Effect of parallel resonance on the electron energy distribution function in a 60 MHz capacitively coupled plasma

In general,as the radio frequency(RF)power increases in a capacitively coupled plasma(CCP),the power transfer efficiency decreases because the resistance of the CCP decreases.In this work,a parallel resonance circuit is applied to improve the power transfer efficiency at high RF power,and the effect of the parallel resonance on the electron energy distribution function(EEDF)is investigated in a 60 MHz CCP.The CCP consists of a power feed line,the electrodes,and plasma.The reactance of the CCP is positive at 60 MHz and acts like an inductive load.A vacuum variable capacitor(VVC)is connected in parallel with the inductive load,and then the parallel resonance between the VVC and the inductive load can be achieved.As the capacitance of the VVC approaches the parallel resonance condition,the equivalent resistance of the parallel circuit is considerably larger than that without the VVC,and the current flowing through the matching network is greatly reduced.Therefore,the power transfer efficiency of the discharge is improved from 76%,70%,and 68%to 81%,77%,and 76%at RF powers of 100 W,150 W,and 200 W,respectively.At parallel resonance conditions,the electron heating in bulk plasma is enhanced,which cannot be achieved without the VVC even at the higher RF powers.This enhancement of electron heating results in the evolution of the shape of the EEDF from a biMaxwellian distribution to a distribution with the smaller temperature difference between high-energy electrons and low-energy electrons.Due to the parallel resonance effect,the electron density increases by approximately 4%,18%,and 21%at RF powers of 100 W,150 W,and 200 W,respectively.

Simulation of the spatio-temporal evolution of the electron energy distribution function in a pulsed hollow-cathode discharge

This article presents the 2D simulation results of a nanosecond pulsed hollow cathode discharge obtained through a combination of fluid and kinetic models.The spatio-temporal evolution of the electron energy distribution function(EEDF)of the plasma column and electrical characteristics of the nanosecond pulsed hollow cathode discharge at a gas pressure of 5 Torr are studied.The results show that the discharge development starts with the formation of an ionization front at the anode surface.The ionization front splits into two parts in the cathode cavity while propagating along its lateral surfaces.The ionization front formation leads to an increase in the fast isotropic EEDF component at its front,as well as in the anisotropic EEDF component.The accelerated electrons enter the cathode cavity,which significantly contributes to the formation of the highenergy EEDF component and EEDF anisotropy.

Effect of Surface Potential Barrier on the Electron Energy Distribution of NEA Photocathodes

By calculating the energy distribution of electrons reaching the photocathode surface and solving the Schrodinger equation that describes the behavior of an electron tunneling through the surface potential barrier,we obtain an equation to calculate the emitted electron energy distribution of transmission-mode NEA GaAs photocathodes. Accord- ing to the equation,we study the effect of cathode surface potential barrier on the electron energy distribution and find a significant effect of the barrier-Ⅰ thickness or end height,especially the thickness,on the quantum efficiency of the cath- ode. Barrier Ⅱ has an effect on the electron energy spread, and an increase in the vacuum level will lead to a narrower electron energy spread while sacrificing a certain amount of cathode quantum efficiency. The equation is also used to fit the measured electron energy distribution curve of the transmission-mode cathode and the parameters of the surface barri- er are obtained from the fitting. The theoretical curve is in good agreement with the experimental curve.

Diagnosing the Fine Structure of Electron Energy Within the ECRIT Ion Source

The ion source of the electron cyclotron resonance ion thruster （ECRIT） extracts ions from its ECR plasma to generate thrust, and has the property of low gas consumption （2 seem, standard-state cubic centimeter per minute） and high durability. Due to the indispensable effects of the primary electron in gas discharge, it is important to experimentally clarify the electron energy structure within the ion source of the ECRIT through analyzing the electron energy distribution function （EEDF） of the plasma inside the thruster. In this article the Langmuir probe diagnosing method was used to diagnose the EEDF, from which the effective electron temperature, plasma density and the electron energy probability function （EEPF） were deduced. The experimental results show that the magnetic field influences the curves of EEDF and EEPF and make the effective plasma parameter nonuniform. The diagnosed electron temperature and density from sample points increased from 4 eV/2 ×10^16 m-3 to 10 eV/4×10^16 m-3 with increasing distances from both the axis and the screen grid of the ion source. Electron temperature and density peaking near the wall coincided with the discharge process. However, a double Maxwellian electron distribution was unexpectedly observed at the position near the axis of the ion source and about 30 mm from the screen grid. Besides, the double Maxwellian electron distribution was more likely to emerge at high power and a low gas flow rate. These phenomena were believed to relate to the arrangements of the gas inlets and the magnetic field where the double Maxwellian electron distribution exits. The results of this research may enhance the understanding of the plasma generation process in the ion source of this type and help to improve its performance.

