COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Space Charge Issues in High Brightness Electron (Plasma)Beams for X-ray FEL’s Luca Serafini, INFN-Milan and University of Milan Electron beams for X-ray FEL’s are cold relativistic plasmas propagating through the Linac in laminar flow (up to GeV’s) To reach high brightness ( I > kA,  n < 1  m) one needs Many Thanks to: SPARC&PLASMONX Project team 1) Transport the beam through a gentle funnel made by RF and acceleration focusing counteracting space charge # betatron oscillations << 1 # plasma oscillations ~ 1 transverse laminarity 2) # synchrotron oscillations ~ 1/4 (with velocity bunching) longitudinal laminarity

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Reaching the goal brightness is critically dependent on matching the beam to the invariant envelope condition ( the funnel) FODO-like transport is forbidden up to 150 MeV and not reccommended up to 1 GeV SPARXino: a GeV LNF to drive a 5-10 nm radiation wavelength 1 kA 500 A Insensitive to quad misalignment

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 L.S., J.B. Rosenzweig, PRE 55 (1997) 7565 Cold Relativistic Plasma-Beams in Laminar Flow with time dependent Space Charge Fields Betatron wavelength photocath. therm. emittance Plasma wavelength (sp. ch. oscillation) norm. amplit. of RF focusing Accelerating gradient Linac length # Betatron oscill. ~ 0.3 # Plasma oscill. ~ 1 # Synchrotron oscill. ~ 1/4 At Linac exit

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Parmela simulation of SPARC photoinjector up to 150 MeV (velocity bunching with X-band RF cavity) C. Ronsivalle

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Schematic View of the Envelope Equations (HOMDYN model)

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Emittance Compensation: Controlled Damping of Plasma Oscillation Hokuto Iijima L. Serafini, J. B. Rosenzweig, Phys. Rev. E 55 (1997) Brillouin Flow 100 A ==> 150 MeV

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Brief Review of Beam Dinamycs in Photo-Injectors The beam generated at the photocathode surface behaves like a Single Component Relativistic Cold Plasma all the way up to the injector exit (150 MeV, 1 GeV with compression) It is a quasi-laminar beam both in transverse (laminar flow) and longitudinal plane (lack of synchrotron motion) Normalized focusing gradient (solenoid +RF foc.)

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 S.C.R.C.P. or Laminar Plasma- Beam Plasma launched at relativistic velocities along the propagation axis with equivalent ionization = 1/  2 ; plasma confinement provided by external focusing (solenoids, ponderomotive RF focusing, acceleration) Spread in plasma frequency along the bunch  strong time-dependent space charge effects  inter-slice dynamics © M. Serafini Liouvillian emittance = foil volume Projected emittance (shadow) >> slice emittance (foil thickness)

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Final emittance = 0.4  m Matching onto the Local Emittance Max., Example of an optimized matching M. Ferrario et al., “HOMDYN Study For The LCLS RF Photo-Injector ”, Proc. of the 2 nd ICFA Adv. Acc. Workshop on “The Physics of High Brightness Beams”, UCLA, Nov., 1999, also in SLAC-PUB-8400

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Movable Emittance-Meter Measuring Emittance SPARC emittance envelope

Emittance Envelope Bz field Z= 170 cm Z= 120 cm Z= 85 cm

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Bunch Microscopy, Inter-Slice dynamics

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Laser Pulse Shaping Experiment: a SPARC-BNL/DUV-SLAC/LCLS Collaboration The Beer-Can Distribution

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 e-beam measurement Q=70 pC Gaussian Flat top

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 e-beam temporal distribution Q=70 pC, after Dazzler optimization

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 e-beam temporal distribution Q=300 pC

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Inter-slice dynamics brings to projected emittance oscillations which are reversible  emittance correctionthis can be described by a multi-envelope code like HOMDYNthe prescription to reach full emittance correction is to match the beam onto the invariant envelope (beam equilibr. mode) LS and JR, PRE 55 (1997) 2575 S.C.R.C.P. or Laminar Plasma-Beam Intra-slice dynamics is affected by space charge field non-linearities (partially reversible, unless wave-breaking is reached) to model intra-slice dynamics we need a multi-particle code (Parmela)the prescription to avoid wave-breaking and irreversible slice emittance growth is to use uniform cylindrical charge density distribution (flat top laser pulses, spatially uniform)

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 The Blow-Out regime: from Pancakes to Waterbag Serafini ==> Luiten ==> Rosenzweig  Use any temporally shaped ultra-short pulse  Longitudinal expansion of well-chosen  shaped radial profile  Uniform ellipsoidal beam created!  Linear space-charge fields (3D)==>

