REVIEW 3 major objections 6 minor 1 cited by
A Multiscale Eulerian Vlasov-Rosenbluth-Fokker-Planck Algorithm for Thermonuclear Burning Plasmas
T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash
Pith's one-line read The paper constructs a two-grid Vlasov-Rosenbluth-Fokker-Planck scheme for fusion alphas whose conservative sink/source transfer recovers the original single-population equation in the continuum without requiring strict scale separation.
desk verdict Solid algorithmic step for multiscale alpha slowing-down, with an acknowledged but under-scrutinized approximation in the sink model. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The machinery is a two-grid population split: energetic alphas $f_\alpha$ live on a grid $\Omega_\alpha$ scaled to the 3.5 MeV birth speed, ash $f_A$ lives on a finer grid $\Omega_A$ scaled to the thermal speed, and the two are coupled by a sink $S_{\alpha\to A}=\nu_{\alpha\to A}f_\alpha$ that is nonzero only in the overlap $\Omega_\alpha\cap\Omega_A$, plus a matched source $S_{A\leftarrow\alpha}$. The sink rate $\nu_{\alpha\to A}$ is obtained by reducing the Rosenbluth-Fokker-Planck collision operator against cold Maxwellian ions to its leading Gaussian term; the source is mapped back by bilinear interpolation and corrected through a variational projection onto $\{1,w_\parallel,w^2\}$, which enforces discrete mass, momentum, and energy conservation. A grid-scale temperature floor $\delta T_\alpha=m_\alpha\Delta v_\alpha^2$ is added to the $\alpha$-electron diffusion coefficient to smooth the near-zero-velocity singularity while canceling in the electron energy equation. This construction gives detailed balance in the continuum, so adding the two population equations returns the original single-population Vlasov-Fokker-Planck equation.
What would settle it
Run the 0D2V slowdown benchmark of Section 5.1 with a beam-like $\alpha$ birth source and $v_\alpha/v_{th,A}\approx 10$, then compare the two-grid $f_\alpha$, ash distribution, and electron-temperature history against a fully resolved single-population simulation. If the agreement does not improve with grid refinement, or if the overlap-region indicator $\hat{A}^M_{\gamma'}\cdot\nabla_v\ln f_\alpha$ is comparable to $\exp(-w^2/v_{th,\gamma'}^2)$ during the simulation, the simplified sink model is controlling the transfer rather than negligible, and the no-scale-separation claim is falsified.
Extended reading notes
Core claim
The central claim is constructive: write the total $\alpha$ distribution as a sum of energetic and ash populations, evolve each on its own grid, and connect them with a sink $S_{\alpha\to A}$ on the energetic side and a source $S_{A\leftarrow\alpha}$ on the ash side. Because the two terms are defined to satisfy detailed balance, adding the two population equations returns the original Vlasov-Fokker-Planck equation exactly (Eqs. 11 and 25 summing to Eq. 26), so the split is consistent in the continuum for arbitrary grid scale ratios. The sink rate is not ad hoc: it comes from the asymptotic form of the $\alpha$-ion Rosenbluth-Fokker-Planck collision operator for a fast particle against a cold Maxwellian, retaining the Gaussian term and leaving a velocity-gradient correction for future work. The discrete version then applies a variational additive correction to the interpolated ash source, projecting onto the moments $\{1,w_\parallel,w^2\}$, which restores exact mass, momentum, and energy conservation. The paper demonstrates on 0D2V and 1D2V problems, including a spherical implosion surrogate with DT fusion reactivity, that this construction tracks the known $\propto 1/(v^3+v_c^3)$ slowing-down tail, converges at second order, and forms the ash structure near the fuel-ice interface without resolving that structure on the energetic grid.
Load-bearing premise
The load-bearing premise is that the velocity-space gradient term $\hat{A}^M_{\gamma'}\cdot\nabla_v\ln f_\alpha$ in the reduced collision operator is negligible in the overlap region; if it is not, the simplified Gaussian sink misrepresents the transfer between the energetic and ash populations even though the summed continuum equations remain exact.
