In this paper, a sheath model has been developed to investigate the characteristics of a magnetised dusty plasma sheath in the presence of a
q
-nonextensive distribution of electrons. For this, we ...have established a one-dimensional fluid model. The electrons are considered following the
q
-nonextensive distribution (i.e. the deflection of the electrons for their Maxwell-Boltzmann distribution); however the ions and dust grains are described by fluid equations. According to multi-fluid equations and some dimensionless variables, the dimensionless equations are obtained and solved numerically. The effect of the nonextensivity
q
-parameter on the plasma sheath parameters is examined. A significant change is observed in the quantities characterising the sheath when the electrons evolve far away from their thermodynamic equilibrium Maxwellian (
q
= 1) assumption.
Graphical abstract
Abstract Charging and dynamics of a spherical dust grain injected into a continuous and pulsed radio frequency (RF) discharge have been studied using a one‐dimensional fluid model. First, the plasma ...characteristics of the two types of discharges are computed and compared. In the pulsed discharge, it is found that the central electron density exhibits a periodic variation while the averaged electron density is lower compared to that in the continuous discharge due to the decrease in the total ionization rate. Further, the dust charge is computed using the plasma characteristics. It is found that the dust charge negatively increases as the duty cycle ratio increases. Also, the charge in the pulsed discharge is lower in comparison to the continuous discharge due to the shorter duration of the pulsed RF discharge limiting the amount of energy transferred to electrons. On the other hand, the dust particle remains in the powered sheath region exhibiting a damped oscillation in the two discharges with higher oscillation frequency in the continuous discharge.
A one-dimensional fluid model of an unmagnetized collisional plasma sheath consisting of
q
-non-extensive electrons and singly charged positive ions with finite temperature is developed and ...presented. The ions are described by the fluid model, which is based on the continuity and momentum equations of ions, while the electrons are considered obeying non-extensive distribution according to the Tsallis statistics. In this work, different ion source terms are used in order to compare their contribution. The modified Bohm sheath criterion is determined for different source terms to specify the ion velocity at sheath entrance. The model equations are solved numerically in the plasma-wall transition region. The effect of ion source terms on the collisional electropositive plasma sheath characteristics such as ion and electron density, electric potential, ion velocity, sheath width and space charge is investigated. The influence of the ionization frequency parameter on the sheath behavior has also been studied. The results obtained show a strong impact of ion source terms on the plasma sheath structure. It is also shown that the ion source terms effect increases significantly when the ionization frequency parameter increases.
The present paper numerically investigates the sheath structure in a collisional electronegative plasma in the presence of non-zero ion source term. The plasma sheath contains non-extensively ...distributed electrons, fluid positive ions with finite temperature, and Boltzmann-distributed negative ions. Using the Sagdeev potential method, a modified Bohm sheath criterion is derived to obtain the ion velocity at the sheath entrance that satisfies the sheath formation condition. The impact of the main parameters like electronegativity D, non-extensivity q, ionization frequency
δ
and collision frequency
α
on the sheath characteristics has been examined. The requirement of positive ion velocity to enter the sheath is found to decrease with the increment of
α
and
δ
. Moreover, it is seen that as q, D,
δ
and
α
increase, the normalized electric potential rapidly rises, the peak amplitude of the space charge density increases, and the sheath thickness significantly decreases. Furthermore, as D decreases, the effect of q,
δ
and
α
on the sheath electric potential and the space charge density becomes more important. This study may be useful in various technological applications, including plasma-based surface treatments, plasma etching, and plasma cleaning. This is particularly relevant in the microelectronic and semiconductor industries for manufacturing electronic devices and integrated circuits. Additionally, it could contribute to the enhancement and advancement of techniques in fusion energy research.
