Collective Effects in the 50 MEV Thomx Compact Storage Ring T. Demma, LAL

1. IN2P3 Les deux infinis Collective Effects in the 50 MEV Thomx Compact Storage RingT. Demma, LAL

2. OUTLOOK • Compton physics. Why Compton light sources….. • Thomx the technology. The machine, the laser and the FP cavity • Ions instability : • analytic and numerical estimations of instability • Possible cleaning • Intrabeam scattering : • Limitations for ThomX • Impact on the X-ray flux

3. The ThomX Project • Compton effect • ThomX is a light source based on Compton Back Scattering (CBS) • Why CBS? • CBS is by far the most efficient photon energy amplifier : wdiff=4g2wlaser, ThomX => g~100 => it is possible to have at one’s disposal hard X rays with a relatively low energy electron machine. • Thomx target is a high AVERAGE flux so we need many electrons and photons colliding in a small volume at high frep => CHOICE: • Storage ring + high average power laser amplified in a Fabry Perot resonator (French collaboration among different kinds of expertise )

4. Laser wlaser • photon : wf • Dynamics of the process • Compton Scatteringg (laser)+eg’+e’ • Photon(laser) + electron scattering • Fano, JOSA39(1949)859; • Simulation program: CAIN from Yokoya-san http://lcdev.kek.jp/~yokoya/CAIN/cain235/ q • electron g=Eelectron/mec2 • (scattered electron) • We are interested by using the scattered photon • Scattered photon properties given by the Compton differential cross-section

5. Eelectron=50MeV wf,max • Energy distribution wf in keV • 1rst interest: the energy boost • (no polar. are observed) Energy distribution ~flat with wf,max=4g2wlaser with g~100 (Eelectron=50MeV) wf,max=45000eV if wlaser~ 1eV Compton scattering is the most powerful mechanism to boost photon energies The cut off is dependent on the incidence angle !! (factor two up to p/2) • Sprangle et al. JAP72(1992)5032

6. Compton X ray source: advantages 1 electron – 1 photon • CBS attractiveness : • 1) Photon frequency boost = 4g2 (tunability / electrons or laser energy) • 2) Directivity (relativistic boost) = > f= 1/garound the electron direction • 2) Energy angle dependence => monochromatic by diaphragm • 4) Polarized if needed • 5) Backscattered spectrum cut off => Energy dependence on collision angle

7. collimator wf(keV) q(mrad) • 2nd interest: the angular energy correlation • Compton scattering • Photon_laser+e photon+e’2 body process  wf = f(q) • electron • Sprangle et al. JAP72(1992)5032 •  ~monoenergétic beam by selecting Backscattered photons at wf,max • Eelectron=50MeV

8. Quelle source de lumière Compton? • Quels paramètres? ThomX : démonstrateur Collaboration entre: LAL Orsay, SOLEIL, CELIA Bordeaux, ILE, LMA, Thales • Anneau d’accumulation d’électrons compact = paquets avec une grande frep • Système laser de grande frep et puissance moyenne couplé avec un résonateur optique de grande finesse.

9. Comparaison with other sources M.E.Couprie, O.Marcouille

10. How it works • ThomX scheme and design • Cycle Frep = 20 msec • RF pulse length 3 ms • Energy 50 - 70 MeV • Laser and FP cavity • 2 Ips • Easy integration • Frees the straight sections • CSR line • Acknowledgments to M.Jore, M Lacroix

11. Frequency comb  all the combmust be locked to the cavity •  Feedback with 2 degrees of freedom : • control of the Dilatation & translation • Pulsed_laser/cavity feedback technique • T=2p/wr • Beam • wn= nwr+w0 • n~106 • T. Udem et al. Nature 416 (2002) 233

12. Fabry-Perot cavity • Laser input • e- beam MightyLaser and PLIC experience • Stable solution: 4-mirror cavity as in Femto laser technology • Vacuum and mechanics : MightyLaser experience Digital Pound-Drever-Hall feedback • PLIC and MightyLaser : record in stable finesse locking (30000). • Acknowledgments to F.Zomer, R.Chiche, D.Jheanno, M.Lacroix, R.Cizeron

