Mul$ple Resonance Crossings with Space Charge and Electron Cloud

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1 Mul$ple Resonance Crossings with Space Charge and Electron Cloud G. Franche; EuCARD s, 2 nd Annual Mee$ng , Paris 11/05/2011 G. Franche; 1

2 Overview Resonance crossing phenomena Space charge mul$ple resonance crossing Electron cloud mul$ple resonance crossing Conclusions 11/05/2011 G. Franche; 2

3 The dynamics issue x +[k(s)+k() cos(ωs)] x = k n (s)x n fast frequency slow frequency resonant term Incoherent Force K() cos(ωs)x This force is driven by the weak coupling with the longitudinal plane (here a cosine func$on) Machine Tune slow tune modula$on excited by machine nonlineari$es The slow tune modula$on creates a regime of resonance crossing If the tune modula$on frequency is small with respect to the fast frequency the dynamics can be of a tune migra$on 11/05/2011 G. Franche; 3

4 Transverse- Longitudinal coupling via space charge x z A par$cle experiences a space charge strength from the local bunch density, which is propor$onal to the longitudinal posi$on F exp Transverse space charge force 1 2 z σ z 2 1 r 1 exp 1 2 r σ r 2 longitudinal modula$on transverse 11/05/2011 G. Franche; 4

5 Amplitude dependent detuning from space charge The space charge detuning has different nature from the la;ce nonlinear errors induced detuning Space charge detuning Space charge Standard nonlinear components Nonlinear driving term detuning x /05/2011 G. Franche; 5

6 Mul$ple resonance crossing in bunched beams induced by space charge Pipe Slow halo forma$on x If halo is too large slow beam loss take place z z Bare tune Periodic crossing of a resonance Lattice error or Space Charge Structure Resonance 11/05/2011 G. Franche; 6

the island Large excursion of par$cles locked to compensate the modula$on of the detuning Islands gives a kick to par$cle

7 Classifica$on of resonance crossing Trapping into resonance Sca4ering by resonance although the tune is modulated par$cles remain locked on the resonance Basic phenomena Separatrix crossing par$cles cross the separatrix but do not remain inside the island Large excursion of par$cles locked to compensate the modula$on of the detuning Islands gives a kick to par$cle (sca]ering of the invariant) Adiaba$c All possible intermediate dynamical regimes are possible Non- Adiaba$c 11/05/2011 G. Franche; 7

8 Adiaba$c / Non adiaba$c Regimes Tune on the Fixed point If during 1 revolu$on around the fixed point the island moves less than its size than the par$cle can remain trapped Speed of the fixed point T << 1 characterize the adiaba$c regime A.W. Chao and Month NIM 121, 129 (1974). A. Schoch, CERN Report, CERN 57-23, (1958) A.I. Neishtadt, Sov. J. Plasma Phys. 12, 568 (1986) Size of the island Machine opera>ons typically are in a non adiaba>c regime 6/26/07 G. Franche; 8

9 Mul$ple resonance crossing in SIS100 Q y Qx = 56 DA/ 4 3 Mi$ga$on of long term effects Compensate the resonance Qx + 2 Qy = 56 without exci$ng the resonance 3 Qx = Nonlinearity: Yes Space charge: No Chroma$city: No Dispersion: No COD: No RF: No Q x 2 1 Compensa>on strategy Cancella$on of the driving terms of Qx + 2 Qy = 56 and 3 Qx = 56 at the crossing of the two resonances SIS100 resonances for the Standard seed 1-2/12/2010 Giuliano Franche; 9

10 Beam loss predic$on for SIS100 % of particles intensity 5E11 Nonlinearity: Yes Space charge: Yes Chroma$city: Yes Dispersion: Yes COD: Yes RF: Yes main resonance compensated First bunch error bar error bar x1000 turns Standard seed % of particles Main resonance un- compensated intensity 5E11 Nonlinearity: Yes Space charge: Yes Chroma$city: Yes Dispersion: Yes COD: Yes RF: Yes First bunch error bar error bar x1000 turns 1-2/12/2010 Giuliano Franche; 10