Analysis of electron energy distribution function in a magnetically filtered complex plasma

The electron energy distribution function （EEDF） for a magnetically filtered dusty plasma is studied in a dusty double plasma device where the electron energy can be varied from 0.15 eV to ～ 2.8 eV and plasma density from 10 6 cm-3 to 10 9cm-3 . The characteristics of EEDF for these ranges of plasma parameters are investigated in a pristine plasma as well as in a dusty plasma. The results show that in the presence of dust, there is a drastic modification in EEDF patterns in a plasma with higher electron temperature and density than those in a low temperature and low density plasma produced by the magnetic filter.

A New Insight into Energy Distribution of Electrons in Fuel-Rod Gap in VVER-1000 Nuclear Reactor

In order to calculate the electron energy distribution in the fuel rod gap of a VVER- 1000 nuclear reactor, the Fokker-Planck equation （FPE） governing the non-equilibrium behavior of electrons passing through the fuel-rod gap as an absorber has been solved in this paper. Besides, the Monte Carlo Geant4 code was employed to simulate the electron migration in the fuel-rod gap and the energy distribution of electrons was found. As for the results, the accuracy of the FPE was compared to the Geant4 code outcomes and a satisfactory agreement was found. Also, different percentage of the volatile and noble gas fission fragments produced in fission reactions in fuel rod, i.e. Krypton, Xenon, Iodine, Bromine, Rubidium and Cesium were employed so as to investigate their effects on the electrons＇ energy distribution. The present results show that most of the electrons in the fuel rod＇s gap were within the thermal energy limitation and the tail of the electron energy distribution was far from a Maxwellian distribution. The interesting outcome was that the electron energy distribution is slightly increased due to the accumulation of fission fragments in the gap. It should be noted that solving the FPE for the energy straggling electrons that are penetrating into the fuel-rod gap in the VVER-1000 nuclear reactor has been carried out for the first time using an analytical approach.

Simulations of electron energy distribution of Pd-like Xe system based on OFI

X-ray laser based on OFI is a promising way to realize the table-top X-ray laser.A simple model to describe the electron energy distribution in plasma produced by circularly polarized optical-field-induced ionization is constructed on the basis of ADK tunneling ionization theory.The ionization rate,threshold intensity,residual energy and electron energy distribution of Pd-like Xe system based on optical-field-induced ionization are calculated.The results are useful to further experments on X-ray laser of Pa-like Xe system.

Calculation of the Energy Distribution of Electrons Emitted from Tungsten

The numerical calculation of the energy distribution of electrons emitted by the tungsten, for a triangular barrier and given reflection images, has been carried out. It is shown that the numerical solution of Schrodinger equation is the most effective method of calculation of the transparency of potential barrier among those used in work. I-V characteristics, which were calculated by the application of this method under different conditions, match the experimental data the best. The application of the numerical solution of Schrodinger equation for the calculation of transparency of the potential barrier enables the in-depth analysis of the tunnels phenomena and allows forecasting the effects which can not be received by application of Wentzel-Kramers-Brillouin approximation.

Electron population properties with different energies in a helicon plasma source

The characteristics of electrons play a dominant role in determining the ionization and acceleration processes of plasmas.Compared with electrostatic diagnostics,the optical method is independent of the radio frequency(RF)noise,magnetic field,and electric field.In this paper,an optical emission spectroscope was used to determine the plasma emission spectra,electron excitation energy population distributions(EEEPDs),growth rates of low-energy and highenergy electrons,and their intensity jumps with input powers.The 56 emission lines with the highest signal-to-noise ratio and their corresponding electron excitation energy were used for the translation of the spectrum into EEEPD.One discrete EEEPD has two clear different regions,namely the low-energy electron excitation region(neutral lines with threshold energy of13–15 eV)and the high-energy electron excitation region(ionic lines with threshold energy?19 e V).The EEEPD variations with different diameters of discharge tubes(20 mm,40 mm,and 60 mm)and different input RF powers(200–1800 W)were investigated.By normalized intensity comparison of the ionic and neutral lines,the growth rate of the ionic population was higher than the neutral one,especially when the tube diameter was less than 40 mm and the input power was higher than 1000 W.Moreover,we found that the intensities of low-energy electrons and high-energy electrons jump at different input powers from inductively coupled(H)mode to helicon(W)mode;therefore,the determination of W mode needs to be carefully considered.

