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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

On the effects of reactant stratification and wall curvature in non-premixed rotating detonation combustors

The optimization of non-premixed rotating detonation combustors (RDCs) requires improved understanding of the coupled effects of reactant stratification, fluid property gradients, and complex shock-wave interactions on the detonation wave structure within annular geometries. In the current work, simultaneous orthogonal views of chemiluminescence and hydroxyl planar laser-induced fluorescence (PLIF) are utilized to establish the existence of a dual-wave system characterized by leading and trailing detonation waves that are closely coupled by the local flow physics. These features are persistent over a wide range of mass flow rates and are consistent with prior observations of non-premixed rotating detonations in annular geometries. The detailed instantaneous time sequences are compared with a 3D reactive unsteady Reynolds averaged Navier-Stokes (URANS) simulation to more clearly elucidate the in-situ combustion dynamics and the sensitivity to reactant inlet conditions. It is found that the dual-wave system results from unburned reactants that survive the leading detonation wave in the injector near field and are consumed within a trailing azimuthal reflected-shock combustion (ARSC) zone. By contrast, the injector far field is characterized by rapid mixing due to a sudden drop to subsonic conditions, and the bifurcated detonation wave structure collapses into a stronger, single-wave detonation front with higher overall pressure ratio as compared with the dual-wave system. While each RDC will have different inflow, mixing, and combustion characteristics, the underlying interactions between the stratified reactants and azimuthal wave dynamics identified through the combination of advanced MHz-rate diagnostics and 3D numerical simulations have important implications for the study of detonation wave stability, mode transition, and combustion efficiency in non-premixed annular RDCs.

3D URANS↗
DOE OSTI2025

Implementation of a Mesh refinement algorithm into the quasi-static PIC code QuickPIC

Plasma-based acceleration (PBA) has emerged as a promising candidate for the accelerator technology used to build a future linear collider and/or an advanced light source. In PBA, a trailing or witness particle beam is accelerated in the plasma wave wakefield (WF) created by a laser or particle beam driver. The WF is often nonlinear and involves the crossing of plasma particle trajectories in real space and thus particle-in-cell methods are used. The distance over which the drive beam evolves is several orders of magnitude larger than the wake wavelength. This large disparity in length scales is amenable to the quasi-static approach. Three-dimensional (3D), quasi-static (QS), particle-in-cell (PIC) codes, e.g., QuickPIC, have been shown to provide high fidelity simulation capability with 2-4 orders of magnitude speedup over 3D fully explicit PIC codes. In PBA, the witness beam needs to be matched to the focusing forces of the WF to reduce the emittance growth. In some linear collider designs, the matched spot size of the witness beam can be 2 to 3 orders of magnitude smaller than the spot size (and wavelength) of the wakefield. Such an additional disparity in length scales is ideal for mesh refinement where the WF within the witness beam is described on a finer mesh than the rest of the WF. A mesh refinement scheme is described that has been implemented into the 3D QS PIC code, QuickPIC. Very fine (high) resolution is used in a small spatial region that includes the witness beam and progressively coarser resolutions in the rest of the simulation domain. A fast multigrid Poisson solver has been implemented for the field solve on the refined meshes and a Fast Fourier Transform (FFT) based Poisson solver is used for the coarse mesh. The code has been parallelized with both MPI and OpenMP, and the parallel scalability has also been improved by using pipelining. A preliminary adaptive mesh refinement technique is described to optimize the computational time for simulations with an evolving witness beam size. Several test problems are used to verify that the mesh refinement algorithm provides accurate results. Additionally, the results are benchmarked against highly resolved simulations exhibiting near-azimuthal symmetry, performed using QPAD—a novel hybrid QS PIC code that uses a PIC description in the coordinates (r, ct – z) and a gridless description in the azimuthal angle, Φ.

