IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 2, FEBRUARY 2012 421 A Hybrid Model to Predict Electron and Ion Distributions in Entire Interelectrode Space of a Negative Corona Discharge Pengxiang Wang, Fa-gung Fan, Francisco Zirilli, and Junhong Chen, Member, IEEE Abstract—Atmospheric direct current (dc) corona discharge from thin wires or sharp needles has been widely used as an ion source in many devices such as photocopiers, laser printers, and electronic air cleaners. Existing numerical models to predict the electron distribution in the corona plasma are based on charge continuity equations and the simplified Boltzmann equation. In this paper, negative dc corona discharges produced from a thin wire in dry air are modeled using a hybrid model of modified particle-in-cell plus Monte Carlo collision (PIC-MCC) and a continuum approach. The PIC-MCC model predicts densities of charge carriers and electron kinetic energy distributions in the plasma region, while the continuum model predicts the densities of charge carriers in the unipolar ion region. Results from the hybrid model are compared with those from prior continuum models. Superior to the prior continuum model, the hybrid model is able to predict the voltage–current curve of corona discharges. The PIC-MCC simulation results also suggest the validity of the local approximation used to solve the Boltzmann equation in the prior continuum model. Index Terms—Corona plasma, electron, Monte Carlo methods, particle-in-cell (PIC). I. I NTRODUCTION C ORONA DISCHARGES have attracted much attention in recent years due to their broad applications [1]. The corona discharge is a weakly luminous discharge that usually takes place at or near atmospheric pressure. It is often produced between two asymmetrical electrodes with an electric potential difference. The discharge electrode usually has a small radius of curvature, e.g., a sharp point or a thin wire, and the passive electrode usually has a much larger radius of curvature, e.g., a flat plate or a cylinder. The polarity of the corona is either positive or negative depending on the relative electric potential applied to the discharge electrode with respect to the passive electrode [2]. Fig. 1 shows a direct current (dc) negative corona Manuscript received May 20, 2011; revised July 25, 2011 and September 20, 2011; accepted October 28, 2011. Date of publication December 8, 2011; date of current version February 10, 2012. This work was supported in part by Xerox Corporation through a UAC grant. The work of P. X. Wang was supported by UWM Dissertation Fellowship. P. Wang and J. Chen are with the Department of Mechanical Engineering, University of Wisconsin–Milwaukee, Milwaukee, WI 53211 USA (e-mail: pwang@uwm.edu; jhchen@uwm.edu). F. Fan is with the Mechanical Engineering Sciences Laboratory, Fairport, NY 14450 USA (e-mail: fagung@gmail.com). F. Zirilli is with the Xerox Research Center Webster, Xerox Corporation, Webster, NY 14580 USA (e-mail: Francesco.Zirilli@xerox.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2011.2174806 Fig. 1. Sketch of a negative wire–cylinder corona discharge. The dashed line indicates the outer boundary of the plasma region. Note that the ionization boundary is thinner than the plasma boundary for negative coronas (not to scale). discharge in wire–cylinder geometry. Corona initiates when the electric potential across the electrode gap is sufficiently high that gas ionization occurs near the wire. An active corona plasma region forms adjacent to the discharge wire. The highly nonequilibrium corona plasma contains electrons at a few electronvolts and heavy species (atoms, molecules, and ions) near room temperature. A short distance away from the discharge electrode, the electric field is insufficient to sustain the ionization, and unipolar ions of the same polarity as the discharge wire drift into this region to fill the interelectrode space. In contrast to the uniform positive corona discharge, negative corona discharges appear as discrete points or tufts (Trichel pulses) along the wire [3], [4]. At voltages near the corona onset voltage, only a few tufts appear. They are irregularly spaced along the wire and preferentially appear at imperfections on the surface. As the voltage is increased, the number of tufts increases, and the distribution of tufts becomes more uniform, which is the regime considered by this work. An important application of atmospheric dc corona discharge is the production of unipolar ions for electrostatic charging of various objects. For many decades, photocopiers, laser jet printers, and electrostatic precipitators have relied on the dc corona discharge to charge surfaces or particulates [5], [6]. In