Laser-driven implosions serve as hydrodynamically scaled surrogates both for full-scale inertial confinement fusion (ICF) capsules and, through the same similarity principle, for high-energy-density astrophysical flows such as supernova-interface hydrodynamics. Scale-invariant Rayleigh-Taylor (RT) growth has so far been demonstrated experimentally only at convergence ratio 2.25, with a single-mode azimuthal perturbation and a short-impulse direct drive, comparing OMEGA and National Ignition Facility (NIF) targets that differ by a factor of three in radius and implosion timescale (Sauppe et al., 2020). The open question is the generality and limits of that scale invariance: whether it survives at the convergence ratios of order 10-17 that the source work identifies as necessary (but not sufficient) for surrogacy to ICF implosions, whether it extends to multimode perturbations, and how it breaks down under non-scale-invariant physics — ablative stabilization (predicted to differ between scales), ionization-gradient-driven instability enhancement, and facility-dependent laser-plasma coupling such as cross-beam energy transfer — and whether that ionization-gradient instability physics can be extrapolated to supernova-interface and H II ionization-front conditions. Whether scale invariance survives these regimes is not yet established and is the object of this task.

Background

In inertial confinement fusion (ICF), a millimetre-scale shell containing deuterium-tritium fuel is imploded to fusion conditions by laser-driven ablation, either through direct laser irradiation (direct drive) or using x rays generated inside a high-atomic-number cylindrical cavity called a hohlraum (indirect drive). An implosion is characterized by its convergence ratio, CR=R0/RfCR = R_0/R_f (initial radius divided by final radius); ignition-scale capsule designs operate at CRCR between roughly 10 and 35. During the deceleration phase, the inward-moving dense shell is slowed by the lower-density central fuel or foam core, and the interface between them is unstable to the Rayleigh-Taylor (RT) instability, the growth of perturbations at an interface between fluids of different density when the pressure gradient pushes the lighter fluid against the heavier one. RT growth mixes cold shell material into the central hot spot and is amplified in convergent geometry by Bell-Plesset effects, geometric convergence effects that sharpen perturbation growth beyond the planar result.

Hydrodynamic scaling rests on the invariance of the Euler equations of inviscid fluid dynamics under x→λxx \to \lambda x and t→λtt \to \lambda t: enlarging a target by a factor λ\lambda while stretching the drive pulse so the implosion velocity is unchanged leaves the dimensionless hydrodynamic evolution identical. This scale invariance is what allows small laser facilities to act as surrogates, both for larger ICF drivers (capsule designs are routinely scaled from the 30 kJ OMEGA laser to the 1.8 MJ National Ignition Facility, NIF, and toward proposed next-generation drivers two to four times larger than NIF capsules) and, through the similarity criteria developed by Ryutov et al. (1999) for the laboratory simulation of supernova hydrodynamics, for astrophysical flows such as the mixing of stellar layers in core-collapse supernovae. The difficulty is that many processes in real implosions are not scale-invariant: electron thermal conduction, radiation transport, viscosity, plasma kinetic effects, ionization physics, and laser-plasma interactions.

Two specific non-hydrodynamic mechanisms define the expected limits. First, Bose, Woo, Nora, and Betti (2015) showed by theory and simulation that deceleration-phase RT growth does not scale hydro-equivalently between OMEGA- and NIF-scale direct-drive capsules, because ablative stabilization — the smoothing of RT growth by ablation from the hot spot, driven by thermal conduction and radiation transport — differs between the two scales. Second, Amendt (2008) showed that stepwise changes in the average ion charge ZZ across the fuel-pusher interface of an imploding capsule create an inverted ion-entropy gradient that drives superclassical RT growth (growth exceeding the classical rate) after deceleration onset, principally in low-Atwood-number implosions (Atwood number A=(ρ2−ρ1)/(ρ2+ρ1)A = (\rho_2-\rho_1)/(\rho_2+\rho_1), the normalized density contrast) with low-ZZ pushers; he conjectured that similar enhancement may pertain to supernova phenomena and to ionization fronts in H II regions, the photoionized gas surrounding young massive stars.

