1 Observations of Linear and Nonlinear Dust Acoustic Waves* Bob Merlino, Jon Heinrich Su Hyun Kim and John Meyer Department of Physics and Astronomy The University of Iowa, Iowa City, Iowa *Supported by DOE and NSF

2 Introduction The DAW is the most basic dust density wave involving motion of the dust particles Dispersion relation: Often reaching very high amplitudes with non- sinusoidal waveforms, may develop into shocks Very difficult to see the linear growth phase, except at high neutral pressures where it is nearly quenched Observations discussed in this talk: –Linear growth of DAWs in a drifting dusty plasma –Nonlinear DAWs and second order wave theory –Secondary dust waves associated with nonlinear DAWs

3 Dust acoustic waves (DAW) The DAW wave is spontaneously excited in gas discharge dusty plasmas by an ion-dust streaming instability Dispersion relation from fluid theory –finite T d –Collisions of electrons, ions and dust with neutrals –DC electric field E 0

4 Ion-dust streaming instability P = 100 mtorr E 0 = 100 V/m

5 DAWs in discharge plasmas DAWs are often observed in discharge dusty plasmas at low neutral pressures Solid lines are numerical solutions of the dispersion relation for various experimental parameters The region below a curve signifies that the mode is unstable The points correspond to different experiments Ion drift in discharges are sufficient for instability Phys. Plasmas 16, , 2009

6 Dusty plasma device Dust: silica microspheres (1 mm diameter) Plasma: argon, 10 – 20 Pa, n i ~ m  3, T e  100 T i  2-3 eV CMOS Camera Top View B Dust Tray 532 nm Laser Plasma B Side View Anode g Lens

7 DAWs excited in a drifting dust cloud A secondary dust suspension is trapped by a biased grid 15 cm from the anode. When the bias on the grid is switched off, the grid returns to its floating potential, and the secondary cloud is released. The secondary cloud begins drifting toward the anode. ion drift

8 Drifting dust cloud and DAWs When the center of cloud is about 10 cm from the anode, dust acoustic waves begin to be excited in the quiescent dust cloud. The DAWs begin being excited when they reach the point where the ion drift is sufficient to drive the ion-dust streaming instability

9 Growth rate measurement  n d / n do Distance from anode (cm) t = 0 s t = 0.03 s t = 0.06 s t = 0.09 s Time (s)  n d / n do FIT r d = 0.5  m silica microspheres

10 Comparison to DAW (F, K) theory f (F) f (K)f (K)  (F) (F)  (K) (K) Frequency (Hz) Growth rate (s  1 ) Wavelength (m) Growth rate Frequency

11 Nonlinear dust acoustic waves Spontaneously excited DA waves often grow to very high amplitudes DA waveforms are non-sinusoidal, typically with sharp wave crests and flat wave troughs

12 2 nd order DA wave theory Nonlinearity generates 2 nd harmonic term Simple fluid theory (Stokes’ waves in ocean wave theory) expand  (n d, u d,  ) as a series in the small parameter,  to second order:  0  1    2 SOLUTION

13 Compare 2 nd order theory to data The fit has a second harmonic amplitude of 30% of the first harmonic amplitude. 2 nd order theory captures sharp crests and flat troughs. Higher order theory provides qualitative and quantitative corrections over linear theory – this was a first start. Exp. Theory

14 Secondary dust density waves Secondary dust density waves (SDDW) were observed in the troughs of high amplitude DAWs The SDDW propagated in the direction opposite to the primary DAW SDDW grow in thedust that is displaced by the nonlinear DAW and then restored back Primary DAW Secondary DDW

15 Dust Density (arb)

16 Secondary dust density waves

17 Dust-dust streaming instability We considered the possibility that the SDDW were excited by a dust-dust streaming instability between the background dust and the restoring dust drift. The kinetic dispersion relation was obtained and solved for the parameters of the experiment. The theory give values for the frequency and wavelength (for max. growth) that fit the results (M. Rosenberg)

18 Summary The linear growth of DAWs was observed in a drifting dusty plasma The measured growth rates agreed well with the kinetic theory of DAWs High amplitude (nonlinear ) DAWs exhibit non-sinusoidal waveforms that seem to be accounted for by second-order DAW theory Secondary DDW were observed in the presence of nonlinear DAW which may be excited by a dust-dust streaming instability