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Observations of Linear and Nonlinear Dust Acoustic Waves*

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. Introduction.

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Observations of Linear and Nonlinear Dust Acoustic Waves*

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  1. Observations of Linear andNonlinear Dust Acoustic Waves* Bob Merlino, Jon HeinrichSu Hyun Kim and John MeyerDepartment of Physics and AstronomyThe 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 Td • Collisions of electrons, ions and dust with neutrals • DC electric field E0

  4. Ion-dust streaming instability P = 100 mtorr E0 = 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, 124501, 2009

  6. B B Lens Plasma Anode g 532 nm Laser Side View Dust Tray Top View CMOS Camera Dusty plasma device Dust: silica microspheres (1 mm diameter) Plasma: argon, 10 – 20 Pa, ni ~ 1015 m3, Te  100 Ti  2-3 eV

  7. ion drift DAWs excited in a drifting dust cloud • A secondary dust suspension is trappedby 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.

  8. Drifting dust cloud and DAWs • When the center of cloud is about 10 cm from the anode, dustacoustic 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. rd = 0.5 mm silica microspheres t = 0.09 s t = 0.06 s nd / ndo t = 0.03 s nd / ndo t = 0 s t = 0 s FIT Time (s) Distance from anode (cm) Growth rate measurement

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

  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. 2nd order DA wave theory • Simple fluid theory (Stokes’ waves in ocean wave theory) • expandx(nd, ud, j) as a series in the small parameter, e to second order: x=x0+ e x1+ e2 x2 SOLUTION Nonlinearity generates 2nd harmonic term

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

  14. Primary DAW Secondary DDW 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

  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

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