Linear collider↗
DOE OSTI2023

ECCE sensitivity studies for single hadron transverse single spin asymmetry measurements

Here, we performed feasibility studies for various single transverse spin measurements that are related to the Sivers effect, transversity and the tensor charge, and the Collins fragmentation function. The processes studied include semi-inclusive deep inelastic scattering (SIDIS) where single hadrons (pions and kaons) were detected in addition to the scattered DIS lepton. The data were obtained in pythia6 and geant4 simulated e+p collisions at 18 GeV on 275 GeV, 18 on 100, 10 on 100, and 5 on 41 that use the ECCE detector configuration. Typical DIS kinematics were selected, most notably Q 2 >1 GeV 2 , and cover the x range from 10 -4 to 1. The single spin asymmetries were extracted as a function of x and Q 2 , as well as the semi-inclusive variables z, which corresponds to the momentum fraction the detected hadron carries relative to the struck parton, and P T , which corresponds to the transverse momentum of the detected hadron relative to the virtual photon. They are obtained in azimuthal moments in combinations of the azimuthal angles of the hadron transverse momentum and transverse spin of the nucleon relative to the lepton scattering plane. In order to extract asymmetries, the initially unpolarized MonteCarlo was re-weighted in the true kinematic variables, hadron types and parton flavors based on global fits of fixed target SIDIS experiments and e + e – annihilation data. The expected statistical precision of such measurements is extrapolated to 10 fb –1 and potential systematic uncertainties are approximated given the deviations between true and reconstructed yields. Similar neutron information is obtained by comparing the ECCE e+p pseudo-data with the same from the EIC Yellow Report and scaling the corresponding Yellow Report e+ 3 He pseudo-data uncertainties accordingly. The impact on the knowledge of the Sivers functions, transversity and tensor charges, and the Collins function has then been evaluated in the same phenomenological extractions as in the Yellow Report. Finally, the impact is found to be comparable to that obtained with the parametrized Yellow Report detector and shows that the ECCE detector configuration can fulfill the physics goals on these quantities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

A tutorial on the micro-trench technique for incident ion angle, material erosion, and impurity deposition measurements at plasma-facing surfaces

The micro-trench method is a new technique to measure polar and azimuthal incident ion angles, material erosion, and impurity deposition at plasma-facing surfaces, and has been applied in the DIII-D divertor. This article gives a tutorial of the micro-trench technique consisting of six steps: (1) micro-trench fabrication, (2) pre-exposure measurement of the fabricated micro-trench geometry, (3) tracer material deposition, (4) plasma exposure, (5) post-exposure observation of the tracer material, and (6) post-exposure measurement of the micro-trench geometry. Two criteria need to be satisfied to apply the micro-trench method successfully: (i) uniform impurity deposition on the micro-trench floor, and (ii) erosion dominated by the physical sputtering induced by the impinging ions. Furthermore, when those two criteria are satisfied, post-exposure analysis of the impurity deposition patterns on the micro-trench floor may be used to determine the polar and azimuthal incident ion directions (mean values of the ion angle directions), erosion rate, and impurity deposition rate during plasma exposure without computational interpretation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Dijet Acoplanarity in CUJET3 as a Probe of the Nonperturbative Color Structure of QCD Perfect Fluids

