Plasma Science and Fusion Center Massachusetts Institute of Technology Evgenya Smirnova Massachusetts Institute of Technology UCLA, January 2005 Photonic Band Gap Accelerator Demonstration at MIT

Plasma Science and Fusion Center Massachusetts Institute of Technology 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

Plasma Science and Fusion Center Massachusetts Institute of Technology Motivation: accelerator applications of PBG structures.

Plasma Science and Fusion Center Massachusetts Institute of Technology Motivation Type of accelerator X- and K-band accelerators and klystrons Laser driven accelerators (μm wavelength) ProblemHigher order modes (Wakefields) Low breakdown threshold in metal components PBG solutionPBG resonator suppresses wakefields Dielectric PBG accelerator can be built

Plasma Science and Fusion Center Massachusetts Institute of Technology 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).

Plasma Science and Fusion Center Massachusetts Institute of Technology Photonic Band Gap (PBG) Structures

Plasma Science and Fusion Center Massachusetts Institute of Technology 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).

Plasma Science and Fusion Center Massachusetts Institute of Technology Band Gaps 1D example: Bragg reflector PBG structure arrays reflect waves of certain frequencies while allowing waves of other frequencies to pass through. Band Gaps

Plasma Science and Fusion Center Massachusetts Institute of Technology 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

Plasma Science and Fusion Center Massachusetts Institute of Technology Theory of PBG Structures

Plasma Science and Fusion Center Massachusetts Institute of Technology Maxwell equations in PBG structures 2D square lattice: m,n - integers must satisfy the Floquet theorem Maxwell equations solved Field in PBG structures satisfies Maxwell’s equations: 

Plasma Science and Fusion Center Massachusetts Institute of Technology Solving Maxwell’s equations Finite difference method (metals) Plane wave method (dielectrics) Periodic boundary conditions: Derivatives: Fourier series expansion takes into account periodic boundary conditions

Plasma Science and Fusion Center Massachusetts Institute of Technology plotted along the Irreducible Brillouin zone boundary Brillouin zone and Brillouin diagram Brillouin zone Irreducible Brillouin zone is periodic, only inside the Brillouin zone matter. Brillouin diagram:

Plasma Science and Fusion Center Massachusetts Institute of Technology Global Band Gaps Global band gap: wave cannot propagate in all directions. Example of band gap diagram: square lattice of metal rods, TM waves a b

Plasma Science and Fusion Center Massachusetts Institute of Technology PBG resonators PBG resonators can be studied with many commercial and freeware electromagnetic solvers, such as Superfish, HFSS, Mafia, Microwave Studio, MPB etc. PBG cavity formed by a defect In the presence of band gaps a defect in a PBG structure may form a resonator:

Plasma Science and Fusion Center Massachusetts Institute of Technology 2a Mode selectivity in PBG resonators Pillbox Cavity, TM 01 mode PBG Cavity, triangular lattice a/b=0.15, TM 01 –like mode Operating Point of PBG structure b Single mode operation. No higher order dipole modes. This structure is employed for the MIT PBG accelerator

Plasma Science and Fusion Center Massachusetts Institute of Technology HOM in PBG resonators Only a single mode confined for 0.1  a/b  0.2

Plasma Science and Fusion Center Massachusetts Institute of Technology 2D PBG resonators

Plasma Science and Fusion Center Massachusetts Institute of Technology Resonators for the cold test Cavity 1Cavity 2 Lattice spacing b 1.06 сm1.35 cm Rod radius a0.16 cm0.40 cm a/b Cavity radius3.81 сm4.83 сm Freq. (TM 01 )11.00 GHz Freq. (TM 11 )15.28 GHz17.34 GHz Axial length0.787 сm 10 cm

Plasma Science and Fusion Center Massachusetts Institute of Technology Cold test results Dipole TM 11 mode (confined) TM 01 mode Propagation band (no modes confined) Band gap Confined TM 11 mode Bad for accelerators No confined wakefield modes. Good for accelerators

