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Simulation of Edge and Diffraction Radiation Propagation in the LCLS Bunch Length Monitor Radiation sources Simulation of radiation propagation Bunch length sensitivity of detector signals 10 April 2006 BIG Meeting Henrik Loos [email protected] Layout Diagnostics Focusing DR Bend 200mm 10mm ER SR Mirror Focusing f = 200mm 200mm 10 April 2006 BIG Meeting Henrik Loos [email protected] 38mm Bunch Form Factor Form Factor Bunch length determined by low frequencies Expansion of FF f(k) = 1 – k2 σrms2 λ » 2πσrms BC1: 1cm – 1mm BC2: 1mm - .1mm 10 April 2006 BIG Meeting BC1 FF BC2 FF BC1 Exp BC2 Exp 1 0.8 0.6 0.4 0.2 0 -1 10 10 0 1 10 Wave Number (cm-1) 10 2 Henrik Loos [email protected] 10 3 BC1 Radiation Distribution 10 April 2006 BIG Meeting 0 y (mm) 1 2 3 4 5 -5 Horizontal Pol. 0 5 10 15 x (mm) 20 25 30 20 25 30 0 1 y (mm) Wavelength 1mm 200mm downstream of BC1 Near field integration of “acceleration field” Edge length « λγ² Mainly ER from both bend edges, 4x larger than SR Radiation from Entrance edge hits vacuum chamber 2 3 4 5 -5 Vertical Pol. 0 5 10 15 x (mm) Henrik Loos [email protected] Radiation Simulation Intensity Treat ER as TR Take virtual quanta transverse distribution and propagate radiating part through optical system. E(r) = K1(kr/γ) Radiating part at γ→∞: E(r) = (1-J0(kr))/kr Max intensity at r = λ Intensity falls off at r = γλ 10 April 2006 BIG Meeting 10 10 10 10 10 2 λ = 1mm γ = 500 0 -2 -4 -6 10 -2 10 -1 10 0 10 1 r (mm) Henrik Loos [email protected] 10 2 10 3 Propagation with Gauss-Laguerre Modes 10 April 2006 BIG Meeting Horizontal polarization at magnet edge -20 λ = 1cm γ = 500 -10 y (mm) Use Gauss-Laguerre modes with radial mode number 1 for field of each polarization Needs γ/2 transverse modes to get correct far field distribution 0 10 20 -20 -10 0 x (mm) Henrik Loos [email protected] 10 20 BLM11 Layout Detector 10mm Lenses, f = 300mm Window 100mm BX14 e-Beam 38mm 15mm 200mm 10 April 2006 BIG Meeting Henrik Loos [email protected] CER Transmission Through Optics 40 7 20 at detector 6 10 0 0 Beam Radius (mm) 3 cm-1 15 cm-1 30 200 80 400 600 Position (mm) 800 3 cm-1 15 cm-1 60 Transmission (%) Transmission (%) For one polarization, normalized to total 2π emission 5 4 3 2 40 1 20 0 0 10 April 2006 BIG Meeting 200 400 600 Position (mm) 800 0 0 20 40 60 80 -1 Wavenumber (cm ) Henrik Loos [email protected] 100 Transverse Profile Through Optics Radius (mm) 50 3 cm-1 40 30 20 10 0 100 200 300 400 Dist (mm) 500 600 700 800 500 600 700 800 Radius (mm) 50 15 cm-1 40 30 20 10 0 10 April 2006 BIG Meeting 100 200 300 400 Dist (mm) Henrik Loos [email protected] Interference of CER and CDR 10 April 2006 BIG Meeting 10 Transmission (%) Get field at detector for CER and CDR CDR is not focused on detector Wave front curvature differs from CER Intensity at detector shows narrow fringe pattern Fringes much faster than changes in formfactor CDR can be ignored 8 6 4 CER CDR CER+CDR 2 0 10 12 14 16 18 -1 Wavenumber (cm ) Henrik Loos [email protected] 20 Spectral Efficiency and Bunch Form Factor 1 Pyro Fused Silica CER Quartz Transmission 0.8 0.6 0.4 0.2 0 0 10 20 30 40 50 60 Wavenumber (cm-1) 70 80 90 100 1 26 um 54 um 82 um 111 um 141 um 170 um 200 um Form factor 0.8 0.6 0.4 0.2 0 0 10 April 2006 BIG Meeting 10 20 30 40 50 60 Wavenumber (cm-1) 70 80 90 100 Henrik Loos [email protected] Bunch Length Sensitivity of Detector Signal Introduce high and low pass filters at 10cm-1 and 20cm-1. Low signal for long bunches More transmission of radiation below 10cm-1 needed 4 26 um 54 um 82 um 111 um 141 um 170 um 200 um Efficiency (%) 5 4 3 2 Detector Signal 6 no hp10 hp20 lp10 lp20 3 2 1 1 0 0 10 10 April 2006 BIG Meeting 20 30 40 Wavenumber (cm-1) 50 60 0 0 50 100 150 Bunch Length (m) Henrik Loos [email protected] 200 Summary Study of proposed bunch length monitor after BC1 Main radiation source is edge radiation Simulation of radiation transmission from dipole edge to detector Hole in out-coupling mirror is acceptable Small apertures in optical system cut radiation below 10 cm-1 Monotonic dependence of detector signal to bunch length Good sensitivity for shorter bunches at 200pC but could be problematic for longer bunches at 1nC 10 April 2006 BIG Meeting Henrik Loos [email protected]