Longitudinal Space Charge Instability C. Limborg-Déprey, Z. Huang, J Longitudinal Space Charge Instability C.Limborg-Déprey, Z.Huang, J.Wu, SLAC T.Shaftan, BNL September 24, 2003 LSC observed experimentally Theory Application to LCLS Comparison theory with Simulations Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

DUV FEL TTF W.S. Graves, et al., PAC 2001, p. 2860 M. Huning et al., NIM A 475 (2001) p. 348 TTF Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Motivations Experimental Theory TTF observations M. Huning et al., NIM A 475 (2001) p. 348 DUVFEL observations W.S. Graves, et al., PAC 2001, p. 2860 T.Shaftan et al. experiments at the DUVFEL T.Shaftan et al., PAC03, “Micro-bunching and beam break-up in the DUV FEL accelerator”, also in FEL03 with modeling of mechanism discussed in March at SLAC Z.Huang, T.Shaftan, SLAC-PUB-97, May 2003 Theory Saldin , Schneidmiller, Yurkov, “Longitudinal Space Charge Driven MicroBunching Instability in TTF2 Linac” TESLA-FEL-2003-02,May 2003 Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

The DUVFEL Accelerator RF gun 4.5 MeV Tank 1 Tank 2 Tank 3 Tank 4 35 MeV 75 MeV Spectrometer dipole Chicane Monitor Beam Dump Drive Laser to FEL Positive RF slope Accelerate bunch at RF zero-crossing of tank 4 Spectrometer dipole Zero RF slope Negative Size of the chirped beam image at the monitor 14 is proportional to the bunch length ! Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

The DUVFEL Accelerator Structure with a Large Number Spikes “Zero-phasing” image of uncompressed bunch with a large number of sharp spikes Energy spectrum, derived from the image, horizontal axis is scaled in picoseconds Time or Energy? Frequency spectrum of upper plot. Spectrum shows modulation with harmonics in THz range. Harmonics  sharpness of the spikes. Time, ps Frequency spectrum (THz) Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Modulation dynamics with Compression (~300 pC) Dynamics at “high” (>200 pC) charge differs from the dynamics at “low” charge Uncompressed bunch profile is smooth Experiment on modulation dynamics: Keep chicane constant and increase chirping tank phase (0-13-19-25 degrees) Modulation shows up during compression Process Compression: a} decreases modulation period (C times); b) increases bunch peak current (C times) 100 0° 1.42 ps 50 2 4 6 8 100 -13° 1.24 ps 50 1 2 3 4 5 200 -19° 0.93 ps 100 1 2 3 4 -25° 0.43 ps 200 Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Isolines of constant bunch length This is not CSR! Isolines of constant bunch length CSR-related effect ?  should be sensitive to the bending radius in the chicane magnets Experiment: final bunch length maintained constant while chicane strength changed Compression factor is 1-hR56  there is always a combination of h and R56 that will maintain a constant compression ratio Result of the experiment: in general the modulation is insensitive to the chicane settings 5 10 15 20 25 30 35 40 50 60 70 Tank 2 Phase (Degree) Chicane Current (A) 0.1 0.3 0.6 1 1.2 1.5 1.7 Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Plasma Oscillation in a Coasting Beam Current Density Energy The self-consistent solution is the space charge oscillation Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Longitudinal Space Charge Impedance For a round, parallel electron beams with a uniform transverse cross section of radius rb, the on-axis longitudinal space charge impedance is (cgs units) Free space approximation is good when  /(2) << beam pipe radius Off-axis LSC is smaller and can increase the energy spread Longitudinal Space Charge Impedance (pancake beam) (pencil beam) Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Integral Equation Bunching parameter b at modulation wavelength l = 2p/k Linear evolution of b(k;s) can be described by an integral equation (Heifets, Stupakov, Krinsky; Huang & Kim) For arbitrary initial condition (density and/or energy modulation), this determines the final microbunching Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Including acceleration beam energy r(s) increases in the linac. Generalize the momentum compaction R56’(! s) as the path length change at s due to a small change in  (not ) at : for r À 1 The integral equation for LSC microbunching in the linac is In a drift,  Space charge oscillation When ! 1, R56’=0, b(k,s)=b0(k,s), beam is “frozen” Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Space Charge Oscillation – 2 regimes Density and energy modulation in a drift at distance s At a very large , plasma phase advance (s/c) ¿ 1, beam is “frozen,” energy modulation gets accumulated (Saldin/Schneidmiller/Yurkov, TESLA-FEL-2003-02) LSC acts like a normal impedance at high energies Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Klystron Amplitfication mechanism Saldin, Schneidmiller, Yurkov R56 ri Z(k) Dg rf Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Gain is high enough to amplify the shot noise bunching LCLS Set-UP 3 keV intrinsic energy spread is too small for the high-frequency LSC Gain is high enough to amplify the shot noise bunching Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Solution = Wiggler before BC2 Only CSR Solution = Wiggler before BC2 CSR + LSC Peak gain increased by a factor of 3 Solution = Adding Energy Spread on beam before BC1 “laser heater” 3 keV-> 30 keV before BC1 Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Even More Landau Damping Current design has energy spread 1x10-4 for the FEL Since FEL  ~ 5x10-4, small increase in energy spread is allowed, say 1.7x10-4 Laser heater increases energy spread 3 keV  50 keV Wiggler increases energy spread to 5x10-5 at 4.5 GeV Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Real danger is in fact energy spread >  = 5.10-4 Wiggler   Laser   Elegant (from M.Borland) Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