This paper investigates the influence of the driving frequency on the dynamics of a single dust particle in argon radiofrequency discharge. A one-dimensional fluid model is presented and solved in ...the entire inter-electrode domain using the finite difference method. In order to solve the particle equation of motion, the coefficients describing the amplification and the damping of the dust particle oscillations are analytically calculated around the equilibrium position, these coefficients allow us to find the relation between the plasma and dust parameters. The results obtained cover the discharge characteristics, the charge and the dynamics of the dust particle. It has been found that the driving frequency has a significant effect on not only the discharge properties but also on the damped oscillatory motion and the equilibrium position of the dust particle. Hence, these oscillations become closer to the electrodes with increasing driving frequency whereas the dust equilibrium position becomes relatively farther from the powered electrode when the dust size decreases.
This work investigates the effect of the electron surface recombination coefficient (Ks) on radio-frequency discharge characteristics. This investigation is performed by a fluid model with the ...drift–diffusion approximation. The simulation results show that when the electron recombination rate is larger, the plasma density is lower in the plasma bulk region. It is found that the cycle-averaged electron and ion fluxes decrease adjacent to the electrode, while the electric potential increases in the bulk plasma region as Ks increases from 0.60 to 2.38. Moreover, the reduction in the electron density in the bulk region leads to decrease in the electron power dissipation in this region. The results also show that the electron ohmic heating and pressure heating, which play a crucial role in sustaining the discharge, can be both reduced in the sheath regions with increasing the electrons recombination rate. Finally, it is observed that the plasma characteristics can significantly be changed depending on the electrode surface properties.
Sheath region of an electronegative magnetized plasma consisting of q-nonextensive electrons, Boltzmann distributed negative ions and positive ions with finite temperature is investigated by using a ...steady state fluid model. Considering Sagdeev's pseudo potential method, a modified Bohm criterion is derived. Taking into account the new formation criterion, the fluid model is then solved numerically and the density distribution of charged particles in the sheath region is studied for different values of the initial positive ion velocity at the sheath edge.
The main purpose of the present work is to study the behavior of sheath properties in unmagnetized collisional plasma. The plasma consists of neutral atoms, thermal positive ions and non-extensive ...electrons. The ions are described by fluid model approach, while the electrons are considered following the q-non-extensive distribution and obey the Tsallis statistics. In this study, a steady state one-dimensional fluid model based on the ion continuity and momentum transport equations, in presence of source term, coupled to the Poisson’s equation and non-extensive electrons density equation is developed. The modified Bohm sheath criterion is also determined and studied. The numerical results obtained highlight the effect of the nonextensivity q-parameter and the positive ion temperature on the evolution of the quantities characterizing the plasma sheath, such as charged particles densities, ion velocity, electric potential and sheath thickness. It is seen that as the q-parameter increases, the charged particles densities decrease more rapidly in the sheath region while the normalized electric potential increases strongly, which leads to a significant decrease in sheath thickness. It is also shown that by increasing the ion temperature for constant q, or by increasing the value of q-parameter for constant ion temperature, the ion velocity increases significantly in the sheath.
In this paper, a plasma sheath containing primary electrons, cold positive ions, and secondary electrons is studied using a one‐dimensional fluid model in which the primary electrons are described by ...q‐non‐extensive distribution according to the Tsallis statistics. Based on the Sagdeev potential method and the current balance relation, a modified sheath criterion, and floating potential are established theoretically. The effect of secondary electron emission on q‐non‐extensive plasma sheath characteristics have been numerically examined. A significant change is observed in the quantities characterizing the non‐extensive plasma sheath with the presence of the secondary electrons. It is found that the sheath properties with super‐extensive distribution (q<1) and sub‐extensive distribution (q>1) are different compared with plasma sheath with Maxwell distribution (q=1).
In this work, we have examined the dynamics of a single dust particle in a non-ionized radio-frequency plasma sheath. For this, we have used a steady state one-dimensional time-averaged model where ...the electrons are considered to be in thermal equilibrium, while the positive ions are described by cold fluid equations. The interactions between ions and neutrals are considered. Numerous forces acting on the dust particles, such as electric force, gravitational force, neutral drag force and ion drag force are taken into account. The numerical results show that the ion-neutral collisions have significant effects on the properties of the motion of the dust. The dust oscillation frequency increases and the equilibrium position of the dust particle drops when the coefficient of ion collision increases.
