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ANSYS Eigenmode Results of Full 4m RFQ with Vacuum Ports and 43.8mm Quadrant Radius

ANSYS Eigenmode Results of Full 4m RFQ with Vacuum Ports and 43.8mm Quadrant Radius. Study Performed. Use Pete’s latest 4m RFQ internal models Vacuum ports only on major top vane Vacuum ports on top and bottom Find all eigenmodes and Q between 300 to 400 MHz (quadrupole and both dipoles)

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ANSYS Eigenmode Results of Full 4m RFQ with Vacuum Ports and 43.8mm Quadrant Radius

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  1. ANSYS Eigenmode Results of Full 4m RFQ with Vacuum Ports and 43.8mm Quadrant Radius

  2. Study Performed • Use Pete’s latest 4m RFQ internal models • Vacuum ports only on major top vane • Vacuum ports on top and bottom • Find all eigenmodes and Q between 300 to 400 MHz (quadrupole and both dipoles) • Use symmetry planes where possible

  3. Symmetry Planes • Different vacuum port configurations imply vertical asymmetry ∴ Use two quadrants of half (2m) of RFQ • Once it’s confirmed how vacuum ports affect fields, need to confirm longitudinal modes ∴ Use just one quadrant but full 4m length

  4. With One or Two Vac Ports Vacuum ports top & bottom Vacuum ports top only Removing the bottom vacuum port increases frequencies by 25 kHz Open squares indicate theoretical modes, missing due to symmetry

  5. Confirming Missing Odd Modes Two quadrants, longitudinal symmetry One quadrant, full 4m long Full 4m-long RFQ model confirms missing modes, but slightly poorer mesh quality shifts whole spectra up ~0.5MHz

  6. Mesh Quality Results converge for vanetip mesh size < 2mm and quadrant mesh size < 15mm. Results in previous slides for one quadrant of full 4m RFQ are on limit of memory, using 2mm vanetip and 12mm bulk quadrant mesh sizes, but are sufficiently accurate.

  7. Electric Field in Vane Gap for Different Longitudinal Modes TE210: 324.5MHz

  8. Electric Field in Vane Gap for Different Longitudinal Modes TE211: 327.7MHz

  9. Electric Field in Vane Gap for Different Longitudinal Modes TE212: 334.6MHz

  10. Electric Field in Vane Gap for Different Longitudinal Modes TE213: 345.3MHz

  11. Electric Field in Vane Gap for Different Longitudinal Modes TE214: 359.9MHz

  12. Electric Field in Vane Gap for Different Longitudinal Modes TE215: 378.0MHz

  13. Electric Field in Vane Gap for Different Longitudinal Modes TE216: 397.2MHz

  14. Absolute Electric Field of First Four Longitudinal Modes

  15. Conclusions • Mesh density sufficient to solve 4m RFQ • Longitudinal modes well resolved • …however the fundamental is not flat! • Fundamental TE210 mode is ~0.5MHz too high so adjust quadrant radius to 44mm • Next nearest modes ~3MHz away. All have high Q so should not cross-talk • Vacuum port asymmetry  25kHz shift

  16. New stuff hot off the press!

  17. (Talk I’ve found possibly explaining non-flat field) Example of a frequency error at a single point x0 Suppose the local error is a delta function at some point x0. Local error magnitude is defined as G. This is the new resonant frequency of the cavity in terms of local frequency error G This relates the cavity frequency change to G. is the new wavefunction

  18. (Talk I’ve found possibly explaining non-flat field) Fractional vane-voltage error Each of the higher modes m contributes a term proportional to the voltage value of each mode at the point of the perturbing error, divided by the mode index m squared so nearest modes in frequency contribute most. An analytic solution exists for this summation. It is.

  19. (Talk I’ve found possibly explaining non-flat field) Dependence of the fractional voltage error at each point x on the parameters. The fractional voltage error at each point increases with the fractional cavity frequency error and as the square of the vane length to wavelength ratio. This next graph shows that if the local error at some point x0 causes the local resonant frequency to increase, the local voltage decreases, and vice versa.

  20. (Talk I’ve found possibly explaining non-flat field) m=0 and 1 m=0 m=1 to 20 Perturbed voltage distribution for problem with a d-function error at the vane end, where x0/lV = 0, lV/l = 2 and dw0/w0 = 0.01. V (x) 0 x/lV / l x V

  21. As-Designed End RegionNo Radial Matcher

  22. As-Designed End RegionWith Radial Matcher

  23. On-Tune End RegionNo Radial Matcher

  24. On-Tune End RegionWith Radial Matcher

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