recent years, corona plasmas have been widely used to generate nanomaterials [7]. In addition to useful ions, energetic electrons produced in the corona discharge have led to undesirable ozone production [8]–[11] and deposition of silicon dioxide on the 0093-3813/$26.00 © 2011 IEEE 422 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 2, FEBRUARY 2012 discharge electrode [12], [13]. The authors have previously developed a comprehensive numerical model to predict the distribution and the production rate of ozone in a dc corona discharge along a thin wire in both dry air [14]–[16] and humid air [17]. The model combines predicted electron distributions with plasma chemistry and transport phenomena [18], [19]. In addition to successfully predicting the ozone production rate in the dc corona, the model explains the experimental data and unveils the underlying mechanisms for ozone production in a corona plasma environment. However, the existing numerical model [18], [19] to predict the electron distribution in the corona plasma is based on charge continuity equations and the simplified Boltzmann equation, in which a local approximation is used to independently solve the electron number density distribution and the electron kinetic energy distribution. This particular approach depends on the validity of the local approximation [20], [21]. Also, this fluid approach is not applicable when the size of the discharge electrode or the discharge gap is comparable to or much smaller than the mean free path (mfp) of electrons and ions in the corona discharge, for instance, in the case of corona discharges from nanostructures. A kinetic-theory-based method such as Monte Carlo simulation and direct solution of the Boltzmann equation should be used in this case. Both particle-in-cell (PIC) [22], [23] and Monte Carlo collision (MCC) [24]–[26] methods and the hybrid of PIC and MCC [24], [27]–[33] have been widely used in modeling various plasmas except weakly ionized corona plasmas. In this paper, we report on the modeling of negative dc corona discharges from a thin wire in dry air using a coupled method of PIC-MCC and continuum approach. Results from the hybrid model are compared with those from prior continuum model for electron and ion distributions. In particular, the hybrid model will be used to predict charge carrier distributions in the whole interelectrode space, which provides additional valuable information, such as the voltage–current (V –I) curve, that the prior continuum model cannot provide. II. H YBRID PIC-MCC AND C ONTINUUM M ODEL A. Computational Domain The negative corona discharge from a wire with a radius of 63.5 μm is studied, and the discharge gap (distance between two electrodes) is 2 mm. The computational domain (Fig. 2) for the simulation is the entire interelectrode space bounded by the discharge electrode surface (r = a) and the grounded electrode (r = ro ), which includes both the corona plasma region and the unipolar ion region. A modified PIC-MCC model is used to solve the electron distribution in the corona plasma region, while a continuum model is used for solving the ion distributions in the plasma region and all species in the unipolar ion region. The ith particle at location ri is indicated by the blue solid circle. The cell containing the particle is bounded by two consecutive nodes at Rj and Rj+1 . The distributions of charge carriers in the discharge are assumed to be 1-D, which is the same as that used in our prior continuum model to facilitate the comparison. The total number of cells was determined by the required accuracy of the electric field. In the present study, the electric Fig. 2. Computational domain for the hybrid model. The solid blue circle indicates a particle present at ri in a cell bounded by Rj and Rj+1 . field distribution without space charges solved by the numerical model was compared with that obtained from an analytic solution. When the difference between electric field distributions obtained by the two methods was within acceptable tolerance, then the cell size was employed in the modeling. The computational domain (2 mm) was divided into 900 000 cells along the radial direction with a cell length of Δr. This cell size is much smaller than the Debye length of the system, which could lead to greater numerical noise. In order to reduce the numerical noise, number densities of electrons in the modified PIC-MCC model were the average values over each cell in a period after the total number of electrons started to fluctuate in a small range. B. Algorithm A computational flowchart of the hybrid scheme is shown in Fig. 3. The initial field distribution is set by solving the Laplace’s equation with an applied