Lecture 5 Damping Ring basics Exercise solution

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Lecture 5 Damping Ring basicsExercise solution
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Thin Lens FODO Cell
In thin lens approximation and representing
dipoles as drift spaces the matrix of a FODO cell
can be written as
Comparing this with the matrix of a periodic
structure evaluate the betatron phase advance
??and the Twiss functions ?? and ?? at the center
of QF (optionally QD) Optional Observe the
behavior of ?? and ?D as a function of ? what
happens at 180º?
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Solution
or
?F ?D 0
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?F (blue) and ?D (magenta) vs phase advance for
FODO cell
L1.5 m
For ?180º ?F?? and ?D?0 The motion is unstable