7) Benchmarking of the trapping in 1 synchrotron oscillation for "standard" synchrotron tunes
The seventh step is to benchmark the trapping of 1 test particle during
1 synchrotron oscillation with a synchrotron tune which produces
one synchrotron oscillation in 1000 turns.
As Qs = 1E-3 the bunch length of step6 should be here reduced of factor 15
to keep in both cases the same momentum spread. Also the number of particles in the
bunch should be reduced of a factor 15 to keep the nominal tuneshifts
Dqx = -0.1, Dqy = -0.1365.
Here are the
Parameters used for step 7.
The test particle has the following initial coordinates:
x = 5mm, px = y = py = 0 and z = 2.5 sigma_z, pz = 0.
We compare the trapping by plotting the evolution of
the single particle emittance
e_x = bet_x px^2 + 2 a_x x px + gamma_x x^2
of the test particle
(normalized with the initial value) vs. number of turns.
Note that the maximum amplitude of the invariant do not follow the pattern of
step 6.
As the motion of the islands is to fast
to crossing the particle orbit in an adiabatic regime is lost:
no trapping occurs. We are now in presence of the "scattering" regime.
SIMPSONS
MICROMAP