Using the CUJET3=DGLV+VISHNU jet-medium interaction framework, we show that dijet azimuthal acoplanarity in high energy A + A collisions is sensitive to possible non-perturbative enhancement of the jet transport coefficient, $\hat{q}$(T,E), in the QCD crossover temperature T ~ 150–300 MeV range. With jet-medium couplings constrained by global RHIC& LHC χ 2 fits to nuclear modification data on R AA (p T > 20) GeV, we compare predictions of the medium induced dijet transverse momentum squared, $Q_s^2~\langle \hat{q}L\rangle~ΔΦ^2E^2$, in two models of the temperature, T, and jet energy E dependence of the jet medium transport coefficient, $\hat{q}$(T,E)). In one model, wQGP, the chromo degrees of freedom (dof) are approximated by a perturbative dielectric gas of quark and gluons dof. In the second model, sQGMP, we consider a nonperturbative partially confined semi-Quark-Gluon-Monopole-Plasma with emergent color magnetic dof constrained by lattice QCD data. Unlike the slow variation of the scaled jet transport coefficient, $\hat{q}_{wQGP}/T^3$, the sQGMP model $\hat{q}_{sQGMP}/T^3$ features a sharp maximum in the QCD confinement crossover T range. We show that the dijet path averaged medium induced azimuthal acoplanarity, Δφ 2 , in sQGMP is robustly ~ 2 times larger than in perturbative wQGP. even though the radiative energy loss in both models is very similar as needed to fit the same R AA data. Future A+A dijet acoplanarity measurements constrained together with single jet R AA and ν n measurements therefore appears to be a promising strategy to search for possible signatures of critical opalescence like phenomena in the QCD confinement temperature range.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

General balance functions of identified charged hadron pairs of (π, Κ, ρ) in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV

First measurements of balance functions (BFs) of all combinations of identified charged hadron (π, Κ, ρ) pairs in Pb–Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV recorded by the ALICE detector are presented. The BF measurements are carried out as two-dimensional differential correlators versus the relative rapidity (Δy) and azimuthal angle (Δφ) of hadron pairs, and studied as a function of collision centrality. The Δφ dependence of BFs is expected to be sensitive to the light quark diffusivity in the quark–gluon plasma. While the BF azimuthal widths of all pairs substantially decrease from peripheral to central collisions, the longitudinal widths exhibit mixed behaviors: BFs of ππ and cross-species pairs narrow significantly in more central collisions, whereas those of KK and pp are found to be independent of collision centrality. This dichotomy is qualitatively consistent with the presence of strong radial flow effects and the existence of two stages of quark production in relativistic heavy-ion collisions. Finally, the first measurements of the collision centrality evolution of BF integrals are presented, with the observation that charge balancing fractions are nearly independent of collision centrality in Pb–Pb collisions. Overall, the results presented provide new and challenging constraints for theoretical models of hadron production and transport in relativistic heavy-ion collisions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Spatial imaging of polarized deuterons at the Electron-Ion Collider

We study diffractive vector meson production at small-x in the collision of electrons and polarized deuterons e + d $\uparrow$ . We consider the polarization dependence of the nuclear wave function of the deuteron, which results in an azimuthal angular dependence of the produced vector meson when the deuteron is transversely polarized. The Fourier coefficients extracted from the azimuthal angular dependence of the vector meson differential cross-section exhibit notable differences between longitudinally and transversely polarized deuterons. The angular dependence of the extracted effective deuteron radius provides direct insight into the structure of the polarized deuteron wave function. Furthermore, we observe slightly increased gluon saturation effects when the deuteron is longitudinally polarized compared to the transversely polarized case. The small-x observables studied in this work will be accessible at the future Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Optimizing the Orientation of Solar Photovoltaic Systems Considering the Effects of Irradiation and Cell Temperature Models with Dust Accumulation

To cope with the growing installation capacities of solar photovoltaic (PV) systems in desert areas, it is necessary to revisit the energy production models and the optimal angles of PV panels given the significant impacts of ambient temperature, wind speed, dust accumulation, and cleaning frequency. In this study, these four factors are examined for four PV technologies (polycrystalline, microcrystalline, monocrystalline, and thin-film) at three cities in Jordan, Egypt, and Tunisia using precise ground-level meteo-solar measurements. Different models are compared to estimate the diffuse irradiance, as well as account for the effects of operating temperature, wind speed, and dust accumulation on energy production and optimal tilt and azimuth angles of the panels. The results reveal 1.5 % higher energy production estimates using the isotropic model, compared to the anisotropic model in the summer months. Considering the cooling effect of wind speed decreases the operating cell temperature drops by up to 7.05 % for thin film panels. The annually produced energy decreases by 24 % when the panels are cleaned bi-monthly. When the dust accumulation rate doubles, the energy production decreases by ~10 % for all studied cases. Also, the variations in optimal tilt and azimuth angles with dust accumulation rate are within ~3.0 degrees .

