Twiss parameter of a FODO lattice

This example shows how to calulate and plot the Twiss parameter of a FOOD lattice.

import numpy as np
import apace as ap

D1 = ap.Drift("D1", length=0.55)
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_CELL", [q1, d1, b1, d1, q2, d1, b1, d1, q1])
fodo_ring = ap.Lattice("FODO_RING", [fodo_cell] * 8)

Output some info on the FODO lattice

print(
    f"Overview of {fodo_ring.name}",
    f"Num of elements: {len(fodo_ring.sequence)}",
    f"Lattice Length : {fodo_ring.length}",
    f"Cell Length    : {fodo_cell.length}",
    sep="\n",
)

Create a new Twiss object to calculate the Twiss parameter

twiss = ap.Twiss(fodo_ring)

print(
    f"Twiss parameter of {fodo_ring.name}",
    f"Stable in x-plane: {twiss.stable_x}",
    f"Stable in y-plane: {twiss.stable_y}",
    f"Horizontal tune  : {twiss.tune_x:.3f}",
    f"Vertical tune    : {twiss.tune_y:.3f}",
    f"Max beta x       : {np.max(twiss.beta_x):.3f}",
    f"Max beta y       : {np.max(twiss.beta_y):.3f}",
    sep="\n",
)

Use the builtin plot_lattice utility function to plot the Twiss parameter

from apace.plot import TwissPlot

fig = TwissPlot(twiss, fodo_ring).fig