Revised Knudsen-layer reduction of fusion reactivity

Albright, B. J.; Molvig, Kim; Huang, Chengkun; Simakov, Andrei N.; Dodd, E. S.; Hoffman, N. M.; Kagan, Grigory; Schmit, Paul

doi:10.1063/1.4833639

Cited by 47 publications

(38 citation statements)

References 14 publications

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“…The difference between the curves shows the impact each individual kinetic effect has on the yields. The (c) Knudsenmodified ion distribution function (f K , dashed) [35], area normalized to the original Maxwellian distribution function (f M , solid line), shows how tail ions are depleted for an average D 3 He ion for a typical strongly kinetic regime (∼0.3 mg=cm 3 ) Knudsen number of N K ¼ 2.…”

Section: Fig 4 (Color Online) Measured (A) Dd and (B) Dmentioning

confidence: 99%

“…As a first step to begin exploring this hydro-kinetic transition, a reduced ion kinetic (RIK) model that includes gradient-diffusion and loss-term approximations to several transport processes was implemented within a 1D radiation-hydrodynamics code [33,34]. This model includes the effects of kinetic transport of ion mass, momentum, and thermal energy and reduction in fusion reactivity owing to Knudsen-layer modification of ion-distribution tails when the ion mean-free path around bang time approaches the shell radius [16,35]. The model requires empirically determined parameters to calibrate its various flux terms.…”

Section: Prl 112 185001 (2014) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

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Exploration of the Transition from the Hydrodynamiclike to the Strongly Kinetic Regime in Shock-Driven Implosions

et al. 2014

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Clear evidence of the transition from hydrodynamiclike to strongly kinetic shock-driven implosions is, for the first time, revealed and quantitatively assessed. Implosions with a range of initial equimolar D 3 He gas densities show that as the density is decreased, hydrodynamic simulations strongly diverge from and increasingly overpredict the observed nuclear yields, from a factor of ∼2 at 3.1 mg=cm 3 to a factor of 100 at 0.14 mg=cm 3 . (The corresponding Knudsen number, the ratio of ion mean-free path to minimum shell radius, varied from 0.3 to 9; similarly, the ratio of fusion burn duration to ion diffusion time, another figure of merit of kinetic effects, varied from 0.3 to 14.) This result is shown to be unrelated to the effects of hydrodynamic mix. As a first step to garner insight into this transition, a reduced ion kinetic (RIK) model that includes gradient-diffusion and loss-term approximations to several transport processes was implemented within the framework of a one-dimensional radiation-transport code. After empirical calibration, the RIK simulations reproduce the observed yield trends, largely as a result of ion diffusion and the depletion of the reacting tail ions. Inertial confinement fusion implosions, whether for ignition [1] or nonignition [2,3] experiments, are nearly exclusively modeled as hydrodynamic in nature with a single average-ion fluid and fluid electrons [4,5]. However, in the early phase of virtually all inertial fusion implosions, strong shocks are launched into the capsule where they increase in strength and speed as they converge to the center and abruptly and significantly increase the ion temperature in the central plasma region. In this process, and in the rebound of the shock from the center, which initiates a burst of fusion reactions (i.e., the fusion shock burn or shock flash [6]), the mean-free path for ion-ion collisions can become, especially for lower-density fueled implosions, sufficiently long that both the shock front itself and the resulting central plasma are inadequately described by hydrodynamic modeling. This process and the transition of regimes from hydrodynamiclike to strongly kinetic are the focus of this Letter.Recent kinetic and multiple-ion-fluid simulations have begun to explore deviations from average-ion hydrodynamic models, particularly during the shock phase of implosions when such effects are potentially paramount. For example, in an effort to explain observed yield anomalies in multiple-ion fuels of D 3 He, DT, and DT 3 He [7][8][9], researchers have investigated multiple-ionfluid effects [10][11][12] as well as utilized a hybrid fluidkinetic model [13,14]. Other modeling work has included ion viscosity and nonlocal ion transport [15] in order to reduce discrepancies with shock-generated nuclear yields. Very recently, a model for Knudsen layer losses of energetic ions [16], based in part on earlier work [17], was explored for a variety of plastic capsule implosions with relatively thick walls, all largely ablatively driven (not shock driven) a...

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Section: Fig 4 (Color Online) Measured (A) Dd and (B) Dmentioning

confidence: 99%

Section: Prl 112 185001 (2014) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Exploration of the Transition from the Hydrodynamiclike to the Strongly Kinetic Regime in Shock-Driven Implosions

et al. 2014

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“…This simulation technique incorporates reduced models of ion kinetic effects in a 1D fluid-based radiation-hydrodynamic code, to represent the effects of kinetic transport of ion mass, momentum, and thermal energy, and reduction in fusion reactivity owing to modified ion-distribution tails when λ ii ∼R shell . 16,40,41 As was described in Ref. [6], model parameters were constrained by the measured DD and D 3 He yields, DD-burn-averaged T i , DD bang time, and the laser absorption fraction.…”

Section: Modelsmentioning

confidence: 99%

Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging

et al. 2015

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The significance and nature of ion kinetic effects in D 3 He-filled, shock-driven inertial confinement fusion implosions is assessed through measurements of fusion burn profiles. Over this series of experiments the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, N K ) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al. Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatially-resolved measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantites to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows that models including ion transport effects are able to better match the experimental results. In implosions characterized by large Knudsen numbers (N K ∼3), the fusion burn profiles predicted by hydrodynamics simulations that exclude ion mean free path effects are peaked far from the origin, in stark disagreement with the experimentally observed profiles, which are centrally-peaked. In contrast, a hydrodynamics simulation that includes a model of ion diffusion is able to qualitatively match the measured profile shapes. Therefore, ion diffusion or diffusion-like processes are identified as a plausible explanation of the observed trends, though further refinement of the models is needed for a more complete and quantitative understanding of ion kinetic effects.

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“…This work was followed by more accurate calculations by Albright et al [27], Schmit et al [28], Tang et al [29], Davidovits and Fisch [30] and Cohen et al [31]. All these studies considered the perfectly planar or spherical models and relied either on direct numerical solution [28,29,30,31] or phenomenological assumptions that affect the structure of the kinetic equation, thereby introducing uncontrollable modifications to the reactivity [26,27].…”

Section: Suprathermal Ionsmentioning

confidence: 99%

Kinetic studies of ICF implosions

Kagan

Herrmann

Kim

et al. 2016

J. Phys.: Conf. Ser.

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Abstract. Kinetic effects on inertial confinement fusion have been investigated. In particular, inter-ion-species diffusion and suprathermal ion distribution have been analyzed. The former drives separation of the fuel constituents in the hot reacting core and governs mix at the shell/fuel interface. The latter underlie measurements obtained with nuclear diagnostics, including the fusion yield and inferred ion burn temperatures. Basic mechanisms behind and practical consequences from these effects are discussed.

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Revised Knudsen-layer reduction of fusion reactivity

Cited by 47 publications

References 14 publications

Exploration of the Transition from the Hydrodynamiclike to the Strongly Kinetic Regime in Shock-Driven Implosions

Exploration of the Transition from the Hydrodynamiclike to the Strongly Kinetic Regime in Shock-Driven Implosions

Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging

Kinetic studies of ICF implosions

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