Editorial extensions
If this is right
- Multiscale alpha slowing-down problems with speed-ratio factors of hundreds can be run on two moderate uniform grids, making kinetic treatment of energetic particles in cryogenic DT ice layers computationally affordable.
- Discrete mass, momentum, and energy conservation removes the need for ad hoc global renormalization in long implosion simulations, so electron heating and alpha energy deposition stay consistent with the kinetic populations.
- Because the split reduces to the original Vlasov-Fokker-Planck equation in the continuum, the method is verifiable by grid refinement against a one-population solver at moderate scale separation, and its errors shrink at second order.
- The scheme resolves the formation of the thermal ash structure even when that structure is far narrower than the energetic grid spacing, so sharp features near fuel-ice interfaces are captured rather than smeared or aliased.
- In layered capsule surrogates the method localizes alpha heating near the ice-vapor interface, predicting that ash accumulates there while the cold ice remains largely unaffected; this is a concrete observable for burn modeling.
Reading between the lines
- The dropped velocity-gradient term becomes the main risk when the alpha population is strongly anisotropic: the current sink removes particles at a rate that does not depend on pitch angle, whereas the full collision operator would transfer more particles from directions where the distribution is steep. A narrow-pitch birth source would expose this, so a two-grid versus fully-resolved comparison o
- All reported benchmarks have electron collisions as the dominant slowing-down channel entering the overlap region; the sink model is not tested where ion collisions thermalize alphas first, such as low electron density or high-Z fuel. A case with $v_\alpha/v_{th,A}$ near 10 and comparable electron and ion drag would stress the claim that scale separation need not be strict.
- The conservation projection uses only the moments $\{1,w_\parallel,w^2\}$; for magnetized or perpendicular-heating scenarios one would want at least $w_\perp^2$ in the basis, and without it the source reconstruction could bias the perpendicular temperature even if global energy is conserved.
- A practical extension the authors hint at is replacing the simplified sink with the full gradient-dependent term; since that term depends on $\nabla_v f_\alpha$, an implicit formulation would be needed, but it would also let the method inherit rigorous scale-separation-free convergence in the overlap region without an auxiliary model.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes an Eulerian two-grid algorithm for the Vlasov-Rosenbluth-Fokker-Planck equation, targeting the multiscale problem of fusion-born alpha particles slowing down into a thermal ash population in burning plasmas. The energetic and thermal populations are represented on separate velocity grids with independent scaling and shift velocities, coupled by a Gaussian-based sink term on the energetic grid and a conservatively projected source term on the ash grid. The sink rate is derived from a reduced collision operator for energetic ions against Maxwellian thermal species, and a temperature floor is introduced to regularize near-zero-velocity singularities. The discretization uses conservative finite differences, Chang-Cooper fluxes, a nonlinearly implicit BDF2 time integrator, and a variational projection that enforces discrete mass, momentum, and energy conservation. The method is tested on 0D2V slowing-down and electron-heating benchmarks, a 1D2V spherical slowing-down problem, a two-grid convergence study, and a 1D2V layered ICF implosion surrogate. The central claim is that the two-grid formulation is consistent with the original VFP equation in the continuum limit, conservative, and valid for arbitrary velocity-scale separation between the alpha and ash grids.
Significance. If fully validated, the method would be a practically valuable alternative to AMR or dynamically adapted grids for kinetic simulations of burning ICF plasmas, since it avoids the strict scale-separation requirement of Peigney et al. and comes with an explicit conservation structure. The paper has several genuine strengths: the continuum consistency argument (Eqs. (11)+(25)=(26)) is exact by construction; the sink rate is derived from collision physics rather than fitted to the benchmarks; the mass, momentum, and energy projection step is explicit and preserves the relevant moments; and the benchmark suite extends from homogeneous slowing-down to a self-consistent ICF-like implosion. However, the central fidelity claim is not yet fully supported. The sink-rate derivation drops a velocity-gradient term that can act as a source, the analytic references share the same asymptotic slowing-down model used to motivate the sink, and the convergence study compares two-grid solutions against finer two-grid solutions rather than against a single-population reference.
