Tune Diagram

This example shows how to use the plot_tune_diagram function to visualise resonance lines up to certain orders.

import matplotlib.pyplot as plt

from pyhdtoolkit.plotting.styles import _SPHINX_GALLERY_PARAMS
from pyhdtoolkit.plotting.tune import plot_tune_diagram
from pyhdtoolkit.utils import logging

logging.config_logger(level="error")
plt.rcParams.update(_SPHINX_GALLERY_PARAMS)  # for readability of this tutorial

The tune diagram allows on to visualise resonance lines up to certain orders, and to know where the working point of the machine stands compared to these resonances By default, the plot_tune_diagram function will plot all resonance lines up to the specified order, with line thickness decreasing with the resonance order. The max order is set 6, as the graph becomes unreadable above this value.

fig, ax = plt.subplots(figsize=(10, 10))
plot_tune_diagram(max_order=5)
plt.show()

One can add their machine’s working point onto the figure with a new matplotlib plotting command. The graph is limited to the ranges [0, 1] on each axis as the fractional part of the tunes is what determines stability.

Tip

Remember that when thinking about tunes, only the fractional part is relevant when determining the stability. As so, plot that value onto the graph, or it would be way out of range

fig, ax = plt.subplots(figsize=(10, 10))
plot_tune_diagram(max_order=5)
plt.scatter(0.35, 0.29, marker="o", color="red")  # this is close to a third order resonance
plt.show()

On the previous plot, it is not obvious that our working point is close to a third order resonance. One may then want to differentiate the origin of each line, aka knowing which resonance order is responsible for each given line. This makes it easier to see the resonances near your working point.

fig, ax = plt.subplots(figsize=(10, 10))
plot_tune_diagram(
    max_order=6,
    differentiate_orders=True,  # different orders will have a different color and linestyle
    legend_title="Resonance Lines",  # if given, legend is added to figure
)
plt.scatter(0.35, 0.29, marker="o", color="red")  # this is close to a third order resonance
plt.xlim(0, 0.5)  # limit the x-axis to the range [0, 0.5] for visibility
plt.ylim(0, 0.5)  # limit the y-axis to the range [0, 0.5] for visibility
plt.show()

It is now much easier to identify the resonances lines near our working point :)

References

The use of the following functions, methods, classes and modules is shown in this example:

• tune: plot_tune_diagram