Laminar Velocity Bunching A. Bacci V – LI 2 FE Collaboration meeting, March 2011, Frascati

Giotto – Genetic Interface for OpTimising Tracking with Optics New Genetic code able to find, more or less complex,beam-line configurations, useful to answer at many different problems, by using fully 3D simulations. The search for the best beam-line settings is driven by a fitness function which can by freely defined from the user. The fitness function can be wrote using all data computed by the tracking code (Astra), or computed by a post processor, which is dedicated to multi bunches simulations: PosZ, time, En,Den,SigZ,Xemit,sigX,divergX,Yemit,SigY,divergY,emitY Multi bunches post_pro:SCurrent(NSpike), SemitX(Nspike),SemitY,Sdist(Nspike) All variable definite in the Astra input file (or in the Astra generator) can be chosen as a Giotto variable to be optimized (genes) (ex. Phi(1)…Phi(50),maxe(1),maxb(1), sig_x,sig_clock --- No limit in the number) A typical simulation works with 3-15 variables and takes from 1h up to 2 days (by using a quite old 8 core workstation) - The speed scale linearly with the cpu number. Giotto can be switched from Genetic Optimizations to Statistical Analysis. Each Astra variable can be analyzed and the sampling interval used for the optimization analysis becomes the jitters interval, which can be sampled in uniform o Gaussion way – A statistical analysis is quite fast; 300 test cases take just some hours. Used for Vbunching strongly space charge dominated – TNSA Proton Acceleration – Laser Comb - Single spike FEL, ecc… --- Next upgrade (switchable Astra-Tstep-Homdybn) ---

Q=1nC – sig_x=0.5 mm – dt=10ps Flat-Top C=11.3 emit=1.2 [mm-mrad] E=170 MeV Best Emit&Curr Push-up Energy by VI,VII,VIII,IX cavities C=10.6 emit=2.0 [mm-mrad] E=340 MeV 1)2) Current & emit distribution Is it necessary to add coils on the III S-band Cavity? The emittance and envelope are in opposition of phase (emit.correction) 1Slice=σ z,s =3.8 μm = 1KA σ z =78 μm Full velocity bunching -Sband

Envelope equation for a round Kapchinskii-Vladimirski beam. Ellipsoidal uniform charge distribution with and rms longitudinal semi-axis : External forces: VB longitudinal focusing gradient Internal forces: space-charge – emittance pressure Longitudinal laminarity (space- charge/emit): VB Compression in longitudinal beam laminarity regime :

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

Under particular conditions (*) it is possible to find an Analytical solution (*)

All VB 9 TW VB over-compression – 3 TW on crest – 3 TW VB 5 TW – 4 on crest E=170 MeV E=340 MeV

Electron density, current and ρ z Conclusion: New simulations with C band cavities are under study. These will be performed by Giotto controlling the ρ z parameters along the simulation. The analytical study needs further considerations.

Short bunches: the compressing factor can be pushed at very high values: It is not true for very short bunch! Considering A=(R/L) >> 1 Very strong de-bunching: Sub-fs e- 1 pC SPARC First attempt