Oscillations of magnetoresistance in a clean hollow cylinder with fluctuating radius

We consider magnetic oscillations of resistivity of a clean hollow cylinder with fluctuating radius $R$, threaded by magnetic flux $\mathrm{\Phi }$. We demonstrate, that for very weak fluctuations $\mathrm{\Delta }R\ll p_F^{-1}$ the oscillations have a standard period $2{\mathrm{\Phi }}_0$ (where ${\mathrm{\Phi }}_0=\pi c\mathrm{\hslash }\mathrm{/}2e$), characteristic for oscillations in a clean system, while for $\mathrm{\Delta }R\gg p_F^{-1}$ they become ${\mathrm{\Phi }}_0$-periodic, which was expected only for dirty systems with $R\gg l$. The work is motivated by observation of predominantly ${\mathrm{\Phi }}_0$-periodic magnetic oscillations in very clean Bismuth wires.