major comments (3)
- [Section 3, Eqs. (21) and (24)] The sink rate in Eq. (24) omits the velocity-gradient term \(\hat{\mathbf{A}}^M_{\gamma'} \cdot \nabla_v \ln f_\alpha\) that appears in the reduced collision operator Eq. (21), even though the authors note that this term can act as a source. The consistency argument following Eqs. (11)+(25)=(26) only proves that the numerical sink and source cancel when the two equations are summed; it does not prove that \(f_\alpha\) and \(f_A\) individually evolve according to the original collision operator. Since the dropped term is most significant precisely in the overlap region \(\Omega_\alpha \cap \Omega_A\), where \(f_\alpha\) has large gradients, the energetic/ash partition is biased by construction, and the statement that the formulation 'remains valid for arbitrary values of \(v^*_\alpha/v^*_A\)' is not supported. The manuscript should either provide a quantitative bound or numerical evidence that the dropped term is small in the regimes of interest, or add a benchmark that specifically exercises this term against a single-population reference solution.
- [Section 5.4, Eq. (78) and Figure 10] The convergence study compares two-grid solutions on coarse grids to a two-grid solution on a finer grid, so it verifies the order of the spatial and velocity discretizations but cannot detect a systematic error introduced by the sink model, because both the coarse and reference solutions use the same split and the same dropped term. In addition, the velocity-space study modifies the source variance with a grid-dependent floor, \(\Delta v_\alpha := \Delta v_\alpha + \Delta v_{\alpha,256\times128}\), which affects the smoothness of the reference solution and therefore the interpretation of the reported second-order rate. A comparison against a single-population VFP solution at moderate scale separation, or a manufactured solution with an independent sink term, is needed to validate the split itself rather than only the discretization.
- [Sections 5.1 and 5.2] The semi-analytical references used in the 0D2V benchmarks are based on the same asymptotic slowing-down theory used to derive the sink rate. Equation (68) is the standard \(1/(v^3+v_c^3)\) distribution, and the ODE model in Eqs. (72)-(74) tracks only bulk temperatures, so it is not sensitive to the velocity-space structure of the sink in the overlap region. Agreement with these references therefore partly reflects self-consistency of the model rather than an independent test of the split dynamics. The qualitative agreement in Section 5.2, where \(\Omega_A\) becomes comparable to \(\Omega_\alpha\), is encouraging, but the test does not exercise the dropped gradient term in Eq. (21). A test with a strongly anisotropic or strongly non-Maxwellian alpha distribution in the overlap region, or a comparison of higher velocity moments, would substantially strengthen the validation.
minor comments (6)
- [Eq. (42)] The symbol \(\Omega^*_A\) is used in the overlap condition but is not defined; earlier Eq. (12) uses \(\Omega_\alpha \cap \Omega_A\). Please define the effective ash-domain mapping on the alpha grid.
- [Eqs. (51) and (58)] The definition of the shifted parallel coordinate is inconsistent between these equations: Eq. (58) includes the unit vector \(\mathbf{e}_\parallel\), while Eq. (51) does not. This makes the projection basis in Eq. (50) ambiguous.
- [Section 4.2, Eq. (43)] The activation function \(\beta\) introduces empirically chosen parameters \(\chi=2\) and \(n_{\min}\), but the sensitivity of the results to these parameters is not discussed. A brief parameter study or a justification of the chosen values would improve reproducibility.
- [References] Reference [8] spells the journal name as 'Erophysics Letters'; it should be 'Europhysics Letters'. The author list of reference [35] also appears garbled and should be corrected.
- [Section 5.4] The smoothing floor added to the fusion source variance in the velocity-space convergence study is an important detail for interpreting Figure 10; it should be stated in the main text before the convergence claim is made, rather than only in the paragraph describing the study.
