Researching | Accounting for speckle-scale beam bending in classical ray tracing schemes for propagating realistic pulses in indirect drive ignition conditions

Journals >Matter and Radiation at Extremes >Volume 8 >Issue 2 >Page 025901 > Article

Matter and Radiation at Extremes
Vol. 8, Issue 2, 025901 (2023)

Accounting for speckle-scale beam bending in classical ray tracing schemes for propagating realistic pulses in indirect drive ignition conditions

C. Ruyer^1、2、a), P. Loiseau^1、2, G. Riazuelo^1、2, R. Riquier¹, A. Debayle^1、2, P. E. Masson-Laborde^1、2, and O. Morice¹

Author Affiliations

¹CEA, DAM, DIF, F-91297 Arpajon, France

²CEA, LMCE, Université Paris-Saclay, 91680 Bruyères-le-Châtel, France

show less

DOI: 10.1063/5.0124360 Cite this Article

C. Ruyer, P. Loiseau, G. Riazuelo, R. Riquier, A. Debayle, P. E. Masson-Laborde, O. Morice. Accounting for speckle-scale beam bending in classical ray tracing schemes for propagating realistic pulses in indirect drive ignition conditions[J]. Matter and Radiation at Extremes, 2023, 8(2): 025901 Copy Citation Text

show less

Abstract

We propose a semi-analytical modeling of smoothed laser beam deviation induced by plasma flows. Based on a Gaussian description of speckles, the model includes spatial, temporal, and polarization smoothing techniques, through fits coming from hydrodynamic simulations with a paraxial description of electromagnetic waves. This beam bending model is then incorporated into a ray tracing algorithm and carefully validated. When applied as a post-process to the propagation of the inner cone in a full-scale simulation of a National Ignition Facility (NIF) experiment, the beam bending along the path of the laser affects the refraction conditions inside the hohlraum and the energy deposition, and could explain some anomalous refraction measurements, namely, the so-called glint observed in some NIF experiments.

\frac{1}{k_{0}} \frac{d 〈 {k ⊥ 〉}_{k_{⊥}}}{d x} \cdot \frac{v_{d}}{| v_{d} |} = \frac{- 1}{2} \frac{n_{e}}{n_{c}} {⟨\nabla_{⊥} \frac{δ n_{e}}{n_{e}}⟩}_{⊥},

(1)

View in Article

{⟨X⟩}_{⊥} = \frac{\int d r_{⊥} X (r) I (r)}{\int d r_{⊥} I (r)},

(2)

View in Article

{⟨X⟩}_{k_{⊥}} = \frac{\int d k_{⊥} X (k) I (k)}{\int d k_{⊥} I (k)},

(3)

View in Article

(\frac{\partial^{2}}{\partial t^{2}} + 2 γ_{0} | k | c_{s} \frac{\partial}{\partial t} + c_{s}^{2} k^{2}) \frac{δ n_{e}}{n_{e}} = A_{| k |} \frac{c_{s}^{2} k^{2} I_{0}}{n_{c} v_{g} T_{e}} \frac{α_{k}}{α_{f}} g (k) e^{i v_{d} \cdot k t} .

(4)

View in Article

α_{k} [M_{0} \cos (θ)] = \frac{- Z^{'} (ζ_{e})}{2} \frac{\sum_{i} Z^{'} (ζ_{i}) \frac{Z_{i} T_{e}}{T_{i}} \frac{Z_{i} n_{e}}{n_{i}}}{Z^{'} (ξ_{e}) + \sum_{i} Z^{'} (ζ_{i}) \frac{Z_{i} T_{e}}{T_{i}} \frac{Z_{i} n_{e}}{n_{i}}},

(5)

View in Article

ζ_{e / i} = \frac{- k_{⊥} \cdot v_{d}}{| k_{⊥} |} \sqrt{\frac{m_{e / i}}{2 T_{e / i}}},

(6)

View in Article

α_{f} [M_{0} \cos (θ)] = \frac{κ}{1 - M_{0}^{2} \cos^{2} θ + 2 i γ_{0} | M_{0} | \cos θ},

(7)

View in Article

\cos (θ) = \frac{k_{⊥} \cdot v_{d}}{| k_{⊥} | | v_{d} |},

(8)

View in Article

κ = \frac{Z_{i} T_{e}}{m_{i} c_{s}^{2}},

(9)

View in Article

\begin{gathered} A_{k} (u) = \frac{1}{2} + Z_{i} (\frac{0.074}{u^{2}} + \frac{0.88}{u^{4 / 7}} + \frac{2.54}{1 + 5.5 u^{2}}) Ω, \\ u = | k_{⊥} | λ_{mfp} \sqrt{Z_{i}}, \\ Ω = \{\begin{cases} 1 & if | k_{⊥} \cdot v_{d} | / ν_{e i} < 1, \\ 0 & elsewhere, \end{cases} \end{gathered}

