1. Measurement of the Charge of a Particle in a Dusty Plasma Jerome Fung, Swarthmore College July 30, 2004

2. Introduction What is a dusty plasma? Why do we care about dusty plasmas? Making dusty plasma crystals The importance of electric charge Theory: Vertical resonance methods Preliminary results Sound speed methods

3. What is a plasma? Plasma: ionized gas –Contains positive ions, negative electrons, and neutral particles –4th state of matter: hotter than gases –Most abundant state of matter in the universe: found in stars, fluorescent light bulbs! High Voltage CathodeAnode Low Pressure Gas P L A S M A

4. plasma = electrons + ions What is a dusty plasma? small particle of solid matter becomes negatively charged absorbs electrons and ions & neutral gas

5. Solar system Rings of Saturn Comet tails Fundamental science Coulomb crystals Waves Manufacturing Particle contamination (Si wafer processing) Who cares about dusty plasmas?

6. Dusty Plasma Crystals Small (micron-sized) particles in plasma disperse into 2-D lattice Exhibits properties of solid crystal –Order of crystal lattice

7. Making Dusty Plasma Crystals Argon RF plasma 20 mTorr 8 - 20 W Polymer microspheres diameter 8.09  0.18  m

8. Voilà!

9. Particle Interactions and Forces Electrostatic ( F e = q E ) –Levitating sheath electric field –Horizontal particle confinement –Interparticle interactions Gravitational ( F g = m g ) Ion drag force, gas drag, thermophoresis qE mg ∑F = 0

10. Charge matters! Electrostatic force is the most significant –Many interactions, all depend on q –Most experiments/theory require knowledge of q Measurement techniques –Vertical Resonance (Melzer et al., Phys. Lett. A 191,1994) –Variation of vertical resonance (Goree) –Sound speed methods Natural phonons Laser-induced longitudinal / transverse waves

11. Vertical Resonance Method Key idea: modulate levitating RF electric field to “shake” crystal up and down, measure amplitude of oscillation –In practice, modulate voltage on electrodes –View oscillations via side view video camera Observe resonance ⇒ measure resonance frequency ⇒ determine particle charge!

12. Vertical Resonance: Theory Damped, driven oscillator equation: Resonance frequency: n i = plasma ion density (ions/unit volume)

13. Vertical Resonance: Issues Original method: requires measurement of ion density –Must be measured with a Langmuir probe in the bulk plasma, above the sheath –Problem: method requires extrapolation of ion density in bulk plasma to sheath –Large uncertainties in q, ~50% in original papers Modified method –Does not require ion density measurement –Makes assumption about the variation of the sheath electric field, which has been tested experimentally –Should result in smaller uncertainties

14. Preliminary Results: Resonance Curve n i ≈ 2 × 10 15 m -3 ω o /2π = 10.08 ± 0.01 Hz m ≈ 4.2 × 10 -13 kg q ≈ 3000 e

15. Vertical Resonance: Variation Assumes linear dependence on height for the electric field in the sheath Uses more easily measured quantities (e.g. plasma potential) instead of ion density q ≈ 9000 e

16. Sound Speed Methods Charge determined from material properties of plasma crystal Natural phonons Laser-induced pulses –Longitudinal –Transverse

17. Longitudinal Pulse

18. Conclusions Knowing charge necessary for lots of interesting experiments / theory with dusty plasma crystals Charge measured with 2 vertical resonance methods Further analysis of data from these methods and from sound speed methods is ongoing

19. Acknowledgements This project would not have been possible without the advice and assistance of Dr. Bin Liu and my advisor, Prof. John A. Goree. Several useful discussions with V. Nosenko and K. Pacha were also had. Work supported by an NSF REU grant.