Tune shift with amplitude of the system. When the tune reaches resonant values, it can be unstable, and thus a tune-shift with amplitude can limit the stability region, or dynamic aperture. In classical mechanics, a simple example of a system with tune shift with amplitude is a pendulum. In accelerator physics, both the transverse and the longitudinal dynamics show tune shift with amplitude. A simple model of the transverse dynamics is of an oscillator with a single sextupole, it is referred to as the Hénon map. Another model for this case is the Standard Map. An important example is the typical case of distributed
Precursor (physics) a period corresponding to that of the highest-frequency component of the original impulse; with increasing time, components with lower and lower frequencies arrive, so the period of the precursor becomes longer and longer until the lowest-frequency component arrives. As more and more components arrive, the amplitude of the precursor also increases. The particular type of precursor characterized by increasing period and amplitude is known as the high-frequency Sommerfeld precursor. In a region of anomalous dispersion, where low-frequency components have faster group velocities than high-frequency ones, the opposite of the above situation occurs: the onset of the precursor is characterized by