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Chromaticity Effects on Transition Crossing

Chromaticity Effects on Transition Crossing . Y. Alexahin (FNAL APC). PIP meeting, April 3 , 2013. 2. Motivation. Losses at transition energy can limit beam intensity due to high dose.

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Chromaticity Effects on Transition Crossing

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  1. Chromaticity Effects on Transition Crossing Y. Alexahin (FNAL APC) PIP meeting, April 3, 2013

  2. 2 Motivation Losses at transition energy can limit beam intensity due to high dose Total number of protons and the integrated dose at two BLMs vs. time for three values of initial intensity (13, 14 and 15 turns injection). Transition Crossing – Y.Alexahin, PIP meeting, 04/03/2013

  3. 3 Off-Momentum Slippage Factor From S.Y.Lee book:  0.049 With chromaticitiesQx,y~ 01=0.04 and 1 is increased by a factor of ~2. Does it matter? W/o much analysis we tried last year “to play by the book” introducing changes to reduce 1 Chromaticities up the ramp as of 03/26/2012 (special settings for studies) Transition Crossing – Y.Alexahin, PIP meeting, 04/03/2013

  4. 4 Bare Lattice Momentum Compaction vs Chromaticity With chromaticitiesQx= +20, Qy= -201 was reduced to ~0, but the losses went up! May be tracking simulations will clarify the situation? Transition Crossing – Y.Alexahin, PIP meeting, 04/03/2013

  5. 5 T-Crossing Simulations (Instantaneous Phase Jump) Eini=3.66GeV  Efin=4.77GeV (Etr=4.18GeV) p p Initial Final, 1=0.1  (rad)  (rad) p p Final, 1=0 Final, 1=-0.05  (rad)  (rad) Obviously the best case! May be there are more important factors than 1 ? Transition Crossing – Y.Alexahin, PIP meeting, 04/03/2013

  6. 6 Chromaticity Effect Using action-angle variables for the transverse motion and z=s-v0t and p for longitudinal: Equation of motion for z=s-v0t : Looking for a stationary solution (dz/ds=0) we obtain betatron amplitude-dependent momentum shift p : negligible! With Qx= +20, Qy= -20 and r.m.s.=0.5m, 0=-0.001, Ax=3, Ay=0  p =-6.e-4 Ax=0, Ay=3 p =+6.e-4 - But tracking shows that the ramp is too fast for p to change appreciably Transition Crossing – Y.Alexahin, PIP meeting, 04/03/2013

  7. 7 (Really Big) Umstatter Effect In a weakly focusing FODO lattice 0 = 1/Qx2 Due to transverse space charge Qx= Qx0 –QSC(Ix, Iy, z, p) QSC(max) can be as large as 0.1 at transition, 0.075 taken in simulations which showed some effect of chromaticity on the tails: p p Qx= +20, Qy= -20 Qx= 0, Qy= 0  (rad)  (rad) Most likely the increase in losses at transition was the result of a better survival of protons with experimental settings before transition  stronger space charge. Let us restore those settings and try different chromaticity at transition. Transition Crossing – Y.Alexahin, PIP meeting, 04/03/2013

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