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Mechanism for magnetic field generation and growth in Rayleigh-Taylor unstable inertial confinement fusion plasmas
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10.1063/1.4742176
/content/aip/journal/pop/19/8/10.1063/1.4742176
http://aip.metastore.ingenta.com/content/aip/journal/pop/19/8/10.1063/1.4742176

Figures

Image of FIG. 1.
FIG. 1.

Hall-MHD 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 Hall-MHD are identical to the Euler solutions.

Image of FIG. 2.
FIG. 2.

Froude number as a function of spike position for several values of A = 0.1, 0.3, 0.5, 0.9. Note re-acceleration of bubble and spike following terminal velocity for low A. Reference 11 shows that there is no re-acceleration for high A. Note 4 stages in RTI growth.

Image of FIG. 3.
FIG. 3.

Fluid density (a), total magnitude of electric field (b), out-of-plane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the linear RTI growth (stage 2 of Fig. 2).

Image of FIG. 4.
FIG. 4.

Fluid density (a), total magnitude of electric field (b), out-of-plane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the early nonlinear RTI growth (stage 3 of Fig. 2).

Image of FIG. 5.
FIG. 5.

Fluid density (a), total magnitude of electric field (b), out-of-plane magnetic field (c), and fluid vorticity (d) when . This represents the solutions during the late nonlinear RTI growth (stage 4 of Fig. 2).

Image of FIG. 6.
FIG. 6.

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.

Image of FIG. 7.
FIG. 7.

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 single-mode universal ).

Image of FIG. 8.
FIG. 8.

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.

Image of FIG. 9.
FIG. 9.

Scale-length of compared to the scale-length of and the scale-length of for several times, (a), (b), and (c). All quantities are normalized in these figures and are values of the cross-section for all x along the mid-plane in y. Note that the scale-length of the peak magnetic field corresponds to the region with the sharpest density gradient. More importantly, follows the same profile and scale-lengths as .

Image of FIG. 10.
FIG. 10.

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).

Image of FIG. 11.
FIG. 11.

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).

Image of FIG. 12.
FIG. 12.

Dependence of time-averaged magnetic field on initial perturbation amplitude over an ion sound transit time. Note the linear dependence.

Image of FIG. 13.
FIG. 13.

Early time evolution and late-time evolution of a random multimode perturbation for ion density (a), and for out-of-plane magnetic field () (b). The density and temperature profiles have the same morphology as .

Image of FIG. 14.
FIG. 14.

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.

Image of FIG. 15.
FIG. 15.

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.

Image of FIG. 16.
FIG. 16.

Perpendicular electron thermal conductivity as a function of for NIF relevant parameter regimes.

Tables

Generic image for table
Table I.

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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/content/aip/journal/pop/19/8/10.1063/1.4742176
2012-08-07
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Mechanism for magnetic field generation and growth in Rayleigh-Taylor unstable inertial confinement fusion plasmas
http://aip.metastore.ingenta.com/content/aip/journal/pop/19/8/10.1063/1.4742176
10.1063/1.4742176
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