 27 cm -2 s -1 RHIC pp, AuAu 250 GeV,100 GeV/n e + ,e  4 × 10 32 cm -2 s -1 DAFNE 0.5 GeV e + ,e  7 × 10 32 cm -2 s -1 BEPC-II 1.89 GeV e + ,e  2 × 10 31 cm -2 s -1 VEPP-4M 5.5 GeV e + ,e  1 × 10 32 cm -2 s -1 VEPP-2000 1 GeV under construction: e + ,e  4 × 7 TeV 8 × 10 35 cm -2 s -1 SuperKEKB 1 × 10 27 cm -2 s -1 NICA AuAu 4.5 GeV/n stopped: AdA (1961) – first collider (e + ,e  ) ISR (1971) – first hadron collider (pp) SLC (1988) – first (and only) linear collider + 19 others LEP (1988) – highest energy e + ,e  collider (104.6 GeV) HERA (1992) – first (and only) electron-ion collider KEKB (1999) – highest luminosity collider (2.1 × 10 34 cm -2 s -1 ) 4

Luminosity  L   N Number of events per second: process       L 2 n f c ( , , x z s ct ) ( , , x z s ct dxdzdsdt ) b 0 1 2 x z s t , , , 2 y  1  2 For Gaussian distributions,   2 ( ) y e y   non-equal beam profiles: 2 y  , , y x z s N N n f  1 2 b 0 L           2 2 2 2 2 1 x 2 x 1 z 2 z How many interacts?       32 2 1 24 2 L 10 cm s 10 cm process ~ ~ 10  6 f 12 10 Hz 0 11 N ~10 Compare to bunch Other particles do not interact with each other but with opposite bunch field 5

Linear beam-beam effects Linear focusing Beam-beam force for Gaussian bunches Perturbation: thin axisymmetric linear lens.          cos sin sin 1 0   0 0 0 0 0    M             sin cos sin p 1 0 0 0 0 0 The sign depends on particles type.            cos sin p sin sin Focusing for   0 0 0 0 0 0 0                particle-antiparticle sin p cos p sin cos sin 0 0 0 0 0 0 0 0 6 beams.

Linear beam-beam effects (2) 1 1                 1 Tr( ) cos cos sin M p 0 0 0 2 2         cos cos sin 0 0     p / 2 0 N r  *  * p   , 2 e x z      Beam-beam parameter     x z ,  2 ( ) 4 x z , x z 1 arccos(cos                2 sin ) cos cos 2 sin  0 0 0 0 0 2  = 0.3  = 0.2  = 0.1  = 0.05  =0.025  =0.075  =0.15  =0.25 7

Dynamic beta            cos cos 2 sin sin sin 0 0 0 0     sin sin     0 0 0 0              2 2 2 2 1 (cos 2 sin ) sin 4 cos sin (2 ) sin 0 0 0 0 0 0   0      2 (1960s) 1 4 cot (2 ) 0 One of the reasons to choose  = 0.3  = 0.2 working point close to half-  = 0.1 integer resonance: additional  = 0.05 (dynamic) bonus final focusing 8

Dynamic emittance (1990s) In electron synchrotron radiative beam emittance: BetaX 5 BetaY WS  3 H r / 55 BetaX   0  2 e BetaY RING Beta - function, cm x 4 2 J 32 3 1/ r X 0 3       2 2 H s ( ) ( ) ( ) s D s 2 ( ) ( ) s D s D s '( ) ( ) s D s '( ) x x x 2 Perturbed  -function (dynamic beta) 1 0 10 20 30 40 50 propagates to arcs and modifies H(s). Current, mA e1 -5 1,2x10 e2 WS as 0,09 e1 bs WS -5 1,0x10 0,08 e2 RING a b RING 0,07 VEPP-2000 -6 8,0x10 Emittance 0,06 Size, mm examples 0,05 -6 6,0x10 0,04 0,03 -6 4,0x10 0,02 0,01 -6 2,0x10 0,00 0 10 20 30 40 50 0,0 Current, mA 0 10 20 30 40 50 9 Current, mA

Dynamic beta & emittance 44  44 mA 2 Beam profile monitors at VEPP-2000 2  2 mA 2 10