- [Eq. (78)] The L2 error norm sums over \(N_r\) coarse-grid points in the numerator but over \(N_{r,\mathrm{ref}}\) reference-grid points in the denominator; please clarify how the reference is interpolated for the velocity-space study, where the sentence about interpolation refers only to the position-space study.
Circularity Check
The two-grid consistency proof is a cancellation identity by construction, and the main slowing-down benchmarks share the same asymptotic model that defines the sink; the method still has independent content, so circularity is partial rather than total.
-
self definitional
[Sec. 3, after Eq. (26) (detailed-balance/consistency argument)]
"This can be readily verified by defining the total distribution function of α particles as the sum of α and ash species, f_α := f_α + f_A, and adding Eqs. (25) and (11): ... which recovers the original form of the Fokker-Planck equation for α particles. Consequently, the new formulation remains valid for arbitrary values of v*_α/v*_A."
The sum identity (26) is guaranteed by construction: S_A←α is defined to equal S_α→A, and f_α total is defined as f_α + f_A, so the numerical sink and source cancel identically when the two population equations are added. This cancellation is not a test that either population individually evolves under the original Rosenbluth operator; it is a definitional property of the split. The paper nevertheless invokes it to conclude validity for arbitrary v*_α/v*_A, even though the energetic-population equation uses the truncated sink rate (24) that drops the bA^M·∇_v ln f_α term, which the paper itself notes can act as a source. The formal claim therefore reduces to the construction of the split.
-
other
[Sec. 5.1, Eq. (68); linked to Sec. 3, Eq. (24)]
"This allows us to derive a simplified form of the collision operator and, consequently, a semi-analytical model for comparison with our multiscale two-grid scheme. ... The semi-analytical steady-state α-particle distribution function is given by: f∞_α(v)=S0 τ_s/(4π(v^3+v_c^3)), v ∈ [v_c, v_α]."
The reference solution in the principal verification is the steady state of the same asymptotic slowing-down/friction model used to construct the sink rate in Eq. (24): Maxwellian target distributions and collisional friction (with the same Rosenbluth-potential reduction). Agreement with Eq. (68) therefore confirms that the two-grid discretization reproduces the simplified model that was put into the sink; it cannot validate the discarded bA^M·∇_v ln f_α term or the claim that the split matches the full collision operator when the grids overlap. This is a validation self-consistency rather than an independent test, although the Sec. 5.2 heating ODE comparison is more independent, which limits the circularity.
full rationale
The central numerical method is not fitted to the benchmarks: the sink rate (24) is derived from collision physics with stated approximations, and parameters such as the activation-function χ and floor density n_min are regularization knobs rather than data fits. The main circularity is the use of the constructed cancellation identity (26) as evidence of validity for arbitrary scale separation; this is a definitional property of the source/sink pair. The 0D and 1D slowing-down benchmarks use the same asymptotic theory that defines the sink, so they are partly self-consistent; the 0D heating ODE test and the layered-implosion surrogate provide more independent support. Self-citations to the authors' prior iFP discretization work are not load-bearing circularity here, because that code has been applied and exercised outside the present paper and no uniqueness theorem is invoked. The dropped gradient term in Eq. (24) is a genuine correctness limitation of the split, but it is not a circularity; it belongs to the accuracy/validity assessment rather than to the circularity score. Overall, the derivation is not equivalent to its inputs, but several load-bearing justifications reduce to the construction itself, giving a partial circularity score of 4.
Assumptions & free parameters
free parameters (3)
- chi =
2
- n_min =
not specified
- delta_T_alpha prefactor =
1 (instead of 1/2)
assumptions (8)
- domain assumption Rosenbluth-Fokker-Planck collision operator (Eqs. (2)-(4)) models ion-ion Coulomb collisions.
- domain assumption Ion-electron collisions use the Lenard-Bernstein operator, valid for v_i << v_th,e (Eq. (5)).
