DUST CHARGE VARIATION IN A NON- THERMAL PLASMA Abid Ali Abid Department of Applied Physics, Federal Urdu University of Arts, Science and Technology, Islamabad 44000, Pakistan National Centre for Physics, Quaid-e-Azam University Campus, Islamabad.

What is a Dusty (Complex) Plasma   “ Dust” = small particles of solid matter, 10 nm – 1 mm,   Acomplex plasma can be comprised of electrons, ions, and dust particles   Dust particles may be made of dielectric, metallic, and ice particles (viz. silicates, graphite, magnetite, amorphous carbons, etc.).   mass: billions times heavier than protons: not constant Refs: Geortz (1989); Mendis & Rosenberg (1994); Verheest (2000); Shukla and Mamun (2002).

Occurrence   Dusty plasmas are most common in interplanetary space, interstellar medium, interstellar clouds, comets, planetary rings, earth atmospheres, etc. Dust in interplanetary space and in comet: (Wurden et al. 1999). The appearance of interplanetary dust particles (courtesy of Dr. Scott Messenger, WU) Mysterious spokes of Sarurn’s B-ring (courtesy of Jet Propulsion Laboratory (JPL)). ion tail dust tail

Occurrence   Dusty plasma are also observed in laboratory, i.e.  dc and rf discharges,  Plasma processing reactors,  Semiconductor industry [2], .  fusion plasma devises.   Solid-fuel combustion products,   Plasma chemistry   nanotechnology, etc. 4 Semiconductor industry “particulates” or “particles” [2] G.S. Selwyn, Plasma Sources Sci. Tehcnol. 3, 340 (1994)

Non-Maxwellian Velocity Distribution Functions   When the plasma particles move faster than their thermal speeds, the Maxwellian distribution becomes inadequate to study the behavior of superthermal particles appropriately.   A non-Maxwellian distribution can be described by a new kappa distribution, which is given by [1]. (1) (1)   Where is the effective thermal speed,   Г is gamma function   ƙ -parameter shows the superthermality effects and always ƙ > 3/2.   For small ƙ values, it represents a power-law distribution in velocity with high energy tails.   For ƙ ∞ the distribution function reduces to Maxwellian distribution [1] V. M. Vasyliunas, J. Geoohys. Res. 73, 2839 (1968). [1] V. M. Vasyliunas, J. Geoohys. Res. 73, 2839 (1968).

Non-Maxwellian (cont.)   Recently, a considerable attention has been focused in studying collective dusty modes in the presence of non- Maxwellian distribution, which is a generalized case of the Maxwellian distribution.   It is taken into consideration due to due to the external forces acting on space and astrophysical environments [3], for example.   Ionosphere.   Auroral zone plasmas.   Mesosphere.   Lower thermosphere.   Solar wind.   Interstellar medium..   Interstellar medium.   Magnetoshpere, etc. [3] V. Pierrad, and M.Lazar, Sol. Phys. 267, 153 (2010).

Charging mechanisms I electron I ion I ion   Electron emission  secondary emission due to e - impact   Photoemission   Thermionic emission    positive charge - +   Charging by collecting electrons and ions only charge  negative charge I electron I ion I electron emission e-e- Electron thermal speed >> ion thermal speed so the grains charge to a negative potential relative to the plasma, until the condition is achieved. Refs: Whipple et al. (1985); Northrop (1992); Choi and Kushner (1994); Young et al. (1994); Barkan et al. (1994) Mamun and Shukla (2003).

Dust Grain Surface Potential in A Non- Maxwellian Dusty Plasma with Boltzmannian Negative Ions   Where is the fundamental charging equation for dust grain created by the electrons and positive/negative ions in an generalized ƙ –DF   When the dust charge attains its steady state value (viz. q d =const), the current balance equation comes into play caused by the electrons and positive/negative ions in non-Maxwellian plasmas and can be expressed [4], as (2) (3) Where (3) with [4] N. Rubab, and G. Murtaza, Phys. Scr. 74, 178 (2006). [4] N. Rubab, and G. Murtaza, Phys. Scr. 74, 178 (2006).

