The Propagation of Electromagnetic Wave in Atmospheric Pressure Plasma Zhonghe Jiang XiWei Hu Shu Zhang Minghai Liu Huazhong University of Science & Technology Workshop on ITER Simulation May2006, PKU, Beijing, China May2006, PKU, Beijing, China

Section one I I Introduction and promotion II results II Numerical results IIIComparisons between analytic III Comparisons between analytic and numerical solutions and numerical solutions

I Introduction When the EM wave propagates in atmospheric pressure plasma layer, its electric field will disturbs the electrons of plasma, and the electrons will dissipate their energy by colliding with neutrals of plasma. So the energy of EM wave will be absorbed by the atmospheric plasma, and the level of dissipated energy strongly depends on the collision frequency between the electrons and neutrals. When the EM wave propagates in atmospheric pressure plasma layer, its electric field will disturbs the electrons of plasma, and the electrons will dissipate their energy by colliding with neutrals of plasma. So the energy of EM wave will be absorbed by the atmospheric plasma, and the level of dissipated energy strongly depends on the collision frequency between the electrons and neutrals.

The characteristics of EM wave in APP Amplitude attenuated strongly through electron-neutrals collision frequency (ν e0 ), the characteristic time or length of wave attenuation are less than one period or one wave length. Amplitude attenuated strongly through electron-neutrals collision frequency (ν e0 ), the characteristic time or length of wave attenuation are less than one period or one wave length. Phase shifted both by electron density (n e ) and collision frequency. Phase shifted both by electron density (n e ) and collision frequency. Reflectivity n e ’ collision frequency Reflectivity of incident EM Wave depends both on electron density gradient (n e ’ ), and collision frequency

Combine Combine wave and electron motion equations, we have got an integral-differential equation: Obtain numerically full solutions of EM wave field in space and time domain Obtain numerically full solutions of EM wave field in space and time domain

II Numerical results Phase shift Δφ Transmissivity T Reflectivity R Absorptivity A Phase shift Δφ Transmissivity T Reflectivity R Absorptivity A Thickness of plasma d Electron density n e Thickness of plasma d Electron density n e Collision frequency ν e0 Collision frequency ν e0

Three models of n e (x) ∫n e {m} (x) dx =N e =constant, m=1,2,3. 1.The bell-like profile 2. The trapezium profile 3. The linear profile

Effects of profiles

Electron density is Bell-like profile

Determination E 0 — incident electric field of EM wave, E 0 — incident electric field of EM wave, E 1 — transmitted electric field, E 1 — transmitted electric field, E 2 — reflected electric field E 2 — reflected electric field Transmissivity: Transmissivity: T=E 1 /E 0, T db =-20 lg (T). Reflectivity: Reflectivity: R=E 2 /E 0, R db =-20 lg (R).  Absorptivity: A=1 - T 2 - R 2

The transmitted plane wave E 1

The reflected plane wave E 2

The phase shift | Δφ |

The transmissivity T db

The reflectivity R db

The absorptivity A

Briefly summary All four quantities Δφ, T, R, A depend on All four quantities Δφ, T, R, A depend on --the electron density n e (x), --the collision frequency ν e0, --the thickness of plasma layer d. But, the d is well known in the experiments. But, the d is well known in the experiments.

Briefly summary (cont.) So, all four quantities Δφ, T, R, A can be used to diagnose both andν e0 of APP (Atmospheric Pressure Plasma): So, all four quantities Δφ, T, R, A can be used to diagnose both andν e0 of APP (Atmospheric Pressure Plasma): --linear average electron density --linear average electron density ν e0 --electron-neutrals collision frequency, ν e0 --electron-neutrals collision frequency, hence the linear average neutral hence the linear average neutral density. density. But, the best quantities for diagnostics are Δφ and T But, the best quantities for diagnostics are Δφ and T

The method of electron density diagnostics in APP

III Comparisons between analytic and numerical solutions

The Appleton formula

The conclusion When the reflected wave is weak, the phase shift Δφ transmissivity T obtained from analytic and numerical solutions are agreed well. When the reflected wave is weak, the phase shift Δφ and transmissivity T obtained from analytic and numerical solutions are agreed well. when the wave reflected strongly, we have to take the numerical full solutions of microwave passed through the APP to diagnose the when the wave reflected strongly, we have to take the numerical full solutions of microwave passed through the APP to diagnose the --linear average electron density --linear average electron density --electron-neutrals collision frequency ν e0 --electron-neutrals collision frequency ν e0 then the linear average neutral density then the linear average neutral density

Section Two: Two-dimensional numerical simulation in APP

I I Introduction

s-polarized p-polarized

Combine Maxwell’s Combine Maxwell’s and electron motion equations, we have got a set of integral-differential equations: S-polarized equations: S-polarized integral-differential equations: P-polarized equations: P-polarized integral-differential equations:

Finite-difference-time-domain (FDTD) Finite-difference-time-domain (FDTD)

II Comparisons II Comparisons between one dimensional and two dimensional solutions

The electron density of two-dimensional simulation is Bell-like profile along the Y axis, and is uniform along X axis

III III Numerical results Phase shift Δφ Transmissivity T Reflectivity R Absorptivity A Phase shift Δφ Transmissivity T Reflectivity R Absorptivity A Thickness of plasma d Electron density n e Thickness of plasma d Electron density n e Incident angle θ Incident angle θ Polarization s, p Polarization s, p Collision frequency ν e0 Collision frequency ν e0

The phaseshift | Δφ |

The transmissivity T db

The reflectivity R db

The absorptivity A

The conclusion Like one-dimensional results, all four quantities Δφ, T, R, A are be sensitive to n e, ν e0, d. Like one-dimensional results, all four quantities Δφ, T, R, A are be sensitive to n e, ν e0, d. For the two-dimensional case, the all four quantities Δφ, T, R, A also depend on the incident angle. For the two-dimensional case, the all four quantities Δφ, T, R, A also depend on the incident angle. The polarized mode of EM wave can take effect on the above parameters when the electron density n e ’ and incident angle are high enough. The polarized mode of EM wave can take effect on the above parameters when the electron density gradient n e ’ and incident angle are high enough.