Tune Measurement

Get tune from Fourier-Transform of transversal particle oscillation at fixed position

Lattice file:

{
  "version": "2.0",
  "title": "FODO Lattice",
  "info": "This is the simplest possible strong focusing lattice. (from Klaus Wille Chapter 3.13.3)",
  "root": "FODO",
  "elements": {
    "D1": ["Drift", {"length": 0.55}],
    "Q1": ["Quadrupole", {"length": 0.2, "k1": 1.2}],
    "Q2": ["Quadrupole", {"length": 0.4, "k1": -1.2}],
    "B1": ["Dipole", {"length": 1.5, "angle": 0.392701, "e1": 0.1963505, "e2": 0.1963505}]
  },
  "lattices": {
    "FODO": ["Q1", "D1", "B1", "D1", "Q2", "D1", "B1", "D1", "Q1"]
  }
}

Some imports …

import numpy as np
from pathlib import Path
from scipy.fftpack import fft
import apace as ap
import matplotlib.pyplot as plt
from math import sqrt

Load FODO lattice from file

fodo = ap.Lattice.from_file("../data/lattices/fodo_cell.json")

Create particle distribution

n_particles = 5
n_turns = 50
position = 0
dist = ap.distribution(n_particles, x_dist="uniform", x_width=0.002, x_center=0.001)

matrix_tracking = ap.TrackingMatrix(fodo, dist, turns=n_turns, watch_points=[0])

Plot x-x’ phase space

plt.subplot(2, 2, 1)

for i in range(n_particles):
    plt.plot(matrix_tracking.x[:, i], matrix_tracking.x_dds[:, i], "o")

plt.xlabel("x / m")
plt.ylabel("x'")

freq = np.linspace(0.0, 1.0 / (2.0 * fodo.length / 299_792_458), n_turns // 2)
fft_tracking = 2.0 / n_turns * np.abs(fft(matrix_tracking.x[:, -1])[: n_turns // 2])
main_freq = freq[np.argmax(fft_tracking)]

# Plot horizontal frequency spectrum
plt.subplot(2, 2, 2)
plt.plot(freq, fft_tracking)
plt.xlabel("Freq / Hz")
plt.ylabel("Fourier transform")
plt.axvline(x=main_freq, color="k")

# Plot horizontal offset for fixed position
plt.subplot(2, 2, 3)
plt.plot(matrix_tracking.orbit_position, matrix_tracking.x[:, -1], "rx")
plt.xlabel(f"orbit position / s")
plt.ylabel(f"horizontal offset x at fixed position {position} / m")

# Plot horizontal offset for multiple positions
matrix_tracking_all_positions = ap.TrackingMatrix(fodo, dist, turns=n_turns)

plt.subplot(2, 2, 4)
plt.plot(
    matrix_tracking_all_positions.orbit_position,
    matrix_tracking_all_positions.x[:, -1],
    linewidth=0.5,
)
plt.plot(matrix_tracking.orbit_position, matrix_tracking.x[:, -1], "rx")
plt.xlabel("orbit position / s")
plt.ylabel("horizontal offset for all positions / m")


plt.gcf().set_size_inches(16, 8)