All the simulations are based on theory just described Let’s compare this theory with results from space charge simulation codes Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Simulations Simulations description +/- 5% 40k/200k particles Distribution generated using the Halton sequence of numbers Longitudinal distribution 2.65 m of drift With 3 cases studied 6MeV, 1nC 6 MeV , 2nC 12 MeV, 1nC +/- 5% Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Half a plasma period, 12 MeV, 1nC,  = 250 m Oscillation of density characterized by “ modulation amplitude” current density  energy But, 1- Residual energy modulation after half a period 2- Line density modulation amplitude strongly increased Two parameters have also evolved along the beamline : - uncorrelated energy spread - transverse beam size Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

6 MeV, 2nC,  = 100 m 30 cm 65 cm 110 cm Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

150 cm 190 cm 230 cm 265 cm Shift + broadening Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Evolution with energy 6 MeV , +/- 5% 12 MeV , +/- 5% ½ plasma period shorter for shorter wavelengths line density modulation  with shorter wavelengths Energy modulation  with shorter wavelengths Amplitude Energy modulation gets larger than for 6 MeV Uncorrelated energy spread gets larger by 60% Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Comparison with theory Transverse beam size evolution along beamline taken into account (Radial variation of green’s function for 2D ) Evolution of peak current NOT taken into account yet Absence of dip in 6MeV curve : “Coasting beam “ against “bunched beam” with edge effects Intrinsic energy spread Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Evolution transverse profile 6 MeV , 1nC, +/- 5% Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

3D model – impedance with r dependency 1-D model: transverse uniform pancake beam with longitudinal modulation where, rb is the radius of the pancake beam. need to find realistic effective rb radius dependence of impedance increases energy spread and so damping define Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

LSC in accelerating structures Initial beam 6MeV No energy spread, Current modulation M drift 67 cm Linac 3m linac 3m drift 1m Summary PARMELA simulations Summary Theory [Huang,Wu] Courtesy of Z.Huang Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

LSC in gun Modulation introduced on the laser (as in real life) Difficulties to study the effect for the LCLS pulse Study of  = 50 m , dz = 5 m z ~ 5 mm Nz x Nr ~ 1000 x 20 200k particles Per longitudinal bin ~ 200 particles , 1/200 ~7%  For initial modulation of less than 7% modulation of current density at gun exit is in noise Case studied :  = 50 m, 100 m, 250 m, 500 m, 1000 m For +/-10% and +/- 20% initial modulation amplitude Other cases under study  < 50 m but for a shorter pulse than the LCLS pulse Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

+/-5% , = 50 m C.Limborg,Z.Huang,T.Shaftan,J.Wu Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

+/-5% , = 100 m +/-5% , = 250 m C.Limborg,Z.Huang,T.Shaftan,J.Wu Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

+/-5% , = 500 m +/-5% , = 1000 m Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

+/-10% +/-20% C.Limborg,Z.Huang,T.Shaftan,J.Wu Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Noise Level = 4% C.Limborg,Z.Huang,T.Shaftan,J.Wu Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

LSC along the LCLS Modulation introduced on the laser (as in real life) Difficulties to study the effect for the LCLS pulse Study of  = 50 m , dz = 5 m z ~ 5 mm Nz x Nr ~ 1000 x 20 200k particles Per longitudinal bin ~ 200 particles , 1/200 ~7%  For initial modulation of less than 7% , modulation in noise Case studied :  = 50 m, 100 m, 250 m, 500 m, 1000 m For +/-10% and +/- 20% initial modulation amplitude Other cases under study  < 100 m but for a shorter pulse than the LCLS pulse Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

