# Nonlinear Phenomena and High Intensity Accelerators

This article explores the nonlinear phenomena observed in space charge dominated beams and the importance of high control of beam quality in high intensity accelerators. It includes examples like the Montague resonance and insights from the Bologna group, CERN PS group, and others.

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## About Nonlinear Phenomena and High Intensity Accelerators

PowerPoint presentation about 'Nonlinear Phenomena and High Intensity Accelerators'. This presentation describes the topic on This article explores the nonlinear phenomena observed in space charge dominated beams and the importance of high control of beam quality in high intensity accelerators. It includes examples like the Montague resonance and insights from the Bologna group, CERN PS group, and others.. The key topics included in this slideshow are Nonlinear phenomena, space charge, high intensity accelerators, beam quality, SNS,. Download this presentation absolutely free.

## Presentation Transcript

1. Nonlinear phenomena in space-charge dominated beams. Nonlinear phenomena in space-charge dominated beams. 1. Why? 2. Collective (purely!) nonlinearity 3. Influence of distributions functions 4. "Montague" resonance example 5. Outlook Acknowledgments: G. Franchetti, A. Franchi, G. Turchetti/Bologna group , CERN PS group, and others Ingo Hofmann GSI Darmstadt Coulomb05 Senigallia, September 12, 2005

2. High Intensity Accelerators High Intensity Accelerators Needs: High intensity accelerators (SNS, JPARC, FAIR at GSI, ...) require small fractional loss and high control of beam quality: - SNS: <10 -4 1 ms - JPARC: <10 -3 400 ms - FAIR (U 28+ ): <10 -2 1000 ms - others (far away): Transmutation, HIF, etc. space charge & nonlinear dynamics are combined sources of beam degradation and loss

3. J-PARC KEK/JAERI, Japan

4. SNS Spallation Neutron Source Oakridge, USA SNS Spallation Neutron Source Oakridge, USA

5. FAIR project of GSI Facility for Antiprotons and Ions 900 Mio FAIR project of GSI Facility for Antiprotons and Ions 900 Mio Code predictions of loss needed storage time of first bunch in SIS 100 ~ 1 s with Q ~ 0.2...0.3 loss must not exceed ~ few % avoid "vacuum breakdown" & sc magnet protection from neutrons (40 kW heavy ion beam)

6. 2 classes of problems in accelerators & beams 2 classes of problems in accelerators & beams Space charge = "mean field" (macroscopic) Coulomb effect 1. Machine (lattice) dominated problems space charge significant in high-intensity accelerators lattice, injection, impedances ... design and operation in specific projects: J-PARC (talk by S. Machida), SNS (talk by S. Cousineau), FAIR (talk by G. Franchetti) 2. "Pure" beam physics cases space charge challenging aspect isolate some phenomena test our understanding numerous talks at this meeting 2 benefits from 3 !

7. Analytical work & simulation & experiments needed Analytical work & simulation & experiments needed No one believes in simulation results except the one who performed the calculation, and everyone believes the experimental results except the one who performed the experiment. At GSI various efforts in comparing space charge effects in experiments with theory since mid-nineties: e-cooling experiments at ESR on longitudinal resistive waves and equilibria (1997) longitudinal bunch oscillations space charge tune shifts measured (1996) quadrupolar oscillations space charge tune shifts measured (1998) experiments at CERN-PS with CERN-PS-group (2002-04) (talks by G. Franchetti/theory and E. Metral/experiments) experiments at GSI synchrotron SIS18 (ongoing)

8. Linear coupling without space charge: 1970's: Schindl, Teng, 2002: Metral (crossing) Linear coupling without space charge: 1970's: Schindl, Teng, 2002: Metral (crossing)

9. New RGM device at GSI SIS18 New RGM device at GSI SIS18 rest gas ionization monitor high sampling rate (10 ms) fast measurement (0.5 ms) new quality of dynamical experiments T. Giacomini, P. Forck (GSI)

10. Measurements at SIS18 (PHD Andrea Franchi) (low intensity) Measurements at SIS18 (PHD Andrea Franchi) (low intensity)

11. Dynamical crossing in progress (low intensity) - now ready for high intensity Dynamical crossing in progress (low intensity) - now ready for high intensity Rest gas ionization profile monitor Rest gas ionization profile monitor frames every 10 ms (later turn by turn) frames every 10 ms (later turn by turn)

12. Nonlinear collective effects in linear coupling introduced by space charge Nonlinear collective effects in linear coupling introduced by space charge 2D coasting beam Second order moments

13. Space charge: dynamical tune shift causes saturation of exchange by feedback on space charge force Space charge: dynamical tune shift causes saturation of exchange by feedback on space charge force PRL 94, 2005 coherent resonance shift (from Vlasov equation) modifying "single particle" resonance condition work based on solving Chernin's second order equations

14. Dynamical crossing "wrong" direction: "barrier" effect of space charge Dynamical crossing "wrong" direction: "barrier" effect of space charge

15. Collective nonlinearity may have strong effects, although single-particle motion linear Collective nonlinearity may have strong effects, although single-particle motion linear coherent frequency shift in resonance condition mQ x + nQ y = N + Q coh (Q x , Q y assumed to include single-particle space charge shifts) Q coh causes strong de-tuning response bounded asymmetry when resonance is slowly crossed ("barrier") distribution function becomes relevant mixing? "mixing" by synchrotron motion in bunched beams might destroy coherence

