Extremely efficient Zevatron in rotating AGN magnetospheres

A novel model of particle acceleration in the magnetospheres of rotating active galactic nuclei (AGN) is constructed.The particle energies may be boosted up to $10^{21}$eV in a two step mechanism: In the first stage, the Langmuir waves are centrifugally excited and amplified by means of a parametric process that efficiently pumps rotational energy to excite electrostatic fields. In the second stage, the electrostatic energy is transferred to particle kinetic energy via Landau damping made possible by rapid "Langmuir collapse". The time-scale for parametric pumping of Langmuir waves turns out to be small compared to the kinematic time-scale, indicating high efficiency of the first process. The second process of "Langmuir collapse" - the creation of caverns or low density regions - also happens rapidly for the characteristic parameters of the AGN magnetosphere. The Langmuir collapse creates appropriate conditions for transferring electric energy to boost up already high particle energies to much higher values. It is further shown that various energy loss mechanism are relatively weak, and do not impose any significant constraints on maximum achievable energies.