MI-0178

Beta Function Distortions from Systematic and Random Gradient Errors in Combined Function and Quadrupole Magnets for Lattice RRV7

S. D. Holmes

July 31, 1996

This note updates information presented in MI-0160 to reflect the newly considered lattice, RRV7. The primary change relative to the lattice RRV6 is that the phase advance/cell has been adjusted slightly to reduce sensitivity to systematic skew quadrupole and octupole components. Tables 1 and 2 are affected and presented here. It should be noted that these tables now present gradient errors in Fermilab "units" rather than as a percentage gradient error, and that roll sensitivity is now referenced to 0.5 mr.

Table 1: Recycler tune shifts, rms b-function distortions, and minimum tune split arising from a systematic gradient and skew quadrupole error of 1x10-4 of nominal in the combined function and quadrupole magnets. Recycler lattice RRV7.
  Dnx Dnx Dbx/bx(rms) Dby/by(rms) Dnmin
           
Gradient Magnet (4.1m)          
integrated gradient
DB'L/BL=.0001/inch 		.028 -.028 28x10-4 35x10-4  
skew quadrupole
DB'sL/BL=.0001/inch 		        16x10-4
           
Gradient Magnet (2.7m)          
integrated gradient
DB'L/BL=.0001/inch 		.0096 -.0096 21x10-4 33x10-4  
skew quadrupole
DB'sL/BL=.0001/inch 		        2x10-4
           
Quadrupole magnets          
integrated strength

DB'L/B'L=.0001

.0004 -.0004 2.7x10-4 3.9x10-4  

 

Table 2: Recycler rms b-function distortions, and minimum tune split arising from a random gradient errors of 1x10-4 of nominal, a random transverse displacement of 0.25 mm (in the long combined function magnets), and a 0.1 mr roll in the combined function and quadrupole magnets. Recycler lattice RRV7.
  Dbx/bx(rms) Dby/by(rms) Dnmin
       
Gradient Magnet (4.1m)      
integrated gradient
sB'L/BL=.0001/inch		 158x104 174x10-4  
transverse displacement
sd=.00025 m		 25x10-4 44x10-4  
skew quadrupole
DB'sL/BL=.0001/inch		     96x10-4
roll
sf=.0005 		    31x10-4
       
Gradient Magnet (2.7m)      
integrated gradient
sB'L/BL=.0001/inch		 70x10-4 71x10-4  
skew quadrupole
DB'sL/BL=.0001/inch		     39x10-4
roll
sf=.0005		     24x10-4
       
Quadrupole magnets      
integrated strength
sB'L/B'L=.0001		 4.9X10-4 5.0X10-4  
roll
sf>=.0005		     14X10-4

Conclusions

Tables 1 and 2 show the rms b-function distortion around the ring and the minimum tune split expected for the designated errors. With the exception of the tune split arising from a systematic skew quadrupole component, the sensitivities are very similar to RRV6. The splitting of the horizontal and vertical phase advance has reduced the coupling sensitivity in RRV7 by nearly a factor of 50 relative to RRV6.

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