14 SOLAR ENERGY↗
DOE OSTI2022

Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

The Naval Research Laboratory ‘Mag Noh problem’, described in this paper, is a self-similar magnetized implosion flow, which contains a fast magnetohydrodynamic (MHD) outward propagating shock of constant velocity. We generalize the classic Noh ( OSTI Tech. Rep. 577058, 1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$ . Our self-similar solutions are indeed realized when we solve the initial value MHD problem with the finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field and a shock wave.

Mechanics↗
DOE OSTI2021

Evidence of Alfvenic Poynting Flux as the Primary Driver of Auroral Motion During a Geomagnetic Substorm

Geomagnetic substorms are major energy transfer events where energy stored in the Earth's magnetotail is released into the ionosphere. Substorm phenomena, including auroral activities, earthward Poynting flux, magnetic field dipolarization, etc, have been extensively studied. However, the complex interplay among them is not fully understood. In a fortuitous event on June 7, 2013, the twin Van Allen Probes (separated by 0.4 h in local time) observed bursts of earthward Alfvenic Poynting flux in the vicinity of the plasma sheet boundary layer (PSBL). The Poynting flux bursts correlate with enhancements of auroral brightness around the footpoints of both spacecraft. This indicates a temporal and spatial correlation between the auroral brightening and Poynting flux bursts, and that the auroral motion is directly linked to the perpendicular expansion of the Alfven wave. These observations suggest that the Alfvenic Poynting flux is a primary driver for the auroral electron acceleration. Furthermore, around the time of auroral brightening, a dipolarization was seen to propagate more than 4 h in local time during a 20 min period. The azimuthal phase speed of this dipolarization (2 deg/min) is too small to explain the azimuthal motion of the aurora (13.6 deg/min), but the dipolarization could be related to the generation of the Alfvenic Poynting flux through phase mixing at strong density gradients like those in the PSBL.

58 GEOSCIENCES↗
DOE OSTI2024

Modeling the Contribution of Precipitation Loss to a Radiation Belt Electron Dropout Observed by Van Allen Probes

A drift-diffusion model is used to simulate the low-altitude electron distribution, accounting for azimuthal drift, pitch angle diffusion, and atmospheric backscattering effects during a rapid electron dropout event on 21st August 2013, at L = 4.5. Additional external loss effects are introduced during times when the low-altitude electron distribution cannot be reproduced by diffusion alone. Here, the model utilizes low-altitude electron count rate data from five POES/MetOp satellites to quantify pitch angle diffusion rates. Low-altitude data provides critical constraint on the model because it includes the drift loss cone region where the electron distribution in longitude is highly dependent on the balance between azimuthal drift and pitch angle diffusion. Furthermore, a newly derived angular response function for the detectors onboard POES/MetOp is employed to accurately incorporate the bounce loss cone measurements, which have been previously contaminated by electrons from outside the nominal field-of-view. While constrained by low-altitude data, the model also shows reasonable agreement with high-altitude data. Pitch angle diffusion rates during the event are quantified and are faster at lower energies. Precipitation is determined to account for all of the total loss observed for 450 keV electrons, 88% for 600 keV and 38% for 900 keV. Predictions made in the MeV range are deemed unreliable as the integral energy channels E3 and P6 fail to provide the necessary constraint at relativistic energies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Observational Evidence for Wind‐Driven Low‐Pass Filtering of Infrasound at Short Range

Infrasound from controlled explosions provides a unique opportunity to isolate atmospheric effects on propagation. We report observations from two campaigns in May and October 2024, each featuring 10‐ton TNT‐equivalent controlled surface chemical explosions recorded by a dense network of 31 single‐sensor stations within 23 km. Despite identical sources, the observed wavefields were very different. October signals followed a near‐unimodal period–distance trend, whereas May signals exhibited a pronounced azimuthal bifurcation in both period and celerity. Downwind paths largely preserved the short‐period baseline observed in October, while upwind paths showed systematically longer periods caused by wind‐driven low‐pass filtering. This study provides the first direct observational evidence that tropospheric winds can impose azimuth‐dependent low‐pass filtering at local ranges, without the influence of measured temperature inversions. Thus, the structure of the atmosphere can modify the spectral characteristics of low‐frequency acoustic waves even at a distance of only a few kilometers.

