ANALYTICAL DESCRIPTION OF BETATRON OSCILLATIONS IN LINEAR MACHINES

O.E. Shishaninª

Moscow State Industrial University, Moscow, Russia

Abstract

As pointed out by Wiedemann, there are three basic periodic lattices using usually in storage rings [1, 2]. Among these are the FODO, Chasman-Green lattice and triplet. They have not sextupole and octopole lenses and define so-called linear machines. To facilitate the calculations the consideration is restricted only to systems with quadrupole magnets. The equations of small deviations are derived in linear approximation. It is established that these expressions are specific differential equations with periodic coefficients and small parameter of the highest derivative. The Hill equations with a formula for the angular velocity determine the charged particle dynamics.

ª – corresponding author

Paper 

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