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THz generation and transport Sara Casalbuoni DESY Hamburg

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S. Casalbuoni, DESY Overview Motivation Design goals Simulation tools - POP ZEMAX - Mathematica code (B. Schmidt, DESY) THz beam extraction Optical design Simulation of the THz radiation transfer line Summary and outlook

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S. Casalbuoni, DESY Motivation CDR/CTR 140 m, = 1000, E el = 500 MeV Bunch length measurements with interferometer

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S. Casalbuoni, DESY Design goals Flat frequency response Low frequency response limit as low as possible BUT –Finite dimensions of transfer line tube and mirrors ( ɸ ≈ 200mm) –Long transfer line ~20m High frequency structures expected from μbunching up to 30THz(10μm)

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S. Casalbuoni, DESY 30THz Diamond window

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S. Casalbuoni, DESY Vacuum needed from B. Schmidt

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S. Casalbuoni, DESY Simulation Tools ZEMAX Commercially available POP (Physical Optic Propagation) B. Schmidt (DESY) Mathematica 2 CODES Huygens-Fresnel principle : Every point of a wave front may be considered as a centre of a secondary disturbance which gives rise to spherical wavelets, and the wave-front at any later instant may be regarded as the envelope of these wavelets. The secondary wavelets mutually interfere. ƞ ξ y x L d first order second order Fraunhofer near field, Fresnel ≃L finite size screen Kirchhoff integral

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S. Casalbuoni, DESY Input for CTR Fourier Transform with respect to the longitudinal coordinate ζ=z-vt of the radial electric field E r of a uniform bunch charge distribution of radius ρ moving with velocity v in straight line uniform motion (M. Geitz, PhD Thesis).

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S. Casalbuoni, DESY Ginzburg-Frank Valid: - if CTR screen radius ≳ effective CTR radius a ≳ λ -if L ≫ λ 2 ⇒ far field (Castellano & Verzilov, Phy.Rev.ST-Accel. Beams,1998) ⇒ frequency independent

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S. Casalbuoni, DESY from P. Schmüser Both conditions satisfied =300 μm L=10m a=30mm

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S. Casalbuoni, DESY from P. Schmüser Finite size CTR screen =1.5mm L=20m a=30mm

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S. Casalbuoni, DESY from P. Schmüser Near field =300 μm L=0.5m a=30mm

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S. Casalbuoni, DESY L=0.5m a=30mm from P. Schmüser Both conditions violated =1.5mm and exact SQRT

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S. Casalbuoni, DESY ZEMAX Commercially available POP (Physical Optic Propagation) B. Schmidt (DESY) Mathematica Both make use of scalar Fresnel diffraction theory 2 CODES Valid if objects and apertures >> λ |x-ξ|,|y-η|<<L ξ ƞ x y L Fourier transform of Simulation Tools

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S. Casalbuoni, DESY Free propagation if a ≲ λ and/or L ≲ λ 2 ⇒ I (x, L,ω) frequency dependent L=1 m; a=10 mm; =1000

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S. Casalbuoni, DESY Dimensions of the CTR screen window =20mm L=40mm; =1000 λ=1.5mm ⇒ f=200GHz

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S. Casalbuoni, DESY CDR screen intensity @window/@screen 0.75 0.55 0.78 20 mm ɸ=20 mm, slit=1mm ʘʘ ʘ window =20mm L=40mm; =1000 λ=1.5mm ⇒ f=200GHz ɸ=20 mm

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S. Casalbuoni, DESY Optical design: technical drawing from O. Peters

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S. Casalbuoni, DESY Optical design CTR screen ɸ =25mm diamond window ɸ =20mm M1 f=630mm ɸ =188mm M2 f=4500mm ɸ =188mm M3 f=3500mm ɸ =188mm M4 f=3000mm ɸ =188mm M5 f=100mm ɸ =100mm final screen 40mm 560mm 3410mm 8990mm 3100mm 2400mm 100mm M1 600mm M2 M3 M4 M5 8990mm 2400mm 100mm 3100mm 3410mm

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S. Casalbuoni, DESY Simulation of the THz radiation transfer line with ideal thin lenses λ=1.5mm ⇒ f=200GHz; =1000 Intensity @final screen/@window=0.49 CTR screen ɸ =25mm Diamond window ɸ =20mm M1 M2 M3 M4 M5 final screen ɸ =8mm

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S. Casalbuoni, DESY Simulation of the THz radiation transfer line with ideal thin lenses λ=1.5mm ⇒ f=200GHz =1000 CTRscreen ɸ =25mm Diamond window ɸ =20mm Intensity @final screen/@window=0.49

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S. Casalbuoni, DESY Good also for a Gaussian beam λ=1.5mm ⇒ f=200GHz =1000 CTRscreen ɸ =25mm Diamond window ɸ =20mm

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S. Casalbuoni, DESY Simulation of the THz radiation transfer line at different frequencies Intensity @final screen/@window 0.49 0.90 0.99

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S. Casalbuoni, DESY Transfer function λ(mm) 3 0.3 0.03

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S. Casalbuoni, DESY Half screen and horizontal polarization: frequency response Intensity @final screen/@window 0.52 0.91 0.99 ʘ

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S. Casalbuoni, DESY Gaussian beam λ=500nm M3 M4 M5 final screen w 0 =1mm Diamond window ɸ =20mm M1 M2

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S. Casalbuoni, DESY Summary and outlook 2 simulation tools: very good agreement Optical design for the THz beam line transfer @140m in TTF2: tested for CTR, CDR and Gaussian beam Outlook -”ideal” mirror surface -tests for stability against beam displacement and mirrors misalignment -effect of tilting CTR screen

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S. Casalbuoni, DESY Electric field of a charge in the laboratory system q observation point θ ⃔

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S. Casalbuoni, DESY L ≫ λ 2 ⇒ far field characteristic size of the CTR screen

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S. Casalbuoni, DESY Paraboloid mirrors CTR screen ɸ =25mm Diamond window ɸ =20mm M1 M2 M3 M4 M5 final screen

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S. Casalbuoni, DESY Paraboloid mirrors

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S. Casalbuoni, DESY Transfer function

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S. Casalbuoni, DESY Paraboloid mirrors: half screen and horizontal polarization Half CTR screen ɸ =25mm Diamond window ɸ =20mm M1 M2 M3 M4 M5 final screen Intensity @final screen/@window 0.64

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