H3-5 Mode conversion of downward-propagating Langmuir waves in the topside ionosphere

Transcription

1 E N G I N E E R I N G H3-5 Mode conversion of downward-propagating Langmuir waves in the topside ionosphere Nikolai G. Lehtinen, Nicholas L. Bunch, and Umran S. Inan STAR Laboratory, Stanford University, Stanford, CA, U.S.A. NRSM, Boulder, CO January 11, 2013 E N G I N E E R I N G Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

2 Outline StanfordFWM E N G I N E E R I N G 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

3 Outline StanfordFWM Algorithm description (cold plasma) 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

4 StanfordFWM Algorithm description (cold plasma) StanfordFWM capabilities and applications Capabilities: Arbitrary plane stratified anisotropic medium Arbitrary configuration of harmonically varying currents Stable against the swamping instability by evanescent waves Efficient use of the computer resources, easily parallelized Previous applications (VLF waves in cold plasma): Trans-ionospheric propagation Earth-ionosphere waveguide propagation Scattering on D-region disturbances Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

5 StanfordFWM Algorithm description (cold plasma) z N e B ε k z M z k+1 z k y x z 2 z 1 =0 We work in Fourier (horizontal wave vector k ) domain: 1 For each k = const (Snell s law) = find k z, E and H in each layer for each of 4 plane wave modes (2 up, 2 down) 2 Use continuity of E and H between layers to find reflection coefficients ˆR u,d (2 2) and mode amplitudes u, d (of length 2) Recursion order ˆR u k+1 ˆR u k and u k u k+1 provides stability against swamping of solution by evanescent waves Represent source currents as boundary conditions on E and H between layers 3 Inverse Fourier transform from k to r Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

6 Outline StanfordFWM Generalization to warm plasma 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

7 Hydro-electro-dynamic equations [ v m t StanfordFWM Generalization to warm plasma E H = ε 0 + qnv q = e t H E = µ 0 t pn γ = const adiabatic, γ = 3 ] = p n + q [E + v (B 0 + µ 0 H)] mνv + (v )v n t + (nv) = 0 No ions = ω ω LH (HF range). Linearize for small disturbances E, H, v, p e iωt ; 6 components E, H, v z and p are continuous between slabs; 3 upward and 3 downward mode amplitudes u and d; Generalization of stable recursive calculation of reflection coefficients ˆR u,d (3 3) and amplitudes u and d is staightforward. Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

8 Important plasma parameters StanfordFWM Generalization to warm plasma Electron sound speed Dimensionless parameters γp0 c s = mn 0 Note: X = q2 n 0 mε 0 ω 2, Y = qb 0 mω, Z = ν ( ω, U = 1 + iz, Γ = cs ) 2 c X = ω 2 p/ω 2, Y = ω H /ω, where ω p and ω H are plasma and gyro frequencies of electrons; Γ = (2γ/3)(E th /E 0 ) = 2E th /E 0, where E th is the thermal energy and E 0 = mc 2 is the rest energy of an electron. We consider non-relativistic plasma only, i.e. Γ 1. Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

9 Outline Comparisons with previous calculations E N G I N E E R I N G 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

10 Comparisons with previous calculations E N G I N E E R I N G Simulated ramp of N e B 0, ν, T e = const = Y, Z, Γ = const. N e = N e (z) = X = X(z). Important dimensionless parameter is k 0 Λ, where Λ = X dx/dz Gradient is simulated as a sinusoidal ramp of X Λ is evaluated at z = 0 zmax 0 zmin X1 X0 X2 Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

11 Outline Comparisons with previous calculations Budden and Jones [1987] 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

12 Comparisons with previous calculations Budden and Jones [1987] Parameters used in the simulation f = 65 khz, Y = 0.5, Z = 10 5, Γ = , k 0 Λ = , θ B = 64.2 Budden and Jones [1987] used a similar but unstable FWM approach Conversion of electrostatic ES mode incident onto a gradient of increasing N e into extraordinary right-handed RX and ordinary left-handed LO modes Path in the CMA diagram At X 1 (bottom): LO, RX, ES; at X 2 (top): no waves small attenuation of propagating waves exact X 1,2 are not very important. Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