voltage and geometrical parameters of the computational domain. The PIC-MCC is then used to obtain distributions of electrons, positive ions, and negative ions (ne , np , and nn , respectively) with the initial field distribution and an assumed number density of electrons at the wire surface ( ne_bd ). With known ne , np , and nn in the corona plasma region, boundary conditions of the continuum model are determined, and the continuum model can be solved. After the continuum model calculation is performed, distributions of charge carriers in the whole space between two discharge electrodes are obtained. Thereafter, the field distribution with space charges can be updated by solving the Maxwell’s (Poisson’s) equation. The effect of space charges on the electric field is relatively small compared with the effect of electric field on the space charges. Therefore, when the number of electrons fluctuates within a small range, the electric field distribution tends to be stable. The computed stable field strength on the wire surface (Es ) is then compared with that estimated by Peek’s formula (Ep ) [19], [34] 0.0308 6 Ep = 3.1 × 10 δ 1 + √ (V /m) (1) δr WANG et al.: HYBRID MODEL TO PREDICT ELECTRON AND ION DISTRIBUTIONS 423 basic idea of PIC-MCC is to use a small number of superparticles to represent a large number of real particles (electrons, positive ions, and negative ions) in the corona plasma. The superparticles are assumed to have the same charge-to-mass ratio as real particles. Some seed electrons are released into the cells in the computational domain from the boundary with a spatially uniform initial number distribution and a normal distribution in the velocity space. Like real particles, superparticles move in the electric field following Newtonian equations of motion dri = vi dt dvi = F (ri ) m dt Fig. 3. Computational flowchart for implementing the hybrid PIC-MCC and continuum model. E = −∇φ Flowchart for an explicit PIC scheme with MCC handler. where δ= T0 P T P0 and r is the electrode radius in meters, T0 and P0 are the standard temperature and pressure, respectively, and T and P are the actual temperature and pressure of air, respectively. If the difference between Es and Ep is not acceptable, then a new value of n e_bd is assumed to start a new computation loop. The procedure is performed until the difference between Es and Ep is less than 0.1%. Implementation details of the PIC-MCC method have been described by Birdsall and Langdon [22] and Vahedi and Surendra [29] and, thus, are briefly summarized here. Fig. 4 shows a flowchart of the PIC-MCC computational scheme. The (3) where ri and vi are the position and the velocity of particles, respectively, subscript i indicates the particle index, t is the time, and m is the particle mass; in the present model, the mass of electrons is 9.1094 × 10−31 kg, the mass of ions is the mean value of nitrogen and oxygen molecules (4.8106 × 10−26 kg), and F = qE is the electrostatic force applied on the particle with E and q as the electric field and the charge carried by the particle. Because the mass of ions is much larger than that of electrons, ions move much slower in the electric field. It is very time consuming to track ionic species in the PIC-MCC model from one boundary to the other. In the parametric studies, we found that distributions of ions move forward always with a stable front. With this characteristic, the value of the stable front can be used as the boundary condition to solve distributions of ions using the continuum model. Therefore, the modified PIC-MCC model is used to track all electrons within the plasma region and only selected ions at the flow front. With this approach, the distribution of ions can be obtained during the electron transit time instead of the ion transit time. Thus, the computation time is significantly reduced. The electrostatic force is derived from the electric potential calculated through Maxwell’s equation ∇2 φ = −e(np − ne − nn )/ε0 Fig. 4. (2) (4) (5) where φ is the electric potential, ε0 is the permittivity of free space, and e is the elementary charge. The charge carrier densities (ne , np , and nn ) in each cell are derived from the particle positions ri , by a weighting technique. In cylindrical system, r is the position along the radial axis. For example, a superparticle at ri is assumed as a charge cloud with charge nc , which is assigned between the two neighboring cells RJ and RJ+1 with subscripts J and J + 1 as the cell index (Fig. 2) RJ+1 − ri Δr ri − RJ . = nc Δr nJ = nc nJ+1 (6) (7) The electric field at each node point (cell boundary) is then obtained from Maxwell’s equation. Since the particle may fall anywhere in the mesh, the electrostatic