Electron Fluid Model Research Articles

Simple relations for electron temperature and potential in dilute cold plasma flows

This short note presents concise semi-analytical expressions for electron temperature and potential in unsteady dilute cold plasma flows. The analysis is based on the detailed fluid model for electrons. Ionizations and normalized electron number density gradients are neglected, and the transport properties are assumed as local constants. Flow is unsteady and Maxwell's equations are adopted in the analysis. With these treatments, the partial differential equations for unsteady electron temperature and potential degenerate as ordinary differential equations. Along an electron streamline, two simple formulas for unsteady electron temperature and plasma potential are obtained. These formulas offer some insights, for example, the electron temperature and plasma potential distributions along an electron streamline include two exponential functions: one for spatial distance along a streamline and the other for time.

Relativistic harmonics for turbulent wakefield diagnostics

The propagation properties of relativistic harmonics excited in a plasma with an intense laser pulse is investigated theoretically and numerically. Focusing on the frequency separation, a cold electron fluid model in two spatial dimension is discussed to obtain the harmonic amplitude. The theoretical predictions are verified by performing particle-in-cell simulations in two spatial dimensions. When the laser amplitude is large, the strong ponderomotive force expels the electrons, creating a large amplitude density structures associated with the wakefield. The harmonics propagate obliquely with respect to the laser propagation direction, which is well represented by the structure of the high density layer resulting from the transverse poderomotive force. We also discuss a possible experimental setup to observe the density structures relevant to wakefield.

Effect of air breakdown on microwave pulse energy transmission**Project supported by the National Natural Science Foundation of China (Grant No. 61501358) and the Fundamental Research Funds for the Central Universities,China.

The energy transmission of the long microwave pulse for the frequency of 2.45 GHz and 5.8 GHz is studied by using the electron fluid model, where the rate coefficients are deduced from the Boltzmann equation solver named BOLSIG+. The breakdown thresholds for different air pressures and incident pulse parameters are predicted, which show good agreement with the experimental data. Below the breakdown threshold, the transmitted pulse energy is proportional to the square of the incident electric field amplitude. When the incident electric field amplitude higher than the breakdown threshold increases, the transmitted pulse energy decreases monotonously at a high air pressure, while at a low air pressure it first decreases and then increases. We also compare the pulse energy transmission for the frequency of 2.45 GHz with the case of 5.8 GHz.

A simple model for electron temperature in dilute plasma flows

In this short note, we present some work on investigating electron temperatures and potentials in steady dilute plasma flows. The analysis is based on the detailed fluid model for electrons. Ionizations, normalized electron number density gradients, and magnetic fields are neglected. The transport properties are assumed as local constants. With these treatments, the partial differential equation for electron temperature degenerates as an ordinary differential equation. Along an electron streamline, two simple formulas for electron temperature and plasma potential are obtained. These formulas offer some insights, e.g., the electron temperature and plasma potential distributions along an electron streamline include two exponential functions, and the one for plasma potential includes an extra linear distribution function.

Computational studies of suppression of microwave gas breakdown by crossed dc magnetic field using electron fluid model

The gas breakdown induced by a square microwave pulse with a crossed dc magnetic field is investigated using the electron fluid model, in which the accurate electron energy distribution functions are adopted. Simulation results show that at low gas pressures the dc magnetic field of a few tenths of a tesla can prolong the breakdown formation time by reducing the mean electron energy. With the gas pressure increasing, the higher dc magnetic field is required to suppress the microwave breakdown. The electric field along the microwave propagation direction generated due to the motion of electrons obviously increases with the dc magnetic field, but it is much less than the incident electric field. The breakdown predictions of the electron fluid model agree very well with the particle-in-cell-Monte Carlo collision simulations as well as the scaling law for the microwave gas breakdown.

