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Aslaninejad, M.

Paper Title Page
THPC003 Sum of Emittance in the Presence of a Linear Coupling 2975
 
  • M. Aslaninejad, H. Ghasem
    IPM, Tehran
 
  In this article, the influence of linear coupling due to skew quadrupoles on the transverse equations of motion and emittances in accelerators is studied*. We first introduce the definition of the transverse single particle emittances using the Floquet transformation in alternating gradient as well as the constant focusing rings, then in the presence of the linear coupling, due to skew quadrupoles we introduce the coupled differential equations governing the particles motion and try to solve them by a direct method and also using the normal modes of motion to find the relation between the two transverse emittances. Based on smooth approximation and using the normal modes** we solve the equations of motion of a test charged particle and derive two new formulas for the sum of the emittances, and the conditions under which this sum is invariant.

*P. J.Bryant, CERN Acclerator School, CERN, PROCEEDINGS, 94-01, Vol. I.
**E. Metral, CERN/PS 2001-066(AE).