Ray-tracing laser-deposition model for plasma particle-in-cell simulation

Abdullah Hyder; Kirill Lezhnin; Samuel Totorica; Will Fox

REVIEW 1 major objections 5 minor 27 references

Ray-tracing laser-deposition model for plasma particle-in-cell simulation

T0 review · 1 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A ray-tracing laser-heating model reproduces FLASH absorption to 0.34 percent and runs in-line in a particle-in-cell code.

desk verdict A practical, honest methods paper: the equations are restatements of Dawson and Shearer, but the cell-based scheme with analytic turning-point treatment is a genuinely useful, verified implementation for PIC codes, with the main gap being an untested reflection-layer closure. read the letter →

arxiv 2412.08543 v1 pith:MHRXHWCV submitted 2024-12-11 physics.plasm-ph physics.comp-ph

Abdullah Hyder , Will Fox , Kirill Lezhnin , Samuel Totorica This is my paper · ORCID

classification physics.plasm-phphysics.comp-ph

keywords raytracinginversebremsstrahlungparticle-in-cellsimulationlaser-plasmainteractionobliqueincidencecriticalsurfacelaserenergydepositionhigh-energy-densityplasma

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Laser-heated high-energy-density plasmas are usually modeled with radiation-hydrodynamics codes that assume local equilibrium, but kinetic particle-in-cell (PIC) methods can resolve non-Maxwellian effects that matter in these systems. The paper develops a laser-energy-deposition module that runs in-line inside a PIC code without resolving the laser wavelength: it traces the laser intensity along one-dimensional rays, applies inverse-bremsstrahlung absorption with oblique-incidence and reflection corrections, and deposits the absorbed energy to electrons as randomized momentum kicks. The authors verify the module against analytic absorption profiles in uniform and linear density plasmas, against a 1 ns energy-conservation test, and against the 2-D ray-tracing code FLASH, where total absorbed power agrees to 0.34 percent at normal incidence and 1.16 percent at oblique incidence. If the paper is right, kinetic simulations gain a cheap, validated way to include realistic laser heating, making direct kinetic-versus-radiation-hydrodynamics comparisons possible for laser-ablation and laser-solid interaction experiments.

What carries the argument

The load-bearing object is the inverse-bremsstrahlung absorption coefficient $K = K_0 n_e^2/(n_{\mathrm{cr}}\sqrt{1-n_e/n_{\mathrm{cr}}})$, specialized to oblique incidence by replacing $n_{\mathrm{cr}}$ with $n_m = n_{\mathrm{cr}}\cos^2\theta_0$ and using the projected intensity $I_{z0}=I_{s0}\cos\theta_0$. Along each one-dimensional ray the intensity evolves as $I_z(z')=I_{z0}\exp(-\int_{z_0}^{z'} K_z\,\mathrm{d}z)$, and the power deposited in a cell is $P_{\mathrm{abs}}=-\Delta I_z/\Delta z$. The singularity at the reflection point is handled analytically: between the last grid point $z_r$ and the turning point $z_m$, the density is assumed linear, the integral $\int_{z_r}^{z_m} K_z\,\mathrm{d}z$ is evaluated in closed form, and the additional absorbed power is tallied into the cell at $z_r$. The particle-heating step converts $P_{\mathrm{abs}}$ into a per-electron energy $H = P_{\mathrm{abs}}\Delta t_{\mathrm{heating}}/n_e$ and delivers it via independent Gaussian momentum kicks, so the average electron energy gain is $H$.

What would settle it

Run the module on a density profile that is strongly nonlinear over a single grid cell at the turning point, such as an exponential ramp, and compare the computed absorption profile and total power against a fine-resolution analytic integration or a 2-D ray-tracing code; if the total absorbed power or the peak height at the reflection layer differs by more than a few percent, the linear-density assumption at the critical surface is falsified.

