= Large-speed approximation for circular-trap kicks
{title2=$f_p\simeq f_T\Delta x/(2\pi R)$}
The exact separated-kick response is $f_p=f_T\Delta x/(C+\Delta x)$ for circumference $C=2\pi R$. Its relative correction to the independent-kick estimate is controlled by $\Delta x/C$. For a localized well with force-induced speed bounded by $\epsilon v_T$, $\Delta x/C\leq(w/C)\epsilon^2/(1-\epsilon)$. Thus high speed is sufficient when the support width is below one circumference. The local straight-force approximation also requires a narrow trap on the curved track.
Back to article page
