Surfatron acceleration of the high energy protons in the relativistic jets

TL;DR

This paper investigates how high-energy protons can be accelerated to ultra-high energies in relativistic jets through a surfatron mechanism involving electrostatic waves and spiral structures, providing formulas for maximum energy and spectrum.

Contribution

It introduces a novel surfatron acceleration model for protons in relativistic jets, deriving maximum energy and spectrum expressions based on jet parameters.

Findings

Protons can reach energies up to approximately 10^19 eV.

The model predicts specific energy spectra for accelerated protons.

Electrostatic waves with spiral structures facilitate proton acceleration.

Abstract

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