Validity of the two-term Boltzmann approximation employed in the fluid model for high-power microwave breakdown in gas

The electron energy distribution function （EEDF）, predicted by the Boltzmann equation solver BOLSIG＋ based on the two-term approximation, is introduced into the fluid model for simulating the high-power microwave （HPM） breakdown in argon, nitrogen, and air, and its validity is examined by comparing with the results of particle-in-cell Monte Carlo collision （PIC/MCC） simulations as well as the experimental data. Numerical results show that, the breakdown time of the fluid model with the Maxwellian EEDF matches that of the PIC/MCC simulations in nitrogen; however, in argon under high pressures, the results from the Maxwellian EEDF were poor. This is due to an overestimation of the energy tail of the Maxwellian EEDF in argon breakdown. The prediction of the fluid model with the BOLSIG＋ EEDF, however, agrees very well with the PIC/MCC prediction in nitrogen and argon over a wide range of pressures. The accuracy of the fluid model with the BOLSIG＋ EEDF is also verified by the experimental results of the air breakdown.

Two-Dimensional Self-Consistent Kinetic Model for Solenoidal Inductively Coupled Plasma

A two-dimensional self-consistent kinetic model was developed to study the influence of the various factors on the electron energy distribution function. These factors include gas pressure the driving frequency, the radius and length of the inductively coupled plasma equipment, the amplitude of the radio-frequency coil current, and the number of turns of rf coils. The spatial profiles of the rf electric field and power density have also been calculated under the same parameters. Numerical results show that the electron energy distribution functions are significantly modified and the spatial profiles of the rf electric field and rf power density are also demonstrated.

Short-pulse high-power microwave breakdown at high pressures

The fluid model is proposed to investigate the gas breakdown driven by a short-pulse（such as a Gaussian pulse） highpower microwave at high pressures.However,the fluid model requires specification of the electron energy distribution function（EEDF）;the common assumption of a Maxwellian EEDF can result in the inaccurate breakdown prediction when the electrons are not in equilibrium.We confirm that the influence of the incident pulse shape on the EEDF is tiny at high pressures by using the particle-in-cell Monte Carlo collision（PIC-MCC） model.As a result,the EEDF for a rectangular microwave pulse directly derived from the Boltzmann equation solver Bolsig＋ is introduced into the fluid model for predicting the breakdown threshold of the non-rectangular pulse over a wide range of pressures,and the obtained results are very well matched with those of the PIC-MCC simulations.The time evolution of a non-rectangular pulse breakdown in gas,obtained by the fluid model with the EEDF from Bolsig＋,is presented and analyzed at different pressures.In addition,the effect of the incident pulse shape on the gas breakdown is discussed.

Optimization of Langmuir Probe System Parameters in a Stationary Laboratory Plasma

In order to obtain creditable data an applicable method to optimize parameters of the Langmuir probes and circuits in a stationary laboratory device is investigated and an experimental criterion of the probe dimension is developed. To obtain the electron temperature and density the Electron Energy Distribution Function （EEDF） approach with less computing time and more accurate results is applied, instead of the conventional slope approach. Moreover the influence of the vessel wall materials on the plasma density is discussed briefly, indicating that the dielectric wall is helpful to enhancing the electron density.

Self-consistent Kinetic Description of the Low-Pressure Solenoidal Inductively Coupled Argon Discharge

Using an one-dimensional slab model, we have studied the electron energy distribution, the anomalous skin effect, and power absorption in the solenoidal-inductively-coupled argon discharge under low pressures (≤ 1.33 Pa). The electron energy distribution function and rf electromagnetic field in the plasma are determined self-consistently by the linearized Bolztmann equation incorporating with the Maxwell equations. The numerical results show that, at low pressures, the electron energy distribution function exhibits a non-Maxwellian distribution with a long high-energy tail. The anomalous skin effect is greatly enhanced under low pressures and the negative power absorption is also obtained.