RLE Progress Report No - Research Laboratory of Electronics - MIT

More documents

Recommendations

Info

1 0.1 ne Te Ti 0.01 100 200 300 400 Location from target (z) in µ m Figure 1: Laser produced plasma in TRIDENT; n e in units of n e /n cr , T e and T i in keV (from Ref.1). The basic experimental setup is illustrated in Figure 13 of our last report 2 , where a laser beam is focused into a plasma that is created from a plastic foil. 1 The plasma is approximately homogeneous along the beam path, but changes its density and temperature as it flows away from the target. By focusing the laser at different positions from the target, experimentalists have studied the SRS backscattering for the different parameters shown in Figure 1. Considering a weak nonlinear interaction of the five waves, we express this as nonlinearly coupled field amplitudes that change slowly in time and space. The equations that describe the interaction between the slowly varying amplitudes ( a 1 , a , 2 a , 3 a and 4 a , for the Laser, BEMW, 5 EPW, BEPW and IAW, respectively) are: ( ∂ + v ∂ + γ ) a = −K a SRS a , (1) t g1 x 1 1 t + vg2∂ x + 2 ) 2 = 2 1 3 3 ( ∂ γ a K a SRS a , (2) ( ∂ + v ∂ + γ ) a = K a a − K a a , (3) t g3 x 3 3 SRS 1 2 t + vg4∂ x + 4) a4 = LDI t + vg5∂ x + 5) a5 = LDI 3 LDI ( ∂ γ K a a , (4) 3 5 ( ∂ γ K a a . (5) 4 4 5 2 In Eqs. (1)–(5), a = W / ω , W , v and g γ are the wave action density, wave energy density, group velocity and damping rate of mode . The nonlinear coupling coefficients are: K SRS ≈ 2 ε o 1/ 2 2 e k ⎛ ω ⎞ 3 pe , m e ⎜ ⎟ 4 ⎝ω1ω 2ω 3 ⎠ K LDI ≈ 2 ε o m e 1/ 2 e ω pe ⎛ ω ⎞ 5 4v ⎜ ⎟ . Te ⎝ω3ω 4 ⎠ Such model equations have also been considered in the past 3 but their solution was not explored in much detail nor related to experiments in relatively homogeneous plasmas. 2 R. J. Focia, A. Bers, and A. K. Ram., “Plasma Electrodynamics and Applications: Section 5 – Electromagnetic Decay Instability in Single Hot Spot Geometry”, Progress Report No. 142, MIT Research Laboratory of Electronics, Cambridge, 2000 (http://rleweb.mit.edu/Publications/pr142/bers142.pdf). 3 J. A. Heikkinen and S. J. Karttunen, “Intensity Saturation of Stimulated Raman Scattering by Ion-Wave Coupling,” Phys. Fluids, 29(4), 1291 (1986).
We transformed Eqs. (1)–(5) according to the convenient normalization: a ← a / ao , t ← γ bt , x ← γ b x / v , g 3 v ← v /v and g g g3 γ ← γ / γ ; where b γ a = K SRS a , o γ b = K LDI a and o G = γ a / γ . b We then numerically integrated the resulting equations: Figure 2: (a) Time evolution of field amplitudes, and (b) time evolution of SRS reflectivity. ( ∂ + v ∂ + γ ) a = −Ga a , (6) t g1 x 1 1 t + vg2∂ x + 2 ) a2 = 1 2 3 3 ( ∂ γ Ga a , (7) ( ∂ + v ∂ + γ ) a = Ga a − a a , (8) t g3 x 3 3 1 t + v g 4∂ x + 4 ) a4 = t + v g 5∂ x + 5) a5 = 2 3 5 4 5 ( ∂ γ a a , (9) ( ∂ γ a a . (10) 3 4 For the parameters of the mentioned experiment we find that SRS reaches a saturated state in a time that is much shorter than the laser pulse length ( ≈ 200psec) and in a region that is shorter than the interaction region length ( ≈ 200µ m ). As an illustration, Figure 2(a) shows the time evolution of the field amplitudes near the beginning of the simulation box, for the plasma parameters at 280 µm from the target ( T e = 0. 7 keV , T i = 0. 16 keV , n = 0. 03n ), and the laser cr 15 2 parameters λ = 0. 524 µ m and intensity I o ≅ 6× 10 Watts / cm . In this case, the corresponding normalized equation parameters are: v ≈ −v ≈ 30 , v ≈ v 1. 0 , v g1 ≈ 30 , v g5 ≈ 0, γ ≈ γ 0 , g1 g2 g4 g3 = 1 2 ≈ γ 3 = 0.68, γ 4 = 0. 53, γ 4 = 0. 08 and G = 0. 52 . Since the group velocity of the laser and the BEMW are the same, the calculation of the SRS reflectivity is straightforward: % SRS = ω 2 a2 / ω1a , at the 1 boundary where the laser enters the simulation box. Figure 2(b) shows the time evolution of the SRS reflectivity for the parameters given before. Finally, we ran our simulation for the different parameters observed in experiments, and found a reasonably good agreement between numeric calculation and experimental observations (for
Page 1 and 2: Plasma Electrodynamics and Applicat
Page 3 and 4: 1. Results of Recent Single Hot Spo
Page 5 and 6: ps FWHM, coincident in time with th
Page 7 and 8: (a) (b) Figure 3: (a) Time-resolved
Page 9: 2. Saturation of Stimulated Raman B
Page 13 and 14: 3. Modes in Density Depleted Wavegu
Page 15 and 16: In Eq. (2), α = −k x , ( ) z o
Page 17 and 18: 5. Emission From Electron Bernstein
Page 19 and 20: the X-B conversion process is optim
Page 21: appear in Proceedings of the 18th I

RLE Progress Report No - Research Laboratory of Electronics - MIT

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?