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Engineering Solution to Modulation-Induced Field Tilt • Modulations affect field flatness of RFQ • Moving from one end of RFQ to the other: Modulation Depth UP Capacitance DOWN Frequency UP Voltage DOWN • Can counteract this by varying bulk inductance • Can do this by changing quadrant radius, but this affects how you join sections together • Equivalent, preferred method: cut grooves in walls • Now, all sections have same quadrant radius, but each section has its own groove depth • This makes all sections have same frequency, despite modulations, so flattens field in full 4m Frequency of Cells When Cavity Sections Have Different Quadrant Radii Simplified 4m Test Model Replicating Effects of Modulations on Voltage Simplified 4m Model Ideas 1 Using the same smaller radius of 44.1 throughout and using a radius to increase the internal volume. Advantage: Would allow use of large custom cutter for bulk of profile. Disadvantage: How to join new radius to large radius without introducing sharp corners. Disadvantage with this design is need for many passes of ball nose cutter An alternative is......... Best design by far from a machining point of view. Still needs ball nose to make profile but flat can be made more conventionally. Scott’s calcs should still hold true. BUT now we have introduced an asymmetry which bring the dipole modes closer? Ideas 2 Bottom of flat cut-out is perfectly flush with bottom of already-cut circle. 0mm Only corners of flat need cutting in. Bottom of flat is definitely cut in by a small amount. 3mm Narrow flat, cut quite deep. 6mm If square cut used, linear change in frequency with cut depth Easier to use ball-ended cutter Large version Using diam 25 ball nose cutter Cutter Small version Using same diam 25 ball nose cutter Ideas 3 Section 1 & 2 (first 50cm) have 44.1mm quadrant radius with no cut Ball cut depth = 2.55mm normally into wall for Section 2 (last 50cm) ‘Depth’ defined as normal cut into wall Ball cut depth = 4.1mm normally into wall for Sections 3 & 4 ‘Depth’ defined as normal cut into wall Modulations with Cavity Frequency Corrected Using Grooves in Wall Cell 220 (in last 50cm of Section 2) Uncorrected Frequency = 324.121 MHz Corrected Frequency = 323.276 MHz Cell 307 (in Section 4) Uncorrected Frequency = 324.664 MHz Corrected Frequency = 323.111 MHz Non-linear change in area of circular cut makes non-linear frequency dependence Question from Pete: “Ahhhh.... But machining here affects the relative ‘sticky-out-ness’ of the tuners! Is this a problem?” NO! We’ll deal with it. If these cuts into the wall make the field 70% flatter than if no cuts were made, then the tuners won’t be needed as much anyway. Sections 1 & 2 (first 50cm) need no groove cut into wall. Section 2 (last 50cm) needs a 2.55mm deep groove cut into wall. Sections 3 & 4 need a 4.1mm deep groove cut into wall. Looking from high energy end........ Looking from section 2 to 1........ Small step at junction of section 2 to 3........ Keep cutback same distance from cooling pocket COOLING CHANNEL