13. Expected beams characteristics • Injector, ring, laser, Fabry-Perot resonator and the source

14. Tasks of the X line • Table 1 Continuous beam detection and monitoring •  Slits and focus device • Beam transport(40 cm diameter beam pipe section) • Table 2 Complete beam characterisation  Demonstration experiments • Imaging • Spectroscopy and diffraction experiments • 3 m

15. Available X-ray beam • ~ 1.5 m • Beryllium window • 50 mm • θ ~ 16 mrad • (opening cone ½ angle) • X beam energy ~ 10-45 KeV • IP • Ee = 50 MeV • normalized dσ/ Ex • Flux 1013ph/sec • Trans. size at IP ~ 70 μm • frep (e-/laser) ~ 20 MHz • EX(KeV) • frep inj. ~ 50 Hz • EX (KeV) • ph/mm2/mrad2/0.1%bw • EX (KeV) • ~ 30 mrad • θ(rad) • θ(rad)

16. ThomX Scientific Case • K-edge imaging (Pbwhite, Hg vermilion…) of a Van-Gogh’s painting • J. Dik et al., Analytical Chemistry, 2008, 80, 6436 • Cultural heritage and medical science • Transfer of the SR techniques to these new machines. Many fields can be interested… • At present two contributors: Medical field (ESRF, INSERM Grenoble) Cultural Heritage (C2RMF CNRS – Louvre Museum) Painting analysis • Physiopathology and Contrast agents, • Dynamic Contrast Enhancement SRCT • Convection Enhanced Delivery =>Stereotactic Synchrotron RT Paleontology Non-destructive analysis • Biston et al, Cancer Res 2004, 64, 2317-23 • Imaging, • Mammography • Microtomography • J Cereb Blood Flow and Metab, 2007. 27 (2):292-303. • Journal of Radiology 53, 226-237 (2005) • Acknowledgments to G.Le Duc, P.Walter

17. Collective effects • With nominal parameters conventional sources of instability (RW, SC,.. ) are controllable but some, more exotic, have to be carefully estimated: • Ions instability : Electrons beam transverse instability due to ions from residual gas in the vacuum chamber • analytic and numerical estimations of instability • estimations of maximal potential and longitudinal displacement of ions for cleaning • Intrabeam scattering : • comparison between Mtingwa and Bane’s model • Limitations for ThomX • Impact on the X-ray flux

18. Ion instability Electrons Molecules of the residual gas Ions Ions Attractive force between electron beam ad ions Ions will oscillate in the potential well of the electrons

19. LinearTheory of Ion Instability (K. Ohmi) • The equations of motion for electrons and ions are expressed as: • to obtain a solution with the following form • Where: • the threshold and growth rate are obtained as:

20. Analytic estimation • Vertical case • Betatron tune =0.17 • For circular beam (in ThomXsx=0.2mm; sy=0.1 mm) • Fions=Fbeam : for small values of the dimensions (available only on few ring points)

21. Optical Functions

22. Instability threshold vs bunch dimensions

23. (Preliminary) Numerical Estimate IONTR developed by K. Ohmi (KEK) • Weak-strong approximation • Electron beam is a rigid gaussian • Ions are regarded as Marco-particles • The interaction between them is based on Bassetti-Erskine formula •  function variation can be taken into account • The effect of a bunch-by-bunch feedback system is included • Assumptions for ThomX: •  function variation taken into account • Only CO ions represented by 1000 MP localized at 10 IP uniformly spaced around the ring • 1 bunch • ni/ne=1 • No effect is observed below ni/ne=1

24. Ions countermeasures • Computed ion density threshold is high however ion could accumulate during the long storing time around the ring and countermeasure could be needed if accumulation continues to value comparable to the threshold. • Decrease Ion density by keeping low vacuum pressure • Insert gap in the filling scheme to clean the ions • Use of feedback system to keep under control the instability • Clearing electrodes • Ions could be collected by the electrodes • A detailed study is needed to asses their efficacy • •Introducing gaps makes motion of ions unstable. • •Ions might be collected on electrodes with smaller voltage. • A simulation is necessary for studying the effectiveness of the electrodes.