A hybrid model for low pressure inductively coupled plasmas combining a fluid model for electrons with a plasma-potential-dependent energy distribution and a fluid-Monte Carlo model for ions

A hybrid plasma model is utilized for the simulation of inductively coupled plasmas (ICPs). It consists of a plasma fluid model coupling fluid with Maxwell’s equations and a Monte Carlo (MC) particle tracing model utilized for the calculation of the ion mobility in high electrostatic fields (sheaths). The model is applied to low pressure Argon plasma in the gaseous electronics conference (GEC) reference cell. Following measurements of electron energy distribution function (EEDF) in low pressure ICPs, a three-temperature EEDF is considered; it is formulated with a generalized equation and depends on the local plasma potential. The use of a predefined formula for the EEDF entails a low computational cost: All parameters affected by the EEDF are calculated as functions of the plasma potential and the mean electron energy once and before the solution of the model. The model results are validated by a comparison with spatially resolved (on axial and radial distance) measurements of electron density, electron temperature, and plasma potential. Both the calculation of the ion mobility by the MC model and the consideration of the three-temperature EEDF are critical for the accuracy of the model results. The very good agreement of the model results with the measurements and the low computational cost in combination with the flexibility of the code utilized for the numerical solution manifest the potential of the hybrid plasma model for the simulation of low pressure ICPs.

Verification of gyrokinetic particle simulation of current-driven instability in fusion plasmas. III. Collisionless tearing mode

A finite-mass electron fluid model for low frequency electromagnetic fluctuations, particularly the collisionless tearing mode, has been implemented in the gyrokinetic toroidal code. Using this fluid model, linear properties of the collisionless tearing mode have been verified. Simulations verify that the linear growth rate of the single collisionless tearing mode is proportional to De2, where De is the electron skin depth. On the other hand, the growth rate of a double tearing mode is proportional to De in the parameter regime of fusion plasmas.

The electric field in capacitively coupled RF discharges: a smooth step model that includes thermal and dynamic effects

The electric field in radio-frequency driven capacitively coupled plasmas (RF-CCP) is studied, taking thermal (finite electron temperature) and dynamic (finite electron mass) effects into account. Two dimensionless numbers are introduced, the ratios of the electron Debye length to the minimum plasma gradient length l (typically the sheath thickness) and of the RF frequency to the electron plasma frequency . Assuming both numbers small but finite, an asymptotic expansion of an electron fluid model is carried out up to quadratic order inclusively. An expression for the electric field is obtained which yields (i) the space charge field in the sheath, (ii) the generalized Ohmic and ambipolar field in the plasma, and (iii) a smooth interpolation for the transition in between. The new expression is a direct generalization of the Advanced Algebraic Approximation (AAA) proposed by the same author (2009 J. Phys. D: Appl. Phys. 42 194009), which can be recovered for , and of the established Step Model (SM) by Godyak (1976 Sov. J. Plasma Phys. 2 78), which corresponds to the simultaneous limits , . A comparison of the hereby proposed Smooth Step Model (SSM) with a numerical solution of the full dynamic problem proves very satisfactory.

Numerical studies on plasma plume flows from a cluster of electric propulsion devices

Several hybrid fluid–particle simulations are performed to investigate the plasma plume flows from a cluster of Hall thrusters. These simulations adopt a detailed fluid electron model to describe electron properties. A general finite element solver is developed to solve for these electron properties, and the cathode geometry, facility effects, and vacuum chamber background pressure are included in the simulations; these are compared with available experimental data, and indicate that the cathode had effects on some flow property distributions. They also clearly display charge exchange collision effects and the clustering effects. There exist complex three-dimensional near field structures in the ion number density with Hall thrusters in operation. With four thrusters in operation, a severe impingement is expected right behind the cluster center. Compared with axisymmetric simulations, these three-dimensional simulations have several improvements. When compared with the Boltzmann relation, the detailed fluid electron model displays superiority in predicting the electron temperature as well.

