Ayyaswamy Venkattraman

Frequency response of atmospheric pressure gas breakdown in micro/nanogaps

In this paper, we study gas breakdown in micro/nanogaps at atmospheric pressure from low RF to high millimeter band. For gaps larger than about 10 μm, the breakdown voltage agrees with macroscale vacuum experiments, exhibiting a sharp decrease at a critical frequency, due to transition between the boundary- and diffusion-controlled regimes, and a gradual increase at very high frequencies as a result of inefficient energy transfer by field. For sub-micron gaps, a much lower breakdown is obtained almost independent of frequency because of the dominance of field emission.

Pre-breakdown evaluation of gas discharge mechanisms in microgaps

The individual contributions of various gas discharge mechanisms to total pre-breakdown current in microgaps are quantified numerically. The variation of contributions of field emission and secondary electron emission with increasing electric field shows contrasting behavior even for a given gap size. The total current near breakdown decreases rapidly with gap size indicating that microscale discharges operate in a high-current, low-voltage regime. This study provides the first such analysis of breakdown mechanisms and aids in the formulation of physics-based theories for microscale breakdown.

Cathode fall model and current-voltage characteristics of field emission driven direct current microplasmas

The post-breakdown characteristics of field emission driven microplasma are studied theoretically and numerically. A cathode fall model assuming a linearly varying electric field is used to obtain equations governing the operation of steady state field emission driven microplasmas. The results obtained from the model by solving these equations are compared with particle-in-cell with Monte Carlo collisions simulation results for parameters including the plasma potential, cathode fall thickness, ion number density in the cathode fall, and current density vs voltage curves. The model shows good overall agreement with the simulations but results in slightly overpredicted values for the plasma potential and the cathode fall thickness attributed to the assumed electric field profile. The current density vs voltage curves obtained show an arc region characterized by negative slope as well as an abnormal glow discharge characterized by a positive slope in gaps as small as 10 μm operating at atmospheric pressure. The model also retrieves the traditional macroscale current vs voltage theory in the absence of field emission.

Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

A Lennard-Jones (LJ) binary interaction model for dilute gases is obtained by representing the exact scattering angle as a polynomial expansion in non-dimensional collision variables. Rigorous theoretical verification of the model is performed by comparison with exact values of diffusion and viscosity cross sections and related collision integrals. The collision quantities given by the polynomial approximation model agree within 3.5% with those of the exact LJ scattering. The proposed model is compared in detail with the generalized soft sphere (GSS) model which is the closest in terms of fidelity among existing direct simulation Monte Carlo collision models. The GSS models performance for the collision integral used in the first approximate of viscosity coefficient is comparable to the proposed model for most reduced temperatures. However, other collision integrals deviate significantly, even at moderate reduced temperatures. The high fidelity of the proposed model at low reduced temperatures enables non-equilibrium simulations of gases with deep LJ potential well such as metallic vapors. The model is based on the scattering angle as opposed to viscosity or diffusion coefficients and provides a direct link to molecular dynamics simulations.

Electric field enhancement due to a saw-tooth asperity in a channel and implications on microscale gas breakdown

The electric field enhancement due to an isolated saw-tooth asperity in an infinite channel is considered with the goal of providing some inputs to the choice of field enhancement factors used to describe microscale gas breakdown. The Schwarz–Christoffel transformation is used to map the interior of the channel to the upper half of the transformed plane. The expression for the electric field in the transformed plane is then used to determine the electric field distribution in the channel as well as field enhancement near the asperity. The effective field enhancement factor is determined and its dependence on operating and geometrical parameters is studied. While the effective field enhancement factor depends only weakly on the height of the asperity in comparison to the channel, it is influenced significantly by the base angles of the asperity. Due to the strong dependence of field emission current density on electric field, the effective field enhancement factor (βeff) is shown to vary rapidly with the applied electric field irrespective of the geometrical parameters. This variation is included in the analysis of microscale gas breakdown and compared with results obtained using a constant βeff as is done traditionally. Even though results for a varying βeff may be approximately reproduced using an equivalent constant βeff independent of E-field, it might be important for a range of operating conditions. This is confirmed by extracting βeff from experimental data for breakdown in argon microgaps with plane-parallel cathodes and comparing its dependence on the E-field. While the use of two-dimensional asperities is shown to be a minor disadvantage of the proposed approach in its current form, it can potentially help in developing predictive capabilities as opposed to treating βeff as a curve-fitting parameter.

