Saturation of the Ion-Acoustic Instability in a Weakly Ionized Plasma

The spatial saturation and the frequency dependence of the energy spectrum of ionacoustic waves in a low-pressure discharge in helium in the pressure range 0.03-0.2 Torr has been investigated. In the high-pressure region the spectrum is peaked around the most unstable frequency predicted by linear theory [i.e., ${\omega }_{\mathrm{Peak}}\sim \left(\frac{1}{\sqrt{3}}\right){\omega }_i$], and the wave energy saturates at the modest value of $\frac{W}{n{T}_e}\simeq {10}^{-5\mathrm{}}$. At low pressures the wave energy increases and varies with frequency according to $W\left(\omega \right)\propto {\omega }^{-\alpha }$, with $\alpha$ assuming values between 2.2 and 2.8.