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 \((2+ε)\), the plasma oscillation is exponentially enhanced with time, where \({=}\{1+(3/2)\ (n{π}a/l₀)²\}ω₀\) 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.