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Rayonnement électromagnétique de solitons d’une antenne à plasma confiné

Rayonnement électromagnétique de solitons d’une antenne à plasma confiné. G.Dubost A.Bellossi 14th Colloque International sur la compatibilité Electromagnétique ,session C4 Bio- électromagnétisme, CEM 2008 Paris, « Les Cordeliers » 20-23 mai 2008. wave amplifier. Confined plasma.

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Rayonnement électromagnétique de solitons d’une antenne à plasma confiné

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  1. Rayonnement électromagnétique de solitons d’une antenne à plasma confiné G.Dubost A.Bellossi 14th Colloque International sur la compatibilité Electromagnétique ,session C4 Bio- électromagnétisme, CEM 2008 Paris, « Les Cordeliers » 20-23 mai 2008.

  2. wave amplifier Confined plasma Transmitter Spectrum analyser loop Square wave generator Antenna tuner

  3. The confined plasma antennaPo=k.To.no is the argon gas pressure With Po =6.65 103 Pascals, To=300 K: no=1.6 1024 /m3 is the neutral argon density. k is the Boltzmann constant. For a neutral gas with an ionization degree α equal to:0.01 we have: n=1.6 1022 /m3 =α.n0 n is the electronic and ion densities.

  4. SOLITONThe hydrodynamic theory explains the soliton øM=e.ФM/k.Te is the max normalized potential between two ions. Te is the electron temperature.ØMis given by the following equation :exp(ØM )+(V/Cs )[(V/Cs )2- 2. ØM ]1/2 =(1+ V/Cs )with Cs =(kTe /mi )1/2 , mi being the ion mass.V is the speed of the soliton ψ ,which is a solution of the non linear equation of Kortweg-de-Vries (b):∂ψ/∂η+ψ.(∂ψ/∂ξ)+(1/2)∂3ψ/∂ξ3 =0ξ=µ1/2 (x/D-ωi t) , η= µ3/2 ωi t , ωi =e(n/ miε0)1/2 .

  5. ωi is the plasma ionic pulsation such that: • tr =1/ ωi <<T=1/f • tr is the relaxation time • f is the modulation frequency

  6. SOLITON (following)The first order solution ψ=µø is: Ψ=3v0 /ch2 [(v0 /2)1/2 (ξ-v0 η)] (d) • Δn is the ion density used to generate one soliton of max amplitude ψM =3v0 =Δn/n. The soliton speed is :V=Cs (1+v0 ) and depends of its max amplitude . • We found a limited development of the first order :v0 =[(øM]3/3. With:ψM =µøM , • we find: µ =(øM)2 ,and :ψM = [øM]3 . • The potential near the ion is equal to:

  7. SOLITON (following) • Ф=(e/4πε0 r).exp(-r/D√2). • ø=(L/r). exp(-r/D√2). • With :L=e2/4πεo kTe :Landau length. • D=( 1/e)[εo kTe /2n]1/2 :Debye screen length • For weak correlations:L<<D that is :ø<<1 . • As d=n-1/3<D , d being the mean distance between two ions ,we have øM for r =d. Then: • øM=(L/d). exp(-d/D√2 ) :potential sheath • ψM =3vO =[L/d). exp(-d/D√2) ]3=Δn/n • The sheath of electrons around each activ ion is near D.

  8. SOLITON (following) • Numerical application • For Te =3.104 K, mi =6.6310-26 kg, Cs = 2500 m/s # V, n=1.61022 /m3 ,Ti=300 K we obtain: • L=5.610-4µm, D=0.067 µm, d=0.04 µm • øM =9.10-3 , Δn=1016/m3, ψM=7.10-7, • ФM=23 mV, µ=8.10-5, vi =(2kTi/ mi)1/2 • vi=324 m/s(mean ion speed)

  9. It is a very small plasma antennaWhen 0.2 <f<100 Khz we measured an electric field : 2 106 <E<3.5 1011 V/m at a distance of 0.4 meter from the confined plasma antenna.The antenna length 2h related to the wavelength is equal to :-in air medium :2hf/c-in the plasma :2hf/CsFor 0.2 <f<100 Khz ,2h=0.45 meters and Cs =2500 m/s we have: 3 10-7 < 2hf/c < 1.5 10-4 in air 0.04 < 2hf/Cs<18 in plasmac/Cs is # the ratio :mass ion/mass electron.

  10. Experimental results • We measured the magnetic induction field with a loop at r0 .We deduced the electric field E ,the magnetic induction field Band the spectral density (u)ffor θ=π/2 : • Z=50 ohms • Zo=377 ohms • P: measured power. R: loop radius . • With R=6 mm, ro= 0.4 m , see the results:

  11. Useful radiations from measurements (θ=π/2) E=3.2 1019 P1/2 / f2 r3 B=2.3 103 P1/2 / f r2 (u)f=8.8 10-4 (1/r2)(dP/df) Pr=2.2 106 P E(V/m), B(T) , (u)f (J.s/m3). P, f ,r , dP/df are measured power (watts), modulation frequency (Hertz),distance (m) spectral width(W/Hz). Pr is the whole radiated power.

  12. Table 1 valid for r=0.4 m.

  13. Generating the whole solitons by one pulse with an ion density: E: electric field deduced at the distance r and θ =π/2. V :volume of the plasma tube. Numerical application with the two parameters P and f : ( Δn)f =(2.91032 /f 2)P1/2. The pressure applied on the internal surface of the plasma tube is : Wr=(1/2)mi.(vi)2(Δn)fwith: vi=(2kTi/mi)1/2=324 m/s, V=0.17 liters,2h=0.45m

  14. Tube internal parameters Table 2. (Δn)fis per m3 , Wr in Pascals , Ns= (Δn)f/Δn=2.9 1016 P1/2/ f2 is the soliton number.

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