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Extended reading notes

Core claim

The central claim is that a reduced one-dimensional ray-trace can reproduce the laser absorption of a full multidimensional ray-tracing code in realistic laser-ablation profiles, provided the global oblique-incidence effect is included through the modified turning-point density $n_m = n_{\mathrm{cr}}\cos^2\theta_0$ and the reflection-layer absorption is handled by an analytic linear-density solution. The model evolves the laser intensity envelope through $\mathrm{d}I_z/\mathrm{d}z = -K_z I_z$, with the inverse-bremsstrahlung coefficient $K_z = K_0 (n_e^2/n_{\mathrm{cr}})/(\cos\theta_0 \sqrt{1-n_e/n_m})$, and deposits absorbed power to electrons through Gaussian momentum kicks whose average energy gain is $H = P_{\mathrm{abs}}/n_e\,\Delta t_{\mathrm{heating}}$. Benchmarks show exact agreement with the analytic solutions for constant and linear density profiles, total absorbed power matching FLASH to 0.34 percent at normal incidence and 1.16 percent at oblique incidence, and energy conservation over a 1 ns fully absorbing run. The paper presents this capability as enabling in-line kinetic modeling of laser-heated high-energy-density plasmas, with companion works extending the comparison to the subsequent dynamical evolution.

Load-bearing premise

The model's accuracy at the critical surface rests on the assumption that the electron density varies linearly between the last grid cell and the reflection point; if the density profile is strongly curved or under-resolved there, the analytic absorption tally for that cell could be wrong, and since most laser energy is deposited in the reflection layer, the total absorption profile would follow.

Editorial extensions

If this is right

Kinetic PIC simulations of laser-solid interactions and expanding ablated plasmas can incorporate inverse-bremsstrahlung laser absorption without resolving the laser wavelength or frequency.
On the tested LaserSlab profiles, total absorbed power from the module agrees with the 2-D ray-tracing radiation-hydrodynamics code FLASH to 0.34 percent at normal incidence and 1.16 percent at oblique incidence.
The analytic reflection-layer treatment resolves the divergence of the absorption coefficient at the critical surface and reproduces the exact absorption profile for a linear density ramp, so reflection-dominated deposition can be captured on coarse grids.
Transverse laser intensity profiles and time-dependent pulses are supported by launching one 1-D ray trace per transverse cell and prescribing $I_0(t)$, allowing realistic experimental laser spots to be modeled.
The ray-trace and particle-kick steps can be sub-cycled relative to the PIC timestep, and the global data gather is restricted to a finite subdomain, keeping the module inexpensive enough for large simulations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper only demonstrates the reflection-layer formula on linear and smooth FLASH density profiles; extending it to strongly curved or under-resolved critical surfaces would require a piecewise reconstruction of $n_e(z)$ in the reflection cell, and an exponential-profile benchmark would test that extension.
The Gaussian-kick heating scheme is the simplest option and is not designed to capture the Langdon super-Gaussian distortion of the electron distribution; kinetic studies of distribution shape would need the Langevin-style IB kicking scheme the paper flags as future work.
For plasmas whose scale length along the target normal grows to order a laser diameter, the no-in-plane-refraction assumption will break down; a natural extension is to add a local density-gradient refraction step so rays bend within the simulation plane.
A partially reflecting energy-conservation test, with nonzero outgoing intensity, would isolate how well the finite-difference deposition conserves energy in the reflection cell and would complement the fully absorbing 1 ns test shown here.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper does what it says: it gives a workable in-line ray-tracing inverse-bremsstrahlung deposition module for PIC, with a clean treatment of oblique incidence and the reflection singularity. The governing physics is not new—Dawson (1964) and Shearer (1971) are correctly cited as the sources—but the numerical scheme is: stopping the trapezoidal integration one cell before the turning point, assuming a linear density profile in that last cell, and depositing the analytically integrated absorption there (Eqs. 11–15). That is a real practical contribution, and the benchmarks back it up. I checked the central algebra myself: Eq. 14 follows from Eq. 7 under the linear profile, and Eqs. 17–19 conserve energy on average as claimed. The agreement with FLASH to sub-percent levels in total absorption is credible, and the paper is refreshingly explicit about what it does not include (1-D rays only, Gaussian kicks, no Langdon effect).

