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In this paper we have developed a model to study the role of both electron and ion nonthermalities on dust acoustic wave propagation in a complex plasma in presence of positively charged dust grains. Secondary electron emission from dust grains has been considered as the source of positive dust charging. As secondary emission current depends on the flux of primary electrons, nonthermality of primary electrons changes the expression of secondary emission current from that of earlier work where primary electrons were thermal. Expression of nonthermal electron current flowing to the positively charged dust grains and consequently the expression of secondary electron current flowing out of the dust grains have been first time calculated in this paper, whereas the expression for nonthermal ion current flowing to the positively charged dust grains is present in existing literature. Dispersion relation of dust acoustic wave has been derived. From this dispersion relation real frequency and growth rate of the wave have been calculated. Results have been plotted for different strength of nonthermalities of electrons and ions.

Existence of energetic electrons with energies up to 100 keV was observed at and near the Earth’s bow shock [

Nonthermal plasmas are also widely used in many technical applications, including plasma display panels, energy saving lamps, devices for microbial decontamination and ozonisers [

Theoretical investigations of nonthermal plasmas have been considerably important since early nineties. Motivated by the observations of solitary structures with density depletions made by Freza and Viking satellites [

Dusty plasma has become a challenging field of plasma research since early nineties of the last century after detection of dust particles in different satellite observations. In space environment enormous amount of meteoric material condenses into dust particles and is suspended in the Earth’s mesosphere between 80 - 100 Km. The presence of dust at such a low altitude where the Debye length and the mean free path is small, constitutes a “dusty plasma”, as compared to the “dust in plasma” at higher “satellite orbit” altitudes. The Earth’s atmosphere at these low altitudes also presents us with anomalous physical phenomena like noctilucent clouds, polar summer mesospheric echoes (PMSE) and sporadic sodium layers. The occurrence of each of these phenomena has been researched extensively in the literature, and in some or the other way each of these phenomena has been linked with the presence of charged dust in the lower earth atmosphere [

Polar mesospheric summer echoes (PMSEs) and Noctilucent clouds (NLCs) are an intriguing example of the effects of charging of ice particles in a plasma. These are unusual atmospheric effects connected with charged ice particles in the Earth’s mesosphere, at about 85 km altitude. The “echoes” refers to unusually strong radar backscattering which is not completely understood, but thought to be connected to electron density anomalies associated with the charged ice. Although there is no consensus on the mechanism for producing PMSEs, the current thinking is that the enhanced radar backscatter is caused by some irregularity structure in the electron density profile such as steep density gradients. Rocket measurements seem to indicate that the ice particles are charged positively [

Since the dust is one of the charged fluid components of the plasma, it can support wave modes in the same way that an ordinary plasma supports ion acoustic waves. The Dust acoustic wave (DAW) is a compressional disturbance which propagates through the dust and directly involves the dynamics of the dust particles. Since the dust particles are relatively massive, DAW is a very low frequency wave, just a few Hz typically and propagates at a speed of a few cm/s [

Effects of nonthermal electrons on nonlinear dust acoustic solitary waves have been investigated in presence of negatively charged dust grains [

In this paper we have developed a model to study the role of both electron and ion nonthermalities on dust acoustic wave propagation in a complex plasma in presence of positively charged dust grains. Secondary electron emission process has considered as the source of positive dust charging. Expression of nonthermal ion current in presence of positively charged dust grains was evaluated in reference [

If the secondary electron emission from dust grains is taken into account then dust grains may be positively charged for high value of the secondary electron yield which is the ratio of the emitted electrons to the incident electrons. If the background electrons are nonthermally distributed the grain charging current and consequently the secondary electron current will be modified from its expression for thermal electrons. In this section we shall evaluate the primary electron current flowing to the positively charged dust grains. The induced secondary electron current flowing out of the positively charged dust grains has also been evaluated in this paper. Non thermal ion current flowing to the positively charged dust grains were evaluated by Sarkar and Maity (2013) will be mentioned here.