(10)

View in Article

\frac{δ n_{e} (k, t)}{n_{e}} = α_{k} A_{| k |} \frac{I_{0} g (k)}{n_{c} v_{g} T_{e}} f (k, t),

(11)

View in Article

f (k, t) = 1 + a_{+} e^{g_{+} c_{s} | k | t} - a_{-} e^{g_{-} c_{s} | k | t},

(12)

View in Article

a_{\pm} = \frac{- i M_{0} \cos (θ) - γ_{0} \mp i \sqrt{1 - γ_{0}^{2}}}{2 i \sqrt{1 - γ_{0}^{2}}},

(13)

View in Article

g_{\pm} = - γ_{0} \pm i \sqrt{1 - γ_{0}^{2}} - i M_{0} \cos (θ) .

(14)

View in Article

\begin{align} \frac{d θ}{d x} & = \frac{1}{k_{0}} \frac{d {〈 k_{⊥} 〉}_{⊥}}{d x} \cdot \frac{v_{d}}{| v_{d} |} \\ = \frac{- 1}{2} \frac{n_{e}}{n_{c}} \frac{I_{0}}{n_{c} v_{g} T_{e}} \int \frac{d^{2} k}{{(2 π)}^{2}} \frac{i k \cdot v_{d}}{| v_{d} |} α_{k} A_{| k |} g (k) f (k, t) {〈 e^{i k \cdot r_{⊥}} 〉}_{⊥} . \end{align}

(15)

View in Article

\frac{d θ}{d x} = - \frac{n_{e}}{n_{c}} \frac{I_{0}}{2 v_{g} n_{c} T_{e}} \frac{1}{σ} G (t),

(16)

View in Article

\begin{align} G & = \frac{σ^{3}}{8 π} I \int_{- \infty}^{\infty} d k k^{2} A_{k} e^{- k^{2} σ^{2} / 4} \\ \times \int_{0}^{π} d θ α_{k / f} [M_{0} \cos (θ)] \cos (θ) f (k, t) . \end{align}

(17)

View in Article

\frac{d θ_{SSD}}{d x} = {⟨\sum_{s} \frac{d θ_{s}}{d x}⟩}_{t},

(18)

View in Article

\frac{d θ_{SSD}}{d x} = - S \frac{n_{0}}{n_{c}} \frac{I_{0}}{2 v_{g} n_{c} T_{e}} \frac{{⟨ G ⟩}_{τ}_{SSD}}{σ},

(19)

View in Article

S = \sum_{s} \frac{I_{s} / I_{0}}{{[1 + {(x - x_{s})}^{2} / z_{c}^{2}]}^{3 / 2}} .

(20)

View in Article

τ_{SSD} = β \frac{2 π}{ω_{m} (2 Δ + 1)} = β T_{SSD} .

(21)

View in Article

{⟨ X ⟩}_{τ}_{SSD} = \frac{1}{τ_{SSD}} \int_{0}^{τ_{SSD}} X (t) d t,

(22)

View in Article

\begin{align} {⟨ G ⟩}_{τ}_{SSD} & ≃ \frac{σ^{3}}{8 π} I \int_{- \infty}^{\infty} d k k^{2} A_{k} e^{- k^{2} σ^{2} / 4} \\ \times \int_{0}^{π} d θ α_{k / f} [M_{0} \cos (θ)] \cos (θ) \\ \times (1 + a_{+} \frac{e^{g_{+} c_{s} | k | τ_{SSD}} - 1}{g_{+} c_{s} | k | τ_{SSD}} - a_{-} \frac{e^{g_{-} c_{s} | k | τ_{SSD}} - 1}{g_{-} c_{s} | k | τ_{SSD}}) . \end{align}

(23)

View in Article

\begin{gathered} \frac{d k}{d s} = - k_{0} \frac{\nabla n_{e}}{2 n_{c} η} - k_{0} S \frac{n_{0}}{n_{c}} \frac{I_{0}}{2 v_{g} n_{c} T_{e}} \frac{{⟨ G ⟩}_{τ}_{SSD}}{σ} \frac{v_{⊥}}{| v_{⊥} |}, \\ \frac{d r}{d s} = \frac{k v_{g}}{ω_{0}}, \\ v_{⊥} = v_{d} - \frac{v_{d} \cdot k}{| k |^{2}} k, \end{gathered}

(24)

View in Article

Figures&Tables (9)

References (89)

Copy Citation Text

C. Ruyer, P. Loiseau, G. Riazuelo, R. Riquier, A. Debayle, P. E. Masson-Laborde, O. Morice. Accounting for speckle-scale beam bending in classical ray tracing schemes for propagating realistic pulses in indirect drive ignition conditions[J]. Matter and Radiation at Extremes, 2023, 8(2): 025901

Download Citation

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address