Excitation of Plasma Oscillations by Parametric Resonance

A typical example of parametric resonance of plasma oscillations is theoretically investigated. When the width of a plasma slab is periodically perturbed with frequency \((2+\varepsilon)\varOmega\), the plasma oscillation is exponentially enhanced with time, where \(\varOmega{=}\{1+(3/2)\ (n{\pi}a/l_{0})^{2}\}\omega_{0}\) is the characteristic frequency of the plasma slab, ω ₀ being the plasma frequency, a the Debye length, l ₀ the width of the slab, n an integer, and | ε |≪1. The growth rate γ _R is given by γ _R ² =(1/4)(σ ² - ε ² )ω ₀ ² , where σ=( n π a / l ₀ ) ² h , h being the ratio of change of width to l ₀ . In a magnetic field the Bernstein mode is also excited by parametric resonance.