Some Researches on Dusty Plasmas

More documents

Recommendations

Info

Bohm velocity, which is the same as the ion-acoustic speed. Thus wake effects associated with this flow are to be expected. One of the first experiments carried out at Oxford related to probe-induced particle circulation in a plasma crystal [1]. The apparatus is illustrated in Figure 1; a capacitively coupled R.F. discharge in argon was employed, the lower electrode being driven at 13.56 MHz, through a matching network. A Langmuir probe was used to determine the plasma parameters prior to inserting the dust particles. On introducing the dust particles, however, the plasma crystal was significantly affected by the probe. Particle circulation was induced around a stable crystalline island, as shown in Figure 2 (and the associated video). A complete theory of the phenomenon has not been carried out. It would involve modification of the electric field in the sheath and also a change in the momentum of the positive ions arriving at the plasma crystal. An estimate was made, however, of the bulk modulus of the crystal K = – Δ P/( Δ V/V 0 ), knowing the momentum carried by the impinging dust particles and the increased density of the crystal. This enabled us to calculate the sound speed in the crystal, c s = (K/ ρ ) ½ = 0.019 m/sec, which was comparable to other published measurements. 3. Effect of laser light on a plasma crystal. Another experiment performed in Oxford was carried out using a focussed low power (maximum power ~150 mW/mm 2 ) HeNe laser beam (632.8 nm) to fracture a crystal [2, 3]. The laser beam was normally used to provide illumination for the dust particles, via a lens to produce a fan of light. When the lens was inadvertently omitted from the system, however, it was found that the focussed beam could drill a hole through the plasma crystal, as shown in Figure 3 (see also the video). A certain threshold power was required to knock particles out of the plasma crystal, not surprisingly. The power of the beam could be changed by using a calibrated variable neutral density filter. Measurements were made of the velocities acquired by the particles when higher laser powers were employed, see Figure 4. The radiation pressure of the beam, (E 2 /Z)/c, although small, was sufficiently high to explain the observed results. When first reported, at a small meeting at Bad Honnef, the audience did not accept this explanation. But within a few months other laboratories were employing such techniques, sometimes using a light chopper to produce a series of radiation pulses. 4. Damped dust oscillations as a plasma sheath diagnostic. It has already been mentioned that many experiments have been carried out for dust particles residing in the space charge sheath adjacent to the plasma. In equilibrium the most important forces on the charged dust particle are the electric force and the weight, the ion drag being less important. The method that we have employed at Oxford to measure the charge was to observe damped oscillations around the equilibrium position [4]. Other workers have employed forced oscillations, where a low-frequency voltage is applied either to a probe or to the adjacent electrode, we believed, however, that the use of such techniques must disturb the plasma. In our case the dust particles were simply dropped into the plasma. When the dust particle is in motion the damping is due to collisions with neutral atoms and the expression for the drag force due to Epstein has been employed. The potential distribution in the sheath was assumed to be parabolic in nature, leading to the following simple equation of motion for the dust particles. 2
M & z +γ z& + κ (z-z eq ) = 0 (1) where M is the particle mass, γ the drag constant, κ is the restoring constant and z is the height above the electrode. <strong>Some</strong> experimental results are shown in Figure 5. The values of the charge on the dust particle, deduced from these measurements, are shown in Figure 6. 5. Parabolic sheath potentials and their implications for the charge on levitated dust particles. Following the work described in the previous paragraph, a number of different sheath models were examined as illustrated in Figure 7 [5]. It was found that a parabolic fit to the potential distributions was surprisingly accurate, for relevant ranges of potential. Even the well-known Child-Langmuir Law, V ∝ x 4/3 , can be wellrepresented by a parabola for a limited range of potential. Using a parabolic potential distribution the charge on dust particles was determined by measuring their height above the electrode. It would appear that this simple method had not previously been used. Results are shown in Figure 8, where they are compared with those obtained from the damped oscillation method. It is seen that the agreement is good at the higher pressure (13.33 Pa) and not quite so good at the lower pressure (6.67 Pa). 6. On the orbital motion limited theory for a small body at floating potential in a Maxwellian plasma. In a paper with the above title [6] we have shown that the O.M.L. (orbital motion limited) theory is incorrect for Maxwellian plasmas, at least for the case where T i is less than or equal to T e . This theory has been extensively employed by workers in the field of dusty plasmas. I shall not go through the details of the aforementioned paper, but I shall explain why the theory is wrong. The principles used in the O.M.L. theory are the conservation of energy and the conservation of angular momentum. The first of these gives the following equation ½M v 2 = ½M v p 2 + eV p = 0 (2) where v p is the velocity at the surface of the dust particle (or probe), V p < 0. Conservation of angular momentum gives, for an ion grazing the surface of the dust particle Mvh p = Mv p r p (3) where h is the impact parameter, as shown in Figure 9, and h p is the impact parameter for a particle which grazes the surface of the dust particle (or probe). h p = r p (1-V p /V 0 ) ½ (4) The initial energy of the ion is denoted by eV o . The expression given by equation (4) represents an effective target radius of the dust particle (or probe) for ions of that particular energy, (according to this theory). On integrating over a Maxwellian velocity distribution one can readily obtain the following expression for the ion current. 3
Page 2 and 3: Overview The importance of dusty p
Page 4 and 5: Experimental Set-up
Page 6 and 7: The fracture of a plasma crystal by
Page 8 and 9: Measurement of charge using damped
Page 10 and 11: Measurement of charge using the bal
Page 12 and 13: The orbital motion limited (OML) th
Page 14 and 15: The floating potential of spherical
Page 16 and 17: The floating potential of spherical
Page 18 and 19: On the drag on an object immersed i
Page 22 and 23: I= 4π r p 2 n o e(kT i /2π ) ½ (
Page 24 and 25: The first and second terms on the R
Page 26: data and fit for P = 13.33 Pa while

Some Researches on Dusty Plasmas

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?