1. Ultra-short electron bunches by Velocity Bunching as required for Plasma Wave Acceleration Alberto Bacci (Sparc Group, infn Milano) EAAC2013, 3-7 June, Isola d’Elba, Italy

2. 1)The Velocity Bunching (VB) and Laminar VB (LBV); a VB compressing technique characterized by a peculiar equilibrium between the external RF long. focusing force and internal space-charge defocusing force. 2) Longitudinal envelope equation analysis in case of strong compression (at low energy, space charge effect in z,pz phase space) – suggestions for optimizations. 3) Simulations on an ideal IV cavities Linac to study VB performances. 4) Simulations on the SPARC layout. outline

3. beam length shorter than cooperation length (around or below 1fs) examples: The SPARX project J. Rosenzweig, et al., NIMA 593 (2008) LCLS, 20pC, single x-ray spike at 1.5 nm Y.Ding, et al. PRL 102 (2009) Ultra short bunches (why we are interested …) High charge ultra short bunches as Plasma Driver in PWFA (after burner) Wake amplitude ; Low charge bunches as witness in PWFA Low or ultra low charge bunches for external injection in LWFA bunch fig. of merit Plama Wave Accelerators (Gradient ~ 1-10 GV/cm) FEL SASE Single Spike in X-ray range

4. VB and Laminar VB 1 SPARC untrue for high aspect-ratio bunches emittance compensation constant envelop Emit.Conp. with or without VB

5. small enough to favor compression, “malleable” bunch big enough to damp the Energy spread and stop the overcompression F int. 1) the compression stars with a prevalence of the RF longitudinal Force K z 2) Space-charge effects controlled by σ x, σ z, stop the overcompression regime and start a ΔT damping 3) long. laminarity is matained by a faster Ɛ term damping VS Space-charge term Laminar VB – in three steps: Beam freezing and long. laminarity … maintain the longitudinal laminarity along the whole compression (low energy) > preventing over-compression, permitting an energy spread damping toghether with the emittance compensation The compression must be performed with a proper control of the envelope or current density Laminar VB key idea

6. small enough to favor compression, “malleable” bunch big enough to damp the Energy spread and stop the overcompression F int. Beam freezing and long. laminarity … maintain the longitudinal laminarity along the whole compression (low energy) > preventing over-compression, permitting an energy spread damping toghether with the emittance compensation The compression must be performed with a proper control of the envelope or current density Laminar VB key idea 1) the compression stars with a prevalence of the RF longitudinal Force K z 2) Space-charge effects controlled by σ x, σ z, stop the overcompression regime and start a ΔT damping 3) long. laminarity is matained by a faster Ɛ term damping VS Space-charge term Laminar VB – in three steps:

7. For an Ellipsoidal uniform charge distribution External force: VB longitudinal focusing gradient Internal forces: space-charge – emittance pressure Laminar parameter (space- charge/emit): A optimiztion Code, like GIOTTO ables to drive Astra can be successfully used The bunch compression optimization can be controlled by imposing different ρ z values along simulations; e.g. by using an optimization code. Longitudinal Envelope eq.’s suggestions 2 GIOTTO repository: http://pcfasci.fisica.unimi.it/Pagine/GIOTTO/GIOTTO.htm constraints

8. Envelope analysis vs simulation σ z ‘’ [mm] from simulation σ x [cm] ΔE rms [MeV] σ z [mm] RF term v term I term Ɛ z term RF term + v term + I term + Ɛ z term σ z ‘’ [mm] from Envelope eq. Sparc-case Q b = 20pC C f = 8

9. VB over-compression – 3 TW LVB on 5 TW – last 4 TW on crest

10. Equilibrium between space charge and longitudinal compression is preserved until the LINAC end; No over compression – Longitudinal Laminar Beam

11. ΔE/E: ~1·10 -4 30k macro particles simulations An ideal IV cavities Linac 3 I s [A] Δγ/γ[%]emitσ t [fs] 1850.060.041.0 2860.09 1.5 7250.130.165.2 4000.040.1810fs 5000.060.2212fs QbQb

12. 3m drift at 12 m ~ 3 µ C ~ 40 = 3.4µ Q b = 15 pC 4.1 SPARC layout

13. SPARC layout – STATISTICAL ANSLYSIS Laser – RF Gun jitters = 80 fsecInjection phase jitters = 100 fsec Q b = 15 pC 150 runs

14. Compression factor ~ 15 Carlo Benedetti - Aladin Plasma Wake Field Accelerator Driver 4.2

15. Conclusions: These simulations show as it’s possible to drive single spike FEL or PWFA, LWFA by using only the VB technique. We have seen very short bunches from 12 fs down to 1 fs, with ΔE < 150KeV and generated with short Linacs 12-15 meters.

16. Thanks for your attention