Cavity Field Maps (TESLA & 3 rd Harmonic Cavity) Undulator Wakes. Estimation of CSR Effects for FLASH2HGHG

Transcription

1 Cavity Field Maps (TESLA & 3 rd Harmonic Cavity) Undulator Wakes Estimation of CSR Effects for FLASHHGHG

2 Cavity Field Maps (TESLA & 3 rd Harmonic Cavity) 3D field map files for ASTRA in E3D format files are available on home page TESLA field maps more info (= discrete coupler kicks) in: 3 rd harmonic cavity new calculations from E. Gjonai(DG, nd and 3 rd order)

3 orientation: origin: in the middle of cell 5 (= middle of cavity) files: E3D_3_9GHz-order.dat E3D_3_9GHz-3order.dat E3D_3_9GHz-order_yrot.dat E3D_3_9GHz-3order_yrot.dat nd order, orientation 1 3 rd order nd order, orientation 3 rd order mesh: x/m from to with stepwidth/m = y/m z/m in 060 steps discrete coupler kicks: see document

4 Undulator Wakes matlab function for longitudinal wake of undulator function [ Kern ] = kern_undulator( xy_param,z_param,du,nu1,nu,gamma,lambda_u,k ) calculates kernel function for undulator trajectory for finite and infinite undulator, local or periode-averaged (only for infinite undulator), 1d beam or cross-section averaged, on axis or offset (for 1d beam) space charge contribution is excluded by approach as for all 1d CSR models: rigid bunch approximation!!! it calculates wake kernel for longitudinal field: E( ( test-length) test) e( test) period averaged: E( ( test-length) test) e( test) test E( ( test-length) test) e 0 z test it is essentially tail head interaction but: for 3d and/or offset, there is a head tail contribution!!!

5 files and docu: undulator_docu.ppt (definition, docu& examples) Two Methods for the Calculation of CSR Fields (TESLA-FEL ) kern_undulator.m Matlab example1.m example conv_fft.m convolution example: γ = 500MeV / c β = β = 10 m = c = 0 m o ε = ε = 1µm γ c c x x xx xy y y yy = ε β x x bunch 1: q λ( s) = exp πσ s q = 0.5 nc cq πσ s = ka 1 s σ s λ bunch : ( s) = exp ( 1+ mcos( ks) ) q = 0.1nC cq πσ s q πσ s = ka 1 s σ s m = 0.0 k = π/ ( 800 nm)

6 FLASH, SEEDING undulator infinite undulator, periodic wake, Nav= 50 bunch1 (0.5 nc), coarsedu = 1 µm, finedu = 0.5 µm γ = 500MeV / m c λ = 3.15 cm u K =.83 o bunch (0.1 nc, modulated), du = µm bunch (0.1 nc, modulated), du = µm, Nsigma= 4, Nstep= 5 bunch (0.1 nc, modulated), du = µm, (Nsigma= 3, Nstep= 13)

7 Estimation of CSR Effects for FLASHHGHG beam: energy ~ 1 GeV current ~ 1 ka slice energy spread ~ 0.15 MeV modulation wavelength ~ 66 nm modulation amplitude ~ 0.75 MeV sigma_x(before chicane) ~ 110 um norm. hor. slice emittance ~ 0.6 um norm. vert. slice emittance ~ 0.7 um chicane: magnet length = 0.1 m drift length = 0.5 m middle drift = 0. m curvature radius (in magnets) ~ 14.5 m R56 ~ 53 um

8 some estimations: charge in one wavelength q λ λ = I 0.89 pc c half of that charge can be compressed q = q λ (3) rms length after ideal compression σ = r56 σ E E 8 nm (1) scaling of steady state csr of gaussian bunch 5 MV/m current spikes Iˆ = cq 6.7 ka πσ (3) rms length with smearing σ ( r σ E ) = 56 E + r51σ x + r51r 5 xx + + r5σ x ( r σ E ) + ( z / R) σ 56 E x () (1) required resolution () required step width σ<< σ(0) (3) rough estimation

9 steady state csr integrated steady state csr

10 CSRtrack simulation: required resolution ~ 7 nm << σ min = r 56 σ E /E required step width ~ 0.3 mm << R magnet σ min /σ x simulation of a short sub-range length = 16 um 1E6 particles gaussianprofile with 6σ= 16 um

11 without self effects E λ/(r 56 ).5 MeV slice ~ 5 wavelength norm. hor. slice emittance = um norm. vert. slice emittance = um

12 with self effects E λ/(r 56 ).5 MeV slice ~ 5 wavelength norm. hor. slice emittance = um norm. vert. slice emittance = um