- domain assumption Electrons are a fluid with a single temperature, governed by Eq. (7).
- domain assumption DT fusion source is isotropic, delta-like in speed, with Maxwellian-averaged Bosch-Hale reactivity (Eqs. (8)-(9), (A.1)).
- domain assumption The thermal ion background in the sink derivation is a local Maxwellian (Eq. (14)).
- ad hoc to paper The velocity-gradient term in Eq. (21) is dropped when defining the sink (Eq. (24)).
- ad hoc to paper The temperature floor delta_T_alpha = m_alpha Delta v_alpha^2 regularizes the singularity and vanishes in the continuum limit (Eq. (64)).
- ad hoc to paper The sink activation function beta (Eq. (43)) with chi=2 and n_min avoids numerical issues at low alpha density.
Cite this review
Pith. "Pith review of A Multiscale Eulerian Vlasov-Rosenbluth-Fokker-Planck Algorithm for Thermonuclear Burning Plasmas." pith.science (2026). https://pith.science/paper/OBCTOBVQ
@misc{pith2026250606672,
author = {Pith},
title = {Pith review of: A Multiscale Eulerian Vlasov-Rosenbluth-Fokker-Planck Algorithm for Thermonuclear Burning Plasmas},
year = {2026},
howpublished = {\url{https://pith.science/paper/OBCTOBVQ}},
note = {Machine review of arXiv:2506.06672}
}
read the original abstract
Accurate treatment of energetic fusion byproducts in laboratory plasmas often requires a kinetic description, owing to their large birth kinetic energy and long mean-free-paths compared with the characteristic system scale lengths. For example, alpha particles produced by deuterium--tritium fusion reactions are born at high energies (\SI{3.5}{MeV}) and predominantly slow down through interactions with electrons traveling at comparable speeds. As an alpha particle slows, its distribution collapses near the background ion-thermal speed, forming a sharp structure in velocity space. Such sharp features pose numerical challenges in grid-based Eulerian methods: capturing the full alpha-particle energies demands a large velocity domain, while resolving the near-thermal region requires a sufficiently fine mesh. Inspired by the work of Peigney et al.[J. Comput. Phys. 278 (2014)], we present a two-grid approach that splits the alpha-particle distribution into energetic (suprathermal) and ash (thermal) components. A Gaussian-based sink term transfers particles from the energetic population to the ash population as they slow to the thermal regime, and a conservative projection scheme ensures that mass, momentum, and energy of the alpha and ash interactions are preserved. Unlike the formulation of Peigney, our method does not require a strict asymptotic separation of velocity scales, which can, in principle, be arbitrary. We demonstrate the robustness of this approach on challenging multiscale problems, including a surrogate for an igniting inertial confinement fusion capsule.
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Forward citations
Cited by 1 Pith paper
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A Multi-Species Reactive-Boltzmann Formulation for Self-Consistent Kinetic Simulation of Burning Fusion Plasmas
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Reference graph
Works this paper leans on
-
[1]
Abu-Shawareb, et al., Lawson criterion for ignition exceeded in an inertial fusion experiment, Physics. Rev. Lett. 129 (2022) 075001
work page 2022
-
[2]
B. E. Peigney, O. Larroche, V. Tikhonchuk, Fokker–planck kinetic modeling of suprathermal𝛼-particles in a fusion plasma, Journal of Computational Physics 278 (2014) 416–444
