Xiwei HU, Zhonghe JIANG, Shu ZHANG and Minghai LIU

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 LIU Huazhong University of Science &Technology Wuhan, P. R. China August 30, 2006

2. IIntroductionand motivationIIOne dimensional solutionIIITwo dimensional solutionIVConclusions

3. IIntroduction and motivation

4. 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 transfer 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.

5. The electron fluid motion equation • f0 is the microwave frequency, • νee , νei and νe0 is the collision frequency of electron-electron, electron-ion and electron-neutral, respectively.

6. Pure plasma (produced by strong laser):νe=νee＋νei, Pure magnetized plasma (in magnetic confinement devices, e.g. tokamak): νe=0, The mixing of plasma and neutral (in ionosphere or in low pressure discharge): νe=νe0. In all of above cases:νe / f0 << 1 Taking the WKB (or ekonal) approximation The solution of electron fluid equation is

7. The Appleton formula

8. Whenp＝50 – 760 Torr νe0≈６－４66G(109) Hz, electron density of APP ne ≈1010– 1012 cm-3, correspondent cut off frequency ωc≈２- 20 GHz, so νe0 ≥or >>ωc≈2πf0. f0 : frequency of electromagnetic wave

9. The goal of our work • Study 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.

10. II One dimensional case II.1 The integral-differential equation II.2 The numerical method, basic wave form and precision check II.3 The comparisons with the Appleton formula II.4 Outline of numerical results

11. II.1The integral-differential equation

12. The coupled set of equations • Begin with the EM wave equation • Coupled with the electron fluid motion equation

13. Combinewave and electron motion equations, we have got a integral-differential equation: • Obtain numerically the full solutions of EM wave field in space and time domain

14. II.2The numerical method, precision check and basic wave forms

15. Numerical Method • Compiler: Visual C++ 6.0 • Algorithm: —average implicit difference method for differential part —composite Simpson integral method for integral part

16. Check the precision of the code • Compare the numerical phase shift with the analytic result inνe0 =0. • The analytic formula for phase shift

17. Bell-like electron density profile

18. Phase shift Δφ when νe0 =0

19. Waveform of Ey (x)ne = 0.5 nc，d = 2 λ0, νe0 = 0.1 ω0

20. Wave forms: passed plasma, passed vacuum, interference, phase shift.ne = 0.5 nc，d = 2 λ0, νe0 = 1.0 ω0

21. The reflected plane wave E2

22. II.3 The comparison with the Appleton formula

24. Brief summary (1) • When n0 /nc <1, the reflected wave is weak, the Δφ andT obtained from analytic (Appleton) formula and numerical solutions are agree well. • When n0 /nc >1, the wave reflected strongly, the Appleton formula is no longer correct. We have to take the full solutions of time and space to describe the behaviors of a microwave passed through the APP.

25. II.4 Outline of numerical resultsPhase shift ΔφTransmissivity TReflectivity RAbsorptivity A

26. Determination • E0—incident electric field of EM wave, E1—transmitted electric field, E2—reflected electric field • Transmissivity: T=E1 /E0 , Tdb =-20 lg (T). • Reflectivity: R=E2 /E0 , Rdb =-20 lg (R). • Absorptivity: A=1 - T2 - R2

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

28. Effects of profiles are not important

29. The phase shift | Δφ |

30. Briefly summary (2) 1.\Δφ\ increases withn0andd. 2. When νe0 → 0，\Δφ\ → the maximum value in pure (collisionless) plasmas. 3. Then, \Δφ\ decreases withνe0/ω0increasing. 4. When νe0/ω0 >>1, Δφ→0 –the pure neutral gas case.

31. The transmissivity Tdb and The absorptivity A reach their maximum atνe0/ω0 ≈1

32. Briefly summary (3) • All four quantities Δφ, T, R, A depend on --the electron density ne(x), --the collision frequency νe0 , --the plasma layer width d.

33. 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 passed 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 .

34. TdB seems a simple function of the product of n and d • Let TdB (nd)=F(ne , νe) • When νe> 1, F(ne , νe) = Const. • When νe < 1 , F(ne , νe) increases slowly with ne

35. F(ne ,νe )

36. 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

37. III.1Geometric graph for FDTDIntegral-differential equations

38. When microwave obliquely incident into an APP layer • The propagation of wave becomes a problem at least in two dimension space. • Then, the incidence angleθand thepolarization (S or P mode) of incident wave will influence the attenuation and phase shift of wave.

39. The equations in two dimension case • Maxwell equation for the microwave. • Electron fluid motion equation for the electrons.

40. s-polarized p-polarized

41. Combine Maxwell’s and motion equationsintegral-differential equations • S-polarized integral-differential equations: • P-polarized integral-differential equations:

42. III.2Comparison between one and two dimensional results in normal incident case

44. III.3The numerical resultsabout the effects of incidence angles and polarizations

45. The influence of incidence angle

47. The effects of the density profile

48. IVConclusion

49. 1. When nmax /nc >1, the Appleton formula should be replayed by the numerical solutions. 2. The larger the microwave incidence angle 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.

50. 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.