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Initial (not-too-optimized) PARMELA study Standard LCLS injector conditions –120 MV/m peak on-axis field Beam initial conditions chosen to: –Avoid image charge effects (  b limit) –Produce emittance compensation Parameters: –Q=0.33 nC –Initial longit. Gaussian  t =33 fs (cutoff at 3  ) –Trans. Gaussian with  x =0.77 mm (cutoff at 1.8  ). Final bunch length 1.3 mm (full), 117 A. At low energy (only) the ellipsoidal beam shape is visible –Transition to emittance dominated regime destroys shape (it is no longer needed!) Initial (not-too-optimized) PARMELA study Standard LCLS injector conditions –120 MV/m peak on-axis field Beam initial conditions chosen to: –Avoid image charge effects (  b limit) –Produce emittance compensation Parameters: –Q=0.33 nC –Initial longit. Gaussian  t =33 fs (cutoff at 3  ) –Trans. Gaussian with  x =0.77 mm (cutoff at 1.8  ). Final bunch length 1.3 mm (full), 117 A. At low energy (only) the ellipsoidal beam shape is visible –Transition to emittance dominated regime destroys shape (it is no longer needed!) Beam distribution showing ellipsoidal boundary (12.5 MeV) Initial PARMELA simulation study J.B. Rosenzweig (UCLA) Beam distribution at high energy shows Boundary collapse (71.5 MeV)

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Emittance compensation is very good: <0.9 mm-mrad Much higher current than standard operation (117 A v. 48 A) Extremely small energy spread –Shorter beam –Approx. linear space charge Emittance compensation is very good: <0.9 mm-mrad Much higher current than standard operation (117 A v. 48 A) Extremely small energy spread –Shorter beam –Approx. linear space charge Beam size evolution RMS emittance evolution Final longitudinal phase space

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Velocity Bunching - Domain of Application : low energy linac section RF field pushes particles in bunch tail more than in bunch head Velocity Bunching: a way to increase brightness Spread of absolute velocitiesRequires a Spread of absolute velocities on a rectilinear path T = 5 MeV T = 25 MeV Collective effects only in transverse plane (longit. space charge negligible) Maximum compressionMaximum compression limited by non linearities of RF field (curvature)

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 What do we need to perform “Advanced” Velocity Bunching ? I > 500 A  n ~ 1  m “Advanced” “Advanced” Velocity Bunching V.B. has been demonstrated at a number of laboratories Good compression ratio ( C > 10, I > kA) - No emittance preservation None of these systems was designed for optimizing velocity bunchingNone of these systems was designed for optimizing velocity bunching Yes 10 < 0.3 ps 0.2 nC CTR 4 S-band Velocity BunchingLLNL Yes > ps (rms) 1 nC Femotsecond Streak Camera 1 S-band Velocity BunchingUTNL-18L > 3156 Comp. Ratio BNL-DUVFELUCLABNL-ATF No 0.37 ps (rms) 0.04 nC zero-phasing method S-band Ballistic 0.5 ps (rms) 0.39 ps (rms) Bunch width No Solenoid field 0.2 nC Charge zero-phasing methodCTRMeasurement 4 S-bandPWT Acc. Structure Velocity BunchingBallisticMethod

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 To be published on JJAP

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Streak Images of Electron Bunch Injected Phase -70 O Minimum! 200 psec range 50 psec range Injected Phase -1 O

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Velocity LLNL - PLEIADES

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Velocity bunching concept  A quarter of synchrotron oscillation performed inside a RF bucket  Extraction at the resonant (synchronous) velocity (  =  r )  Injection of a short bunch at  =0 (zero field point) rr   r trapped untrapped separatrix Synchr. Wav.     inj. extr.

COULOMB’05, Senigallia, Italy, Sept. 14th 2005  Works as well with speed of light RF waves,  r =1  Extraction performed at quasi-resonant velocity (    )  Injection still at  =0, no bucket but similar pattern of Poincarè lines Velocity bunching concept

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Compression during acceleration Velocity Bunching: the very first simulation* Current scaling with energy I/  = const. Courtesy of D. Yeremian, SLAC *L.S., M.Ferrario, AIP CP 581 (2001) 87

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Average current vs. RF compressor phase In SPARC photoinjector LOW COMPRESSION MEDIUM COMPRESSION HIGH COMPRESSION OVER- COMPRESSION  z = 4 mm  z = 1 mm Overcompression, i.e. loss of longitudinal laminarity, slice mixing, irreversible sp. ch. emittance growth

