Nonlinear dynamical modelling of chaotic electrostatic ion cyclotron oscillations by jerk equations

Plasma being a nonlinear and complex system, is capable of sustaining a wide spectrum of waves, oscillations and instabilities. These fluctuations interact nonlinearly amongst themselves and also with particles: electrons/ions and thus lead to nonlinear wave-wave or wave-particle interaction. In the presence of coherent waves the particles are accelerated whereas irregular oscillations can give rise to particle heating which is also called stochastic heating. Particle orbits are known to be randomized by the wave fields such that their motion can also become stochastic. For fusion to be sustained one needs a very high temperature plasma for an extended duration. It quite common to deploy external waves like electron cyclotron waves or ion cyclotron waves for plasma heating and current drive. These external waves also work only in certain regimes. Conventional plasma techniques have been able to answer several of the observations of the above processes related to heating transport etc, but nonlinear dynamics as a tool has helped in comprehending the plasma oscillations better. We have for the first time obtained a Third Order nonlinear ordinary differential equation (TONLODE) also known as jerk equation to describe the electrostatic ion cyclotron plasma oscillations in a magnetic field. The interesting feature of this equation is that it does not require an external forcing term to obtain chaotic behaviour.