EEHG 101: The Basics of Echo-7 Joel EEHG 101: The Basics of Echo-7 Joel Frederico & Pierre-Louis Pernet | Prof. Tor Raubenheimer | SLAC ARD, 2010

Motivations for Echo-7: The Free Electrons Lasers (FEL) The fourth generation of light sources Many projects around the world The LCLS at SLAC commissioned last year Beam of coherent ultrafast high intensity X-rays One billion time brighter than any previous sources Resolution of molecular and even atomic processes Open a new dimension: the time Pierre

Motivations for Echo-7: ESASE, HGHG, & EEGH Self-Amplified Spontaneous Emission (SASE), e.g. LCLS Radiations are coming from the initial shot in the beam Excellent spatial coherence High-Gain Harmonic Generation (HGHG) FEL seeding with a laser Needs of shorter undulators Echo Enhanced Harmonic Generation (EEHG) Need a proof-of-concept experiment Pierre

Echo Overview: The Big Picture How to get fine energy structure? Via laser modulator + chicane Creates energy modulation Convert to density modulation: modulator + chicane Joel

Echo Overview: Analogy with Injector Laser on cathode produces non-relativistic electron pulse Accelerated and energy chirped by RF cavity Pulse compressed by velocity bunching (drift section) Bunching in accelerator Beam comes from injector Energy changed by laser modulator Pulse compressed by path-length differences in a chicane Joel z U

Concepts: Accelerator Components Injector Subharmonic Buncher Laser Modulator Chicane Radiator Joel

Concepts: Subharmonic Buncher RF Cavity Head gets too little energy Tail gets too much energy Results in linear energy chirp Pulse in general can be accelerated Drift (Non-relativistic) Tail catches up with head Pulse is compressed! z U Pierre

Concepts: Laser Modulator Similar to chirping the beam - sinusoidal energy modulation Beam passes through undulator with a laser Quasi-sinusoidal path (alternating B- field) Confusing! So let’s follow a particle... Joel

Concepts: Laser Modulator Beam travels with βz=c (Unphysical) Beam travels slower (Physical) Laser field is constant for a particular particle Light passes, beam sees oscillating laser field But the particle oscillates... Particle oscillates with the field (synchronism condition) In one period, positive and negative work is done Positive work is always done So total work done is zero! Total work done is positive! Joel

Concepts: Laser Modulator Particles at different phases receive different energies Sinusoidal modulation in z But particles are relativistic: Only energy changes, Velocity stays ~c No bunching occurs Joel +θ -θ p0 p0+δ

Concepts: Chicane - Design Similar to drift in subharmonic buncher Larger momentum particles Composed of four bend magnets Shorter path length Move forward in bunch Equal strength and length Vice versa for smaller momentum Pierre +θ -θ p0 p0+δ

Concepts: Chicane - Overcompressing the bunch Momentum compaction: Large R56 for the first chicane Energy strips in phase space Uniform longitudinal density distribution Pierre

Concepts: Energy Strips to Density Modulation More standard use of laser modulator + chicane Laser Modulator: Larger energy modulation than previously Not so much that structure washes out Joel

Concepts: Convert Energy Structure to Density Chicane rotates phase space Bunches beam Overbunching would destroy structure Project to z-axis: Note superharmonic density modulation! Joel

Concepts: Bunching Factor Indicates amount of bunching at a harmonic n There is a peak at n = 7. An undulator tuned to this harmonic should have a decent signal Pierre

Concepts: Final Radiator The last undulator is a radiator Generation of attosecond X-ray pulses Saturation of the radiation after only a couple of undulator sections Pierre

Echo-7: Phase Space Joel

Echo-7: Phase Space

Echo-7: Phase Space

Echo-7: Phase Space

Echo-7: Phase Space

Echo-7: Phase Space

Echo 7: Preserving Phase Space Structure CSR, ISR Laser spot size finite Doesn’t provide uniform fields Field errors Mixes phase space Can occur in chicane, modulator Trim errors, misalignments, etc. Density modulation is delicate! Pierre

Citations/Acknowledgements Papers/Books Introduction to the Physics of the Free Electron Laser, J. Murphy & C. Pellegrini Echo-enabled harmonic generation free electron laser, D. Xiang & G. Stupakov, PRSTAB Image Credits Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation, G. Stupakov, PRL http://www.ikp.physik.tu- darmstadt.de/richter/fel/overview.html Fundamentals of Beam Physics, J. Rosenzweig