Beam Tilt Calculation in Particle Accelerators
Explore the intricate process of beam tilt calculation in particle accelerators, where transverse impedance leads to betatron motion, generating a closed orbit distortion. Key parameters and components are discussed, shedding light on the complexities of beam behavior.
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Presentation Transcript
Beam tilt calculation Zhang Yuan Xu Gang Sun Yuansheng
Beam tilt calculation When a beam bunch traverses a transverse impedance , the bunch head generates a transverse wake field that kicks the bunch tail, generating a betatron motion of the tail relative to the head. In a storage ring, in a steady state, this kick to the bunch tail produces a transverse closed orbit (e.g. in the y-direction) of the bunch tail relative to the bunch head, which means the beam now has a y-z tilt. v a b
Beam-tilt calculation z kick 1 = ( z ) N r xco w [ ( z s ) f s ( )] ds (1) e z 2 c 1 = W ( z ) * * L (2) m + + 2 * m 1 * b 1 ( ) z m 0 2 z 1 = 2 2 f ( z ) e (3) 2 The transverse kick is proportional to the transverse displacement of the bunch head.
Beam-tilt calculation Close orbit distortion ( ) s 0 = ( ) cos( | ( ) ( ) |) u s s s (4) 0 2 n si ( si t ) ( s ) = du ( z , t ) ( z ) cos( | ( t ) ( s ) |) 2 n (5) = u ( z t , ) du ( z t , ) s ( t ( ) ) = ( z ) cos( | t ( ) s ( ) |) ds (6) si 2 n
Parameter Unit Value [N] GeV 120 [N] 3.79E+11 [ ] mm 2.14 z [ ] m 69.97 x m 0.8 x 0.8578 x 2025/4/16
Beam tilt calculation component is dominant ) ( W 1z If the object considered is cylindrically symmetric the dipolar 2 c 1 = W ( 1 z ) * * L 3 * b z c b = 05 . 0 ( m Beam pipe = = 17 1 7 1 1 3 . 2 * 10 ( s ) 3 . 5 * 10 ( m ) c 2025/4/16
= -4m 69 97 . ( m ) 0 . 7 * 10 ) 4 x X 1 . 16 * 10 ( m ) max 2025/4/16
End 2025/4/16