The soft spots are proportionate. The reflection-layer closure in Eqs. 13–15 is load-bearing because the absorption coefficient diverges at the turning point, yet it is tested only on a linear profile where the assumption is exact by construction and on one smooth FLASH snapshot. That leaves a genuine verification gap for curved, noisy, or under-resolved density profiles at the critical surface. A grid-convergence scan and a curved-profile test would close it. The FLASH comparison also uses a deliberately matched Coulomb logarithm and a static snapshot, so the dynamical behavior in a running PIC simulation is deferred to companion papers. And the code and input decks are not released, which limits independent reproduction. None of these are fatal; they are exactly the kind of thing that should be checked in review or in the companion papers.

This is a solid, honest methods paper with verified algebra and useful benchmarks. The right audience is anyone coupling laser heating into kinetic PIC simulations, and the paper deserves a serious referee rather than a desk rejection. I would send it out, asking the referee to push for a curved-profile test or at least a grid-convergence check, and to clarify the status of code release. If those are addressed, it is a straightforward accept.

Referee Report

1 major / 5 minor

Summary. The paper describes a reduced ray-tracing model for inverse-bremsstrahlung laser energy deposition in a kinetic particle-in-cell code. The model follows the laser intensity along rays in one dimension with Shearer's oblique-incidence corrections, uses a linear-density analytic closure at the reflection point, and converts the absorbed power into randomized momentum kicks to electrons. It is implemented in PSC. Benchmarking consists of an exact comparison for uniform and linear density profiles, an energy-conservation run, and a comparison with two-dimensional FLASH ray-tracing calculations for normal and oblique incidence.

Significance. If accepted, this is a useful engineering contribution: it provides an inexpensive, sub-cycled laser-heating module that does not require resolving the laser wavelength and therefore enables kinetic PIC studies of laser-heated high-energy-density plasmas. I checked the central algebra and found it sound: Eq. (14) follows exactly from Eqs. (7) and (13), and Eq. (19) shows that the random kick delivers the intended average energy H. The paper is candid about its limitations, including the user-specified Coulomb logarithm and the simple isotropic Gaussian kick, and the companion papers give further dynamical benchmarking. The main missing piece is a demonstration that the reflection-layer closure, which dominates the deposited energy, is robust for density profiles that are not linear and for varying grid resolution.

major comments (1)

[Sec. III B, Eqs. (12)-(15); Figs. 3 and 5] The reflection-layer closure is the least-supported part of the verification claim. Equations (13) and (15) assume that the density is exactly linear between the last grid point zr and the reflection point zm and that all absorption in [zr, zm] is deposited into the single cell at zr. This assumption is exact for the linear-density benchmark of Fig. 3 by construction, and the FLASH comparison in Fig. 5 uses one smooth snapshot. Because Kz diverges as ne approaches nm, the majority of the absorbed energy is controlled by this last-cell closure, so in realistic kinetic runs with curved, noisy, or under-resolved density near the critical surface the error is not bounded by the present benchmarks. I request either an additional benchmark with a curved density profile (for example, exponential or sinusoidal) compared with a high-resolution or analytically integrated reference, including a grid-convergence scan in z, or an explicit error estimate for the linear assumption in the reflection layer.

minor comments (5)