Theory and analysis of operating modes in microplasmas assisted by field emitting cathodesa)

Motivated by the recent interest in the development of novel diamond-based cathodes, we study microplasmas assisted by field emitting cathodes with large field enhancement factors using a simplified model and comparisons with particle-in-cell with Monte Carlo collision (PIC-MCC) simulations and experiments. The model used to determine current-voltage characteristics assumes a linearly varying electric field in the sheath and predicts transition from an abnormal glow to arc mode at moderate current densities in a 1 mm argon gap. The influence of an external circuit is also considered to show the dependence of current as a function of the applied voltage, including potential drop across external resistors. PIC-MCC simulations confirm the validity of the model and also show the significant non-equilibrium nature of these low-temperature microplasmas with electron temperatures ∼1 eV and ion temperatures ∼0.07 eV in the quasi-neutral region. The model is also used to explain experimental data reported for a 1 ...

Modeling of Viscous Shock Tube Using ES-BGK Model Kinetic Equations

The viscous effects on unsteady shock wave propagation are investigated by numerical solution of the Boltzmann model kinetic equations. The kinetic equations are solved for two unsteady non-equilibrium flow problems, namely, the one-dimensional Riemann problem and a two-dimensional viscous shock-tube. The numerical method comprises the discrete velocity method in the velocity space and the finite volume discretization in physical space using various flux schemes. The discrete version of H-theorem is applied for analysis of accuracy of the numerical solution as well as of the onset of non-equilibrium. Simulations show that the maximum entropy generation rate in viscous shock tube occurs in the boundary layer / shock wave interaction region. The entropy generation rate is used to determine the time-variation of the speed of propagation of shock, contact discontinuity and rarefaction waves.

Generalized criterion for thermo-field emission driven electrical breakdown of gases

Microdischarges operating in an ambient gas with both thermionic and field emission from the cathode are considered theoretically to predict pre-breakdown current density vs voltage as well as breakdown voltages. The integrals in the thermo-field current density expression lead to a breakdown criterion that does not have a simple closed-form and requires the use of optimization techniques to obtain the breakdown voltage. The breakdown voltage is shown to be a non-monotonic function of both cathode temperature and gap size. The proposed framework can be applied with no additional effort to gas breakdown driven by other cathode emission mechanisms.

Non-Equilibrium Flow Modeling Using High-Order Schemes for the Boltzmann Model Equations

We consider application of higher-order schemes to the Boltzmann model equations with a goal to develop a deterministic computational approach that is accurate and efficient for simulating flows involving a wide range of Knudsen numbers. The kinetic equations are solved for two non-equilibrium flow problems, namely, the structure of a normal shock wave and an unsteady two-dimensional shock tube. The numerical method comprises the discrete velocity method in the velocity space and the finite volume discretization in physical space with different numerical flux schemes: the first-order, the second-order minmod flux limiter as well as a third-order WENO scheme. The normal shock wave solutions using BGK and ES collision models are compared to the DSMC simulations. The solution for unsteady shock tube is compared to the Navier-Stokes simulations at low Knudsen numbers and the rarefaction effects in such flow are also discussed. It is observed that a higher-order flux scheme provides a better convergence rate and, hence, reduces the computational effort. The entropy generation rate is shown to be a very sensitive indicator of the onset of non-equilibrium as well as accuracy of a numerical scheme and consistency of boundary conditions in both flow problems.

Field enhancement factor dependence on electric field and implications on microscale gas breakdown: Theory and experimental interpretation

In this letter, we obtain a better understanding of effective field enhancement factors (β eff) in the context of microscale gas breakdown with specific emphasis on its dependence on applied electric field. The theoretical dependence of β eff on electric field for various hemi-ellipsoidal asperities indicates that the value of β eff decreases with increasing electric field. The interpretation of experimental data using a typical one-dimensional modified Paschen law indicates a qualitatively similar electric field dependence even though the data could not be completely explained using a single effective asperity size. The values of β eff extracted from seven independent experimental datasets for microscale breakdown of argon and air are shown to be consistent and an empirical dependence on electric field is determined.