Abstract
RayleighTaylor instabilities(RTI) in inertial confinement fusion(ICF) implosions are expected to generate magnetic fields at the gasice interface and at the iceablator interface. The focus here is on the gasice interface where the temperature gradient is the largest. A HallMHD model is used to study the magnetic field generation and growth for 2D singlemode and multimode RTI in a stratified twofluid plasma, the two fluids being ions and electrons. Selfgenerated magnetic fields are observed and these fields grow as the RTI progresses via the term in the generalized Ohm’s law. Srinivasan et al. [Phys. Rev. Lett. 108, 165002 (2012)] present results of the magnetic field generation and growth, and some scaling studies in 2dimensions. The results presented here study the mechanism behind the magnetic field generation and growth, which is related to fluidvorticity generation by RTI. The magnetic field wraps around the bubbles and spikes and concentrates in flux bundles at the perturbed gasice interface where fluidvorticity is large. Additionally, the results of Srinivasan et al. [Phys. Rev. Lett. 108, 165002 (2012)] are described in greater detail. Additional scaling studies are performed to determine the growth of the selfgenerated magnetic field as a function of density, acceleration, perturbation wavelength, Atwood number, and ion mass.
This study was supported by the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DEAC5206NA25396. The authors wish to acknowledge the discussions with Dr. Guy Dimonte from Los Alamos National Laboratory during the course of this study and suggestions offered by him to improve this manuscript. The authors also wish to acknowledge the use of the WARPX code, which was developed at the University of Washington.
I. INTRODUCTION
II. NUMERICAL METHOD AND PLASMA MODEL
III. 2D SINGLEMODE RTI
A. Problem description and background
B. Singlemode RTI benchmark
C. Selfgenerated magnetic field in the linear and nonlinear stages of RTI
D. Initial condition: Effect of using a colinear and perturbation
E. Magnetic field scaling
IV. 2D MULTIMODE RTI
V. DISCUSSION
Key Topics
 Magnetic fields
 116.0
 Rayleigh Taylor instabilities
 38.0
 Vortex dynamics
 21.0
 Inertial confinement
 15.0
 Magnetic fluids
 11.0
Figures
HallMHD and Euler solutions of the spike and bubble positions (a) and the spike and bubble velocities (b) to benchmark the plasma results to neutral fluid results in WARPX. Note that the RTI solutions obtained using HallMHD are identical to the Euler solutions.
HallMHD and Euler solutions of the spike and bubble positions (a) and the spike and bubble velocities (b) to benchmark the plasma results to neutral fluid results in WARPX. Note that the RTI solutions obtained using HallMHD are identical to the Euler solutions.
Froude number as a function of spike position for several values of A = 0.1, 0.3, 0.5, 0.9. Note reacceleration of bubble and spike following terminal velocity for low A. Reference 11 shows that there is no reacceleration for high A. Note 4 stages in RTI growth.
Froude number as a function of spike position for several values of A = 0.1, 0.3, 0.5, 0.9. Note reacceleration of bubble and spike following terminal velocity for low A. Reference 11 shows that there is no reacceleration for high A. Note 4 stages in RTI growth.
Fluid density (a), total magnitude of electric field (b), outofplane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the linear RTI growth (stage 2 of Fig. 2).
Fluid density (a), total magnitude of electric field (b), outofplane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the linear RTI growth (stage 2 of Fig. 2).
Fluid density (a), total magnitude of electric field (b), outofplane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the early nonlinear RTI growth (stage 3 of Fig. 2).
Fluid density (a), total magnitude of electric field (b), outofplane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the early nonlinear RTI growth (stage 3 of Fig. 2).
Fluid density (a), total magnitude of electric field (b), outofplane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the late nonlinear RTI growth (stage 4 of Fig. 2).
