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 H uazhong U niversity of S cience & T echnology Wuhan, P. R. China
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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
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
Whenp＝50 – 760 Torr
electron density of APP
ne ≈1010– 1012 cm-3,
correspondent cut off frequency
ωc≈２- 20 GHz,
νe0 ≥or >>ωc≈2πf0.
f0 : frequency of electromagnetic wave
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
Visual C++ 6.0
—average implicit difference method for differential part
—composite Simpson integral method for integral part
The comparison with the Appleton formula
E1—transmitted electric field,
E2—reflected electric field
T=E1 /E0 , Tdb =-20 lg (T).
R=E2 /E0 , Rdb =-20 lg (R).
The bell-like profile
2. The trapezium profile
3. The linear profile
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.
--the electron density ne(x),
--the collision frequency νe0 ,
--the plasma layer width d.
TdB (nd)=F(ne , νe)
F(ne , νe) = Const.
F(ne , νe) increases slowly with ne
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
Combine Maxwell’s and motion equationsintegral-differential equations
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.
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.