Dynamics and stability of one-dimensional plasma with periodic boundary

We extend the method proposed by Miller and Rouet to formulate analytic solutions for the electric potential and field in a one-dimensional plasma satisfying periodic boundary conditions. We have also devised an event-driven algorithm to follow the time evolution of the system and to study its dynamical properties. In a dynamical system, the presence of positive Lyapunov exponents indicates that the system is chaotic. Of particular interest is the value of the largest (maximal) Lyapunov exponent which is usually sufficient to point toward the degree of chaos in the system. Using our new approach for defining the phase-space distance in systems with periodic boundary, we have employed our algorithm to find the largest Lyapunov exponent in the periodic plasma. Results obtained from our algorithm will be discussed with a view to exploring the dependence of chaotic properties of the system on its initial state.