Fluid density (a), total magnitude of electric field (b), outofplane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the late nonlinear RTI growth (stage 4 of Fig. 2).
as a function of the normalized time (a), as a function of the normalized spike position (b), and for the spike as a function of thenormalized time . and are the same as Fig. 1. Note exponential growth of the peak magnetic field as a function of time.
as a function of the normalized time (a), as a function of the normalized spike position (b), and for the spike as a function of thenormalized time . and are the same as Fig. 1. Note exponential growth of the peak magnetic field as a function of time.
scaling as a function of spike position () (a) by varying density, acceleration, wavelength, Atwood number, and ion mass. (with a corresponding and ) is when the spike and bubble transition from exponential growth to a terminal velocity stage, which also corresponds to when the dependence of on goes from linear to exponential. Plot (b) shows the normalized magnetic field for each of the RTI parameters (the singlemode universal ).
scaling as a function of spike position () (a) by varying density, acceleration, wavelength, Atwood number, and ion mass. (with a corresponding and ) is when the spike and bubble transition from exponential growth to a terminal velocity stage, which also corresponds to when the dependence of on goes from linear to exponential. Plot (b) shows the normalized magnetic field for each of the RTI parameters (the singlemode universal ).
as a function of spike position () for the nominal case with and without the Hall term (Term II in Eq. (8)). Note that the Hall term does not significantly affect the generation and growth of the magnetic field.
as a function of spike position () for the nominal case with and without the Hall term (Term II in Eq. (8)). Note that the Hall term does not significantly affect the generation and growth of the magnetic field.
Scalelength of compared to the scalelength of and the scalelength of for several times, (a), (b), and (c). All quantities are normalized in these figures and are values of the crosssection for all x along the midplane in y. Note that the scalelength of the peak magnetic field corresponds to the region with the sharpest density gradient. More importantly, follows the same profile and scalelengths as .
Scalelength of compared to the scalelength of and the scalelength of for several times, (a), (b), and (c). All quantities are normalized in these figures and are values of the crosssection for all x along the midplane in y. Note that the scalelength of the peak magnetic field corresponds to the region with the sharpest density gradient. More importantly, follows the same profile and scalelengths as .
Evolution of as a function of (a) (blue line), the location of 5 sound transit times (dashed cyan), and the location of where the exponential RT growth ends (also where the linear relationship between and ends). Corresponding plots of as a function of are shown in (b).
Evolution of as a function of (a) (blue line), the location of 5 sound transit times (dashed cyan), and the location of where the exponential RT growth ends (also where the linear relationship between and ends). Corresponding plots of as a function of are shown in (b).
Evolution of as a function of (a) (blue line), the location of 5 sound transit times (dashed cyan), and the location of for . Corresponding plots of as a function of are shown in (b).
Evolution of as a function of (a) (blue line), the location of 5 sound transit times (dashed cyan), and the location of for . Corresponding plots of as a function of are shown in (b).
Dependence of timeaveraged magnetic field on initial perturbation amplitude over an ion sound transit time. Note the linear dependence.
Dependence of timeaveraged magnetic field on initial perturbation amplitude over an ion sound transit time. Note the linear dependence.
Early time evolution and latetime evolution of a random multimode perturbation for ion density (a), and for outofplane magnetic field () (b). The density and temperature profiles have the same morphology as .
Early time evolution and latetime evolution of a random multimode perturbation for ion density (a), and for outofplane magnetic field () (b). The density and temperature profiles have the same morphology as .
The bubble position as a function of time for a random multimode perturbation using several values of A. Note that there is a dependence of the early time solution.
The bubble position as a function of time for a random multimode perturbation using several values of A. Note that there is a dependence of the early time solution.
as a function of spike position (a), and normalized which is the multimode universal f(h/L) (b) for a random multimode perturbation by varying RTI parameters.
as a function of spike position (a), and normalized which is the multimode universal f(h/L) (b) for a random multimode perturbation by varying RTI parameters.
Perpendicular electron thermal conductivity as a function of for NIF relevant parameter regimes.
Perpendicular electron thermal conductivity as a function of for NIF relevant parameter regimes.
Tables
Summary of spike position as a function of time, peak magnetic field as a function of time, and peak magnetic field as a function of spike position for different stages of RTI.
Summary of spike position as a function of time, peak magnetic field as a function of time, and peak magnetic field as a function of spike position for different stages of RTI.
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