25. Ion potential • Ion potential maximum at IPs • Possibility to clear ions with polarized BPMs • Necessity to have longitudinal displacement of the ions

26. Combined effect of IBS and CBS on X ray flux e- e- hn E hn’ E-DE photon • IBS : coulomb scattering inside the bunch • Emittance and energy spread degradation • CBS : random energy excitation • Energy spread degradation e-

27. Comparison of Mtingwa and Bane’s model for ThomX • Both models are based on the integration of the diffential equation concerning energy spread and emittances • Mtingwa • does not consider approximation, • but it is a low integration (slowly convergent integral to be calculated at each longitudinal position in the ring • Bane : • faster model based on mean values of optical function, and a quick convergent integral • But it consideres high energy approximation (to be cheked for ThomX

28. Validity of the Bane’s model for THOMX • Bane does a variable change • It conseidered to simplify the Mtingwa model that a, b<<1 • Inducing the major (65%) error in the longitudinal plane : in this region a, b=0.35 for the nomina lattice • Then, it simplify the integral, which induces the rets of the error • In the horizontal axis, • Considering a,b<<1 elso introduced the error • It is partially compensated with an other approximation <<

29. Bane’s model introduces • 4% of over estimation of the energy spread increase on 20 ms • 3% of over estimation of the horizontal emittance on 20 ms • This model can be used for ThomX, with a negligeable over estimation of the calculated quatities

30. Mean over a cycle of 20ms CBS+IBS CBS+IBS • Asolute mean increase larger for higher charge, But the relative one is lower • Impact on the brillance ? • Flux reduction of 24% averaged over a clycle

32. Conclusion • Compton X Rays source • Collaboration established, CDR published • Financing!!!! Equipex (French minister), Ile-de-France Region, CNRS-IN2P3, Université Paris Sud XI • TDR phase close to the end • Construction should start by the end of this year • IONS Analytical and numerical estimations show that we are confident about ions • But needs of more simulations also including space charge force • Ions can also be cleaned by polarised BPMs Achievable voltages for the BPMs • But needs to evaluate more precisely the ion longitudinal displacement • Even if ions instability can arise after few cycles, a gap between injection could be added : • to be evaluated • IBS/CBS Faster numerical evaluation with the Bane’s model • Effect on the brilliance is being evaluated with numerical and analytical calculations

33. Ions countermeasures • A) Decrease the ion density • a) Better vacuum pressure • •This might be an ultimate cure, but may be difficult. • + • electrode • b) Clearing electrode • 2a • rc • •A condition where an ion is not trapped in a potential well by a dc beam, • ion • (A. Poncet) • - • •Introducing gaps makes motion of ions unstable. • •Ions might be collected on electrodes with smaller voltage. • A simulation is necessary for studying the effectiveness of the electrodes.

34. Maximum longitudinal displacement of ions • Accumulation points where ions does not take longitudinal speed • BPMs are located near these points except at the symmetric IP where a vacuum pump is placed • Longitudinal displacement of ions along the ring should be evaluated versus time and ion transverse and longitudinal position along the ring

35. Combined effect of IBS and CBS on X ray flux e- e- hn E hn’ E-DE photon • IBS : coulomb scattering inside the bunch • Emittance and energy spread degradation • CBS : random energy excitation • Energy spread degradation e- CBS • 30% reduction on the X ray flux CBS+IBS

36. Beam-Beam Collisions a) energy, angles, polarization (convolution) b) Collision angle (luminosity loss, energy shift, jitter….) c) Beam focussing => hourglass effect N.Artemiev