Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment (2024)

Authorization Required

×

×

• 

  Figure 1

  (a)Cutaway characteristic target geometry (gold-lined depleted uranium hohlraum surrounding an HDC capsule) with some features labeled. The capsule, $\sim 2\mathrm{mm}$ diameter, at the center of the hohlraum, $\sim 1\mathrm{cm}$ height, occupies a small fraction of the volume. Laser beams (not shown) enter the target at the top and bottom apertures called laser entrance holes (LEH’s) (outer beams: 44° and 50°, inner beams: 23° and 30° relative to the vertical axis of symmetry). The LEH washer forms the LEH aperture. The “starburst” allows imaging of the DT fuel layer during experiment preparation as cryogenic DT liquid is flowed into the capsule via the “fill tube.” (b)Total laser power (blue) vs time and simulated [16] hohlraum radiation temperature ($T_{\mathrm{rad}}$) (red) vs time for experiment N210808 are shown with a few key elements, discussed in the text, labeled. The “picket” of the laser pulse delivers the first significant burst of energy to the hohlraum and is key to controlling implosion compressibility and hydrodynamic stability. The “foot” of the laser pulse is the duration of the pulse before the rise to peak power—it sets the entropy of the DT fuel via a series of shock waves. The capsule ablation pressure is directly related to $T_{\mathrm{rad}}$ and the ablator composition (which in this case is high density carbon, HDC). A key aspect shown is the laser typically turns off $\approx 1\mathrm{ns}$ before bang time (denoted “coast-time” duration), of order the hohlraum cooling time [17]. Increasing late-time x-ray drive results in reduced coast time which enhances the conversion of implosion kinetic energy to DT internal energy [18, 19]. (c)Imaging data from experiments: neutron images [20] are taken at three lines of sight: (0,0) (technically at $\theta =5.75$ and $\varphi =225$), (90,315), and (90,213) in target-chamber coordinates [$(\theta ,\varphi )$ are the respective polar and azimuthal angles measured from the top looking down of the NIF target chamber in degrees]. All images are $100\mu \mathrm{m}$ square. Imaging data are used to reconstruct the hot spot plasma volume needed for inferring pressure and other plasma properties.

  Reuse & Permissions

• 

  Figure 2

  Simulated hot spot powers of Eq.(1) as a function of time from a model of N210808 [16]. Note that the negative $pdV$ rate of work is a loss comparable to the radiation loss and exceeds the conduction loss, even before peak $\alpha$-heating power is obtained, which is why satisfying the self-heating condition, $f_{\alpha }{Q}_{\alpha }>f_B{Q}_{B,\mathrm{D}\mathrm{T}}+Q_e$, is necessary but not sufficient for determining ignition of an ICF implosion. After the time of peak $\alpha$-heating power the negative $pdV$ work is the dominant power loss.

  Reuse & Permissions

• 

  Figure 3

  NIF DT shot data (symbols) are plotted in the space of time-averaged inferred hot spot pressure (${\overline{P}}_{\mathrm{HS}}$) and hot spot radius (${\overline{R}}_{\mathrm{HS}}$). The black dashed curve denotes the ignition boundary from Eq.(2). Data from the hybrid-$E$ series are highlighted in red. DT shot N210808 is the datum in the upper-right of the plot, shown as the probability distribution from Markov chain MonteCarlo (MCMC) analysis with a contour enclosing 80% of the distribution.

  Reuse & Permissions

• 

  Figure 4

  NIF DT shot data (symbols) are plotted in the space of inferred Lawson parameter and hot spot thermal temperature. The black curve denotes the ignition boundary from Eq.(3). The dotted and dashed curves show how the ignition boundary moves to higher temperature under different assumptions of mixing of high-$Z$ material into the DT resulting in enhancement of bremsstrahlung x-ray losses (dotted: a 50% increase in bremsstrahlung, $f_B=1.5$; and dashed: a 100% increase, $f_B=2.0$). Data from the hybrid-$E$ series is highlighted in red. In this analysis, the NTOF inferred DD ion temperature, $T_i(\mathrm{D}\mathrm{D})$, is used as an estimate of $T_{\mathrm{th}}$ as previous work [112] measuring electron temperature ($T_e$) has shown that $T_e\approx T_i(\mathrm{D}\mathrm{D})\le T_i(\mathrm{D}\mathrm{T})$ for these types of implosions.

  Reuse & Permissions

• 

  Figure 5

  NIF DT shot data are plotted against the ignition metrics of $\alpha$ energy to hot spot energy fraction, Eq.(4) (left) and Eq.(5) (right). The ordinate is the yield amplification ($Y_{\mathrm{amp}}$). Data from the hybrid-$E$ series are highlighted in red. On the left, inferred quantities from both 0D (closed symbols and red oval probability distribution) and 1D (open symbols and purple oval probability distribution) hot spot models are shown.

  Reuse & Permissions

• 

  Figure 6

  NIF DT shot data (symbols) is plotted in the space of fuel areal-density [$\rho R$, hot spot only (top) and total (bottom)] and hot spot thermal temperature. The curves denote the ignition boundaries published in Cheng etal. [116], Tipton [115], Atzeni and Meyer-ter-Vehn [108], and Coutant [117].

  Reuse & Permissions

• 

  Figure 7

  The contour plot of $H$ shows the dependence upon $f_B$ and $T$. At fixed $T$, higher $f_B$ lowers $H$ essentially reflecting the fact that enhanced bremsstrahlung cooling makes the ignition temperature higher than it would be for pure DT and this makes ignition more difficult to achieve. If the implosion can be engineered to have a high enough optical depth to reabsorb bremsstrahlung x rays ($f_B<1$), the ignition temperature is reduced.

  Reuse & Permissions

×