force acting on the 424 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 2, FEBRUARY 2012 TABLE I E LECTRON -I MPACT R EACTIONS C ONSIDERED IN THE P RESENT M ODEL particle is interpolated using the electric field at the nearest node points by inverse weighting RJ+1 − ri ri − RJ E(ri ) = EJ + EJ+1 . (8) Δr Δr After the electrons move one time step (Δt) following Newtonian equations of motion [(2) and (3)], they are ready for collision with neutral molecules. The collisions are tracked with the Monte Carlo scheme. The spatial information of charged particles is recorded to calculate the new electric field distribution by solving Maxwell’s equation in a new computation loop. In the current modified PIC method, the electric field is solved at each period of time (multiple time steps) instead of each PIC loop to accumulate the particles in each cell. The average value of particle number is then used to compute the number density to obtain the source term in Maxwell’s equation. In the MCC scheme, oxygen and nitrogen molecules are assumed to be the background species, and their number densities are assumed to be constant. The major electron-impact reactions considered in the model are shown in Table I. These Fig. 5. Oxygen cross-sectional data used in the model. Fig. 6. Nitrogen cross-sectional data used in the model. electron-impact reactions and the associated collision cross sections used are the same as those used in the prior model [18]. The total number of reactions accounted for in this work is 39, including elastic collisions for N2 and O2 , 20 excitations for N2 and 11 excitations for O2 , dissociations for N2 and O2 , ionizations for N2 and O2 , and two attachments for O2 . A complete compilation of collision cross-sectional data can be found in [35] and [36]. Figs. 5 and 6 show the collision crosssectional data set used for O2 and N2 in this model. Of course, there are many more electron-impact reactions occurring in the atmospheric corona discharge, such as step ionizations, manybody collisions, and attachment and detachment processes, which, in general, are also important to describe plasma properties. However, due to the extremely small ionization degree in the corona discharge, effects of these secondary reactions on the corona plasma properties are negligible [18]. Since ionic species do not have sufficient energy to contribute to ionization, collisions between ions and neutral molecules do not affect the distribution of electrons and are thus neglected. Considering the stability and the accuracy of the PIC-MCC simulation, the time step should be chosen carefully [22], [33], [37]. On one hand, larger time steps lead to particles moving out of the domain boundary without any collisions and thus result in inaccuracies. On the other hand, smaller time steps make the computation more expensive. In the present work, the time step is chosen as Δt = 5 × 10−14 s after a series of trial studies. This value agrees well with the selection in the study by Hong et al. [37]. WANG et al.: HYBRID MODEL TO PREDICT ELECTRON AND ION DISTRIBUTIONS 425 For the continuum model, continuity equations of ne , np , and nn are solved from the following equations, and more details about the continuum model can be found in [18] and [19]: d(rne μe E) = (α − β)ne μe E rdr d(rnp μp E) = −αne μe E rdr d(rnn μn E) = βne μe E. rdr (9) (10) (11) C. Boundary Conditions The electrodes in the discharge system are equipotential, which results in the Dirichlet boundary conditions for the electric potential. In the hybrid method, the boundary conditions for Maxwell’s equation (3) are the applied voltage at the discharge electrode V (a) = VHV V (ro ) = 0 at the grounded electrode. (12) (13) Only one boundary condition is required for each species density at the corona discharge electrode (electron and negative ion) or at the plasma boundary (positive ion). Since the number density of positive ions in the unipolar ion region of a negative discharge is negligible, the boundary condition for positive ions is defined at the plasma boundary to save computational time. Boundary conditions for positive and negative ions are their densities in the background neutral air. In this paper, these two densities are assumed as zero since densities of both positive and negative ions in the atmosphere are much lower than those in an active corona plasma region np (rp ) = 0 at the plasma boundary nn (a) = 0 at the discharge electrode. (14) (15) However, the electron density is strongly coupled with the electric field in a corona discharge. The Katpzov hypothesis suggests that the electric field at the discharge electrode increases proportionally with the increasing voltage below the corona onset