C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Optimum electron distribution for space charge dominated beams C.Limborg-Deprey Minimum emittance Ellipsoidal electron bunch Comparison with “Beer Can” nominal case Optimization for S-Band and L-Band guns Sensitivity Generation of 3D-ellipsoidal laser pulse Tolerances on “stacker” Simulation Conclusions Is the production of such a pulse realistic?

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Minimum emittance: Intrinsic limits Intrinsic emittance for metal cathode for copper measured 0.6 mm.mrad per mm [1,2,3] theoretical is 0.3 mm.mrad per mm Space Charge Limit Minimum radius or electrons cannot leave cathode for metal cathodes r minimum = 0.82/0.26 mm at 54 MV/m for a 1/0.1nC r minimum = 1.34/0.42 mm at 20 MV/m for a 1/0.1nC RF emittance 10 degrees acceptable for small  RF, gives 0.15 mm.mrad for S-Band For a single slice out of 100, it reduces to nearly 0 Space charge Strong non-linear effects if local charge density varies Ideal Emitted pulse = Uniform charge density inside 3D-Ellipsoid volume Charge density remains constant as the space charge force is linear Perfect emittance compensation is achieved with linear optics elements   space charge ==0

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Ellipsoidal Emission pulse Beer Can shape is not the optimum Ideal Emitted pulse = Ellipsoid Ideally differs from Laser pulse by Shottky effect Electrons are uniformly distributed inside a 3D ellipsoid volume r max = 1.2 mm Pulse length Radius fwhm = 10 ps Pulse length Line Density

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Gun S1S2 L MV/m L MV/m ‘Laser Heater’ ‘RF Deflecting cavity’ TCAV1 3 screen emittance measurement 6 MeV  = 1.6  m  ,un. = 3keV 63 MeV  = 1.08  m  ,un. = 3keV 135 MeV  = 1.07  m  ,un. = 3keV DL1 135 MeV  = 1.07  m  ,un. = 40keV Spectrometer Linac tunnel UV Laser 200  J,  = 255 nm, 10ps, r = 1.2 mm Spectrometer S-Band Gun E peak ~120MV/m S1 L0-1~20 MV/m 6 MeV 63 MeV

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Comparison between“beer can” &“3D ellipsoid” r max = 1.2mm r= 1.2mm

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Comparison between“beer can” &“3D ellipsoid”  = 1.02 mm.mrad;  80% = 0.95 mm.mrad, r = 1.2mm  = 0.71 mm.mrad ;  80% = 0.71 mm.mrad; r = 1mm 3D ellipsoid is even better optimized with r max = 1mm Larger slice emittance for beer can with r = 1mm

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Gaussian Square pulse Ellipsoid with  thermal  = 1.16 mm.mrad  = 2.34 mm.mrad  = 0.75 mm.mrad  = 0.15 mm.mrad no  thermal

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Linear longitudinal Phase Space Beer can 3D-ellipsoid Exit gunEntrance L01 Exit L01 Longitudinal Phase Space Ek [MeV] vs T [ps] The longitudinal phase space gets linear Unfortunately, does not prevent the production of large spikes after bunch compressor  those spikes come from wakefield which follow  ’  ☺☼ lower current density on head and tail might help ☼ LCLS will benefit from lower slice emittance anyway, and better match

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Optimization  = ½(  o  -2  o  +  o ) Smaller r  more mismatch Too short bunch  large mismatch

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Optimization vs pulse length and radius Vs laser pulse lengthVs laser spot size radius Increasing pulse length reduces emittances suggests running 12ps, but too long in LCLS later pulse compression Optimum radius would be between 0.8 and 1mm unfortunately at 0.8 mm, too strong image charge distorts too much the bunch

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Much less sensitive !! Solenoid 1  0.3%  gun  2.5  Solenoid 2% “Beer can”  >  7  Ellipsoid how much distorsion on that perfect shape until we start losing this low sensitivity ? Very low sensitivity to Shottky – Anyway can be compensated for as pulse generated

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Optimization for L-Band Gun 1nC, with little effort in optimizing/retuning  =1.42 mm.mrad;  80% = 1.34 mm.mrad  = 0.93 mm.mrad ;  80% = 0.96 mm.mrad  = 1.02 mm.mrad;  80% = 1.03 mm.mrad L-Band gun 40MV/m,  = 33 ,  at 140 MeV

