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Flat-Beams and Emittance Exchange P. Emma 1, Z. Huang 1, K.-J. Kim 2, Ph. Piot 3 June 23, 2006 Flat-beam gun can produce >100:1 emittance ratio Smaller emittance ( y ) might approach 0.1 m Longitudinal emittance may also approach 0.1 m Larger z is useful to Landau damp -bunching Can we exchange z ↔ x and produce: ( x, y, z ) = (0.1, 0.1, 10) m, or better? [1] SLAC, [2] ANL, [3] FNAL

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transverse emittance: energy spread: 0.2 m at 1 Å, 15 GeV 0.01% at I pk = 4 kA, K 3.5, u 3 cm, … Long. emittance requirement is: z z 60 m Can we reduce x at the expense of z ? RF gun produces both x ~ z ~ few m FEL needs very bright electron beam…

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Gain Length vs. K of FEL at 0.4 Å x,y 1 m, I pk 3.5 kA, 0.01% x,y 0.1 m, I pk 1 kA, 0.01% assume that the beta function in the undulator is optimized to produce the shortest gain length

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Intrinsic energy spread is too small to be a benefit for x-ray SASE FEL Final long. phase space at 14 GeV for initial modulation of 1% at = 15 m heated beam stays cool beam blows up with no heater A beam heater is required, which Landau damps the CSR/LSC micro-bunching instability

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Very Small Energy Spread is Wasted Ming Xie scaling withoutheaterwithheater LCLS Parameters

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How cold is the photo-injector beam? Parmela Simulation TTF measurement simulation measured E/EE/EE/EE/E 3 keV 3 keV t (sec) 3 keV, accelerated to 14 GeV, and compressed 36 3/14 10 6 36 < 1 10 5 Too small to be useful in FEL (no effect on FEL gain when < 1 10 4 ) H. Schlarb, M. Huening

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Generating a Flat Beam (Y. Derbenev), (R. Brinkmann, Y. Derbenev, K. Flöttmann), (D. Edwards …), (Y.-E Sun) UV light rf gun skew quads experimentsimulation X3X4X5X6X7X8 x 0.4 m y 40 m * * Ph. Piot, Y.-E Sun, and K.-J. Kim, Phys. Rev. ST Accel. Beams 9, 031001 (2006) booster cavity

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Injector Simulation (Astra, Impact-T) 2.6-GHz, 1.5-cell RF gun 138 MV/m peak E-field in gun 8 TESLA SC-cavities at 1.3 GHz (216 MeV) round-to-flat converter of 3 skew quads 3D oblate ellipsoid laser pulse 0.6 m per mm radius thermal emittance 36 MV/m peak E-field in TESLA cavities 300 m rms laser spot size on cathode 50 m rms bunch length (80 fs laser pulse) 20 pC bunch charge (34 A)

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Emittance Levels from Simulation Thermal 2D: (0.6 m/mm) (0.3 mm) 0.23 m Transverse 4D: (0.23 m) 2 0.053 m 2 After skew 4D: (9.9 m) (0.0054 m) 0.053 m 2 Longitudinal 2D: 0.080 m

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K.-J. Kim, NIM, A275, 201, (1989) Space-Charge Effects on Emittance Is the small longitudinal emittance consistent with the space charge force? x 300 m, z 50 m, I 34 A, E 0 138 MV/m, 0 45° z 0.13 m not so different than 0.08 m seen in simulation

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Evolution of Transverse Emittances Along Photo-Injector Beamline (to 216 MeV) acc. cavities rf gun skew quads intrinsic x,y 0.23 m 9.9 m 0.084 m 0.0054 m coupled values x z y

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Longitudinal Distributions After Photo-Injector slice energy spread (rms 4 10 6, 0.9 keV) z = 0.080 m y = 0.0054 m x = 9.92 m E 0 = 216 MeV

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x x yyyy y y xxxx Transverse Distributions After Photo-Injector z = 0.080 m y = 0.0054 m x = 9.92 m E 0 = 216 MeV ??

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Emittance Exchange Concept (2002) Electric and magnetic fields k Transverse RF in chicane… x kx Particle at position x in cavity gets acceleration: kx Must include magnetic field and calculate emittance in both planes x = This energy deviation in chicane causes position change: x = k x kx x k = 1 Choose k to cancel initial position: x kx x k = 1 Cornacchia, Emma, PRST AB 5, 084001 (2002)

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Improved Emittance Exchanger (2005) kk R1R1R1R1 RkRkRkRk R1R1R1R1 System modified by K.-J. Kim, 2005 2L2L2L2L R 56 of dog-leg rectangular RF deflecting cavity x, z mapping (ignore y coordinate here)

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If RF deflector voltage is set to: k = 1/ and transverse (bend-plane) and longitudinal emittances are completely exchanged. Full Emittance Exchange