[Sec. III C] The text says the particles are kicked 'via Gaussian kicks, drawn from a uniform distribution for all particles'; since Eq. (17) samples from a standard normal distribution, the phrase 'uniform distribution' should be corrected to 'normal distribution'.
[Sec. III B] There is a missing space in 'the outgoing laser atzr after reflection', and the definition of zr as the grid point immediately before the reflection point should be restated more precisely because zm is found by interpolation and may lie between grid points.
[Sec. IV, Fig. 5 caption] The notation 'Pabs/Pabs z = 0.34%' is not defined; please state explicitly that this is the relative error of the spatially integrated absorbed power between PSC and FLASH.
[Sec. IV, Fig. 4] The energy-conservation test reports 'close agreement' visually but no quantitative final relative error or tolerance; please add the measured relative energy error over the 1 ns run.
[Sec. III B, Eq. (14)] The analytic result in Eq. (14) is correct, but the intermediate substitution from the linear density profile is not shown; a short derivation or an appendix reference would make the closure easier for readers to check.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is a standard inverse-bremsstrahlung ray-tracing model verified against analytic solutions and an independent 2-D ray-tracing code.

full rationale

The paper implements a standard geometric-optics inverse-bremsstrahlung model using equations imported from Dawson and Shearer, and the central verification is against external anchors: closed-form analytic solutions of the same transport equation and the FLASH radiation-hydrodynamics ray-tracing code. Comparing a numerical scheme against analytic solutions of the same governing equations is standard code verification, not a circular derivation, because the code's trapezoidal quadrature and turning-point closure are nontrivial implementations of the equations. In the FLASH cross-benchmark, the Coulomb logarithm was deliberately matched so that both codes use the same absorption coefficient; this is a controlled choice of input parameters, not a fitted parameter renamed as a prediction. The compared quantities—spatial deposition profiles, critical-surface location, maximum penetration depth, and the oblique-incidence correction—are not determined solely by that matched coefficient, so the agreement tests the reduced 1-D model's treatment of reflection and oblique incidence. The energy-conservation test in Fig. 4 checks bookkeeping against the input laser energy and is a consistency test rather than a physics prediction. The cited companion papers [21,22] provide additional dynamical benchmarking by overlapping authors, but they are not load-bearing for the claims made here; the present results are self-contained. No step in the paper reduces by construction to its own inputs, and no load-bearing argument depends on an unverified self-citation.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The model contains no fitted coefficients: Eqs. 2-7 are standard IB theory (Dawson 1964; Johnston-Dawson 1973) plus the Shearer oblique-incidence transform (1971), with laser and plasma quantities supplied by the user. The only user-chosen physics knob is the Coulomb logarithm, deliberately left user-specified to match other codes and experiments. The numerical scheme adds one ad hoc element, the local linear density assumption at the reflection point (Eq. 13). No physical entities are invented.

free parameters (2)

Coulomb logarithm ln(Lambda_IB) = user-specified function; matched to FLASH default in the cross-code test
Section II states 'we keep ln Lambda_IB to be a user-specified function.' The absorption coefficient scales linearly with this choice, so the magnitude of deposition is an input to the model rather than a derived quantity; the FLASH agreement partly reflects matching it exactly.
heating call interval Delta_t_heating
Section III C: user-chosen time between heating module calls; constrained only by H/Te << 1, not fitted to any data. It controls the kick amplitude per call but not the time-averaged deposition.

assumptions (7)

domain assumption Geometric optics holds: laser wavelength is much shorter than plasma density scale lengths, so intensity can be transported along rays.
Section II, opening paragraph: 'This approach is valid when the laser wavelength is much shorter than other scales in the plasma.' This is the standard envelope validity condition.
domain assumption Inverse bremsstrahlung is the only absorption mechanism considered.
Section II uses only the IB coefficient of Eq. 2; resonant, parametric, and other near-critical absorption processes are not included, so the model is restricted to collisional absorption regimes.
domain assumption The plasma appears one-dimensional to the laser: no in-domain refraction, propagation along a fixed axis.
Section II: 'does not include further refraction of the laser in the simulation domain'; the validity limit stated is plasma expansion length much smaller than laser diameter.
ad hoc to paper Between the last grid point and the reflection point the density profile is linear, and zm is obtained by linear interpolation.
Section III B, Eq. 13: introduced specifically to make the singular integral at the reflection point tractable; its accuracy is only tested in the paper against linear or smooth profiles.
domain assumption Particle kicks are small and uncorrelated with particle momenta, so the p dot Delta-p term averages to zero, and Gaussian kicks are an adequate heating model.
Section III C, Eqs. 18-19; the paper states the Gaussian scheme is the simplest possible and that Langdon super-Gaussian effects are deferred to future work.
standard math The high-frequency (Johnston-Dawson) Coulomb logarithm form applies, with a user-supplied function.
Section II, following Ref. 16; the choice of form affects absolute absorption but the user can dial it, which the paper treats as a feature.
domain assumption Electrons alone are heated directly (me much less than mi), ions later via collisions.
Section III C: 'given that me << mi, the heating is applied only to the electrons.'

