Quickstart

A simple example on how to calculate the Twiss parameter for a FODO lattice.

Import apace:

import apace as ap

Create a ring consisting of 8 FODO cells:

d1 = ap.Drift('D1', length=0.55)
b1 = ap.Dipole('B1', length=1.5, angle=0.392701, e1=0.1963505, e2=0.1963505)
q1 = ap.Quadrupole('Q1', length=0.2, k1=1.2)
q2 = ap.Quadrupole('Q2', length=0.4, k1=-1.2)
fodo_cell = ap.Lattice('FODO', [q1, d1, b1, d1, q2, d1, b1, d1, q1])
fodo_ring = ap.Lattice('RING', [fodo_cell] * 8)

Calculate the twiss parameters:

twiss = ap.Twiss(ring)

Plot horizontal and vertical beta functions using matplotlib:

import matplotlib.pyplot as plt
plt.plot(twiss.s, twiss.beta_x, twiss.beta_y, twiss.eta_x)
plt.show()

Note

A FODO lattice is the simplest possible strong focusing lattice consisting out of a horizontal focusing quadrupole (F), a drift space (0), a horizontal defocusing quadrupole (D) and another drift space (0).