Dust Grain-- with Boltzmannian (cont.)   Current of Plasma Species with κ- Distribution To proceed, we simplify (3) by integrating over the non-Maxwellian velocity distribution function and express the volume element as in spherical coordinates. The currents due to electrons, positive ions, and negative ions for negatively charged dust grains, respectively, as and (4) (5) (6)

Dust Grain-- with Boltzmannian (cont.) where The corresponding effective thermal speeds for electrons, positive ions, and negative ions are, respectively, given by and and

Dust Grain-- with Boltzmannian (cont.) By using the relation and the charge-neutrality condition The equilibrium dust grain surface potential in the presence of kappa-DF for a negatively charged dust grains can be obtained by substituting Eqs. (4)-(6) into Eq. (2), [5] as with [5] A. A. Abid, S. Ali, and R. Muhammad, J. Plasma Phys. 79, 1117 (2013). (7)

Dust Grain-- with Boltzmannian (cont.)   The normalized dust grain potential   The normalized dust number density   with   When κ → ∞, we have a κ ∼ 1 and b κ ∼ exp(U). As a consequence, (7) exactly reduces to the earlier results [6] showing the dust grain potential in a Maxwellian dusty plasma [6]. Note that in the absence of negative number density (α=0), Eq. (7) may reproduce Eq.(3) of Ref [7] for isolated dust grains [6] [6] A. A. Mamun, and P. K. Shukla, Phys. Plasmas 10, 1518 (2003). [7] A. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Rev. Lett. 73, 3093 (1994).

Numerical Result and Discussion   For numerical illustration, we have solved Eqs. (7) to study dust surface potential (U) as a function of the normalized dust number density (P).   To examine the effects of various plasma parameters in a non-Maxwellian dusty plasma. The latter contains negative and positive ions (O ₂⁻ and O ₂⁺ ions) in addition to electrons and negatively charged isolated dust grains.   Considered some normalized values, which are consistent with low-temperature laboratory plasmas namely, α=0-0.6, β=1, μ=242.8 γ=0.1-1, σ=0.1-1, and Ref; Amemiya et al. (1998); Amemiya et al. (1999); Vyas et al.( 2002); Mamun and Shukla (2003).

Numerical Boltzmanian Negative ions(cont.)   See that as we increase the value of kappa, the curves tend to approach the Maxwellian case. For κ ∼ 50, our result is exactly in agreement with earlier studies [6], which is in thermodynamic equilibrium.   Interestingly, at lower κ-values, the magnitude of the negative dust surface potential increases and the effect becomes significant when log P is less than −1.75.  Figure 1.The normalized dust surface potential (U = e ϕ d /T e ) versus normalized dust number density parameter (P = 4πn d r d λ 2 0 ) (as given in (7)) for different values of spectral index κ (=2.6,4,50). Other numerical values used are: σ =1, α = 0.4, β = 1, γ = 0.3, μ = 242.8, and Zi = 1 = Zn. [6] A. A. Mamun, and P. K. Shukla, Phys. Plasmas 10, 1518 (2003).

Numerical---- Boltzmanian Negative ions (cont.)   The dependence of negative ion temperature γ (=0.1, 0.5, 1) is shown on the curves of U and P (given by (7)) in Fig. 2.   It is evident from the plot that the magnitude of the dust surface potential increases with the increase of negative ion temperature effect.  Figure 2. The normalized dust surface potential (U) versus normalized dust number density parameter (P) (as given in (7)) for different values of the negative ion-to-electron temperature ratio γ (=0.1, 0.5, 1) with fixed κ = 3 and σ =0.2. Other numerical values are the same as in Fig. 1.

