In the limit of a small Debye length ( lambda D to 0) the analysis of the plasma boundary layer leads to a two-scale problem of a collision free sheath and of a quasi-neutral presheath. Bohm's criterion expresses a necessary condition for the formation of a stationary sheath in front of a negative absorbing wall. The basic features of the plasma-sheath transition and their relation to the Bohm criterion are discussed and illustrated from a simple cold-ion fluid model. A rigorous kinetic analysis of the vicinity of the sheath edge allows one to generalize Bohm's criterion accounting not only for arbitrary ion and electron distributions, but also for general boundary conditions at the wall. It is shown that the generalized sheath condition is (apart from special exceptions) marginally fulfilled and related to a sheath edge field singularity. Due to this singularity, smooth matching of the presheath and sheath solutions requires an additional transition layer. Previous investigations concerning particular problems of the plasma-sheath transition are reviewed in the light of the general relations.

https://iopscience.iop.org/article/10.1088/0022-3727/24/4/001/pdf

The Bohm criterion and sheath formation

The present paper is a wide review on AC surface dielectric barrier discharge (DBD) actuators applied to airflow control. Both electrical and mechanical characteristics of surface DBD are presented and discussed. The first half of the present paper gives the last results concerning typical single plate-to-plate surface DBDs supplied by a sine high voltage. The discharge current, the plasma extension and its morphology are firstly analyzed. Then, time-averaged and time-resolved measurements of the produced electrohydrodynamic force and of the resulting electric wind are commented. The second half of the paper concerns a partial list of approaches having demonstrated a significant modification in the discharge behavior and an increasing of its mechanical performances. Typically, single DBDs can produce mean force and electric wind velocity up to 1 mN/W and 7 m/s, respectively. With multi-DBD designs, velocity up to 11 m/s has been measured and force up to 350 mN/m.

/pdf/electrical-and-mechanical-characteristics-of-surface-ac-1mbx9840kz.pdf

Electrical and mechanical characteristics of surface AC dielectric barrier discharge plasma actuators applied to airflow control

Surface discharges created in dielectric barrier discharge (DBD) configurations have been proposed as actuators for flow control in aerodynamic applications. We focus on DBDs operating in a glow regime, i.e., where the discharge is sustained by ion-induced secondary electron emission from the surface and volume ionization. After a brief discussion of the force per unit volume acting on the flow and due to the momentum transfer from charged particles to neutral molecules, we present calculations of this force based on a two-dimensional fluid model of the surface discharge. We show that this force is of the same nature as the electric wind in a corona discharge. However, the force in a DBD is localized in the cathode sheath region of the discharge expanding along the dielectric surface. While its intensity is much larger than the analogous force in a direct-current corona discharge, it is active during less than one hundred nanoseconds for each discharge pulse and the time-averaged forces in the two cases a...

Electrohydrodynamic force and aerodynamic flow acceleration in surface dielectric barrier discharge

We present a review and analysis of ion energy distributions (IED) arriving at the target of a radio frequency (rf) discharge. We mainly discuss the collisionless regime, which is of great interest to experimentalists and modellers studying high-density discharges in which the sheath is much thinner than in conventional reactive ion etching systems. We assess what has been done so far and determine what factors influence the shape of the IEDs. We also briefly discuss collisional effects on the IEDs. Having determined the important parameters, we perform some particle-in-cell simulations of a collisionless current-driven rf sheath which show that ion modulations in an rf sheath significantly affect the IEDs when ion/rf<1, where ion is the ion transit time and rf is the rf period.