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Stacking pulses 6+6 beamlets of different radii Gaussians Wash out discrete steps of rms value Interferences

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Fighting interferences in Stacker Alternating polarization + appropriate choice of , interference effect is minimized No interferenceInterferences random phases +/- 15 %

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 PARMELA simulations using stacker distributions Beer Can Direct beer can Ellipsoid ideal 50 Beamlets no interference Stacker 12 Beamlets and random phase  = 1.02 mm.mrad;  80% = 0.95 mm.mrad  = 0.71 mm.mrad ;  80% = 0.71 mm.mrad  = 0.80 mm.mrad;  80% = 0.80 mm.mrad IDEAL NOT IDEAL IDEAL

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Stacker Layout Profile shape r pulse energy control delay line imaging optics collimator- magnifier delay slide grating spectral filters photocathode half waveplate polarizing cube launch mirror To the Courtesy of P.Bolton “what to try to avoid…” from P.Bolton

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Production of the 3D ellipsoidal pulse Two solutions proposed Pulse Stacker Too complex Too lossy Uses too much space Technically feasible with many $$$$$$$ for controls, to achieve alignment, timing measurement to adjust amplitude coefficient Spectral Control technique UV shaping using Four-gratings with masking array in dispersive environment Principle : for highly chirp beam projects (t,x) into a 2D surface Use masking matrix (2D) Projects back in (t,x) A second pair of gratings : same for (t,y) masking technology for UV needs to be developed (transmissive or reflective scheme) fluence limits on optics (even worse upstream) efficiency low probably better for space and money than previous solution

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Spectral Control z y x X mask y mask Chirped input, temporally t x y t To cathode In z,y plane In z,x plane

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Conclusion Ideal emission pulse = “ellipsoid” not “beer can” Perfect emittance compensation in high charge regime Works better at high gradient Impressively less sensitive to tuning parameter tolerances are 1 order of magnitude above those defined for “beer can” pulse even using “stacker pulse” More exploration required for L-Band gun Ellipsoidal Laser pulse is aTechnical challenge maybe not worse than “beer can” generation? if direct UV shaping has to considered anyway for “beer can”, the ellipsoid generation shares many of the same difficulties

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 References [1], Sumitomo Industries [2] B.Graves, DUVFEL [3] J.Schmerge, GTF [4] O.J.Luiten, et al. “How to realize uniform 3- dimensional ellipsoidal electron bunches”, Phys.Rev. August 2004 [5 ]

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Computation of of stacker Alternating polarization + appropriate choice of , interference effect is minimized No interference Interferences assuming random phases +/- 15 %

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 S-Band Gun E peak ~120MV/m S1 L0-1~20 MV/m 6 MeV 63 MeV

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Computation using stacker Distributions with 12 Gaussians run and random phase with PARMELA for the LCLS set-up r = 0.8 mm

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Computation using stacker Distributions with 12 Gaussians run and random phase with PARMELA for the LCLS set-up  = 1.02 mm.mrad;  80% = 0.95 mm.mrad  = 0.71 mm.mrad ;  80% = 0.71 mm.mrad  = 0.80 mm.mrad;  80% = 0.80 mm.mrad  = 1.02 mm.mrad;  80% = 0.95 mm.mrad  = 0.69 mm.mrad ;  80% = 0.69 mm.mrad  = 0.79 mm.mrad;  80% = 0.79 mm.mrad r = 1mm r = 0.9 mm

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Production of the 3D ellipsoidal pulse Two solutions proposed pulse stacker Too complex Too lossy Uses too much space Technically feasible with many $$$$$$$ For controls, to achieve alignment, timing For measurement to adjust coefficient UV shaping using Four-gratings with masking array in dispersive environment ELL_Shaper Principle First pair of gratings : projects (t,x) into a 2D surface Use LCD matrix (2D) for partially masking Projects back in (t,x) A second pair of gratings : same for (t,y) Requires high input power (as low efficiency)

C.Limborg-Deprey ERL Workshop, Jefferson March 20th 2005 Stacking pulses Alternating polarization + appropriate choice of , interference effect is minimized No interferenceInterferences random phases +/- 15 % 12 beamlets Gaussians Wash out discrete steps