At end LCLS injector beamline: Current density modulation strongly attenuated residual energy oscillation has amplitude between 2 keV and 4 keV for wavelengths [50 m, 500 m] Impedance defined by Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Conclusion Good agreement Simulations / Theory for drift and Acceleration Discrepancies are under investigation Intrinsic energy spread increase Edge effects for bunched beam More comparisons simulations /theory in high energy regime Difficulties to do simulations for small modulation amplitude Noise Problem Shorter wavelengths, not enough particles More comparisons experiments / simulations “Attenuation” in gun might make situation not as critical as first thought But not enough attenuation : extrapolation from 10% case for wavelengths >100 m : attenuation line density modulation by factor of 3 for wavelengths <100 m : attenuation line density modulation by factor of 4 Beam Heater is under discussion for the LCLS beamline Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

DISCUSSION ON EXPERIMENTAL RESULTS AT DUVFEL from T.Shaftan et al. Theory Institute, ANL , 24 September 2003 C.Limborg,Z.Huang,T.Shaftan,J.Wu

Modulation analysis An example of the chirped beam image. One of the interesting features here is evolution of the modulation wavelength along the bunch, corresponding to nonlinear chirp. Interpretation of double peaks on the left: “overmodulated” periods. Every couple of double spikes in this region represents a single modulation period. Tail of the bunch is folded back over, introducing bright region on the right side of the image (space charge). “Analysis of space charge driven modulation in electron bunch energy spectra”, T. Shaftan and L.H. Yu, BNL preprint.

“Overmodulation” effect Measuring distance E between “double spikes” we can determine amplitude of the energy modulation. where is the energy modulation,  is the modulation frequency “Analysis of space charge driven modulation in electron bunch energy spectra”, T. Shaftan and L.H. Yu, BNL preprint.

Sensitivity to the Transverse Beam Size large linac beam (1 mm) Space charge force is a function of rb Change the beam size of the compressed beam along the accelerator  effect on modulation ? 200 A 40 A small linac beam (250  m) 20 40 60 80 100 5 10 15 25 30 35 G a 200 A 40 A Analytical calculations of “gain” in the modulation by Z. Huang 3 different lattice solutions  3 different RMS beam sizes along the accelerator

Results of the Experiment “Zero-phasing” profiles of the beam (300 pC) for different lattice solutions: Average RMS beam sizes along the accelerator: 0.25 mm, 0.5 mm, 1 mm

IR Radiation Measurements Does modulation enhance any bunching in the bunch longitudinal density ? Experiment: Change the beam size  “modulated” and “non-modulated” bunch profiles We measured CTR from metallic mirror, using IR detector and low-pass IR filters (cut-off of 40 µm, 100 µm, 160 µm) Modulation wavelength = 90 µm (from “zero-phasing”)  expect enhancement of the coherent IR power in this spectral region if bunching Result of the experiment: No difference is found between“modulated” and “non-modulated” beam conditions “Modulated” bunch profile “Non-modulated” bunch profile Bolometer signal, uVs Filters: >40 um >100 um >160 um Wavelength, um

Dependence on Energy 60 MeV 80 MeV 110 MeV Space charge force is a function of  Change the energy of the compressed beam (300 pC) along the accelerator   effect on modulation ? Vary tank 3 energy, maintaining the same all other beam parameters (bunch length, transverse beam size, charge) 80 MeV 110 MeV

(I) Results of the experiment Number of modulation periods and modulation wavelength for different energies is different ! Product is constant: bunch length is the same for different energies Why ? “Experimental investigation of a space charge induced modulation in high-brightness electron beam”, T. Shaftan and Z. Huang, BNL-71491-2003-JA

Model of “Modulation versus Energy” experiment 3 m long linac section Space Charge “kicks” “Initial phase space” Beam: 70 MeV and other parameters of the experiment Slippage “kicks” “Final phase space”, spectrometer Assumptions: 1) Do not take into consideration bunch prehistory before chicane. We did not change anything but energy using tank after chicane. 2) Initial conditions at the end of the chicane  no initial energy modulation, certain amount of initial density modulation (spectral shape is unknown)

(II) Results of the experiment 50 MeV Simulated normalized spectra of energy and density modulations for 50 MeV and 110 MeV With energy increase average spectral frequency of energy modulation shifts toward higher freq. range Therefore modulation wavelength decreases and number of modulation periods increases for higher energy Another words: Plasma oscillations at different frequencies accumulate different phase advance while the bunch travels down to the accelerator. Initial density modulation Final energy modulation Final density modulation Initial density modulation Final energy modulation Final density modulation “Experimental investigation of a space charge induced modulation in high-brightness electron beam”, T. Shaftan and Z. Huang, BNL-71491-2003-JA 110 MeV