Geosciences↗
DOE OSTI2020

Generation of large-volume high-pressure plasma by spatiotemporal control of space charge

Any attempt to scale pressure and volume of nonthermal plasma usually leads to instabilities due to the formation of localized space charge. The control of the plasma is limited by the discharge geometry, type of excitation, and gas composition. This article explores the possibility of controlling the space charge in a discharge with a spatially and temporally varying electric field. It is shown that a phase-staggered sinusoidal excitation to a set of conformal azimuthal electrodes in a cylindrical geometry leads to a traveling electric field. Simulations show that in space charge dominated transport, the charged species are dispersed both in the radial and azimuthal directions. This will lead to better control of the space charge and stable discharges near atmospheric pressures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Spectral solar irradiance on inclined surfaces: A fast Monte Carlo approach

Estimating spectral plane-of-array (POA) solar irradiance on inclined surfaces is an important step in the design and performance evaluation of both photovoltaic and concentrated solar plants. This work introduces a fast, line-by-line spectral, Monte Carlo (MC) radiative transfer model approach to simulate anisotropic distributions of shortwave radiation through the atmosphere as photon bundles impinge on inclined surfaces. This fast Monte Carlo approach reproduces the angular distribution of solar irradiance without the undesirable effects of spatial discretization and thus computes detailed POA irradiance values on surfaces at any orientation and also when surfaces are subjected to the anisotropic ground and atmospheric scattering. Polarization effects are also easily incorporated into this approach that can be considered as direct numerical simulation of the physics involved. Here, we compare our Monte Carlo radiative transfer model with the most widely used empirical transposition model, Perez4, under various conditions. The results show that the Perez4 model reproduces the more detailed Monte Carlo simulations with less than 10% deviation under clear skies for all relevant surface tilt and azimuth angles. When optically thin clouds are present, observed deviations are larger, especially when the receiving surface is strongly tilted. Deviations are also observed for large azimuth angle differences between the receiving surface and the solar position. When optically thick clouds are present, the two models agree within 15% deviation for nearly all surface orientation and tilt angles. The overall deviations are smaller when compared with cases for optically thin clouds. The Perez4 model performs very well (6.0% deviation) in comparison with the detailed MC simulations for all cases, thus validating its widespread use for practical solar applications. When detailed atmospheric profiles and cloud optical properties are available, the proposed fast Monte Carlo radiative model reproduces accurate spectral and angular POA irradiance levels for various atmospheric and cloud cover conditions, surface orientations, and different surface and ground properties.

42 ENGINEERING↗
DOE OSTI2020

Axial magnetic flux amplification in Hall-magnetohydrodynamic simulations of externally magnetized z-pinches

It is shown that externally magnetized gas-puff z-pinches under compression can exhibit robust axial flux amplification under suitable axial boundary conditions. This effect relies upon the Hall term in the generalized Ohm's law to generate azimuthal currents in the presence of a driving axial electric field. Under dynamic compression, the total current tends to flow in a mostly force-free boundary layer, separating the predominately azimuthal field outside the layer and the predominately axial field inside the layer. The effect only appears to occur if the axial boundaries allow for outflow or absorption of electromagnetic energy. The effect is mitigated by imposing either periodic or conducting axial boundary conditions. A semi-analytic equilibrium analysis agrees with steady-state solutions of the time-dependent electron-magnetohydrodynamic equations and provides an estimate of the scaling of the boundary layer as well as suggesting a scenario for the formation of the boundary layer. When operative, the effect can significantly impede plasma compression due to the increase in axial flux that diffuses into the pre-compressed plasma or through the presence of conductors that inhibit movement of the generated axial flux. Several facilities have noted unusual implosion behavior in z-pinch experiments with applied axial fields that does not appear to be explainable within the standard magnetohydrodynamic model. In conclusion, it is suggested that these experiments can be explained by the axial flux amplification and concentration effect

