footprint.rst

Tune footprint and stability diagram

The Line class provides a method to compute and optionally plot the tune footprint as illustrated in the following example.

Table of Contents

Basic usage

See also: xtrack.Line.get_footprint

generated_code_snippets/footprint.py

Footprints produced with a polar grid.

Footprints produced with a uniform grid in action space.

Linear rescale on knobs

In some cases the effects introducing the detuning also introduce other effects (e.g. coupling, or non-linear resonances) that disturb the particles tune measurement. In this case it is possible to rescale quantify the detuning for smaller values of the knobs associate to the detuning effects and rescale to the actual value of the knob. This can be done by the linear_rescale_on_knobs option as illustrated in the following example for a case where the detuning with amplitude is introduced by beam-beam interactions.

See also: xtrack.Line.get_footprint

generated_code_snippets/footprint_with_bb.py

Footprints produced without rescaling beam-beam knob.

Footprints produced with rescaling beam-beam knob.

Stability diagram

Using the amplitude detuning given by the tune footprint, it is possible to evaluate numerically the dispersion integral from https://cds.cern.ch/record/318826 and obtain the stability diagram as in https://doi.org/10.1103/PhysRevSTAB.17.111002.

If the context is xobjects.ContextCupy, both the tracking and the numerical integration are performed on the GPU.

generated_code_snippets/stabilitydiagram.py