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Cite this review

Pith. "Pith review of Ray-tracing laser-deposition model for plasma particle-in-cell simulation." pith.science (2026). https://pith.science/paper/MHRXHWCV

@misc{pith2026241208543,
  author       = {Pith},
  title        = {Pith review of: Ray-tracing laser-deposition model for plasma particle-in-cell simulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MHRXHWCV}},
  note         = {Machine review of arXiv:2412.08543}
}

read the original abstract

We develop a ray-tracing model for laser-plasma interaction suitable for coupling in-line into kinetic particle-in-cell plasma simulation. The model is based on inverse Bremsstrahlung absorption and includes oblique incidence effects and reflection at the critical surface. The energy deposition is given to electrons by randomized kicks to momentum. The model is verified against analytic solutions and a 2-D laser ray-tracing code.

Figures

Figures reproduced from arXiv: 2412.08543 by the authors.

**Figure 3.** FIG. 3. (a) Laser power absorption in a linear electron density [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 2.** FIG. 2. Analytical and numerical laser power deposition [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Temporal evolution of the internal energy areal [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. Testing laser ray tracing and laser energy deposi [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

27 extracted references · 26 canonical work pages

[1]

H. G. Rinderknecht, P. A. Amendt, S. C. Wilks, and G. Collins, Kinetic physics in ICF: present understand- ing and future directions, Plasma Phys. Contr. Fus. 60, 064001 (2018)

work page 2018
[2]

C. N. Danson, C. Haefner, J. Bromage, T. Butcher, J.- C. F. Chanteloup, E. A. Chowdhury, A. Galvanauskas, L. A. Gizzi, J. Hein, D. I. Hillier, and et al., Petawatt and exawatt class lasers worldwide, High Power Laser Sci. Eng. 7, e54 (2019)

work page 2019
[3]

W. Fox, J. Matteucci, C. Moissard, D. B. Schaeffer, A. Bhattacharjee, K. Germaschewski, and S. X. Hu, Ki- netic simulation of magnetic field generation and colli- sionless shock formation in expanding laboratory plas- mas, Phys. Plasmas 25, 102106 (2018)

work page 2018
[4]

D. B. Schaeffer, W. Fox, J. Matteucci, K. V. Lezhnin, A. Bhattacharjee, and K. Germaschewski, Kinetic sim- ulations of piston-driven collisionless shock formation in magnetized laboratory plasmas, Physics of Plasmas 27, 10.1063/1.5123229 (2020). 8

work page doi:10.1063/1.5123229 2020
[5]

K. V. Lezhnin, W. Fox, D. B. Schaeffer, A. Spitkovsky, J. Matteucci, A. Bhattacharjee, and K. Germaschewski, Kinetic simulations of electron pre-energization by mag- netized collisionless shocks in expanding laboratory plas- mas, Astrophys. J. Lett. 908, L52 (2021)

work page 2021
[6]

W. Fox, G. Fiksel, A. Bhattacharjee, P.-Y. Chang, K. Germaschewski, S. X. Hu, and P. M. Nilson, Filamen- tation instability of counterstreaming laser-driven plas- mas, Phys. Rev. Lett. 111, 225002 (2013)

work page 2013
[7]

W. Fox, A. Bhattacharjee, and K. Germaschewski, Fast magnetic reconnection in laser-produced plasma bubbles, Phys. Rev. Lett. 106, 215003 (2011)

work page 2011
[8]

