1、Conference on Computation Physics-2006 (I27) The propagation of a microwave in an atmospheric pressure plasma layer: 1 and 2 dimensional numerical solutions,Xiwei HU, Zhonghe JIANG, Shu ZHANG and Minghai LIUHuazhong University of Science & Technology Wuhan, P. R. China August 30, 2006,I Introduction
2、 and motivation II One dimensional solution III Two dimensional solution IV Conclusions,I Introduction and motivation,The classical mechanism,firstly, the EM wave transfer its wave energy to the quiver kinetic energy of plasma electrons through electric field action of waves. Then, the electrons tra
3、nsfer their kinetic energy to the thermal energy of electrons, ions or neutrals in the plasmas through COLLISIONS between electrons or between electrons and other particles.,The electron fluid motion equation,f0 is the microwave frequency, ee , ei and e0 is the collision frequency of electron-electr
4、on, electron-ion and electron-neutral, respectively.,Pure plasma (produced by strong laser) : e=eeei , Pure magnetized plasma (in magnetic confinement devices, e.g. tokamak): e=0, The mixing of plasma and neutral (in ionosphere or in low pressure discharge): e=e0 . In all of above cases: e / f0 1 Ta
5、king the WKB (or ekonal) approximationThe solution of electron fluid equation is,The Appleton formula,When p50 760 Torre066 G(109) Hz, electron density of APP ne 1010 1012 cm-3 ,correspondent cut off frequencyc- 20 GHz,so e0 or c 2f0. f0 : frequency of electromagnetic wave,The goal of our work,Study
6、 the propagation behaviors of microwave by solving the coupled wave (Maxwell) equation and electron fluid motion equation directly in time and space domain instead of in frequency and wavevector domain.,II One dimensional case,II.1 The integral-differential equation II.2 The numerical method, basic
7、wave form and precision check II.3 The comparisons with the Appleton formula II.4 Outline of numerical results,II.1 The integral-differential equation,The coupled set of equations,Begin with the EM wave equationCoupled with the electron fluid motion equation,Combine wave and electron motion equation
8、s, we have got a integral-differential equation:Obtain numerically the full solutions of EM wave field in space and time domain,II.2 The numerical method, precision check and basic wave forms,Numerical Method,Compiler: Visual C+ 6.0 Algorithm: average implicit difference method for differential part
9、 composite Simpson integral method for integral part,Check the precision of the code,Compare the numerical phase shift with the analytic result in e0 =0. The analytic formula for phase shift,Bell-like electron density profile,Phase shift when e0 =0,Waveform of Ey (x) ne = 0.5 nc，d = 2 0, e0 = 0.1 0,
10、Wave forms: passed plasma, passed vacuum, interference, phase shift. ne = 0.5 nc，d = 2 0, e0 = 1.0 0,The reflected plane wave E2,II.3,The comparison with the Appleton formula,Brief summary (1),When n0 /nc 1, the wave reflected strongly, the Appleton formula is no longer correct. We have to take the
11、full solutions of time and space to describe the behaviors of a microwave passed through the APP.,II.4 Outline of numerical results Phase shift Transmissivity T Reflectivity R Absorptivity A,Determination,E0incident electric field of EM wave,E1transmitted electric field,E2reflected electric field Tr
12、ansmissivity: T=E1 /E0 , Tdb =-20 lg (T). Reflectivity: R=E2 /E0 , Rdb =-20 lg (R). Absorptivity: A=1 - T2 - R2,Three models of ne(x) nem (x) dx =Ne=constant, m=1,2,3.,The bell-like profile2. The trapezium profile3. The linear profile,Effects of profiles are not important,The phase shift | |,1. incr
13、eases with n0 and d. 2. When e0 0 ， the maximum value in pure (collisionless) plasmas. 3. Then, decreases with e0/0 increasing. 4. When e0/ 0 1, 0 the pure neutral gas case.,Briefly summary (2),The transmissivity Tdb and The absorptivity A reach their maximum at e0/0 1,Briefly summary (3),All four q
14、uantities , T, R, A depend on -the electron density ne(x), -the collision frequency e0 , -the plasma layer width d.,is more important than and d,According to the collision damping mechanism, the transferred wave energy is approximately proper to the total number of electrons, which is in the wave pa
15、ssed path.represents the total number of electrons in a volume with unit cross-section and width d when the average linear density of electron is .,TdB seems a simple function of the product of n and d,Let TdB (nd)= F(ne , e) When e 1, F(ne , e) = Const. When e 1 , F(ne , e) increases slowly with ne
16、,F(ne ,e ),III Two dimensional case,III.1 The geometric graph and arithmetic III.2 Comparison between one and two dimensional results in normal incident case III.3 Outline of numerical results,III.1 Geometric graph for FDTD Integral-differential equations,When microwave obliquely incident into an AP
17、P layer,The propagation of wave becomes a problem at least in two dimension space. Then, the incidence angle and the polarization (S or P mode) of incident wave will influence the attenuation and phase shift of wave.,The equations in two dimension case,Maxwell equation for the microwave.Electron flu
18、id motion equation for the electrons.,s-polarized p-polarized,Combine Maxwells and motion equations integral-differential equations,S-polarized integral-differential equations:P-polarized integral-differential equations:,III.2 Comparison between one and two dimensional results in normal incident cas
19、e,III.3 The numerical results about the effects of incidence angles and polarizations,The influence of incidence angle,The effects of the density profile,IV Conclusion,1. When nmax /nc 1, the Appleton formula should be replayed by the numerical solutions. 2. The larger the microwave incidence angle
20、is, the bigger the absorptivity of microwave is. 3. The absorptivity of P (TE) mode is generally larger than the one of S (TM) mode incidence microwave.,4. The bigger the factor is, the better the absorption of APP layer is. 5. The absorptivity reaches it maximum when . 6.The less the gradient of electron density is, the larger (smaller) the absorptivity (reflectivity) is.,Thanks !,
