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Main Injector Slow Extraction Studies

f. Main Injector Slow Extraction Studies. Y. Alexahin, E. Gianfelice-Wendt, J. Johnstone (APC) D. Morris, M.-J. Yang (AD). MI Slow Extraction Group Meeting, June 29, 2012. Issues. 2.

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Main Injector Slow Extraction Studies

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  1. f Main Injector Slow Extraction Studies Y. Alexahin, E. Gianfelice-Wendt, J. Johnstone (APC) D. Morris, M.-J. Yang (AD) MI Slow Extraction Group Meeting, June 29, 2012

  2. Issues 2  What are the optimal conditions for ½-integer resonance extraction?  The amplitude and phase of the quad harmonic?  Nonlinear tuneshift with amplitude?  Where we are:  Tune vs harmonic quad strength and amplitude of oscillations.  TBT optics measurements.  Nonlinear chromaticity  Optimum ES angle vs ES position  Plan of action MI Slow Extraction Group Meeting, June 29, 2012

  3. Theory 3 Model: 2-turn move for  < 0: clockwise counter-clockwise r a0 c /2 Best orientation ()? Optimum parameters? MI Slow Extraction Group Meeting, June 29, 2012

  4. Theory - 2 4 2-turn move for  < 0: clockwise counter-clockwise r a0 c /2 maximum tangential 2-turn step here orientation for maximum 2-turn step in xand maximum x and … allowed ES position With orientation like that (or on the right) Ima < 0 for xES < 0 the extraction trajectory can be diverted from the axis, with the angle +0.0011 for x=31m, x=1.72, xES=-2cm For this reason, and to maximize the step size, 0 <  <  (better << ) MI Slow Extraction Group Meeting, June 29, 2012

  5. Measurements 5 There was a few rounds of measurements: 03/21/12: TBT optics with harmonic quads: “nominal”; off; minimum Qx (QC206=+1.5A, QC328 = -2A); and QC206 = -3A Qx vs amplitude with harmonic quads for minimum Qx TBT optics with vertical kicks at QC206 = -3A (also gives Qx vs amplitude) 04/02/12: Qx vs amplitude with OF on and off (data not saved) 04/10/12: TBT optics and Qx vs amplitude at QC328 = -6.5A 04/25/12: TBT optics with individual harmonic quads offset by 12A from minimum Qx settings Extraction with QC328 = -6.5A attempted Also, Ming-Jen and Denton measured 2nd order chromaticity with OF on and off MI Slow Extraction Group Meeting, June 29, 2012

  6. x - function @ HBPMs 6 measurement HP520 “Nominal” harm. quads, Qx=0.485627 design Q206=+1.5A, Q328=-2A, Qx=0.484487 - John’s algorithm works! Q206=-3A, Q328=-2A, Qx=0.4895 - x @ HP520 goes down, not up! Distance from HP624 (m) MI Slow Extraction Group Meeting, June 29, 2012

  7. QC206 vs QC328 7 HP520 x measurement QC206=-4.5A, QC328=0, Qx=0.4895 - x @ HP520 goes down, not up! nominal Distance from HP624 (m) x QC206=-1A, QC328=-4.5A, Qx=0.4899 - x @ HP520 goes up! Distance from HP624 (m) MI Slow Extraction Group Meeting, June 29, 2012

  8. Closer Look 8 measurement x QC206=-4.5A, QC328=0, Qx=0.4895 ES entrance MAD model nominal Distance from HP624 (m) x QC206=-1A, QC328=-4.5A, Qx=0.4899 - x @ ES larger while max x is smaller Distance from HP624 (m) MI Slow Extraction Group Meeting, June 29, 2012

