Speaker
Dr
Shane Koscielniak
(TRIUMF)
Description
The pendulum equation is the archetype for longitudinal motion within an RF bucket. The restoring force is sinusoidal. The case that the confining potential is composed of fundamental and second harmonic is called "dual harmonic". The solution to the pendulum equation of motion in terms of Jacobi elliptic functions is well known, for 140 years. The solution to the dual harmonic equation, also in terms of elliptic functions, is almost unknown. Here we present the solutions for confined and unbounded motion, with almost arbitrary ratio of the two harmonics. The oscillation frequency as a function of oscillation amplitude is a collateral prediction.
| Paper status | Proceeding files received |
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Author
Dr
Shane Koscielniak
(TRIUMF)