Oscillations of magnetoresistance in a clean hollow cylinder with fluctuating radius

We consider magnetic oscillations of resistivity of a clean (mean free path $l\gg R$) hollow cylinder with fluctuating (with an amplitude of fluctuations $\Delta R\ll\overline{R}$) radius $R$, threaded by magnetic flux $\Phi$. We demonstrate, that for weak fluctuations ($\Delta R\ll p_{\text{F}}^{-1}$) the oscillations have a standard period $2\Phi_0$, characteristic for oscillations in a clean system, while for $\Delta R\gg p_{\text{F}}^{-1}$ they become $\Phi_0$-periodic, which was expected only for dirty systems with $l\ll R$. The work is motivated by observation of predominantly $\Phi_0$-periodic magnetic oscillations in very clean Bismuth wires.