1. The Zipper Structure: A Novel Accelerator Structure Configuration Christopher Nantista SLAC AAC Workshop ’08 Santa Cruz, CA July 31, 2008

2. I present a novel normal-conducting accelerator structure. The design is not necessarily fully optimized and features still need to be added. The concept seems to offer some advantages over traditional structures. When limiting mechanisms are not completely understood, sometimes it’s worth trying something different just to be different. (i.e. It may have virtues not immediately apparent.) Feedback, suggestions and comments are welcome. Opening Statements

3. Some Considerations A  /2 phase advance may offer improved R/Q compared to larger phase advances, since the cell transit time factor can be significantly larger (0.90 vs. 0.64 for a  mode in a simple pillbox). But, if SW, what about empty cells? Biperiodic – off-axis, short,…? Large iris apertures, for large group velocity (TW) or mode spacing (SW), seem to exacerbate breakdown problems in TW structures and reduce shunt impedance in SW structures. What if we decouple power flow/cell coupling from beam irises, and keep the latter as small as short-range wakefield considerations allow? Coupler cells (and those near them) seem to be particularly prone to gradient limiting RF breakdown. Even if pulsed heating is minimized, squeezing the full structure power through such cells seems a bad idea. What if we eliminate coupler cells by coupling to all cells identically? Coupling out HOM power is a problem (slots, chokes, manifolds,…). What if all the cells were heavily coupled, with a wide-open geometry, into an easily damped volume? What if we use the empty cells by interleaving two  /2 modes?

4. The Zipper Structure*  -mode SW “  -mode TW” Because the fields in the central region are equivalent to the  /2 mode, with zero field in every other cell, the interleaved combs don’t couple, despite the irises. A  /2-mode structure that fills like a SW structure but uses all cells like a TW structure. * with apologies to Kroll, et al. (“PLANAR ACCELERATOR STRUCTURES FOR MILLIMETER WAVELENGTHS” PAC ’99) Periodic stubbed waveguides interfaced with square accelerator. The stubs serve to reduce the guide wavelength.

5. excited in quadrature The Basic Circuit coupling irises

6. Consider just the square structure region. What is the R/Q dependance on the iris thickness with simple radiusing and a/ =0.11 (a=0.113648”=2.887 mm)? t (iris thickness) s (side) r/Q (k  /m) Q r (M  /m) |E| pk /|E| a 0.0500”0.75334”18.8855,464.3103.1921.93 0.050”t0.7450”18.4305,370.198.971.66 0.050e20.7591”18.4555,480.5101.1441.57 1.27 mm elliptical tamago asp. rat.=3 round Iris Optimization

7. The Field Patterns Re E Re H

8. blue – real red – -imaginary green – complex mag. cyan – -RF phase/  yellow – beam phase/  magenta – effective field mean(green) = 0.8661 mean(magenta) = 0.8562 mean(magenta)/mean(green) = 0.9885 z (mm) Normalized Amplitude The Axial Field

9. r/Q = 10.896 k  /m Q = 6,369.9 r = 69.408 M  /m E p /E a = ~1.770 a/ = 0.11 = 2.887 mm Design Parameters p = 0.25829” = 6.5606 mm 0.1875” = 4.7625 mm s = 0.7591” = 19.2811 mm = W (half WR75 height) normal conducting (warm) standing-wave (TW to beam) X-band (11.424 GHz) H = 1.4766” = 37.5056 mm

10. f(0)f(  /2)f(  k=(f  -f 0 )/2f  /2 Square structure: 11.2811 GHz11.424 GHz11.5564 GHz0.0120 Stub waveguide:7.7749 GHz9.26171 GHz11.424 GHz0.1970 < -30 dB coupling and dropping (w/ iterations) 1 2 3 Intra-Structure Coupling PERIODIC SUB-STRUCTURES: COMB ISOLATION: coupling through waveguide >> coupling through beam iris HFSS S matrix No coupling between input waveguides at resonance.

11. The required power is: The length of the structure may be limited by the power handling capacity of the waveguide. For critical coupling when the beam is present, we want to match: Large mode spacing due to strong coupling may allow ~23 cells per comb. Iris coupling of each “comb” to input waveguide External Coupling and Length I b = 1 A G = 100 MV/m Q 0 = 6,370 r/Q = 10.9 k  /m 100 MW  L= 0.307m = ~46 cells t i = 88.0 ns Q L = 2,124 Sample Operating Parameters:

12. 1.1016” 1.4766” 0.04761” 0.7500” 0.7591” transition in vertical mitered H-plane bends WR75 Magic-T mitered E-plane bends Feeding RF power is fed in through a Magic-T, slightly offset from axis (because guide wavelength differs fom free-space wavelength), plus bends. Reflected power goes to a load on the fourth port of the Magic-T. This is like a built-in circulator. Structure pairing is not needed. Waveguide height is stepped/tapered down, perhaps as part of coupling irises.

13. HOM/SOM loads Damping and Tuning tuning buttons cutoff end waveguide HOM loads

14. Over a transverse beam size of 100 , the gradient should be flat to the scale of 1.5  10 -9 !  = 0  =  The Octupole Content of Accelerating Gradient G(r,f) = G 0 (1 -  r 4 cos4  )  = ~1.46  10 -5 mm -4 r (mm) Normalized Gradient x (mm) y (mm) Normalized Gradient x

15. For an NLC beam (I b =0.864 A, T b =267 ns) and a gradient of 90 MV/m, a maximum efficiency of  =0.2978 is achieved with  =1.846, T f =90.55 ns, and P RF /L = 195 MW/m. For a CLIC_G beam (I b =1.192 A, T b =155.5 ns) and a gradient of 100 MV/m, a maximum efficiency of  =0.3032 is achieved with  =2.0198, T f = 76.098 ns, and P RF /L = 263.9 MW/m. For optimized CLIC_C and CLIC_G structures:  = 0.24 and.277, respectively*. Efficiency What would be the RF-to-beam power efficiency of such a “zipper structure” if implemented in a linear collider? = energy into beam per unit length per pulse RF energy into structure per unit length per pulse *Alexej Grudiev

16. I’ve not yet completely developed this idea and answered all questions (It’s slightly more than half-baked). However, the zipper structure seems to be a promising structure candidate inasmuch as it appears to offer: good efficiency simple geometry / easy fabrication (low cost) easy heavy damping tunability low breakdown rate? Input/feedback from the community of experts gathered at this workshop is welcome. Any show-stoppers I’ve missed? Concluding Remarks