Fundamental limitations of the local approximation for electron distribution function and fluid model in bounded plasmas

It is shown that the local approximation for computing the electron distribution function depends both on the ratio between the energy relaxation length and a characteristic plasma length and on the ratio between heating and ambipolar electric fields. In particular, the local approximation is not valid at the discharge periphery even at high pressure due to the fact that the ambipolar electric field practically always is larger than the heating electric field.

One-dimensional hybrid-direct kinetic simulation of the discharge plasma in a Hall thruster

In order to model the non-equilibrium plasma within the discharge region of a Hall thruster, the velocity distribution functions (VDFs) must be obtained accurately. A direct kinetic (DK) simulation method that directly solves the plasma Boltzmann equation can achieve better resolution of VDFs in comparison to particle simulations, such as the particle-in-cell (PIC) method that inherently include statistical noise. In this paper, a one-dimensional hybrid-DK simulation, which uses a DK simulation for heavy species and a fluid model for electrons, is developed and compared to a hybrid-PIC simulation. Time-averaged results obtained from the hybrid-DK simulation are in good agreement with hybrid-PIC results and experimental data. It is shown from a comparison of using a kinetic simulation and solving the continuity equation that modeling of the neutral atoms plays an important role for simulations of the Hall thruster discharge plasma. In addition, low and high frequency plasma oscillations are observed. Although the kinetic nature of electrons is not resolved due to the use of a fluid model, the hybrid-DK model provides spatially and temporally well-resolved plasma properties and an improved resolution of VDFs for heavy species with less statistical noise in comparison to the hybrid-PIC method.

On the approximation of transport properties in structured materials using momentum-transfer theory

In this paper, we present a fluid model for electrons and positrons in structured and soft-condensed matter utilizing dilute gas phase cross-sections together with a structure factor for the medium. Generalizations of the Wannier energy and Einstein (Nernst–Townsend) relations to account for coherent scattering effects present in soft-condensed matter are presented along with new expressions directly relating transport properties in the dilute gas and the structured matter phases. The theory is applied to electrons in a benchmark Percus–Yevick model and positrons in liquid argon, and the accuracy is tested against a multi-term solution of Boltzmann's equation (White and Robson 2011 Phys. Rev. E 84 031125).

An FDTD Thin-Wire Model for Modeling Carbon Nanotube Dipoles at THz Regime

This letter presents an effective model for the numerical simulation of carbon nanotube (CNT) antennas by finite-difference time domain (FDTD). The formulation is based on the classical Holland's thin-wire model, which includes the electromagnetic parameters of the CNT. Those parameters are derived by applying the electron-fluid model, acceptable up to the far-infrared regime. The results have been validated for both scattering and radiation problems, through a comparison of previously reported experimental measurements and numerical simulations based on integral equations.

Finite-mass fluid electron simulation of kinetic and inertial Alfvén waves in a sheared magnetic field

The linear behaviors of kinetic and inertial Alfvén waves (KAW/IAW) in a sheared magnetic field are investigated via a finite-mass fluid electron model in finite-β magnetized plasmas. It is found that the KAW and IAW propagate in opposite directions after mode conversion. Here, β is the ratio between plasma and magnetic pressures. The KAW propagates to the singular surface and deposits energy at the resonant point, where the wave resonates with the local electron motion. The IAW propagates away from the singular surface.

Secondary instability of electromagnetic ion-temperature-gradient modes for zonal flow generation

An analytical model for zonal flow generation by toroidal ion-temperature-gradient (ITG) modes, including finite β electromagnetic effects, is derived. The derivation is based on a fluid model for ions and electrons and takes into account both linear and nonlinear β effects. The influence of finite plasma β on the zonal flow growth rate (γZF) scaling is investigated for typical tokamak plasma parameters. The results show the importance of the zonal flows close to marginal stability where γZF/γITG ≫ 1 is obtained. In this region the parameter γZF/γITG increases with β, indicating that the ITG turbulence and associated transport would decrease with β at a faster rate than expected from a purely linear or quasi-linear analysis.