Numerical-----Boltzmanian Negative ions(cont.)   In Figure 3, we note that increase in the negative ion number density causes a significant reduction of electrons via the charge-neutrality condition –Figure 3. The normalized dust surface potential (U) versus normalized dust number density parameter (P) (as given in (7)) for different values of the negative ion number density α (=0, 0.3, 0.6) with κ = 4, γ = 0.5, and σ = 0.2. Other numerical values are the same as in Fig. 1

Dust Grain Surface Potential in A Non-Maxwellian Dusty Plasma with Streaming Negative Ions   For the negative ion current with κ-distribution is given by   Using (4), (5), and (8) into (2), we obtain the equilibrium dust grain surface potential in the presence of kappa distribution for a streaming negatively charged dust grains can be determined [5], as where [5] A. A. Abid, S. Ali, and R. Muhammad, J. Plasma Phys. 79, 1117 (2013). (8) (9)

Dust Grain with Streaming(cont.)  For taking the spectral index κ → ∞, we have a κ ∼ 1, b κ ∼ exp(U), c κ ∼ 0.5, and d κ ∼ 1.9. Hence, Eq. (9) exactly coincides the results of Ref. [6].   Note that in the absence of negative number density (α=0) and negative ion streaming (U ₀ ), Eq. (9) may reproduce Eq.(3) of Ref [7] for isolated dust grains [6] A. A. Mamun, and P. K. Shukla, Phys. Plasmas 10, 1518 (2003). [7] A. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Rev. Lett. 73, 3093 (1994).

Numerical Result and Discussion with negative ion Streaming   Figs. 4 represent how the negative ion streaming speed effects (given by (9)) the dust surface potential or dust charge.   The magnitude of dust surface potential increases as we increases the value of the negative ion streaming speed (U0) –Figure 4. Normalized dust surface potential (U) versus normalized dust number density parameter (P) (as given in (9)) for different values of the negative ion streaming speed U0(= 0.1, 0.5, 1) with κ = 2.6 and σ = 0.2. Other numerical value are the same as in Fig. 1

Numerical with Streaming(cont.)   Figs. 5 represent how the power- law κ-distribution and the negative ion streaming speed effects (given by (9)) modify the dust surface potential or dust charge.  The magnitude of the dust grain potential decreases as we increase the value of kappa parameter Figure 5. Normalized dust surface potential (U) versus normalized dust number density parameter (P) (as given in (9)) for different values of κ(= 2.6, 4, 50) with U0 = 0.1. Other numerical values are the same as in Fig. 1

Conclusions To conclude, we have considered two models for negative ions, the streaming negative ions and the Boltzmannian negative ions and investigated their effects on the charging of dust grain non-Maxwellian dusty plasmas. The behavior of U vs P curves is significantly modified due to the negative ions distributions. Some important results can be listed as follows : To conclude, we have considered two models for negative ions, the streaming negative ions and the Boltzmannian negative ions and investigated their effects on the charging of dust grain non-Maxwellian dusty plasmas. The behavior of U vs P curves is significantly modified due to the negative ions distributions. Some important results can be listed as follows :  By increasing the negative ion density ratio, the strength of dust potential decreases.  The enhancement of the negative ion streaming speed leads to increase the magnitude of the dust potential.

Conclusions(Cont.)  By increasing the spectral index (superthermality effects), the equilibrium dust surface potential decreases and approaches to the Maxwellian case.  While the negative ion number density ratio shows similar effects as was shown in the Maxwellian case.  It is also observed that the negative ion-to-electron temperature ratio would lead to enhance the dust grain surface potential of the negatively charged dust grains.

Future Perspectives  We have to modified the electron and positive/negative ion currents flowing onto dust with a distribution function and calculated dust potential.  One needs to extend this work for investigating the particle behavior by using the other distributions like I. r-q distribution II. Cairns-Tsallis distributions To study the non-thermal behavior of the plasma particles. To study the non-thermal behavior of the plasma particles.  The work can be also extended to obtain the equilibrium and fluctuating currents with these distributions.

List of Publications 1. 1.A. A. Abid, S. Ali and R. Muhammad, J. Plasma Phys. 79, 1117 (2013) A. A. Abid, S. Ali, J. Du and R. Muhammad. " Dust charging processes in the dusty plasma with a generalized power-law velocity (r,q)-distribution " Chinese Phy. B (Under Riview) A. A. Abid, S. Ali, J. Du and A. A. Mamun. “Vasyliunas-Cairns distribution for space plasma species” Phys. Plasmas (Under Riview) A. A. Abid, S. Ali, J. Du and A. A. Mamun "Cairn-Tsallis model for dust charge variation with negative ions" Phys. Plasmas to be submitted soon  .