2) Benchmarking of the Tunes versus particle amplitude. Sextupole OFF.
The second step is to benchmark the dependence of a test particle tunes
from its amplitude.
The amplitude of the particle is here meant as the
effectively maximum amplitude that the particle can have in one betatron
oscillation.
The particle coordinates of the test particles are:
x_0 = 0, ..., 4 sigma_x, p_x0 = y_0 = p_y0 = 0.
The particle amplitude is therefore x = \sqrt{bet_x \gamma_x} x_0.
The same definition applies to the y amplitude.
The lattice nonlinear component is off.
As the bunch space charge is maximum at the center of the bunch, the
test is performed keeping the particle at z=0.
The bare tunes are are Qx = 4.338, Qy = 3.2.
The tunes are computed with an FFT from the motion of a test particle
over 1024 turns.