A finite-difference time-domain simulation of high power microwave generated plasma at atmospheric pressures (original) (raw)
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Plasma formation and propagation during microwave breakdown has been extensively studied during the last decades. Numerical modeling of the strong coupling between the high frequency electromagnetic waves and the plasma is still a challenging topic due to the different time and space scales involved. In this article, an Alternative Direction Implicit (ADI) formulation of the Finite Difference Time Domain method for solving the Maxwell's equations coupled with a simplified plasma model via the electric current is being proposed, leading to a significant reduction of the computational cost as the CFL criterion for stability of the FDTD method is being removed. An energy estimate has been used to prove the unconditional stability of the ADI-FDTD leapfrog scheme as well as its coupled formulation. The computational efficiency and accuracy of this approach has been studied in a simplified case. The proposed method is applied and validated in two dimensional microwave breakdown in air while its computational efficiency allows for fully three dimensional simulations, an important step for understanding the complex nature and evolution of a microwave plasma discharge and its possible applicability as an aerodynamic flow control method.
Numerical Studies of the Low Pressure RF Plasma
ANU, 1990
A one-dimensional, electrostatic particle-in-cell code with non-periodic boundary conditions is used to simulate a low pressure capacitive rf plasma created between two planar electrodes. Ion and electron motion is included and ionising collisions by energetic electrons allow a steady state to be reached and maintained. Realistic values of mi/me are used but there is no attempt to model a real gas and, except for ionisation, no binary collision processes are considered. The simulation plasma is generated by driving one boundary with a sinusoidal rf voltage at a frequency of 10 MHz. The effects of scaling on the steady state, the structure and the impedance of the resulting discharge are investigated. Changes resulting from varying the amplitude of the driving voltage are examined and scaling laws for the plasma potential, electron density and power loss obtained. Sheath heating is shown to be the main electron heating process and power balance is checked. The structure of the rf sheath obtained in the simulation is compared to theoretical models of both the current driven and the voltage driven sheath. Disagreement in the maximum sheath width between the simulation and the model is ascribed to neglect of the period of sheath collapse and the use of an idealised electron density profile in the model. Sheath scaling is shown to underlie the variation of electron density and temperature with rf voltage. The electron sheath interaction is examined and found to differ considerably from current theoretical models. In the range of parameters investigated, it is essential to consider the distortion of the electron velocity distribution in the sheath. A beam-like distribution is observed when the sheath velocity changes rapidly near the time of sheath collapse and an instability develops when electrons are accelerated into the plasma as the sheath expands.
Time-Domain Modeling of RF Antennas and Plasma-Surface Interactions
EPJ Web of Conferences, 2017
Recent advances in finite-difference time-domain (FDTD) modeling techniques allow plasmasurface interactions such as sheath formation and sputtering to be modeled concurrently with the physics of antenna near-and far-field behavior and ICRF power flow. Although typical sheath length scales (micrometers) are much smaller than the wavelengths of fast (tens of cm) and slow (millimeter) waves excited by the antenna, sheath behavior near plasma-facing antenna components can be represented by a sub-grid kinetic sheath boundary condition, from which RF-rectified sheath potential variation over the surface is computed as a function of current flow and local plasma parameters near the wall. These local time-varying sheath potentials can then be used, in tandem with particle-in-cell (PIC) models of the edge plasma, to study sputtering effects. Particle strike energies at the wall can be computed more accurately, consistent with their passage through the known potential of the sheath, such that correspondingly increased accuracy of sputtering yields and heat/particle fluxes to antenna surfaces is obtained. The new simulation capabilities enable timedomain modeling of plasma-surface interactions and ICRF physics in realistic experimental configurations at unprecedented spatial resolution. We will present results/animations from high-performance (10k-100k core) FDTD/PIC simulations of Alcator C-Mod antenna operation.
2012
The modelling of plasma formation during microwave breakdown is a difficult task because of the strong non-linear coupling between Maxwell's equations and plasma equations, and of the large plasma density gradients that form during breakdown. An original Finite Volume Time Domain (FVTD) method has been developed to solve Maxwell's equations coupled with a simplified fluid plasma model and is described in this paper. This method is illustrated with the study of the shielding of a metallic aperture by the plasma generated by an incident high power electromagnetic wave. Typical results obtained with the FVTD method for this shielding problem are shown.
A Numerical Method to Simulate Radio-Frequency Plasma Discharges
Journal of Computational Physics, 2002
A fully conservative and efficient numerical algorithm is developed for fluid simulations of radio-frequency plasma discharges. Results are presented in one and multiple dimensions for a helium discharge. The algorithm produces accurate results even on fairly coarse grids without the use of numerical dissipation. The proposed electron flux discretization is more accurate and efficient than two of the most commonly used discretizations: low-order upwinding (M. S.
Journal of Physics D: Applied Physics, 1996
RF glow-discharge plasmas provide mild energetic ion bombardment of exposed surfaces. The characteristics of a 10 MHz RF glow-discharge Ar plasma are studied by particle-in-cell simulation. The model simulates a spherical plasma device using a one-dimensional plasma model. The code is used to determine the breakdown voltage, V rf , for a given pd , where p is the gas pressure and d is the plasma discharge length. These values are then compared with Paschen's law for the DC case. Also, the breakdown voltage as a function of driver frequency is investigated. Due to the nonlinear capacitance of the plasma, the current and voltage waveforms are found to contain higher harmonic components and sub-harmonic components. Above a certain power level of the driver, sub-harmonics which are indicative of a period-doubling (PD) bifurcation are found to become dominant. The PD thresholds for varying pd , the magnitude of the current and the voltage of the Fourier-analysed components as a function of applied RF voltages are calculated. The PD threshold is always higher than the breakdown threshold. Finally, the pressure-dependence of the sheath width is discussed.
A new hybrid scheme for simulations of highly collisional RF-driven plasmas
Plasma Sources Science and Technology, 2015
This work describes a new 1D hybrid approach for modeling atmospheric pressure discharges featuring complex chemistry. In this approach electrons are described fully kinetically using Particle-In-Cell/Monte-Carlo (PIC/MCC) scheme, whereas the heavy species are modeled within a fluid description. Validity of the popular drift-diffusion approximation is verified against a "full" fluid model accounting for the ion inertia and a fully kinetic PIC/MCC code for ions as well as electrons. The fluid models require knowledge of the momentum exchange frequency and dependence of the ion mobilities on the electric field when the ions are in equilibrium with the latter. To this end an auxiliary Monte-Carlo scheme is constructed. It is demonstrated that the drift-diffusion approximation can overestimate ion transport in simulations of RF-driven discharges with heavy ion species operated in the γ mode at the atmospheric pressure or in all discharge simulations for lower pressures. This can lead to exaggerated plasma densities and incorrect profiles provided by the drift-diffusion models. Therefore, the hybrid code version featuring the full ion fluid model should be favored against the more popular drfit-diffusion model, noting that the suggested numerical scheme for the former model implies only a small additional computational cost.
Numerical Calculations of Some Plasma Parameters of the Capacitively Coupled RF Discharge
Numerical calculations by using a self-consistent model of the collisional sheath for the capaci-tively coupled RF discharge are our target. The results indicated that, at high pressure, the ohmic heating is usually the dominant heating mechanism in the discharge. The power dissipated in the sheath is calculated and compared with the measured data. Moreover, we indicated that, when the gas pressure is increased, the calculated dissipated power is decreased also while the measured input RF power is increased. Furthermore the sheath thickness of the capacitively coupled discharge is calculated and in the same order of the electron oscillation amplitude in the RF field, while the ionization mean free path is shorter than it.