Matteucci, W

J. Matteucci, W. Fox, A. Bhattacharjee, D. B. Schaeffer, C. Moissard, K. Germaschewski, G. Fiksel, and S. X. Hu, Biermann-battery-mediated magnetic reconnection in 3d colliding plasmas, Phys. Rev. Lett. 121, 095001 (2018)

work page 2018

Show all 27 references

[9]

J. M. Dawson, On the Production of Plasma by Giant Pulse Lasers, Phys. Fluids 7, 981 (1964)

1964
[10]

T. B. Kaiser, Laser ray tracing and power deposition on an unstructured three-dimensional grid, Phys. Rev. E61, 895–905 (2000)

2000
[11]

Tzeferacos, M

P. Tzeferacos, M. Fatenejad, N. Flocke, C. Graziani, G. Gregori, D. Lamb, D. Lee, J. Meinecke, A. Scopatz, and K. Weide, FLASH MHD simulations of experiments that study shock-generated magnetic fields, High Energy Dens. Phys. 17, 24 (2015)

2015
[12]

Thoma, D

C. Thoma, D. R. Welch, R. E. Clark, D. V. Rose, and I. E. Golovkin, Hybrid-pic modeling of laser-plasma in- teractions and hot electron generation in gold hohlraum walls, Phys. Plasmas 24, 062707 (2017)

2017
[13]

M. M. Basko and I. P. Tsygvintsev, A hybrid model of laser energy deposition for multi-dimensional simulations of plasmas and metals, Comp. Phys. Comm. 214, 59 (2017)

2017
[14]

T. D. Arber, K. Bennett, C. S. Brady, A. Lawrence- Douglas, M. G. Ramsay, N. J. Sircombe, P. Gillies, R. G. Evans, H. Schmitz, A. R. Bell, and C. P. Ridgers, Con- temporary particle-in-cell approach to laser-plasma mod- elling, Plasma Phys. Control. Fus. 57, 113001 (2015)

2015
[15]

Zhang, F

Y. Zhang, F. Wang, J. Liu, and J. Sun, Simulation of the inverse bremsstrahlung absorption by plasma plume in laser penetration welding, Chem. Phys. Lett.793, 139434 (2022)

2022
[16]

T. W. Johnston and J. M. Dawson, Correct val- ues for high-frequency power absorption by inverse bremsstrahlung in plasmas, Phys. Fluids 16, 722–722 (1973)

1973
[17]

Turnbull, J

D. Turnbull, J. Katz, M. Sherlock, L. Divol, N. R. Shaf- fer, D. J. Strozzi, A. Cola ¨ ıtis, D. H. Edgell, R. K. Fol- lett, K. R. McMillen, P. Michel, A. L. Milder, and D. H. Froula, Inverse bremsstrahlung absorption, Phys. Rev. Lett. 130, 145103 (2023)

2023
[18]

Takizuka and H

T. Takizuka and H. Abe, A binary collision model for plasma simulation with a particle code, J. Comp. Phys. 25, 205 (1977)

1977
[19]

Devriendt and O

R. Devriendt and O. Poujade, Classical molecu- lar dynamic simulations and modeling of inverse bremsstrahlung heating in low Z weakly coupled plas- mas, Phys. Plasmas 29, 073301 (2022)

2022
[20]

Germaschewski, W

K. Germaschewski, W. Fox, S. Abbott, N. Ahmadi, K. Maynard, L. Wang, H. Ruhl, and A. Bhattacharjee, The Plasma Simulation Code: a modern particle-in-cell code with patch-based load-balancing, J. Comp. Phys. 318, 305 (2016)

2016
[21]

K. V. Lezhnin, S. R. Totorica, A. S. Hyder, J. Griff- McMahon, M. B. P. Adams, P. Tzeferacos, A. Diallo, and W. Fox, Particle-in-cell simulations of expanding high energy density plasmas with laser ray tracing (2024), arXiv:2409.17327 [physics.plasm-ph]

