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Photonic Band Gap Accelerator Demonstration at MIT. Evgenya Smirnova Massachusetts Institute of Technology UCLA, January 2005. Outline. Motivation: accelerator applications of photonic band gap (PBG) structures. Photonic band gap structures: definition and examples.
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Photonic Band Gap Accelerator Demonstration at MIT Evgenya Smirnova Massachusetts Institute of Technology UCLA, January 2005
Outline • Motivation: accelerator applications of photonic band gap (PBG) structures. • Photonic band gap structures: definition and examples. • Theory of PBG structures and resonators. • 2D PBG resonators testing. • PBG accelerating structure: cold test • PBG accelerator demonstration
X- and K-band accelerators • High efficiency accelerators are needed • Energy stored in accelerator structure decreases with frequency • Wakefields increase with frequency as f 3 • PBG structure is effective for damping wakefields Idea and first PBG experiments: D.R. Smith et al., AIP Conf. Proc. 398, 518 (1997).
Photonic band gap structures A photonic bandgap (PBG) structure is a one-, two- or three-dimensional periodic metallic and/or dielectric system (for example, of rods).
Band Gaps PBG structure arrays reflect waves of certain frequencies while allowing waves of other frequencies to pass through. Band Gaps 1D example: Bragg reflector
PBG resonators and waveguides 2D PBG structures (arrays of rods) are of main interest for accelerator applications. If a wave of certain frequency cannot propagate through a photonic crystal wall, then a mode can form in a crystal defect. This way we can construct a PBG resonator or PBG waveguide. PBG resonator PBG waveguide Higher order mode PBG resonator
Maxwell equations in PBG structures Field in PBG structures satisfies Maxwell’s equations: must satisfy the Floquet theorem 2D square lattice: m,n - integers Maxwell equations solved
Solving Maxwell’s equations Finite difference method (metals) Plane wave method (dielectrics) Fourier series expansion takes into account periodic boundary conditions Derivatives: Periodic boundary conditions:
Brillouin zone and Brillouin diagram Irreducible Brillouin zone is periodic, only Brillouin zone inside the Brillouin zone matter. Brillouin diagram: plotted along the Irreducible Brillouin zone boundary
a b Global Band Gaps Global band gap: wave cannot propagate in all directions. Example of band gap diagram: square lattice of metal rods, TM waves
PBG resonators In the presence of band gaps a defect in a PBG structure may form a resonator: PBG cavity formed by a defect PBG resonators can be studied with many commercial and freeware electromagnetic solvers, such as Superfish, HFSS, Mafia, Microwave Studio, MPB etc.
Operating Point of PBG structure • Mode selectivity in PBG resonators PBG Cavity, triangular lattice a/b=0.15, TM01 –like mode 2a b Single mode operation. No higher order dipole modes. This structure is employed for the MIT PBG accelerator Pillbox Cavity, TM01 mode
HOM in PBG resonators Only a single mode confined for 0.1a/b 0.2
Cold test results Propagation band (no modes confined) Dipole TM11mode (confined) Band gap TM01 mode TM01 mode No confined wakefield modes. Good for accelerators Confined TM11 mode Bad for accelerators
Brazed PBG resonator Theoretical QHFSS(TM01) = 5300 Measured Qmeasured (TM01) = 2000 Reason for low Q: poor contact between rods and end plates How to improve Q ? Brazing Electroforming A resonator was brazed at CPI: Qbrazed (TM01) = 5000
Accelerator with PBG cells • Design the structure • ● Choose the accelerator parameters • ● Tune the cell to 17.137 GHz • ● Tune the coupler • Cold test the structure ● Tune the coupler ● Tune the cell to 17.137 GHz • Hot test the PBG accelerator
HFSS: accelerator design tool • Accuracy driven adaptive solutions • Optimization tools • Powerful post-processor • Macro language control of calculation.
Dimensions 2 /3 traveling wave cell: L/c = 2 /3 Iris radius scaled to 17 GHz from the SLC design
Tolerances Both: the coupler cell and the TW cell, are sensitive to the rods radii and spacing. Fabrication tolerance of 0.001’’ is a must. Tuning in the cold test is needed.
Electroformed PBG structure PBG accelerator was electroformed by Custom Microwave, Inc. (www.custommicrowave.com). Rods and plates of each cell were grown as a single crystal without connections. The cells were brazed together.
Initial coupling measurements • Measured coupling curves were 40 MHz high. • Two cells of the structure were 20 MHz lower than other cells. Tuning was performed via etching.
Etching Etching was performed in Material Science and Technology division, Los Alamos National Laboratory. Acid solution: 100 ml nitric acid, 275 ml phosphoric acid, 125 ml acetic acid. Masking material: jack-o-lantern candle wax. Etching time: 1 min per 0.0001’’. Etching temperature: 45 C.
Final cold test results • Good agreement between measurement and computation. • Flat field profile in accelerating mode. Measured field profile (bead pull)
MIT PBG experiment setup Beam line PBG Chamber
Accelerator laboratory Linac Load Klystron Spectrometer Coupling waveguide PBG chamber
High power coupling • 2 MW 100 ns pulse was coupled into PBG accelerator • Conditioning time ~ 1 week
Plan of experiment • Align the spectrometer • Measure electron beam acceleration in PBG structure • To be completed in January 2005
Conclusion • Photonic band gap structures present accelerator physicists with new opportunities. • Theory of PBG structures is well elaborated. • MIT PBG experiments prove the existing theories. • Design and fabrication of a PBG accelerator were successful. • MIT 17 GHz PBG accelerator experiment to be completed soon !
Acknowledgement MIT: Chiping Chen Amit Kesar Ivan Mastovsky Michael Shapiro Richard Temkin LANL: Lawrence Earley Randall Edwards Frank Krawczyk Warren Pierce James Potter CPI: Monica Blank Philipp Borchard SLAC: Valery Dolgashev IAP RAS: Mikhail Petelin Custom Microwave: Clency Lee-Yow