Experimentally, Sauppe et al. (2020) demonstrated scale-invariant RT growth for the first time in the high-energy-density regime: directly driven cylindrical implosions with an embedded aluminum marker layer, fielded at OMEGA (scale 1) and NIF (scale 3), produced nearly identical growth factors of about 14 for a single-mode m=20m = 20 azimuthal perturbation as the marker converged inward by a factor of 2.25 and decelerated on a central foam core, despite different laser drive conditions at the two facilities. The simulations used to interpret the experiments required an ad hoc laser power multiplier to represent cross-beam energy transfer (CBET), the exchange of energy between crossing laser beams via scattering from ion-acoustic waves in the blow-off plasma, which differs between facilities and was not modeled from first principles. The authors frame the remaining agenda explicitly: future work will target CR≈10CR \approx 10-17, where Bell-Plesset effects are pronounced and which is 'a necessary but not sufficient condition for surrogacy to ICF implosions', and further extensions 'will examine the breakdown of hydrodynamic scale-invariance in high-energy-density systems, such as the predicted differences in ablative stabilization during deceleration'.

Problem Statement

Determine the generality and limits of hydrodynamic scale invariance for laser-driven convergent implosions in the high-energy-density regime — the property that underpins both the use of small-scale implosions as surrogates for full-scale ICF capsules and, through the same similarity principle (Ryutov et al. 1999), for supernova-relevant astrophysical flows. The question is about the scaling principle itself, not any particular facility, drive, or geometry, and has four linked parts: (i) does scale-invariant Rayleigh-Taylor growth — demonstrated only at convergence ratio 2.25 with a single-mode perturbation and a short-impulse direct drive — persist at convergence ratios of order 10-17, where Bell-Plesset amplification is pronounced and which the source work identifies as a necessary but not sufficient condition for surrogacy to ICF implosions; (ii) does scale invariance extend to multimode perturbations and their nonlinear coupling, rather than the single-mode seeds used so far; (iii) where, and by how much, does scale invariance break down under non-scale-invariant physics — ablative stabilization from hot-spot thermal conduction and radiation transport (predicted to differ between scales by Bose et al. 2015), ionization-gradient-driven instability enhancement (Amendt 2008), and facility-dependent laser-plasma coupling such as cross-beam energy transfer — so that scaled experiments stop being faithful surrogates; and (iv) can the ionization-gradient stability physics identified for ICF capsules be extrapolated to supernova and H II ionization-front conditions, a connection the source work offers only as a conjecture requiring separate domain-specific analysis with gravity, radiative transfer, and astrophysical ionization physics? Part (i) is a separate persistence question that is not settled by the regime map of part (iii).