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Emittance Exchange Limitations 4x4 transfer matrix is four 2x2 blocks 1 : [2]Thanks to Bill Spence. Equal emittances remain equal. (If x 0 = z 0 then x = z. ) Equal, uncoupled emittances cannot be generated from unequal, uncoupled emittances 3. (Setting |A| = ½ produces equal emittances, but then they are highly coupled with 2 0.) [3]E. Courant, in “Perspectives in Modern Physics...,” R.E. Marshak, ed., Interscience Publishers, 1966. [1]K.L. Brown, SLAC-PUB-2370, August 1980. 2

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Parametersymbolvalueunit Electron energy E216MeV Dipole magnet length LBLBLBLB20cm Drift length between dipole magnets L1m Bend angle per dipole magnet 20deg Length of rec. RF cavity LcLcLcLc30cm Initial horizontal norm. emittance x 9.92 mmmm Initial longitudinal norm. emittance z 0.080 mmmm Initial rms bunch length zGzGzGzG51 mmmm Initial rms slice energy spread EGEGEGEG0.9keV Initial energy chirp ( -z slope) h6.9 m1m1m1m1 Initial horizontal beta function xxxx100m Initial horizontal alpha function xxxx0 Emittance Exchanger Parameters

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CSR Suppression with Large Beam Size With this large x and large x, the CSR emittance growth is estimated (1D, elegant) at 0.08 m 0.16 m. x = 100 m zzzz E/EE/EE/EE/E CSR also reduced when horizontal beam size exceeds transverse coherence length:

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Cavity ‘Thick-Lens’ Effect Thick-lens: B y kick, and then x - offset changes add ‘chirp’ to compensate: no mean x -offset l tail head tail head tail head Thin-lens gives no x -offset in cavity

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Energy spread is induced in T-cav due to transverse beam extent ( = kx ) Second-order dispersion is generated in last two bends, which dilutes bend plane ( x ) emittance The right initial energy chirp minimizes the divergence, , after the last bend, which minimizes emittance growth x = 2 x = 2 = kx TcavTcav x = kz Control of Second-Order Dispersive Aberration

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x 2 1/2 The Effect of Initial Chirp Small at System Exit much bigger area increase when large much smaller area increase when small x x The final divergence, , is decreased by the initial chirp shorter bunch in cavity less kick, x = kz, after cavity... For large (left) and small (right), the same x increase produces much larger area increase (emittance growth) when is large ( is Twiss parameter, { 1+ 2 }/ , not energy) x x 0 1/2 min 0 1/2 0 1/2

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Longitudinal Distributions After Exchanger (no CSR) slice energy spread (rms 6 10 5, 13 keV) z = 9.92 m y = 0.0054 m x = 0.084 m E 0 = 216 MeV

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Transverse Distributions After Exchanger (no CSR) x x yyyy y y xxxx z = 9.92 m y = 0.0054 m x = 0.084 m E 0 = 216 MeV

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Transverse phase space (left two plots) and longitudinal phase space (right two plots) before (top) and after (bottom) emittance exchange. BEFORE EXCHANGER AFTER EXCHANGER z 500 m!

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Operating Parameters ValueUnits Bunch charge 20pC Laser rms spot size 300 mmmm Laser rms pulse duration 80fs Peak E-field in rf-gun 138MV/m Launch phase 45deg Peak E-field in TESLA cavities 36MV/m B-field on photocathode 0.191T Cavity off-crest phase 4deg Beam Parameters ValueUnits Before flat beam transformer Transverse emittances 4.96 mmmm Intrinsic transverse emittances 0.23 mmmm Longitudinal emittance 0.071 mmmm Kinetic energy 215.4MeV After transformer Emittance x 9.923 mmmm Emittance y 0.0054 mmmm Longitudinal emittance 0.080 mmmm 0.23 mmmm Operating parameters and ‘achieved’ beam parameters at photo-injector end

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Flat Beam FEL at 0.4 Å Assume und = 3 cm, K = 1.34, x 0.16 m, x,y = 20 m I pk 1 kA, 0.024% at 13.6 GeV (hence z 10 m) Emittance-exchanged beam Round beam x = y 0.16 m Round beam x = y 0.16 m confirmed with Genesis 1.3 Ming Xie, NIMA507, 450 (2003)

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xxxx energy error starts -osc. Unusual System Characteristics k k E/EE/EE/EE/E - tron oscillations disappear Need extremely stable energy (0.5 10 6 rms jitter 10% x -beam size jitter)

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Summary Simulations of flat-beam gun with emittance exchanger suggest possible levels of: z 9.9 m, y 0.0054 m, x 0.16 m Large z -emittance should Landau-damp micro- bunching instabilities Bunch gets longer (50 500 m) and will need to be compressed by 250 to achieve 1 kA CSR needs much closer look Sensitivity to energy jitter may be Achilles heel

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