13 Comparison Comparisons with previous calculations Budden and Jones [1987] Budden and Jones [1987, Fig 2] 0 Present work 10 Power fraction, db ES to ES ES to RX ES to LO n x We reproduced the features of Budden and Jones [1987, Fig 2], such as the effect of the radio window at n x = Y /(1 + Y ) sin θ B = The backscattering ES ES is lower than Budden and Jones [1987] result due to attenuation of ES waves. Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

14 Outline Comparisons with previous calculations Mjølhus [1990] 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

15 Comparisons with previous calculations Mjølhus [1990] Mjølhus [1990] used contour integration in the complex k z -plane; Calculated attenuation A(p) (dimensionless fraction of power) of LO wave when reflected from an upward ramp in N e Parameter is dimensionless factor p = (k 0 Λ) 1/3 Y 1/2 Mjølhus [1990, Fig 10] Present work A(p) p Results are the same, except non-zero A(p) at p due to collisions. Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

16 Outline Comparisons with previous calculations Kim et al [2008] 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

17 Comparisons with previous calculations Kim et al [2008] Kim et al [2008] used a fluid model; Calculated LO attenuation A(p, q) Parameters are dimensionless Mjølhus factors q = (k 0 Λ) 1/3 n x, p = (k 0 Λ) 1/3 Y 1/2 Kim et al [2008, Fig 6] Present work 1.4 q p The peaks are in the same place! Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

18 Outline ES to EM conversion E N G I N E E R I N G 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

19 Outline ES to EM conversion Waves 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

20 Waves ES to EM conversion Waves Consider a small density change around the resonance Path in the CMA diagram At X 1 (bottom): LO, Z, ES; at X 2 (top): LX Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

21 ES to EM conversion Waves Refractive index surfaces at Y < 1 near X = 1 Typical ionosphere, f = 5 MHz X 1 X LO ES (θ<θ res ); Z (θ>θ res ) Z log 10 n X= X=1.025 Y=0.2; Z=3.2e 05; Γ=4.4e 07 Z and ES waves are actually the same, separated by the resonance cone. Also, Z and LX are the same for θ 0. This opens a possibility of conversion ES Z LX. Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

22 Outline ES to EM conversion Stanford FWM results 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

23 0.2 E N G I N E E R I N G Efficency of conversion ES to EM conversion Stanford FWM results The parameter is now L = z max z min, the width of the ramp; k 0 Λ = ( ) 2L 2X0 λ 0 X 2 ES up L(X) up 2 ES up Z down S /S z,out z,in f=5.0 MHz log 10 (2L/λ 0 ) n x n x Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

24 Outline ES to EM conversion Explanation of the conversion efficiency 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

25 Double internal reflection ES to EM conversion Explanation of the conversion efficiency Total internal reflection of upward ES into downward ZB ( backward ) mode on the resonance cone (with S z opposite to k z = k 0 q) As ZB mode propagates downwards to the lower density region, the resonance cone becomes wider and the mode gets further away from it. At some point with q > 0, the downward ZB coalesces with upward ZF ( forward ) mode, and converts to it in the total internal reflection process. The extraordinary ZF mode becomes LX mode above the ramp, without being affected by the resonance at X = 1. Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

26 Outline Conclusions E N G I N E E R I N G 1 Stanford Full-Wave Method (StanfordFWM) Algorithm description (cold plasma) Generalization to warm plasma 2 Comparisons with previous calculations Budden and Jones [1987, doi: /rspa ] Mjølhus [1990, doi: /rs025i006p01321] Kim et al [2008, doi: / ] 3 Conversion of Langmuir into electromagnetic waves in the ionosphere Waves at the top and the bottom of a small N e ramp Stanford FWM results Explanation of the conversion efficiency 4 Conclusions Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,

27 Conclusions Conclusions E N G I N E E R I N G We generalized StanfordFWM to warm plasma Results compare well to previous workers There is efficient conversion ES EM due to total internal reflection mechanism Lehtinen et al (Stanford) Wave conversion in warm plasma January 11,