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A Resonant, THz Slab- Symmetric Dielectric-Based Accelerator R. B. Yoder and J. B. Rosenzweig Neptune Lab, UCLA ICFA Advanced Accelerator Workshop Sardinia, July 2002

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R. Yoder / ICFA Sardinia Outline Introduction: sketch of the idea Basic theory and features Motivation for experiment Wakefield simulations 3D electromagnetic simulation Experimental prospects

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R. Yoder / ICFA Sardinia Why Slab Geometry? Interested in structures in the mm or FIR regime But— there are well-known limitations: Cavity structures: Wakefields ~ 3, leading to bad transverse dynamics Machining tolerances are tough Accelerating fields limited by breakdown Slab structure: Transverse wakefields strongly suppressed Planar structure easy to build and tune Dielectric breakdown limit potentially easier

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R. Yoder / ICFA Sardinia Slab-Symmetric Dielectric- Loaded Accelerator

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R. Yoder / ICFA Sardinia History Dielectric-loaded slow-wave structure for phase- matching is 20+ years old Inverse Cerenkov accelerator (BNL, Omega-P, Columbia, Dartmouth, …) Dielectric wakefield accelerator (ANL, Yale/Omega-P-- current slab work) Planar dielectric waveguide is now under investigation in mm- wave regime at SLAC (M. Hill et al., PRL 87, 2001) Laser-driven resonant slab-structure proposed at UCLA, 1995– phase velocity not set by dielectric properties (Rosenzweig, Murokh, Pellegrini, PRL 74, 1995) This proposal refined: better accelerating mode quality (Tremaine, Rosenzweig, Schoessow, PRE 56, 1997; Rosenzweig, AAC1998) … but optical dimensions still too difficult to operate Now: new THz power source at UCLA— expt possible!

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R. Yoder / ICFA Sardinia Basic physics of the structures “Infinitely” wide in x conducting wall rr Fields must be independent of x Set = 0 (vacuum wavelength of laser) Coupling Q -1 ~ w/ Coupling slit, width w Dispersion relation: = c 2 (k x 2 + k y 2 + k z 2 ) Want: v z = c, i.e. k z = /c Therefore: since k x = 0, must have k y = 0 in gap Resonant k z values obtained as a function of a, b, r dielectric layer

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R. Yoder / ICFA Sardinia Accelerating Modes In the gap (|y| < a) E ~ e ikz [otherwise Fabry-Perot] k y = 0, so E z is constant in y E = 0 E y ~ k z y In the dielectric (a< |y|< b) E z (y) ~ Asin[k y (b–y)] E y (y) ~ A k z /k y cos[k y (b–y)] A ~ E 0 /sin[k y (b–a)], k y = ( r –1) k z E z = 0 at y = b, E z, E y continuous at y = a (Simplest case: perfect slab)

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R. Yoder / ICFA Sardinia A n n E y (a)/E 0 Solutions for accelerating modes = 340 µm resonator, n = 1, 2, 3 E z /E 0 y (µm) E y /E 0

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R. Yoder / ICFA Sardinia Transverse Wakefield Suppression Short pulse ( = 0.4 ps) Long pulse ( = 4 ps) Simulations using OOPIC 200 pC, r = 120 µm, r = 3.9, a = 0.58 mm, b = 1.44 mm WzWz WW

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R. Yoder / ICFA Sardinia Motivation for an experiment UCLA Neptune Lab: Photoinjector beam with good parameters, well understood (E = 11–14 MeV, n = 6π mm mrad, E/E = 0.1%, 4 ps bunch length, chicane compressor, can focus to ~ 20-30 µm “slab” beam) New THz generation experiment beginning, using Neptune CO 2 laser / MARS amplifier (≤ 100 J/pulse) Opportunity for realistic device dimensions using FIR drive power, and potential multi-MW source

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R. Yoder / ICFA Sardinia Nonlinear Difference Frequency Generation (UCLA Elec Eng — S. Tochitsky, P. Musumeci) 10.6 + 10.3 µm 340 µm Non-collinear phase matching in isotropic gallium arsenide crystal Frequency mixing through choice of face angles GaAs transmits well in 100–1000 µm range Limited by dispersion in crystal, damage threshold CO 2 laser a natural source of frequency doublets Maximum power: 100’s of MW at 340 µm with Neptune laser Other possibilities: use low-power tunable laser for several MW at mm- wave (e.g. 300 GHz) First experiments underway

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R. Yoder / ICFA Sardinia Theory vs. Simulation: accelerating mode Structure Q ~ 600, r/Q = 25 k /m, so field = 30 MV/m at 50 MW

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R. Yoder / ICFA Sardinia Resonant fields in GdfidL, time-domain

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R. Yoder / ICFA Sardinia Time-domain simulation: structure fills

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R. Yoder / ICFA Sardinia Time-domain simulation: structure fills

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R. Yoder / ICFA Sardinia Wakefield simulations OOPIC: use resonant structure from GdfidL with ‘real’ beam Longitudinal wakefield period = 340 µm ! Q = 200 pC, a = 115 µm, b = 145 µm, = 3, y = 25 µm Bunch length 1.2 mm Field mostly washed out Bunch length 120 µm Still only 20 kV retarding potential

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R. Yoder / ICFA Sardinia Wakefield measurements seeing energy change is impossible; maybe misalignment could disrupt the beam with FIR bandpass filter can check resonant frequency try adjusting gap and verifying mode analysis Structure resonances (“cold test”) use coupling slots as bandpass filter Breakdown fields need to see if we can break down structure in small high-power spot Energy change Energy gain set by structure size and Q, details of coupling slots, power available, frequency, and laser spot size. Gains of a few MeV are possible Experiments -- and questions:

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R. Yoder / ICFA Sardinia Conclusions Slab structures are attractive for beam quality and gradient; become practical at (sub-)THz We are simulating and planning experiments for Neptune; theory appears to be backed up by simulation Wakefield is important but will be hard to measure Breakdown limit still to be established Acceleration gradients potentially worth the effort

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