Trapping of plasma enabled by pycnoclinic acoustic force

Sound can hold partially ionized sulfur at the center of a spherical bulb. We use the sulfur plasma itself to drive a 180 dB re 20 $\mu \mathrm{Pa}$ sound wave by periodically heating it with microwave pulses at a frequency that matches the lowest order, spherically symmetric, acoustic resonance of the bulb. To clarify the trapping mechanism, we generalize acoustic radiation pressure theory to include gaseous inhomogeneities and find an interaction of high-amplitude sound with density gradients in the gas through which it propagates. This is the pycnoclinic acoustic force (PAF). Though generated by rapidly oscillating sound waves, it has a finite time average and manipulates the plasma through density gradients at its boundary. The PAF is essential for the description of the trap holding a plasma against its own buoyancy as well as understanding convection in the region outside the plasma. It has implications for pulse tubes, thermoacoustic engines, thermal vibrational convection in microgravity, combustion in the presence of sound, and the modeling of Cepheid variable stars.

Figure 1

(a) Pycnoclinic acoustic force holds plasma centrally in a spherical bulb. (b) In the absence of sound, the plasma fills the bulb. The bulb rotates at 50 Hz in both states; otherwise the bulb is prone to sudden extinction. Hexagonal shading in the images is due to the metallic mesh cavity surrounding the bulb. The light emission in the trapped (c) and normal (d) states is qualitatively different. The high-pass filtered signal transitions from sawtooth to sinusoidal in shape near an acoustic resonance. When the plasma is trapped, the peak-to-peak oscillation amplitude is $20\times \text{to}60\times$ larger than in the normal state. Acoustic pressure and velocity in the lowest frequency, spherically symmetric mode are plotted in the inset of (a). High-speed videos of each state as well as of the transition from the normal to the trapped state are available in the Supplemental Material [9].

Figure 2

Plasma size and spatially integrated light emission over time.

Figure 3

Instability periodically generates ejections of warm material from the hot core (a) (shown in Supplemental video S5 [9]). The ejections cool when they reach the glass, lowering the acoustic resonant frequency. Beating between the drive frequency and frequency-shifted sound is seen in the high-pass filtered photodiode signal (b). Microwave heating slowly increases the gas temperature, and when the resonant frequency matches the drive, the sound amplitude rapidly builds up, driving the next ejection.

Figure 4

Periodic ejections in the trapped state increase the heat flow to the quartz bulb, raising its temperature by $\sim 100$ K.