“…The electron energy is sourced from the electrical field of the high-frequency wave when electrons pass through the ECR layer is calculated using a model given in [9,10]. The phase difference between the particle gyromotion and the wave electric field as Ψ = nψ − ωt and the dimensionless variable Γ = γ − 1 are defined, where, n, ψ, ω, γ are the harmonic number, the gyro-phase of electrons, the wave angular frequency, and relativistic factor of electron, respectively.…”