A. Nonthermal primary electron current and primary electron energy

We have calculated it in this section using three dimensional equilibrium state electron velocity distribution function satisfying collisionless Vlasov equation

where a is the electron nonthermal parameter, v_{x}, v_{y}, v_{z} are three components of electron velocity. _{e} is the electron temperature, m_{e} is the electron mass and_{B} is the Boltzmann constant.

Using Orbit Motion Limited (OML) theory [

For nonthermal parameter a = 0, this expression reduces to

where

In this section we have also calculated the average kinetic energy of non thermal electrons. In equilibrium (

Using this distribution function we have calculated the average kinetic energy of non thermal electrons in the form,

For non thermal parameter a = 0, this reduces to

B. Secondary electron current when primary electrons are nonthermal

The orbital motion limited theory based expression for secondary electron current flowing out of the positively charged dust grains in presence of nonthermal electrons will be,

where r_{0} is the grain radius, m_{e} is the electron mass, T_{e} and T_{s} are the primary and secondary electron temperatures, d_{M} is the maximum yield of secondary electrons, which occurs when the impinging electron has the maximum kinetic energy E_{M}. Here _{5,B}(x) is given by,

where

Putting a = 0 in the expression (6) we get back the expression of secondary electron current for thermally distributed primary electrons.

C. Nonthermal ion current

The OML theory based expression for the nonthermal ion current I_{i} is [

where b is the ion nonthermal parameter [

This was evaluated using ion velocity distribution [

Since number of charges on the dust grains fluctuates in space and time, dust charge is a dynamical variable satisfying the grain charging equation

In this section we substitute the expressions of I_{i}, I_{e} and

In equilibrium

From (10) and (11) with (2), (6) and (9) we calculate the equilibrium ion-electron number density ratio in the form,

where

The grain charging frequency for positively charged dust grains in the background of nonthermal electrons, ions and with emitted secondary electrons has been calculated in the form,

where

Linearization of Equations (10) with (2), (6), (9) and (11) leads to the linearized charge variation,

where

We have considered a plasma consisting of non thermal electrons, ions and positively charged inertial dust grains satisfying the equilibrium charge neutrality condition,

The governing equations are

and the Poisson equation

Here m_{d} is the mass of the charged dust grains moving with velocity v_{d} and n_{d} is the dust number density.

Linearizing these basic equations about their equilibrium values we obtain the first order perturbed number densities of primary electrons, secondary electrons, ions and dust grains in the form,

where

Substituting

where

From this dispersion relation we have calculated the real frequency

For numerical estimation we have considered that dust grains are MgO material having _{0} for four sets of values of a and b with s_{i} = 1.0, s_{s} = 1.01 and d_{M} = 24. _{0 }for a=0.05 and b = 0.5. The same have been plotted for a = 0.05, b = 0.0 in _{0} whereas _{0}. Figures 9-12 have been plotted for _{0} with the values (a = 0.05, b = 0.5), (a = 0.05, b = 0.0), (a = 0.0, b = 1.5), and (a = 0.0, b = 0.0) respectively.

In Figures 9-11, _{0}. So dust acoustic wave grows when either of electrons and ions or both are nonthermal. In all the three cases, magnitude of growth rate increases with increasing number of charges on the positively charged dust grains. Magnitude of growth is stronger in first two cases when electrons are nonthermal but rate of increase of the growth with z_{0} in these cases are slower than the case when electrons are thermal but ions are nonthermal.

The effect of both electron and ion nonthermalities on dust acoustic wave propagation in a complex plasma in presence of positively charged dust grains has been investigated in this paper. Secondary electron emission has been considered as the source of positive dust charging. This secondary electron emission process is influenced by the nonthermality of primary electrons hitting the dust grains. Dispersion relation of dust acoustic wave has been obtained with the above mentioned physical effects. From the dispersion relation we have calculated the real frequency

SusmitaSarkar,SubrataBhakta, (2016) Effect of Electron and/or Ion Nonthermality on Dust Acoustic Wave Propagation in a Complex Plasma in Presence of Positively Charged Dust Grains Generated by Secondary Electron Emission Process. Journal of Modern Physics,07,74-86. doi: 10.4236/jmp.2016.71008