On the kinetic and thermodynamic electron temperatures in non-thermal plasmas

Álvarez, Rafael; Cotrino, José; Palmero, Alberto

doi:10.1209/0295-5075/105/15001

Cited by 3 publications

(4 citation statements)

References 32 publications

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“…Figures 2 and 4 show the EEPF and the VDF, respectively, for the nitrogen plasma with its electron kinetic energy T ek = 2.5, 3.0, and 4.5 eV. The electron kinetic energy is defined as 2/3 times the electron mean energy , which is calculated as follows [33]:…”

Section: Resultsmentioning

confidence: 99%

Discussion on population kinetics and number densities of excited species of low‐pressure discharge nitrogen plasma

Akatsuka

Shibata

Nezu

2016

IEEJ Transactions Elec Engng

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A numerical model is constructed to calculate the number densities of some excited species of nitrogen in low-pressure discharge nitrogen plasma, together with simultaneous solution of the self-consistent electron energy distribution function and N 2 -vibration distribution function. We consider species N 2 (X), N 2 (A), N 2 (B), N 2 (C), N 2 (a), N 2 (a ), N + 2 , N + 4 , N( 4 S) and e − . In addition to electron collisional reactions, diffusion losses and molecular relations are included. It is found that the ratio of number densities of N 2 (B) and N 2 (C) states can be a good measure of the electron kinetic temperature. The N 2 (C) state is found to be almost in a corona equilibrium, whereas the N 2 (B) state becomes mainly populated by N 2 (X, v ≥ 6) + N 2 (A) reaction and depopulated by collisional relaxation by the ground-state N 2 (X) molecule.

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Section: Resultsmentioning

confidence: 99%

Discussion on population kinetics and number densities of excited species of low‐pressure discharge nitrogen plasma

Akatsuka

Shibata

Nezu

2016

IEEJ Transactions Elec Engng

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“…Consequently, to determine the temperature of the non-equilibrium system, the distribution function must be approximated to a straight line, which is generally considered to correspond to the local derivative at each energy value in the Boltzmann plot. The definition of temperature in the non-equilibrium state, which does not obey the Maxwell-Boltzmann distribution, has received a great deal of attention in recent years [7,8]. For example, Álvarez et al attempted to describe the out-of-equilibrium free-electrons in cold plasmas and applied the developed theory assuming the electron entropy defined based on the Boltzmann H-theorem [7].…”

Section: Introductionmentioning

confidence: 99%

“…The definition of temperature in the non-equilibrium state, which does not obey the Maxwell-Boltzmann distribution, has received a great deal of attention in recent years [7,8]. For example, Álvarez et al attempted to describe the out-of-equilibrium free-electrons in cold plasmas and applied the developed theory assuming the electron entropy defined based on the Boltzmann H-theorem [7]. Their theory concluded that the partial derivative of the entropy with respect to the electron mean energy as shown in Equation (3) corresponds to the so-called effective temperature T eff simply given as…”

Section: Introductionmentioning

confidence: 99%

“…In this study, the excitation temperature of nonequilibrium plasma is determined using Tsallis statistics, and the results are compared with those obtained using Boltzmann statistics. As Álvarez et al studied from the viewpoint of statistical physics, the temperature is given as a reciprocal value of the partial derivative of the entropy with respect to the internal energy [7]. On the other hand, Akatsuka et al examined another concept of the electron temperature of the non-equilibrium plasma on the relation between the entropy and the energy through the distribution function [8].…”

Section: Introductionmentioning

confidence: 99%

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Reconsideration of Temperature Determined by the Excited-State Population Distribution of Hydrogen Atoms Based on Tsallis Entropy and Its Statistics in Hydrogen Plasma in Non-Equilibrium State

Kikuchi,

Akatsuka

2023

Entropy

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In non-equilibrium plasmas, the temperature cannot be uniquely determined unless the energy-distribution function is approximated as a Maxwell–Boltzmann distribution. To overcome this problem, we applied Tsallis statistics to determine the temperature with respect to the excited-state populations in non-equilibrium state hydrogen plasma, which enables the description of its entropy that obeys q-exponential population distribution in the non-equilibrium state. However, it is quite difficult to apply the q-exponential distribution because it is a self-consistent function that cannot be solved analytically. In this study, a self-consistent iterative scheme was adopted to calculate q-exponential distribution using the similar algorithm of the Hartree–Fock method. Results show that the excited-state population distribution based on Tsallis statistics well captures the non-equilibrium characteristics in the high-energy region, which is far from the equilibrium-Boltzmann distribution. The temperature was calculated using the partial derivative of entropy with respect to the mean energy based on Tsallis statistics and using the coefficient of q-exponential distribution. An analytical expression was derived and compared with Boltzmann statistics, and the distribution was discussed from the viewpoint of statistical physics.

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Discussion on Electron Temperature of Gas-Discharge Plasma with Non-Maxwellian Electron Energy Distribution Function Based on Entropy and Statistical Physics

Akatsuka

Tanaka

2023

Entropy

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Electron temperature is reconsidered for weakly-ionized oxygen and nitrogen plasmas with its discharge pressure of a few hundred Pa, with its electron density of the order of 1017m−3 and in a state of non-equilibrium, based on thermodynamics and statistical physics. The relationship between entropy and electron mean energy is focused on based on the electron energy distribution function (EEDF) calculated with the integro-differential Boltzmann equation for a given reduced electric field E/N. When the Boltzmann equation is solved, chemical kinetic equations are also simultaneously solved to determine essential excited species for the oxygen plasma, while vibrationally excited populations are solved for the nitrogen plasma, since the EEDF should be self-consistently found with the densities of collision counterparts of electrons. Next, the electron mean energy U and entropy S are calculated with the self-consistent EEDF obtained, where the entropy is calculated with the Gibbs’s formula. Then, the “statistical” electron temperature Test is calculated as Test=[∂S/∂U]−1. The difference between Test and the electron kinetic temperature Tekin is discussed, which is defined as [2/(3k)] times of the mean electron energy U=⟨ϵ⟩, as well as the temperature given as a slope of the EEDF for each value of E/N from the viewpoint of statistical physics as well as of elementary processes in the oxygen or nitrogen plasma.

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On the kinetic and thermodynamic electron temperatures in non-thermal plasmas

Cited by 3 publications

References 32 publications

Discussion on population kinetics and number densities of excited species of low‐pressure discharge nitrogen plasma

Discussion on population kinetics and number densities of excited species of low‐pressure discharge nitrogen plasma

Reconsideration of Temperature Determined by the Excited-State Population Distribution of Hydrogen Atoms Based on Tsallis Entropy and Its Statistics in Hydrogen Plasma in Non-Equilibrium State

Discussion on Electron Temperature of Gas-Discharge Plasma with Non-Maxwellian Electron Energy Distribution Function Based on Entropy and Statistical Physics

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