but will preserve its value after the corona is initiated [38]. The electric field on the surface of the corona electrode is constant and equal to a value derived by Peek [39], [40]. Peek’s formula (1) is used to determine the threshold strength of electric field for the corona onset at the discharge electrode. Lowke and D’Alessandro studied the onset corona field and showed good agreement of Peek’s formula with experiments in cylindrical geometries [41]. Therefore, the boundary condition for electrons is replaced by the additional condition for the field strength on the discharge electrode surface Es = Ep . One boundary value of ne (a) generates corresponding distributions of the space charges which affect the field strength at the wire surface Es . The value of ne (a) that makes Es = Ep is the boundary condition of electrons. This approach provides an indirect boundary condition for electron number density. Iterations will be performed until the total number of electrons Fig. 7. Comparison of voltage–current curves fitted from modeling results using (solid curve) the hybrid model and (dashed line) Cooperman’s formula. fluctuates within a small range and the electric field at the discharge electrode is sufficiently close to the value predicted by Peek’s formula. The modified PIC-MCC model and the continuum model are coupled at the plasma boundary, which requires the thickness of the plasma region. The thickness of the plasma region is defined as the radius at which the reduced field E/N equals 80 Td for negative plasmas [19]. In the present work, the thickness of the plasma region is determined each time after the Maxwell’s equation is solved and the field distribution is obtained. Since positive ions are present only within the plasma region, it is not necessary to compute the number density of positive ions outside the plasma region. For electrons and negative ions, the boundary conditions for the continuum model are the number densities computed from the PIC-MCC model. D. Computational Hardware and Parameters The simulation was performed on a supercomputer cluster of IMB LS21 at the Minnesota Supercomputing Institute. Typically, in a 32-processor parallel computation, for a case with total number of superelectrons fluctuating between 1.4 × 106 and 1.5 × 106 , it took about 48 h to complete 5 × 105 time steps (Δt = 5 × 10−14 s) before a converged electric field was obtained for a negative corona. The computing time is consumed mainly by the PIC-MCC model. III. R ESULTS AND D ISCUSSION In order to obtain the relationship between voltage (V ) and current density (J), different values of the applied voltage are computed for a = 63.5 μm wire: −3.2, −3.5, −3.8, and −4.2 kV. At each applied voltage, one value of the current density is obtained by performing the simulation with hybrid model following the procedure described in Section II. A voltage–current curve can be fitted from modeling results by the hybrid model (solid line in Fig. 7). It can be seen that the corona current increases with the increasing voltage, which agrees reasonably well with the result predicted by Cooperman’s formula [42] (dashed line in Fig. 7) Jtot = 4πεo μp V (V − Vi ) d2 ln ad (16) 426 Fig. 8. Electric field distribution in the negative corona discharge with V = −4.2 kV and the effect of space charge on the electric field distribution (result obtained by solving the Laplace’s equation). The wire surface is at 0 µm, and the grounded electrode is at 2000 µm. Fig. 9. Number density distributions of charge carriers in the negative corona discharge with V = −4.2 kV. The position of the plasma boundary is indicated at rp = 382 µm. The wire surface is at 0 µm, and the grounded electrode is at 2000 µm. where Jtot represents the total corona current density, Vi = aEp ln(d/a) is the starting voltage for the corona discharge, μp is the mobility of the positive ions, a is the wire radius, and d is the space between two electrodes. Compared with Cooperman’s formula, the curve fit from the current data shows a stronger nonlinear characteristic and predicts a slightly higher current for a given voltage. Cooperman’s formula considers the case when the electrostatic field (zero space charge) is much larger than the field generated by the space charge alone. This is true at a low discharge current (or voltage). At a high discharge current (or voltage), more space charges are generated, and the electric field generated by the space charge could be significant and Cooperman’s formula tends to underestimate the corona current at a higher voltage as shown in Fig. 7. Distributions of the electric field and charge carriers in the whole interelectrode space with an applied voltage of −4.2 kV are