  9. Phase Space @ ES 9 Design optics used to compute variables @ES from HP520 & HP522 data QC328=-6.5A QC206=-3A “minimum Qx” /2 The ellipse tilt with QC206 is wrong: /2 = 108 > 90 With QC328 it is still wrong: /2 = 145 Inversion of QC206 polarity will give (-) = (+) -  = 216 - 180 = 36 Still some contribution from QC328 may be helpful MI Slow Extraction Group Meeting, June 29, 2012

  10. How it looks in ordinary coordinates 10 QC328=-6.5A From Ming-Jen’s I90 simulations MI Slow Extraction Group Meeting, June 29, 2012

  11. Harmonic Quad Strength 11 To obtain the observed (by eye) beta-beat with MAD K1QC206  0.0011m-2 is needed that gives |G2|0.0055 Another way is to look at the tuneshift: When QC206 is downshifted by 4.5A Qx=0.485  0.4885, so that 0=0.015  =0.0115 that gives |G2|0.0052 One more way is to use the transfer function – would I have known it – to calculate K1QC206 for a given current. The last necessary parameter is MI Slow Extraction Group Meeting, June 29, 2012

  12. Effect of Octupoles 12 Qx From 03/21/12 studies, harm. quads set for minimum Qx (QC206=+1.5A, QC328=-2A), Action variable determined from all HBPM data by a special algorithm Jx (m) Tuneshift with amplitude dQx/dCSI=1.68103 [1/m] (Courant-Snyder Invariant = 2J) MAD8 with octupole components provided by D.Johnson seems to underestimate the effect, while I90 seems to overestimate it. MI Slow Extraction Group Meeting, June 29, 2012

  13. 04/28/12 studies by D.Morris & M.-J. Yang Tune vs Δp/p Harmonic quads?

  14. 2nd Order Chromaticity (/2) 13 *) using more points for p/p>0 **) using transfer function 2.8 T-m/m^3/A (multiplied by 3!/LMRO) ***) increasing the built-in octupole component by 32.5% Correspondence between measured OF effect and I90 is amazing! MAD8 underestimates built-in octupoles by a factor of 1.84 and exaggerates OF (slightly) With this factor in the MAD8 detuning will be dQx/dCSI=1.90103 [1/m] – not too far from the measured dQx/dCSI=1.68103 [1/m]  G4=dQx/dJx/2=dQx/dCSI G4=1.68103 [1/m] MI Slow Extraction Group Meeting, June 29, 2012

  15. Step Size 14 At the stopband boundary (0=-2|G2|) and =0 (left pic.) the step size in x reaches its maximum: - this is just a half of the available ES aperture (14mm). To increase xmax we can increase |G2| (and 0/2) by up to 58% (or reduce G4 by a factor of 4?) x (m) x x x (m) x (m) x (m) /2 = 18 (the same |G2|) 2-turn step =- 6.5mm @ xES=-1cm, x=-0.0003: x=-1cm  -1.2cm over ES With larger |G2| xES can be increased /2 = 108 2-turn step =- 4.5mm @ xES=-2cm, x=+0.0007: x=-2cm  -1.5cm over ES MI Slow Extraction Group Meeting, June 29, 2012

  16. Central Separatrix Area 15 From Leo & John: To begin the squeeze of 95%N = 20 mmmrad out of the central separatrix Ac < 95%N /  |0| - 2|G2| < 0.0016 ( |a0/c| < 0.39 ) At this moment the separatrix extends to xc =1.7mm for /2 = 108 and xc =  5.1mm for /2 = 18 - no problem with xES=-1cm Still,  can be further optimized by mixing QC206 and QC328 MI Slow Extraction Group Meeting, June 29, 2012

  17. Plans 16  Analyze measurement data from 03/21 - 04/25  extract BPM calibration errors  find -functions at important locations (harm. quads, septa)  fit the optics model to the data  Look for optimal harmonic quad configuration (, |G2|)  16-mult for resonance excitation? Extracted beam transport? (Larger step-size  larger emittance)  Simulate extraction with account of nonlinearities and space-charge MI Slow Extraction Group Meeting, June 29, 2012

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