Collisional Penrose process and jets in Kerr naked singularity

In this article, we investigate the possibilities of energy extraction from an over-spinning Kerr spacetime using collisional Penrose process. This phenomenon can produce a high-energy ejecta of particles under certain favourable conditions. Unlike black holes, in this case, the particles endowed with higher energy can escape to infinity. We use this model to explore various possibilities of jet formation in an over-spinning geometry. Primarily we concentrate on the energy extraction associated with collisions taking place on the off-equatorial planes and find the signature of jets from them. We also apply this formalism to a toy model which could be useful in practical astrophysical scenarios. This is motivated from the atomic model where we have considered the decay of a circular orbit because of energy extraction via Penrose mechanism.