shown in Figs. 8 and 9, respectively. From Fig. 8, it can be seen that, at a higher voltage, the space charges distort the electric field distribution compared with the case of without space charges. This makes it possible to keep the electric field near the inner electrode close to the value predicted by Peek’s formula (convergence criterion). At the wire surface, the densities of electrons (ne = 8.78 × 109 m−3 ) and negative ions are at the boundary values. In the region IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 2, FEBRUARY 2012 Fig. 10. Comparison of the number density distributions of charge carriers in the negative corona plasma computed from the continuum model and the hybrid model. Solid curves are the number densities obtained by the hybrid model, and the dashed curves are those obtained by the prior continuum model. close to the wire surface, the electron number density increases with increasing distance from the wire surface, similar to the tendency obtained from the prior continuum model (Fig. 10). The increase in electron number density is due to the larger rate of ionization than attachment. In Fig. 9, beyond the plasma boundary (rp = 382 μm), the electric field is not strong enough to support the ionization. In the unipolar ion region, most of the effective collisions between electrons and neutral molecules are the attachments that produce new negative ions by consuming electrons. Therefore, the number density of negative ions nn still increases with increasing radial position (r) in the unipolar ion region although the increasing r may lead to decreasing number density in the case of a constant particle number. In Fig. 9, the decreasing ne is the result of not only the increasing r but also the attachment collisions. Ionization occurs mainly in the plasma region, so np increases from the boundary value at the plasma boundary to the peak value at the wire surface. Distributions of number densities of space charges in the plasma region computed from the PIC-MCC part of the hybrid model are compared with those from the prior continuum model [18], [19] as shown in Fig. 10. Since the number of particles computed from the PIC-MCC model varies with time, the electron number densities shown in the figure are the time-averaged values from the time when the total number of particles is stable. The difference between the PIC-MCC and the prior continuum models may be partly attributed to the statistical error in the MCC process. In MCC, the electrons which will collide with the molecules are sampled by the collision probability. In each computational loop, only a fraction of the electrons (the probability percent of all electrons) will be considered to collide with molecules, and statistical errors may be generated in the MCC process. Another reason is that the coefficient of ionization and attachment and the mobility of electrons used in the continuum model are fitted from the result of energy solver. In the PIC-MCC model, these parameters are taken as the properties of electrons and are computed directly. The occurrence of ionization or attachment is determined based on the relationship between the kinetic energy of electrons and the collision cross section directly. Nevertheless, the close agreement between the prior continuum model and the PIC-MCC model suggests that the local approximation used to WANG et al.: HYBRID MODEL TO PREDICT ELECTRON AND ION DISTRIBUTIONS 427 with feature sizes much greater than the mfp of charge carriers, the hybrid model is applicable to discharges ranging from microscopic to macroscopic. The hybrid model can thus be used to study corona discharges from nanostructures and across microscale or nanoscale gaps. ACKNOWLEDGMENT Fig. 11. Distributions of the electron mean kinetic energy as a function of the electric field computed from (solid line) the PIC-MCC and (dashed line) the continuum models. Note that the higher electric field is located at the inner electrode. solve the Boltzmann equation in the prior continuum model is valid. The electron mean kinetic energy distribution in the negative corona plasma is shown in Fig. 11. For the prior continuum model, the electron mean kinetic energy distribution is exactly the same for both positive and negative coronas (independent of the discharge polarity) [18], [19]. The PIC-MCC model predicts the electron mean kinetic energy distribution pretty well except that there are some fluctuations due to the nature of the PIC-MCC computation. For both models, the electron mean kinetic energy increases with the increasing electric field. Similar to the continuum model, the electron mean kinetic energy distribution from the PIC-MCC model varies from ∼2 eV at the outer