1. One More 162.5 RFQ Design Renewal ANL Design

2. Several 162.5 MHz RFQ Designs ANL-1LBNL-1LBNL-2ANL-2aANL-2b Vane modulation typeSinusoidal Sinusoidal + trapezoidal Input energy, MeV0.0400.0350.0200.035 Output energy, MeV2.5 2.1 Average radius, mm6.06.050.5216.0 Aperture, mm4.03.953.164.0 Vane width, mm9.012.17.8210.2 Voltage, kV85.090.868.085 Cell number203135212220191 RFQ length, mm45723840404038003501 Transverse phase advance @ I=057 0 - 50 0 Normalize transverse envelope1.29 – 1.33 Maximum field at vane surface, kV179208164185 Norm. transverse acceptance, mm·mrad4.894.797.79

3. Simulation results ANL-1LBNL-1LBNL-2ANL-2aANL-2b Particle loss inside structure, %  0.3 0.050.260.52 Transmission, %>9893.797.8>95>99 Transverse emittance growth, rms11.161.01611 Transverse emittance growth, 99.5% 1.091.03 Longitudinal emittance, rms, keV·nsec0.8250.880.490.62 Longitudinal emittance, rms, keV·deg48.351.128.936.3 Results obtained with different simulation codes: ANL-1, ANL-2a – TRACK, LBNL-1, LBNL-2 – PAMTEQ, ANL-2b – TRANSIT.

4. What is new in This Design Calculation of 3D field distribution in RFQ cell Method of vane profile generation. Using combined vane modulation profile – sinusoidal for gentle buncher and trapezoidal for acceleration. Simulation code.

5. RFQ Cell (DESRFQ) L c i m i L c i+1 L c i+2 m i+1 m i+2 In DESRFQ cell is distance between cross sections with exact quadrupole symmetry. One half of cell is used for field calculation with periodic boundary conditions. This approach produces smooth vane profile but some step in field between cells.

6. RFQ Cell (PARMTEQ) L c i m i L c i+1 L c i+2 m i+1 m i+2 In PARMTEQ cell is space between cross sections with maximum and minimum distances from axis. This approach produces smooth field distribution but some step in vane profile between cells.

7. RFQ Cell (New) DESRFQ cell definition was used for current design. Vane profile for field calculation was constructed using adjacent half-cells. This approach produces smooth field distribution and smooth vane profile. L c i Profile for field calculation L c i+2 m i m i+1 m i+2

8. PRERFQ Code PRERFQ code solves Laplace equation for space limited by modulated vanes using finite difference method. with the following boundary conditions:

9. PRERFQ Simulation Domain with Sinusoidal Modulation Y VaneX Vane miaimiai Longitudinal profiles of RFQ vanes was created using file full-rfq-cells-data.dat a i+1 (Lc i + Lc i+1 ) / 2 aiai m i+1 a i+1 (Lc i + Lc i+1 ) / 2

10. Field for Sinusoidal and Trapezoidal Modulation CST Studio simulation was used for testing PRERFQ results. It was shown good coincidence.

11. Sinusoidal and Trapezoidal Modulation Sinusoidal modulation is most common but not most effective type of RFQ vane modulation. Trapezoidal modulation is more effective for long cells due to better field distribution that leads to higher transit time factor. This type of vane modulation was used in first RFQ. Sinusoidal modulation is preferable for initial RFQ part because it provides low field at electrode surface for short cells.

12. Accelerating Field at Sinusoidal and Trapezoidal Modulation Sinusoidal Modulation Trapezoidal Modulation

13. Maximum Field at Electrode Surface for Trapezoidal Modulation Field between Vanes at Exact Quadrupole Symmetry Cross Section Field between Flat Vanes Voltage, kV70 Exact quadrupole symmetry, kV/cm125.0 Flat vanes, kV/cm128.04

14. PRERFQ Simulation Domain with Trapezoidal Modulation x(z) y(z) z z miaimiai a i+1 (Lc i + Lc i+1 ) / 2 aiai m i+1 a i+1 (Lc i + Lc i+1 ) / 2 Y VaneX Vane Cell profile consists of straight parts with different distances from axis and sinusoidal part between them. Only straight part length is changed for higher energy cells. Sinusoidal part is constant for all cells. This profile provide 16% - 20% higher accelerating efficiency along RFQ part with constant modulation. It leads to about 10% shorter structure.

15. Field Components along RFQ

16. Summary Trapezoidal vane nodulation allows to increase RFQ acceleration efficiency and correspondingly reduce total RFQ length for given output energy. It leads to lower manufacture and operation cost. Total Project – X RFQ length can be reduced about 10%. Trapezoidal modulation causes only relatively small increase of maximum field at vane survace. All other RFQ parameters are kept the same to compare with conventional sinusoidal vane modulation.