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Limitation: longitudinal emitance growth induced byRF curvature Injection Extraction

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Parmela simulation of SPARC photoinjector: velocity bunching w/o higher RF harmonic C. Ronsivalle

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Parmela simulation of SPARC photoinjector: velocity bunching with higher RF harmonic C. Ronsivalle

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Current sensitivity for 1° error in RF compressor phase with IV harmonic cavity C. Ronsivalle D.Alesini et al., PAC05 without with

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Three conditions to preserve emittance during velocity bunching current growing at the same rate as the beam energy (velocity bunching !, not ballistic) (additional external focusing to match onto a parallel envelope (I.E. RFC solution) RF compressor accelerating section longer than a plasma wavelength (2-3 m) Needs a dedicated well optimized lay-out (presently not available): motivation for SPARC project at LNF

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 = 860 A  n = 1.5  m = 450 A  n = 1.0  m

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Intra-slice bunch microscopy for = 860 A,  n = 1.5  m Velocity Bunching has almost no effect on Slice Emittance !

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Velocity Bunching and Magnetic Compression in a FEL Driver: application to Sparxino See papers THPP019, C. Vaccarezza et al. and MOPP015, V. Fusco et al. 500 MeV 450 A860 A

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 L.S., J.B. Rosenzweig, PRE 55 (1997) 7565 Beam at the Sparxino photoinjector exit (with Velocity Bunching) is still space charge dominated (cold relativistic plasma) Laminarityparameter Photocathode thermal emittance Invariant Envelope norm. amplit. of RF focusing Transition Energy between plasma and gas regime Beam matching con- ditions on I. E.

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 See paper THPP019, C. Vaccarezza et al. Further Magnetic Compression with or w/o additional X-band cavity at compressor entrance withoutwith

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Effects of RF cavity misalignment See paper MOPP015, V. Fusco et al. Beam centroid walk-off Observed negligible effect on emittance No quad used! Only the funnel with invariant envelope

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Conclusions The SPARC Project is aiming at producing by LNF electron beams of unique properties in 6D phase space density Investigation on Advanced Velocity Bunching is one of its main goals, with applications ranging from high brightness beam production for FEL Drivers to (see PLASMONX Proj.) advanced plasma acceleration experiments combining fs electron beams with high intensity (>10 20 W/cm 2 ) fs laser beams (plus Thomson X-rays in spontaneous/coerent regime, i.e. a compact X-ray laser) The Sparxino Linac is conceived as a X-FEL Driver based on Adv. Vel. Bunching: it will be a test bench for the theory of relativistic cold plasma-beams

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Physics and Applications of High Brightness Electron Beams Organizers: L. Palumbo (Univ. Roma), J. Rosenzweig (UCLA), L. Serafini (INFN-Milano).

COULOMB’05, Senigallia, Italy, Sept. 14th 2005

This solution represents a beam equilibrium mode that turns out to be the transport mode for achieving minimum emittance at the end of the emittance correction process ( L.S and J.B.R., PRE 55 (1997) 7565 ) The associated plasma frequency is This solution includes (at ) the so-called Brillouin flow (rigid rotation at constant spot-size in a solenoid field) Transverse Dynamics of a quasi-laminar plasma beam (constant current) No slice dependence !

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Emittance Oscillations in Beam- Plasmas Envelope Oscillations drive emittance oscillations ( ) Damped Oscillations (  emittance correction) if the beam is transported under two possible equilibrium conditions connected to each other Brillouin Flow Invariant Envelope

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 TRACE3D PARMELAELEGANT GENESIS HOMDYNPERSEO RETARTREDIABCI POISSON-SUPERFISH MAFIA 0 Matrix0 Matrix I Semi-AnalyticalI Semi-Analytical II TrackingII Tracking III Self-ConsistentIII Self-Consistent

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 B bunch compressors RF & magnetic Pulse Shaping New Working Point How to increase e- Brightness

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Brief Review of Beam Dinamycs in Photo-Injectors The beam undergoes two regimes along the accelerator, photocathode  Linac exit Single Component Relativistic Cold Plasma (laminar beam or plasma-beam with ionization = 1/  2 )  Thermal Beam(gas-beam) laminarity parameter

COULOMB’05, Senigallia, Italy, Sept. 14th 2005 Typical X-FEL Beam   k   k  Plasma beam confined by focusing channel Potential space charge emittance growth Gas Beam ll 