Plasma Science and Fusion Center Massachusetts Institute of Technology Brazed PBG resonator Theoretical Q HFSS (TM 01 ) = 5300 Measured Q measured (TM 01 ) = 2000 Reason for low Q: poor contact between rods and end plates How to improve Q ? BrazingElectroforming A resonator was brazed at CPI: Q brazed (TM01) = 5000

Plasma Science and Fusion Center Massachusetts Institute of Technology PBG accelerating structure

Plasma Science and Fusion Center Massachusetts Institute of Technology Accelerator with PBG cells Design the structure ● Choose the accelerator parameters ● Tune the cell to GHz ● Tune the coupler Cold test the structure ● Tune the coupler ● Tune the cell to GHz Hot test the PBG accelerator

Plasma Science and Fusion Center Massachusetts Institute of Technology HFSS: accelerator design tool Accuracy driven adaptive solutions Optimization tools Powerful post- processor Macro language control of calculation.

Plasma Science and Fusion Center Massachusetts Institute of Technology PBG accelerator parameters PBG disk-loaded structure Disk-loaded waveguide Frequency GHz QwQw rsrs 98 M /m139 M /m [r s /Q]23.4 k /m24.7 k /m Group velocity0.013c0.014c Gradient25.2 P[MW] MV/m 25.1 P[MW] MV/m

Plasma Science and Fusion Center Massachusetts Institute of Technology 2 /3 traveling wave cell: L/c = 2 /3 Iris radius scaled to 17 GHz from the SLC design Dimensions PBG disk- loaded structure Disk-loaded waveguide Rod radius, a1.08 mm Lattice vector, b6.97 mm a/b Cavity radius24.38 mm6.88 mm Cavity length, L5.83 mm Iris radius1.94 mm Frequency GHz

Plasma Science and Fusion Center Massachusetts Institute of Technology 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.

Plasma Science and Fusion Center Massachusetts Institute of Technology Electroformed PBG structure PBG accelerator was electroformed by Custom Microwave, Inc. ( Rods and plates of each cell were grown as a single crystal without connections. The cells were brazed together.

Plasma Science and Fusion Center Massachusetts Institute of Technology 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.

Plasma Science and Fusion Center Massachusetts Institute of Technology 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 ’’. Etching temperature: 45 C.

Plasma Science and Fusion Center Massachusetts Institute of Technology Final cold test results Good agreement between measurement and computation. Flat field profile in accelerating mode. Measured field profile (bead pull)

Plasma Science and Fusion Center Massachusetts Institute of Technology PBG accelerator experiments

Plasma Science and Fusion Center Massachusetts Institute of Technology MIT PBG experiment setup Beam linePBG Chamber

Plasma Science and Fusion Center Massachusetts Institute of Technology Components schematic

Plasma Science and Fusion Center Massachusetts Institute of Technology Accelerator laboratory Load Coupling waveguide PBG chamber Linac Klystron Spectrometer

Plasma Science and Fusion Center Massachusetts Institute of Technology High power coupling 2 MW 100 ns pulse was coupled into PBG accelerator Conditioning time ~ 1 week

Plasma Science and Fusion Center Massachusetts Institute of Technology Plan of experiment Align the spectrometer Measure electron beam acceleration in PBG structure To be completed in January 2005

Plasma Science and Fusion Center Massachusetts Institute of Technology 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 !

Plasma Science and Fusion Center Massachusetts Institute of Technology Acknowledgement MIT: Chiping Chen Amit Kesar Ivan Mastovsky Michael Shapiro Richard Temkin LANL: Lawrence Earley Randall Edwards Frank Krawczyk Warren Pierce James Potter SLAC: Valery Dolgashev CPI: Monica Blank Philipp Borchard Custom Microwave: Clency Lee-Yow IAP RAS: Mikhail Petelin