Acoustic self-oscillation in a spherical microwave plasma

We present a method of sound amplification and self-oscillation in high pressure partially ionized gas. Continuous microwaves incident on partially ionized gas may sustain and amplify an acoustic field if increased ionization during the sound field's adiabatic compression enhances rf power absorption. Amplifying sound in this way enables the generation of high amplitude sound in a cavity containing partially ionized gas without mechanical driving or precise knowledge of its resonance frequency. This method of amplification may open opportunities within thermoacoustics such as using three-dimensional geometries and volumetric gain mechanisms.

Figure 1

Spherical acoustic resonator sits within a microwave cavity. Low levels of ionization in the hot gas within the resonator allow driving sound with amplitude modulated microwaves. Under the right conditions, sound will spontaneously develop in the presence of a continuous wave (i.e., no modulation) microwave field.

Figure 2

Comparison of the acoustic damping time constant, ${\tau }_{\kappa }$, and the acoustic amplification time constant, ${\tau }_{\mathrm{amp}}$, for three incident powers, neutral density $N_0=2.5\times {10}^{19}$ per cc, and microwave quality factor $Q_c=1000$. When ${\tau }_{\mathrm{amp}}<{\tau }_{\kappa }$, the energy added to the acoustic field by the absorbed microwave exceeds the acoustic losses. The increase in amplification time at low temperatures is due to the inability of low temperature plasma to absorb microwaves as described in the text. To illustrate how the quality factor impacts the amplification time, the 2 kW case is shown both with $Q_c=1000$ (solid) and $Q_c=2000$ (dotted).

Figure 3

For each power, acoustic amplification exceeds thermal acoustic damping, ${\tau }_{\mathrm{amp}}<{\tau }_{\kappa }$, to the left of the solid curve. In the region to the right of the dashed line, the electron-neutral collision time is short enough to justify use of the Drude conductivity. Below the dotted line, the microwave penetration depth is larger than the plasma radius, which justifies use of a constant electric field throughout the plasma. The shaded area represents the region in parameter space in which this analysis predicts acoustic self-oscillation for the 2 kW case.