2024 arXiv
[22]

S. R. Totorica, K. Lezhnin, D. J. Hemminga, J. Gonza- lez, J. Sheil, A. Diallo, A. Hyder, and W. Fox, Acceler- ation mechanisms of energetic ion debris in laser-driven tin plasma EUV sources, Appl. Phys. Lett. 124, 174101 (2024)

2024
[23]

Huba, NRL Plasma Formulary(Naval Research Lab., Washington, DC, 2004)

J. Huba, NRL Plasma Formulary(Naval Research Lab., Washington, DC, 2004)

2004
[24]

J. W. Shearer, Effect of oblique incidence on optical ab- sorption of laser light by a plasma, Phys. Fluids 14, 183 (1971)

1971
[25]

Detering, V

F. Detering, V. Y. Bychenkov, W. Rozmus, R. Sydora, and C. Capjack, Langevin representation of laser heating in PIC simulations, Comp. Phys. Comm. 143, 48 (2002)

2002
[26]

A. B. Langdon, Nonlinear inverse bremsstrahlung and heated-electron distributions, Phys. Rev. Lett. 44, 575 (1980)

1980
[27]

FLASH User’s Guide (Flash Center for Computational Science, University of Rochester, 2023)

2023

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

H. G. Rinderknecht, P. A. Amendt, S. C. Wilks, and G. Collins, Kinetic physics in ICF: present understand- ing and future directions, Plasma Phys. Contr. Fus. 60, 064001 (2018)

work page 2018

[2] [2]

C. N. Danson, C. Haefner, J. Bromage, T. Butcher, J.- C. F. Chanteloup, E. A. Chowdhury, A. Galvanauskas, L. A. Gizzi, J. Hein, D. I. Hillier, and et al., Petawatt and exawatt class lasers worldwide, High Power Laser Sci. Eng. 7, e54 (2019)

work page 2019

[3] [3]

W. Fox, J. Matteucci, C. Moissard, D. B. Schaeffer, A. Bhattacharjee, K. Germaschewski, and S. X. Hu, Ki- netic simulation of magnetic field generation and colli- sionless shock formation in expanding laboratory plas- mas, Phys. Plasmas 25, 102106 (2018)

work page 2018

[4] [4]

D. B. Schaeffer, W. Fox, J. Matteucci, K. V. Lezhnin, A. Bhattacharjee, and K. Germaschewski, Kinetic sim- ulations of piston-driven collisionless shock formation in magnetized laboratory plasmas, Physics of Plasmas 27, 10.1063/1.5123229 (2020). 8

work page doi:10.1063/1.5123229 2020

[5] [5]

K. V. Lezhnin, W. Fox, D. B. Schaeffer, A. Spitkovsky, J. Matteucci, A. Bhattacharjee, and K. Germaschewski, Kinetic simulations of electron pre-energization by mag- netized collisionless shocks in expanding laboratory plas- mas, Astrophys. J. Lett. 908, L52 (2021)

work page 2021

[6] [6]

W. Fox, G. Fiksel, A. Bhattacharjee, P.-Y. Chang, K. Germaschewski, S. X. Hu, and P. M. Nilson, Filamen- tation instability of counterstreaming laser-driven plas- mas, Phys. Rev. Lett. 111, 225002 (2013)

work page 2013

[7] [7]

W. Fox, A. Bhattacharjee, and K. Germaschewski, Fast magnetic reconnection in laser-produced plasma bubbles, Phys. Rev. Lett. 106, 215003 (2011)

work page 2011

[8] [8]

Matteucci, W

J. Matteucci, W. Fox, A. Bhattacharjee, D. B. Schaeffer, C. Moissard, K. Germaschewski, G. Fiksel, and S. X. Hu, Biermann-battery-mediated magnetic reconnection in 3d colliding plasmas, Phys. Rev. Lett. 121, 095001 (2018)

work page 2018