boundary to ∼10 eV at the discharge wire surface. The mean energy obtained by the PIC-MCC model is slightly greater than that predicted by the prior continuum model at the plasma boundary where the field strength is low but is slightly smaller than that by the prior continuum model near the wire surface where the field strength is high. This phenomenon physically explains why the number density of electrons predicted by the hybrid model is lower than that obtained by the prior continuum model at the wire surface but higher at the plasma boundary (Fig. 10). IV. C ONCLUSION A hybrid scheme has been developed to predict distributions of electrons, positive ions, and negative ions in the entire discharge gap for a negative wire discharge. A modified PIC-MCC model was used in the corona plasma region, and a continuum model was used in the unipolar ion region. Therefore, the hybrid approach combines the accuracy of the kinetic model and the efficiency of the continuum model. The computed voltage–current characteristic of the discharge agrees well with that obtained by theoretical prediction (Cooperman’s formula). The electron number density distribution and the electron kinetic energy distribution in the corona plasma region computed by the modified PIC-MCC model are similar to those obtained from the prior continuum model, which suggests the validity of the local approximation used to solve the Boltzmann equation in the prior continuum model. Superior to the prior continuum model which applies only to macroscopic discharges The authors would like to thank anonymous reviewers for their insightful comments and the access to the Minnesota Supercomputing Institute at the University of Minnesota, Minneapolis, and the High-Performance Computing Service at the University of Wisconsin, Milwaukee. R EFERENCES [1] L. Bardos and H. Barankova, “Cold atmospheric plasma: Sources, processes, and applications,” Thin Solid Films, vol. 518, no. 23, pp. 6705– 6713, Sep. 2010. [2] L. B. Leob, Electrical Coronas: Their Basic Physical Mechanisms. Berkeley, CA: Univ. California Press, 1965. [3] A. P. 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He is currently working toward the Ph.D. degree in the Department of Mechanical Engineering, University of Wisconsin, Milwaukee. He is a Research Assistant with the Department of Mechanical Engineering, University of Wisconsin. His research interests include numerical simulation of electrical discharges, microscale and nanoscale plasma, and parallel computations. Fa-gung Fan received the M.S. degree in mechanical engineering and the Ph.D. degree in engineering science from Clarkson University, Potsdam, NY, in 1989 and 1995, respectively. His graduate work was on vibration isolation and aerosol dynamics. He was a Member of Research and Technology Staff, Xerox Research Center Webster, Xerox Corporation. He is currently a Principal Engineer with the Mechanical Engineering Sciences Laboratory, Fairport, NY. His research interests include xerography and modeling and simulation of marking processes. Francisco Zirilli received the B.S., M.S., and Ph.D. degrees from Clarkson University, Potsdam, NY, in 1977, 1979, and 1985, respectively. His graduate work focused on the development of finite-difference and finite-element algorithms for the solution of free and mixed convection problems. He has been with the Xerox Research Center Webster, Xerox Corporation, Webster, NY, for 26 years, where he held positions in technology development and product development and design and is currently a Principal Engineer with the Global Development Group. His primary responsibility is the use of computational models in the areas of fluid dynamics and heat transfer applied to the development and design of high-speed marking engines. His areas of interest include numerical simulation of turbulent flows, conjugate heat transfer, free convection heat transfer, and cooling of electronic components. Junhong Chen (M’02) received the B.E. degree in thermal engineering from Tongji University, Shanghai, China, in 1995, and the M.S. and Ph.D. degrees in mechanical engineering from the University of Minnesota, Minneapolis, in 2000 and 2002, respectively. His graduate work focused on dc corona plasmas and corona-enhanced chemical reactions. From 2002 to 2003, he was a Postdoctoral Scholar in chemical engineering with the California Institute of Technology, Pasadena, where he worked on arc plasma synthesis of nanoparticles. He is currently a Professor with the Department of Mechanical Engineering, University of Wisconsin, Milwaukee. His current research interests include corona discharges, plasma reacting flows, and nanotechnology for sustainable energy and environment.