Nonlinear oscillation that indicates chaotic behavior at low frequency in a gas discharge plasma is investigated by analytic and numerical solutions. The electric field in plasma is determined through the Poisson equation by assuming charge distribution: ions distribute spatially uniform, beam electrons from hot cathode are described by an exponentially decreasing distribution, and plasma electrons are in thermal equilibrium and described by the Boltzmann distribution. The electrostatic potential that is obtained analytically by using linear approximation contains the Debye shielding effect. Low frequency motion of the ions in this electric field is calculated numerically. Period-doubling bifurcation and chaotic oscillation are obtained for a region of parameters and they agree with the experimental results qualitatively.
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