/pdf/ion-energy-distributions-in-rf-sheaths-review-analysis-and-4nkqqdneay.pdf

Ion energy distributions in rf sheaths; review, analysis and simulation

A review is presented of the studies in the former Soviet Union and in the USA of the mutual interactions of plasmas and high speed flows and shocks. There are reports from as early as the 1980s of large changes in the standoff distance ahead of a blunt body in ballistic tunnels, significantly reduced drag and modifications of travelling shocks in bounded weakly ionized gases. Energy addition to the flow results in an increase in the local sound speed that leads to expected modifications of the flow and changes to the pressure distribution around a vehicle due to the decrease in local Mach number. The critical question was, did a plasma provide a significant energy multiplier for the system? There have been a large number of experimental studies on the influence of a weakly ionized plasma on relatively low Mach number shocks and inherently also on the influence of the shock on the plasma. This literature is reviewed and illustrated with representative examples. The convergence through more controlled experiments and improved modelling to a physics understanding of the effects being essentially due to heating is outlined. It is demonstrated that the heating in many cases is global; however, tailored experiments with positive columns, dielectric barrier discharges and focused microwave plasmas can produce very localized heating. The latter appears more attractive for energy efficiency in flow control. Tailored localized ionization and thermal effects are also of interest for high speed inlet shock control and for producing reliable ignition for short residence time combustors, and work in these areas is also reviewed.

https://iopscience.iop.org/article/10.1088/0022-3727/38/4/R01/pdf

Plasmas in high speed aerodynamics

An equivalent circuit model is presented for a planar rf plasma reactor The physical properties of the plasma sheath adjacent to the electrodes are incorporated in the model The sheath capacitances and the conduction currents through the sheaths are time varying and have a highly nonlinear dependence on the potentials across the plasma sheaths The model shows that the waveforms of the voltage differences across the sheaths are highly nonsinusoidal and agree with reported measurements

Application of the physics of plasma sheaths to the modeling of rf plasma reactors

A model is presented for the energy distribution of ions bombarding electrode surfaces in planar rf plasma reactors at low pressures, where collisions in the sheath may be ignored. Given the waveform for the voltage difference across the sheath adjacent to an electrode, the model predicts the ion bombardment energy distribution in the limits tr <1/f and tr ≫1/f, where tr is the transit time of the ions across the sheath and f is the frequency of the applied rf voltage. Utilizing sheath voltage waveforms from a previously published equivalent circuit model of a rf reactor [A. Metze, D. W. Ernie, and H. J. Oskam, J. Appl. Phys. 60, 3081 (1986)], the model shows that the ion bombardment energy distribution is bimodal and skewed toward lower ion bombardment energies. The model also demonstrates one of the mechanisms responsible for narrowing of the ion bombardment energy distribution with increasing rf frequency. These results are compared with experimental measurements.

The energy distribution of ions bombarding electrode surfaces in rf plasma reactors

Radial distributions of charged-particle densities and electric field strength in the positive column.

Experimental measurements of the energy distribution and flux of ions bombarding an electrode of a parallel‐plate rf reactor were performed in argon, neon, and a 95% helium‐5% argon mixture using a hemispherical retarding grid energy analyzer. Quadrupole mass analysis was performed to identify the ions which were bombarding the electrode. Frequencies from 2.5 to 20 MHz and pressures from 0.025 to 1.6 Torr were studied. For a given amplitude of the applied rf potential, the ratio of the frequency of the applied rf potential to the reactor gas pressure was found to be the critical parameter in determining the shape of the measured ion bombardment energy distributions. The total ion flux to the electrode surface was found to be proportional to the square of the frequency and insensitive to the reactor gas pressure, for a fixed amplitude of the applied rf potential. These results are discussed with reference to the physics of rf gas discharges.

Pressure and frequency dependence of ion bombardment energy distributions from rf discharges

We have discussed the force contours produced during dielectric barrier discharge on a plasma actuator. There is asymmetry in the direction and magnitude of forces during cathode directed and anode directed discharges. This can be attributed to the difference in the dielectric charging characteristics during positive and negative pulses. Accurate modeling of surface processes on the dielectric is essential to understanding the working of the actuator. Nomenclature n p e n n n , , = densities of electrons, positive ions, and negative ions n p e D D D , , = species diffusivities n p e µ µ µ , , n p e v v v    , , = species mobility = species velocity r e e , 0

Douglas Ernie

Papers

Application of the physics of plasma sheaths to the modeling of rf plasma reactors

The energy distribution of ions bombarding electrode surfaces in rf plasma reactors

Radial distributions of charged-particle densities and electric field strength in the positive column.

Pressure and frequency dependence of ion bombardment energy distributions from rf discharges

Plasma actuator simulation: Force contours and dielectric charging characteristics