Flip-flop (simple linear example) Assume round beams, unperturbed emittance 2 2         * * Nr Nr             e 0 e 0  0   0  cos cos 2 sin     2 0 2 2 1 0 2 0      4 4      2 0 2 2  sin sin 1 1 0 0  2 2                 2 0  0  0  0  b 1 4 cot 2  1,2    0 0 0     1,2 1 2 2  = 0.1          2 2 2  b 1 4 cot b 2 b 0 0 2 0 2  1         2  2 2 b 1 4 cot b 2 b  0 0 1 0 1 2 Self-consistent solutions: equal sizes below threshold  , non-equal above  th . 11

Coherent beam-beam Two beams modes coupling via beam-beam interaction: new eigenmodes.  -mode, unperturbed tune,   =  0 IP  -mode, shifted tune,   =  0 +  0 =  0 +  IP Without going into details,  ~1 K.Hirata, 1988 VEPP-2000  -modes  -modes example 12

Coherent beam-beam Example: coherent beam-beam modes monitoring at VEPP-2000.  -modes  -modes Shifted tune drift with beam current decay. 13

Beam-beam tune spread LHC example: pp − defocusing Linear beam-beam: tune shift Nonlinear beam-beam: tune spread (footprint) 14

Beam-beam limit  * r N Beam-beam parameter saturation ,    e x z , 2      x z , emittance (and beam size) growth 2 ( ) x z , x z Final limit: 1) emittance blowup, 2) lifetime reduction, 3) flip-flop effect J.Seeman (1983) 15

Nonlinear beam-beam limit   * * N r r N     2 e z e z 2       z 2 ( ) 2 z x z x z Typical dependence of specific N n f N  luminosity on beam current 1 b 0 2 L   4 x z (VEPP-2M example) n f N L 1   b 0 2 L   spec N N N 4 1 2 1 x z 16

Distribution deformation LIFETRAC simulations example DAFNE example: beam profile measurements. Vertical profile significantly differs  z = 398  m from Gaussian distribution. “Long” tails – lifetime reduction (+ hard background in detectors). 17

Nonlinear beam-beam 6 th order betatron resonances & synchro-betatron satellites BB-interaction produces: 1) High-order resonance grid 2) Footprint, overlapping resonances FMA: footprint Resonances in normalized amplitudes plain 18 VEPP-4 simulations example (flat e + ,e  beams)

Integrable beam-beam? What can be done to increase significantly beam-beam parameter threshold? Integrability should be implemented! Half-integrability: 1) Round beams (+1 integral of motion >> 1D nonlinearity remains) 2) Crab-waist approach for large Piwinsky angle 3) Vicinity to half-integer resonance. Even closer to full-integrable beam-beam? 1) Round beams + special longitudinal profile? …? 2) Reduction of nonlinear motion dimensions number is very important: diffusion along stochastic layer through additional dimension is suppressed 19

Round beams at e + e - collider Luminosity increase scenario:  Number of bunches (i.e. collision frequency)  Bunch-by-bunch luminosity Round Beams: 2         2    2 2 f 4 f     x y x y L 1 L       2 * r 2   r e y x e   2     1 / 4  Geometric factor: y x    Beam-beam limit enhancement: 0.1  IBS for low energy? Better life time! 02/19

The concept of Round Colliding Beams Axial symmetry of counter beam force together with x-y symmetry of transfer matrix should provide additional integral of motion (angular momentum M z = x  y - xy  ). Particle dynamics remains nonlinear, but becomes 1D. Lattice requirements: • Head-on collisions!    • Small and equal β -functions at IP: x y Round beam    • Equal beam emittances: x y M x = M y    • Equal fractional parts of betatron tunes: x y V.V.Danilov et al., EPAC’96, Barcelona, p.1149, (1996) 03/19

Historic beam-beam simulations “Weak - Strong” “Strong - Strong” I.Nesterenko, D.Shatilov, E.Simonov, in Beam size and luminosity vs. the Proc. of Mini- Workshop on “Round nominal beam-beam parameter beams and related concepts in beam (A. Valishev, E. Perevedentsev, dynamics”, Fermilab, December 5 -6, K. Ohmi, PAC’2003 ) 1996. 04/19