Spin depolarization induced by self-generated magnetic fields during cylindrical implosions

Spin-polarized fuels are promising for inertial confinement fusion due to the enhanced fusion cross section. One significant concern of spin-polarized inertial confinement fusion is whether the nuclei polarization could survive in the implosions and contribute to ignitions. Here we present numerical simulation methods and results of spin dynamics of polarized deuterium-tritium fuels in strong self-generated magnetic fields during the implosions of dense cylindrical shells. The magnetic field generation and evolution is modeled with generalized Ohm's laws combined with hydrodynamic equations. The spin dynamics is investigated with a particle-tracking method, by solving the spin precession equations of tracked particles. Rayleigh-Taylor instabilities and Richtmyer-Meshkov instabilities are found to be the main cause of depolarization. Hydrodynamic instabilities lead to depolarization of nuclei near the hot-spot shell interface, and an asymmetric shock front leads to depolarization of nuclei inside a hot spot. Deuterium polarization is more stable than tritium polarization due to its smaller gyromagnetic ratio. Low-mode perturbations can lead to higher depolarization inside a hot spot than high-mode perturbations. In the multimode simulations, the modes around 16–32 are significant for hot-spot depolarization.

Figure 1

(a) Time evolution of the mass density $\rho$ radial profile in the implosion without initial perturbation. The interface of the hot spot and shell is marked by a white dashed-dotted line, and the shock front position is marked by gray dashed-dotted lines. (b) Time evolution of pressure $p$.

Figure 2

Simulation results for initial perturbation $m=16$ and $A=10\mu \mathrm{m}$ at $t=150$ ps: (a) the distribution of mass density $\rho$, (b) pressure $p$, (c) magnetic fields $B_z$, (d) fraction of depolarized D, (e) fraction of depolarized T, (f) cross-sectional enhancement factor $\delta$.

Figure 3

Simulation results for different initial perturbation amplitudes $A$ with fixed $M=16$. (a) Mass weighted average magnetic field strength $|B_z|$ in the inner region. (b) Fraction of depolarized deuterons in the inner region. (c) Fraction of depolarized tritons in the inner region. (d) Cross-sectional enhancement factor $\delta$ in the inner region. (e) Mass weighted average magnetic field strength $|B_z|$ in the outer region. (f) Fraction of depolarized deuterons in the outer region. (g) Fraction of depolarized tritons in the outer region. (h) Cross-sectional enhancement factor $\delta$ in the outer region.

Figure 4

Simulation results for different initial perturbation mode numbers $m$ with fixed $A=10\mu \mathrm{m}$. (a) Mass weighted average magnetic field strength $|B_z|$ in the inner region. (b) Cross-sectional enhancement factor $\delta$ in the inner region. (c) Mass weighted average magnetic field strength $|B_z|$ in the outer region. (d) Cross-sectional enhancement factor $\delta$ in the outer region.

Figure 5

Multimode random perturbation simulation results. (a) Density $\rho$ at 150 ps. (b) Cross-sectional enhancement factor $\delta$ at 150 ps. (c) Mass weighted average magnetic field strength $|B_z|$ in the inner region for five random initial perturbations. (d) Cross-sectional enhancement factor $\delta$ in the inner region for five random initial perturbations.