11 Transverse- Longitudinal coupling via electron- colud Localized electron cloud The coupling take place only at the loca$on of an electron cloud Pipe s Pipe 11/05/2011 G. Franche; 11

12 In the reference frame of the bunch Pipe s Pipe 11/05/2011 G. Franche; 12

13 But electrons have different wavelength according to their amplitude x 1 ω = ω 0 1+r 2 The slight difference of frequency construct a structure of electron cloud along the bunch Structure of EC rings pinch s Giuliano Franche; 13

14 EC- pinch in dipoles For nominal LHC bunch Based on the ``strong field approxima$on cut at 1 σ z 11/05/2011 G. Franche; 14

x Complex structure of amplitude dependent detuning z z Very complex

15 Mul$ple resonance crossing in bunched beams induced by electron cloud Pipe Slow halo forma$on? x Complex structure of amplitude dependent detuning z z Very complex Periodic crossing of a resonance Bare tune Lattice error or Electron cloud Structure Resonance 11/05/2011 G. Franche; 15

16 1D Modeling of EC incoherent effects BEAM07 1D model of EC pinch Electrons are in two planes moving apart according to the longitudinal posi$on of a par$cle in a bunch 1 localized EC kick excite all structure resonances 11/05/2011 G. Franche; 16

17 Crossing of the 4 th order structure resonance Trapping process for the 1D electron- cloud map In red are show the orbit of the frozen system This resonance crossing in NOT ADIABATIC Sinusoidal Periodic Crossing: Period turns

18 We find the existence of an a]rac$on point, which characterize the trapping of par$cles The same beam dynamics in the reference frame of the a]rac$on point Sinusoidal Periodic Crossing: Period turns

19 Modeling of the EC rings in field free regions R E r =0 Slope (or angle) of the EC ring E r = K ec 1 r E r =0 11/05/2011 G. Franche; 19

20 Tune footprint Example for DQ = 0.2 Tune- footprint of the full bunch EC kicks create a web of high order structure resonances Q y Q x 11/05/2011 G. Franche; 20

21 Example of an es$mate for LHC EC Kicks all dipoles all quad, but EC structure of free pinch x / x =0.06t h Simula$on DQe = 0.1 y / y 0 11/05/2011 G. Franche; 21

22 Conclusion Incoherent effect are caused by the mul$ple crossing of the same resonance by a beam par$cle The single par$cle tune modula$on is caused by transverse- longitudinal coupling created by: chroma$city, space charge, pinched electron cloud The difference between the source of the coupling arises from the type of amplitude dependent detuning created These effect are of relevance for long term storage in high intensity machines and in presence of electron cloud (LHC, SIS100) Source/Feature Detuning Amplitude dependence Driving resonances Chroma$city weak weak no (?) yes Experiment verifica>on Space Charge strong strong/decrease yes/no yes/ongoing Electron Cloud strong/weak strong/decrease yes? Nonlineari$es strong/weak strong/increase yes yes 11/05/2011 G. Franche; 22

23 Thanks to GSI BNL CERN ITEP KEK SLAC/Stanford SRI Univ. Bologna O. Choriny, W. Bayer, O. Boine- Frankenheim, C. Omet, B. Franczak, P. Forck, T. Giacomini, I. Hofmann, M. Kirk, H. Kollmus, T. Mohite, A. Parfenova, P. Schue], P. Spiller W. Fischer G. Arduini, V. Baglin,E. Benede]o, O.E. Berrig, O. Bruening,C. Carli, R. Cappi, M. Giovannozzi, K. Li, M. Mar$ni, E. Metral, R.R. Steeremberg, G. Rumolo, F. Zimmermann P. Zenkevich, A.Bolshakov, V. Kapin K. Ohmi A. Chao A.I. Neishtadt G. Turche;, C. Benede;, A. Bazzani 26/6/2008 G. Franche; 23

Incoherent effect due to electron cloud

Incoherent effect due to electron cloud G. Franche2 ECLOUD 2012 8/6/2012 Isola d Elba Thanks2: G. Arduini, V. Baglin, E. BenedeIo, O.E. Berrig, K. Li, K.Ohmi, E. Metral, G. Rumolo, E. Schaposhnikova, F.