work page 2014
-
[3]
O. Larroche, Kinetic simulations of fuel ion transport in ICF target implosions, European Physical Journal D 27 (2) (2003) 131–146
work page 2003
-
[4]
O. Larroche, Ion fokker-planck simulation of d-3he gas target implosions, Physics of Plasmas 19 (12) (2012)
work page 2012
-
[5]
O. Larroche, An efficient explicit numerical scheme for diffusion-type equations with a highly inhomogeneous and highly anisotropic diffusion tensor, Journal of Computational Physics 223 (1) (2007) 436–450
work page 2007
-
[6]
O. Larroche, H. G. Rinderknecht, M. J. Rosenberg, Nuclear yield reduction in inertial confinement fusion exploding-pusher targets explained by fuel-pusher mixing through hybrid kinetic-fluid modeling, Physical Review E 98 (2018) 031201 (R)
work page 2018
-
[7]
B. E. Peigney, O. Larroche, V. Tikhonchuk, Ion kinetic effects on the ignition and burn of inertial confinement fusion targets: a multi-scale approach, Phys. Plasmas 21 (2014) 122709
work page 2014
-
[8]
A. Inglebert, B. Canaud, , O. Larroche, Species separation and modification of neutron diagnostics in inertial-confinement fusion, Erophysics Letters 107 (6) (2014) 65003
work page 2014
Show all 36 references
-
[9]
R. D. Hazeltine, J. D. Meiss, Plasma Confinement, Addison-Wesley Publishing Company, 1991
1991
-
[10]
Taitano, B
W. Taitano, B. Keenan, L. Chacón, S. Anderson, H. Hammer, A. Simakov, An Eulerian Vlasov-Fokker-Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules, Comp. Phys. Comm. 263 (2021) 107861
2021
-
[11]
H. S. Bosch, G. M. Hale, Improved formulas for fusion cross-sections and thermal reactivities, Nuclear Fusion 32 (1992) 611–631
1992
-
[12]
Haines, K
B. Haines, K. Meaney, J. Kuczek, B. Albright, W. Daughton, N. Hoffman, R. Lester, S. J.P, Simulated signatures of ignition, Physics. Plasmas 31 (2024) 042705
2024
-
[13]
Daniel, W
D. Daniel, W. Taitano, L. Chacón, A fully implicit, scalable, conservative nonlinear relativistic Fokker-Planck 0D-2P solver, Comp. Phys. Comm. 254 (2020) 107361
2020
-
[14]
Taitano, L
W. Taitano, L. Chacón, A. Simakov, An adaptive, conservative, 1D-2V multi-species Vlasov-Fokker-Planck multi-scale solver in planar geometry, J. Comp. Phys. 365 (2018) 173–205
2018
-
[15]
Taitano, L
W. Taitano, L. Chacón, A. Simakov, K. Molvig, A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species, Rosenbluth-Fokker-Planck equation, J. Comp. Phys. 297 (2015) 357– 380
2015
-
[16]
G. D. Byrne, A. C. Hindmarsh, A polyalgorithm for the numerical solution of ordinary differential equations, ACM Trans. Math. Softw. 1 (1) (1975) 71–96
1975
-
[17]
Taitano, L
W. Taitano, L. Chacón, A. Simakov, S. Anderson, A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck solver, Comp. Phys. Comm. 258 (2021) 107547. 24
2021
-
[18]
Taitano, L
W. Taitano, L. Chacón, A. Simakov, An adaptive, conservative 0d-2v multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes, J. Comp. Phys. 318 (2016) 391–420
2016
-
[19]
Taitano, L
W. Taitano, L. Chacón, A. Simakov, An equilibrium-preserving discretization for the nonlinear Rosenbluth-Fokker-Planck operator in arbitrary multi-dimensional geometry, J. Comp. Phys. 339 (2017) 453–460
2017
-
[20]
Anderson, W
S. Anderson, W. Taitano, L. Chacón, A. Simakov, An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system, J. Comp. Phys. 419 (2020) 109686
2020
-
