Abstract
This paper describes the acceleration of high-energy protons captured by electrostatic waves in the frame of a jet arising in the area of instability of a relativistic jet, where spiral structures are excited. The wave has a spatially heterogeneous structure of $\mathrm{exp}(i{k}_{\ensuremath{\parallel}}z+i{m}_{\ensuremath{\phi}}\ensuremath{\phi})$. Protons can be captured in potential wells created by spiral waves, and thereby experience acceleration via a mechanism known as surfatron acceleration. Expressions for the maximum energy (${E}_{p}\ensuremath{\simeq}{10}^{19}\text{ }\text{ }\mathrm{eV}$) and energy spectrum from jet parameters are obtained.
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