Effect of RFQ Modulations on Frequency and Field Flatness

Recap: Tuning the End Region to Achieve Correct Frequency

Final Design

CST and ANSYS results for final geometry, 4m RFQ with flush tuners.

Taking into account meshing accuracy for these large models (see slides 3 & 4), both agree with the frequency being (323.5 ± 0.5) MHz

Original Matcher

No Matcher

Optimised Matcher

New matcher design achieves considerably flatter field and ensures (323.5 ± 0.5) MHz along the entire RFQ

Now: What About Modulations?

• Transverse position of copper in each cell varies

• ∴ Capacitance varies throughout the cell• But surely, on average, capacitance stays

constant if average bore radius is constant?

Average bore radius, r0

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Evidence For Modulation-Induced Field Flatness

Errors

“RF Test of a 324-MHz, 3-MeV, H- RFQ stabilised with PISLs”, TUD02, LINAC’00A. Ueno & Y. Kondo, KEK

“…tuners were set at the design positions (99.5mm from the beam axis)

…The longitudinal field non-uniformity is speculated to be produced by the modulation effect.

…The larger modulation is speculated to have thelarger capacitance.”

Evidence For Modulation-Induced Field Flatness

Errors

“Complete RF design of the HINS RFQ with CST and HFSS”, MOP042, LINAC’08G. Romanov & A. Lunin, Fermilab

My Simulation Strategy

1. Import Simon’s full 4m vane-tips geometry.2. Import vane geometry with tips removed.3. Create cavity vacuum by taking inverse of copper.4. Macro to automate slicing & mesh of one cell.5. Eigenmode solution of each individual cell.

Calculate for each RFQ cell:• Resonant frequency• Q• Voltage at cell centre (position of quadrupole transverse & maximum longitudinal

field)

E-field Plots for Cell 222

Transverse (cell centre)

Longitudinal (x=0 plane)

Comparing HINS & FETS RFQs

Solution?✕Complete redesign of beam dynamics

and modulation parameters to get correct capacitance and frequency for each cell

✕Vary inductance by altering the quadrant radius to suit each modulation

Alter quadrant radius of each 1m section so each section is roughly flat to start with, easing tuning procedure

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Leave quadrant radius at 44.1mm

Increase quadrant radius to ~44.2mm

Increase quadrant radius to ~44.2mm

Change quadrant radius half way along this section?

Next step: Try this solution to see if frequency and voltage do flatten out