51.3: Highly Reliable Modeling of AC Plasma Display Panels with a Three‐ Dimensional Hybrid Simulation

AbstractDischarge characteristics of a PDP cell have been investigated using a three‐dimensional hybrid model with an electron‐fluid and ion‐particle model, which shows improvement of simulation results proved by the comparison with the experimental infrared light emission. The hybrid model represents experimental results very well compared with the conventional two‐fluid model adopting drift‐diffusion approximation for both the electrons and the ions.

A finite-mass fluid electron simulation model for low-frequency electromagnetic waves in magnetized plasmas

A finite-mass fluid electron model has been developed for simulating low-frequency electromagnetic waves in finite-β magnetized plasmas. Here, β is the ratio between plasma and magnetic pressures. It is demonstrated in slab geometry that the model successfully exhibits the linear properties of both the kinetic and inertial Alfvén waves as well as the theoretically predicted collisionless tearing-mode instability.

Fluid electrons with kinetic closure for long wavelength energetic particles driven modes

A kinetic electron closure scheme is presented for the fluid electron model that has been implemented in the GEM code [J. Lang, Y. Chen, S. E. Parker, and G.-Y. Fu, Phys. Plasmas 16, 102101 (2009)]. The most important element of the closure scheme is a complete Ohm’s law for the parallel electric field E∥, derived by combining the quasineutrality condition, the Ampere’s equation and the v∥ moment of the gyrokinetic equations. A discretization method for the closure scheme is presented and studied in detail for a three-dimensional shearless slab plasma. It is found that for long wavelength shear Alfvén waves the kinetic closure scheme is both more accurate and more robust than the previous GEM algorithm [Y. Chen and S. E. Parker, J. Comput. Phys. 189, 463 (2003)], whereas for the ion-gradient-driven instability the previous algorithm is more efficient. The fluid electron model with kinetic electron closure is useful for studying energetic particles driven modes with electron kinetic damping effects.

Linear gyrokinetic simulation of high-n toroidal Alfvén eigenmodes in a burning plasma

A hybrid gyrokinetic ions/massless fluid electron model is used to study the stability of high-n toroidal Alfvén eigenmodes (TAEs) in ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)]. The hybrid model has been implemented in the particle-in-cell turbulence simulation code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)]. The adequacy of the hybrid model for simulating TAEs has been previously demonstrated [J. Lang et al., Phys. Plasmas 16, 102101 (2009)] by comparing the simulated TAE mode frequency and structure with an eigenmode analysis, and the thermal ion kinetic damping effect with analytic theory. By using a global particle-in-cell code the effects of large orbit width and nonlocal mode structures can be accurately included. Damping rate due to numerical filtering is carefully monitored, and convergence with respect to particle number, grid resolution, etc., is thoroughly tested. The simulations show that the most unstable modes in ITER lie in the rage of 10<n<20. Thermal ion pressure effect and alpha particle nonperturbative effect are important in determining the mode radial location and stability threshold. The thermal ion Landau damping rate and radiative damping rate from the simulations are compared with analytical estimates. The thermal ion Landau damping is the dominant damping mechanism. Plasma elongation has a strong stabilizing effect on the alpha driven TAEs. The central alpha particle pressure threshold for the most unstable n=15 mode is about βα(0)=0.7% for the fully shaped ITER equilibrium.

A model for carbon nanotube interconnects

AbstractIn this paper, a semi‐classical one‐dimensional (1D) electron fluid model is built that is based on a classical two‐dimensional electron fluid theory taking into account electron–electron repulsive forces, which are significant in 1D system. We have used 1D fluid model to characterize the carbon nanotube (CNT) as interconnects, built a transmission line model and studied S‐parameters and group delays. We have also compared S‐parameters and group delays of CNT interconnects with the corresponding parameters of Cu interconnects. The results show that the CNT interconnects exhibit superior performance over the Cu interconnects. The results also suggest using CNT as interconnects for radio frequency (RF)/microwave applications. Copyright © 2009 John Wiley & Sons, Ltd.