1. 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

2. 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…

3. 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

4. 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

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

6. How cold is the photo-injector beam? Parmela Simulation TTF measurement simulation measured E/EE/EE/EE/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

7. 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

8. 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)

9. 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

10. 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

11. 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

12. 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

13. x x yyyy y y xxxx Transverse Distributions After Photo-Injector  z = 0.080  m  y = 0.0054  m  x = 9.92  m E 0 = 216 MeV ??

14. 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)

15. 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)

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

17. 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

18. 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 mmmm Initial longitudinal norm. emittance  z 0.080 mmmm Initial rms bunch length zGzGzGzG51 mmmm Initial rms slice energy spread EGEGEGEG0.9keV Initial energy chirp (  -z slope) h6.9 m1m1m1m1 Initial horizontal beta function xxxx100m Initial horizontal alpha function xxxx0 Emittance Exchanger Parameters

19. 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 zzzz E/EE/EE/EE/E CSR also reduced when horizontal beam size exceeds transverse coherence length:

20. 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

21. 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

22.  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

23. 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

24. Transverse Distributions After Exchanger (no CSR) x x yyyy y y xxxx  z = 9.92  m  y = 0.0054  m  x = 0.084  m E 0 = 216 MeV

25. 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!

26. Operating Parameters ValueUnits Bunch charge 20pC Laser rms spot size 300 mmmm 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 mmmm Intrinsic transverse emittances 0.23 mmmm Longitudinal emittance 0.071 mmmm Kinetic energy 215.4MeV After transformer Emittance  x 9.923 mmmm Emittance  y 0.0054 mmmm Longitudinal emittance 0.080 mmmm 0.23 mmmm Operating parameters and ‘achieved’ beam parameters at photo-injector end

27. 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)

28. xxxx energy error starts  -osc. Unusual System Characteristics k k E/EE/EE/EE/E  - tron oscillations disappear Need extremely stable energy (0.5  10  6 rms jitter  10% x -beam size jitter)

29. 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