References

  1. J. P. Sauppe, S. Palaniyappan, B. J. Tobias, J. L. Kline, K. A. Flippo, O. L. Landen, D. Shvarts, S. H. Batha, P. A. Bradley, E. N. Loomis, N. N. Vazirani, C. F. Kawaguchi, L. Kot, D. W. Schmidt, T. H. Day, A. B. Zylstra, and E. Malka, 'Demonstration of Scale-Invariant Rayleigh-Taylor Instability Growth in Laser-Driven Cylindrical Implosion Experiments', Physical Review Letters 124, 185003 (2020). DOI: 10.1103/PhysRevLett.124.185003, https://doi.org/10.1103/PhysRevLett.124.185003
  2. J. P. Sauppe, S. Palaniyappan, J. L. Kline, K. A. Flippo, O. L. Landen, D. Shvarts, S. H. Batha, P. A. Bradley, E. N. Loomis, B. J. Tobias, N. N. Vazirani, C. F. Kawaguchi, L. Kot, D. W. Schmidt, T. H. Day, A. B. Zylstra, and E. Malka, 'Design of Cylindrical Implosion Experiments to Demonstrate Scale-Invariant Rayleigh-Taylor Instability Growth', High Energy Density Physics 36, 100831 (2020). DOI: 10.1016/j.hedp.2020.100831, https://doi.org/10.1016/j.hedp.2020.100831
  3. S. Palaniyappan, J. P. Sauppe, B. J. Tobias, C. F. Kawaguchi, K. A. Flippo, A. B. Zylstra, O. L. Landen, D. Shvarts, E. Malka, S. H. Batha, P. A. Bradley, E. N. Loomis, N. N. Vazirani, L. Kot, D. W. Schmidt, T. H. Day, R. Gonzales, and J. L. Kline, 'Hydro-scaling of direct-drive cylindrical implosions at the OMEGA and the National Ignition Facility', Physics of Plasmas 27, 042708 (2020). DOI: 10.1063/1.5144608, https://doi.org/10.1063/1.5144608
  4. B. Tobias, C. F. Kawaguchi, S. Palaniyappan, J. P. Sauppe, K. A. Flippo, and J. L. Kline, 'Bayesian inference of deceleration-phase Rayleigh-Taylor growth rates in laser-driven cylindrical implosions', High Energy Density Physics 37, 100879 (2020). DOI: 10.1016/j.hedp.2020.100879, https://doi.org/10.1016/j.hedp.2020.100879
  5. A. Bose, K. M. Woo, R. Nora, and R. Betti, 'Hydrodynamic scaling of the deceleration-phase Rayleigh-Taylor instability', Physics of Plasmas 22, 072702 (2015). DOI: 10.1063/1.4923438, https://doi.org/10.1063/1.4923438
  6. Peter Amendt, 'Effects of Ionization Gradients on Inertial-Confinement-Fusion Capsule Hydrodynamic Stability', Physical Review Letters 101, 115004 (2008). DOI: 10.1103/PhysRevLett.101.115004, https://doi.org/10.1103/PhysRevLett.101.115004
  7. P. A. Amendt, J. L. Milovich, S. C. Wilks, C. K. Li, R. D. Petrasso, and F. H. Seguin, 'Electric field and ionization-gradient effects on inertial-confinement-fusion implosions', Plasma Physics and Controlled Fusion 51, 124048 (2009). DOI: 10.1088/0741-3335/51/12/124048, https://doi.org/10.1088/0741-3335/51/12/124048
  8. D. D. Ryutov, R. P. Drake, J. Kane, E. Liang, B. A. Remington, and W. M. Wood-Vasey, 'Similarity Criteria for the Laboratory Simulation of Supernova Hydrodynamics', The Astrophysical Journal 518, 821 (1999). DOI: 10.1086/307293, https://doi.org/10.1086/307293
  9. I. V. Igumenshchev, D. H. Edgell, V. N. Goncharov, J. A. Delettrez, A. V. Maximov, J. F. Myatt, W. Seka, A. Shvydky, S. Skupsky, and C. Stoeckl, 'Crossed-beam energy transfer in implosion experiments on OMEGA', Physics of Plasmas 17, 122708 (2010). DOI: 10.1063/1.3532817, https://doi.org/10.1063/1.3532817
  10. R. K. Follett, I. V. Igumenshchev, A. Colaitis, J. P. Palastro, D. H. Froula, and D. Turnbull, 'Modeling cross-beam energy transfer with sector ray tracing', Physics of Plasmas 32, 022709 (2025). DOI: 10.1063/5.0253858, https://doi.org/10.1063/5.0253858
  11. R. Roycroft, J. P. Sauppe, and P. A. Bradley, 'Double cylinder target design for study of hydrodynamic instabilities in multi-shell ICF', Physics of Plasmas 29, 032704 (2022). DOI: 10.1063/5.0083190, https://doi.org/10.1063/5.0083190
  12. J. P. Sauppe, I. Sagert, T. H. Day, K. A. Flippo, J. L. Kline, L. Kot, S. Palaniyappan, R. A. Roycroft, and D. W. Schmidt, 'Double cylinder implosion experiments at the National Ignition Facility', High Energy Density Physics 53, 101156 (2024). DOI: 10.1016/j.hedp.2024.101156, https://doi.org/10.1016/j.hedp.2024.101156
  13. A. Casner, 'Recent progress in quantifying hydrodynamics instabilities and turbulence in inertial confinement fusion and high-energy-density experiments', Philosophical Transactions of the Royal Society A 379, 20200021 (2021). DOI: 10.1098/rsta.2020.0021, https://doi.org/10.1098/rsta.2020.0021