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Rotational pumping revisited

This paper considers a pure electron plasma, with a small admixture of negative ions, confined in a Penning–Malmberg trap. When a diocotron mode is excited on the plasma, the end sheaths of the plasma are azimuthally distorted. During reflection at a distorted end sheath, an ion steps off of the surface characterizing the drift motion in the plasma interior, and this step produces transport. The diocotron mode transfers canonical angular momentum to the ions, and in response damps. These transport mechanism and associated damping are called rotational pumping. It is particularly strong when the axial bounce motion and the rotational drift motion, in the rotating frame of the mode, satisfy a resonance condition. This paper calculates the transport flux of ions and the associated damping rate of the mode in the resonant regime. Previous papers have discussed the theory and the experimental observation of rotational pumping for the special case of a diocotron mode with azimuthal wave number l = 1, and this paper extends the theory to modes with l≠1, which may sound like a trivial extension, but in fact is not.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Effects of multiply charged ions on microturbulence-driven electron transport in partially magnetized plasmas

Herein, nonlinear interaction between kinetic instabilities in partially magnetized plasmas in the presence of multiply-charged ion streams is investigated using kinetic simulations. It was observed by Hara and Tsikata [Phys. Rev. E 102, 023202 (2020)] that the axial ion-ion two-stream instability (IITSI) due to singly and doubly charged ion streams, coupled with the azimuthal electron cyclotron drift instability (ECDI), enhances cross-field electron transport. In the present study, it is observed that the addition of triply charged ions (as a third ion species) contributes to damping of the excited modes, leading to a reduction in the cross-field electron transport. The net instability-driven electron transport is shown to be a function not only of the azimuthal modes, such as the ECDI, but of the multiple ion species that dictate the development of additional plasma waves. It is found that trapping of the higher ion charge states within the plasma waves results in a broadening of the ion velocity distribution functions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Double cylinder target design for study of hydrodynamic instabilities in multi-shell ICF

Cylindrical implosions are used to study hydrodynamic instability growth for inertial confinement fusion (ICF) applications, as the cylindrical geometry allows for easier diagnostic access while retaining convergence effects. In this work, we use the established cylindrical implosion platform [Palaniyappan et al., Phys. Plasmas 27, 042708 (2020)] to inform the double shell ICF campaign [Montgomery et al., Phys. Plasmas 25, 092706 (2018)]. We present a design for a double cylindrical target as an analogue to the double shell ICF capsule in order to study hydrodynamic instability growth on the high-Z inner shell. Our design work is done with two-dimensional (2D) Eulerian radiation-hydrodynamics simulations, considering the axial uniformity of the implosion and feasibility of measuring the instability growth of pre-seeded single mode sinusoidal perturbations. We discuss in depth the design for a target to be directly driven at the OMEGA laser facility [Boehly et al., Opt. Commun. 133, 495 (1997)]. We evaluate the design for axial implosion symmetry and visibility of instability growth using synthetic radiographs constructed from the simulations, as the instability growth on the inner cylinder is experimentally measured using x-ray radiography of the implosion. We find that the seeded perturbation growth on the inner cylinder should be visible in an experiment, even with axial implosion asymmetry and preheat. We compare our 2D simulations with linear theory predictions for perturbation growth and show that a cylinder with lower azimuthal mode number (mode-20) perturbations compares more favorably with linear theory, while a cylinder with higher azimuthal mode number (mode-40) perturbations at the same starting amplitude saturates and is over-predicted by linear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