[21]
Chacón, G
L. Chacón, G. Chen, D. Knoll, C. Newman, H. Park, W. Taitano, J. Willert, G. Womeldorff, Multiscale hihg-order/low- order (HOLO) algorithms and applications, J. Comp. Phys. 330 (2017) 21–45
2017
-
[22]
Chang, C
J. Chang, C. Cooper, A practical difference scheme for Fokker-Planck equations, J. Comp. Phys. 6 (1970) 1–16
1970
-
[23]
Hammer, H
H. Hammer, H. K. Park, L. Chacón, W. Taitano, A discontinuous finite-element formulation of the gray radiative heat transfer P1 equations using a moving mesh partial differential equation, Transactions of the American Nuclear Society 121 (2019) 795–798
2019
-
[24]
Keenan, A
B. Keenan, A. Simakov, L. Chacón, W. Taitano, Deciphering the kinetic structure of multi-ion plasma shocks, Phys. Rev. E 96 (2017) 053203
2017
-
[25]
B. D. Keenan, A. N. Simakov, W. T. Taitano, L. Chacón, Ion species stratification within strong shocks in two-ion plasmas, Physics of Plasmas 25 (2018) 032103
2018
-
[26]
Keenan, A
B. Keenan, A. Simakov, W. Taitano, L. Chacón, Ion species stratification within strong shocks in two-ion plasmas, Phys. Plasmas 25 (2018) 032103
2018
-
[27]
Keenan, W
B. Keenan, W. Taitano, K. Molvig, Physics of the implosion up until the time of ignition in a revolver (triple-shell) capsule, Phys. Plasmas 27 (2020) 042704
2020
-
[28]
Keenan, W
B. Keenan, W. Taitano, A. Simakov, L. Chacón, B. Albright, Shock-driven kinetic and diffusive mix in high-Z pusher ICF deseigns, Phys. Plasmas 27 (2020) 022704
2020
-
[29]
E. A. Anderson, L. Chacón, W. T. Taitano, A. N. Simakov, B. D. Keenan, Fully kinetic simulations of strong steady-state collisional planar plasma shocks, Physical Review E 104 (5) (2021) 055205
2021
-
[30]
W. T. Taitano, A. N. Simakov, L. Chacón, B. D. Keenan, Yield degradation in inertial-confinementfusion implosions due to shock-driven kinetic fuel-species stratification and viscous heating, Physics of Plasmas 25 (2018) 056310
2018
-
[31]
Mannion, W
O. Mannion, W. Taitano, B. Appelbe, A. Crilly, C. Forrest, V. Glebov, J. Knauer, P. McKenty, Z. Mohamed, C. Stoeckl, B. Keenan, J. Cittenden, P. Adrian, J. Frenje, N. Kabadi, M. G. Johnson, S. Regan, Evidence of non-Maxwellian ion velocity distributions in spherical shock-driv...
2023
-
[32]
Gatu-Johnson, P
M. Gatu-Johnson, P. J. Adrian, B. D. Appelbe, A. J. Crilly, C. J. Forrest, et al., Impact of mid-z gas fill on dynamics and performance of shock-driven implosions at the Omega laser, Physical Review E 109 (2024) 065201
2024
-
[33]
B. L. Reichelt, M. Gatu Johnson, J. H. Kunimune, W. Taitano, P. Adrian, S. Anderson, L. Chacon, T. Evans, C. Forrest, B. Haines, T. Johnson, N. Kabadi, R. Petrasso, I. Ruiz, C. Shuldberg, J. Frenje, C. Li, Experimental observation of kinetic mix enhancement in thin-shell OMEGA...
2025
-
[34]
D. S. Montgomery, W. S. Daughton, B. J. Albright, A. N. Simakov, D. C. Wilson, E. S. Dodd, R. C. Kirkpatrick, R. G. Watt, M. A. Gunderson, E. N. Loomis, E. C. Merritt, T. Cardenas, P. Amendt, J. L. Milovich, H. F. Robey, R. E. Tipton, M. D. Rosen, Design considerations for ind...
2018
-
[35]
Atzeni, V.-t.-V
S. Atzeni, V.-t.-V. J, The physics of inertial fusion: Beam plasma interaciton, hydrodynamics, hot dense matter, Oxford University Press, 2004
2004
-
[36]
Oseledets, Tensor-train decomposition, SIAM J
I. Oseledets, Tensor-train decomposition, SIAM J. Sci. Comput. 33 (5) (2011) 2295–2317. 25
2011
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