Open AccessOn the quasi-stationary approach to solve the electron Boltzmann equation in pulsed plasmas
Author(s) -
Antonio Tejero-del-Caz,
Vasco Guerra,
N. Pinhão,
C. D. Pintassilgo,
L. L. Alves
Publication year - 2021
Publication title -
plasma sources science and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 108
eISSN - 1361-6595
pISSN - 0963-0252
DOI - 10.1088/1361-6595/abf858
Subject(s) - electric field , nanosecond , electron , boltzmann constant , microsecond , boltzmann equation , atomic physics , exponential function , time evolution , pulse (music) , electron density , physics , collisionality , plasma , computational physics , quantum mechanics , mathematics , mathematical analysis , laser , voltage , tokamak
This work analyzes the temporal evolution of the electron kinetics in dry-air plasmas (80% N 2 : 20% O 2 ), excited by electric-field pulses with typical rise-times of 10 −9 and 10 −6 s, applied to a stationary neutral gaseous background at pressures of 10 5 , 133 Pa and temperature of 300 K. The study is based on the solution of the electron Boltzmann equation (EBE), adopting either (i) a time-dependent formulation that considers an intrinsic time evolution for the electron energy distribution function (EEDF), assuming the classical two-term expansion and a space-independent exponential temporal growth of the electron density; or (ii) a quasi-stationary approach, where the time-independent form of the EBE is solved for different values of the reduced electric-field over the duration of the pulse. The EBE was solved using the LisbOn KInetics Boltzmann solver (LoKI-B), whose original capabilities were extended to accept time-dependent non-oscillatory electric fields as input data. The role of electron–electron collisions, under specific conditions, is also reported and discussed. The simulations show that the quasi-stationary approach gives solutions similar to the time-dependent formulation for rise-times longer than the characteristic evolution time of the EEDF, i.e. 20 ns at 10 5 Pa and 20 μ s at 133 Pa, meaning that a quasi-stationary description is possible in a high-collisionality situation and long rise-times (e.g. microsecond pulses at atmospheric pressure), failing for faster rise-times (e.g. nanosecond pulses for both pressures considered here).