16. KV distributions nonlinear effects KV distributions nonlinear effects uniform space charge single particle motion linear (linear lattice) anomalous KV instabilities for strong space charge ( 0 < 0.39) as first shown by Gluckstern space charge tune shift, no spread high degree of coherence (absence of Landau damping)

17. Lack of overlap with single-particle- spectrum Lack of overlap with single-particle- spectrum KV WB G PHD thesis, Ralph Br, GSI (1998)

18. Also in response to octupolar resonance of coasting beams: strong imprint of coherent response Also in response to octupolar resonance of coasting beams: strong imprint of coherent response Gaussian k 3 =125 loss KV k 3 =125 Q x bare machine tune

19. "Detuning" effect of space charge "octupole" with small emittance growth in coasting beam "Detuning" effect of space charge "octupole" with small emittance growth in coasting beam 0 . 9 1 1 . 1 1 . 2 1 . 3 0 1 0 0 2 0 0 3 0 0 4 0 0 0 I / I 0 I [ A ] o c t z e r o s p a c e c h a r g e a s y m p t o t i c e m i t t a n c e g r o w t h Resonance driving << space charge de-tuning

20. In bunched beam "periodic crossing" In bunched beam "periodic crossing" synchrotron motion (and chromaticity - weaker) modulate tune due to space charge ~ 1 ms periodic crossing of resonance depending on 3D amplitude and phase of particles coherence largely destroyed trapped particles may get lost with islands moving out see talks by Giuliano Franchetti / Elias Metral

21. Nonlinear features of "Montague" resonance in coasting beams Nonlinear features of "Montague" resonance in coasting beams Practically important emittance transfer in rings with un- split tunes longitudinal - transverse coupling in linacs Machine independent Explored theoretically + experimentally (CERN-PS) in recent years Good candidate to explore nonlinear space charge physics 2 Q x - 2 Q y ~ 0 2 Q x - 2 Q y = 0 in single-particle picture here coherent effects

22. Emittance coupling in 2D "singular" behavior if bare tune resonance condition is approached Emittance coupling in 2D "singular" behavior if bare tune resonance condition is approached Q ox Q oy (=6.21) from below, assuming x > y

23. Coherent response can be related to unstable modes from KV - Vlasov theory Coherent response can be related to unstable modes from KV - Vlasov theory Q 0y = 6.21 Q 0x = Q 0y Q x = Q y Q x = Q y Unexpected: at 2 Q x - 2 Q y = 0 find all growth rates zero and no exchange in KV-simulation anti-exchange for KV single-particle picture coherent response picture KV Gauss

24. Scaling laws Scaling laws from evaluating dispersion relations found "simple" laws for bandwidth and growth rates stop-band width and exchange rate: g ex weakly dependent on x / y

25. Dynamical crossing Dynamical crossing N ex ~ 34 turns 100 turns 1000 turns "slow" crossing causes emittance exchange complete exchange if N cr >> N ex (more than 10)

26. Space charge "barrier" Space charge "barrier" from left side adiabatic change from right side "barrier" crossing from left is a reversible process

27. Adiabatic non-linear Hamiltonian Adiabatic non-linear Hamiltonian all memory of initial emittance imbalance stored in correlated phase space challenge to analytical modelling (normal forms?)

28. Measurements at CERN PS in 2003 Measurements at CERN PS in 2003 measured agree on "exact resonance" Montague "static" measurement injection at 1.4 GeV x =3 y / 180 ns bunch flying wire after 13.000 turns emittance exchange Q x dependent (Q y =6.21) unsymmetric stopband Q x < Q y x = y from 6.19 ... 6.21 IMPACT 3D idealized simulation "constant focusing" unsymmetric stop-band similar x = y only from 6.205 ... 6.21 try to resolve why less coupling? maximum disagreement codes Vertical tune = 6.21 (fixed)

29. Participating codes Participating codes code comparison started after October 2004 (ICFA-HB2004 workshop)

30. Step 3: nonlinear lattice / coasting beam Step 3: nonlinear lattice / coasting beam codes still agree well among each other! but: again only weak emittance exchange (nearly same as in constant focusing 2D or bunch) and: only minor effect of nonlinear lattice over 10 3 turns! is there more effect by combined nonlinear lattice + synchrotron motion (bunch)?

31. Challenge are measurements on dynamical crossing Challenge are measurements on dynamical crossing k 3 = + 0 k 3 = + 60 k 3 = - 60 2D "slow crossing" exchange experiment Dynamical crossing data from 2003: 40.000 turns slow "dynamical crossing" result resembles very fast crossing of coasting beam (why? synchrotron motion "mixing", collisions?) simulations in preparation

32. Outlook Outlook gained some understanding of 2D coasting beams coherent frequency shifts, distribution function effects nonlinear saturation by de-tuning asymmetry effects for crossing of resonances adiabaticity still under investigation are aspects like experimental evidence of 2D coherence simulation for bunched beams, i.e. 3D effects, with synchrotron motion collisions (C. Benedetti)

33. Suppressed damping and halo production of mismatched beams Suppressed damping and halo production of mismatched beams

34. confirmed in linac simulations ... confirmed in linac simulations ...