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When calculating the spectral opacity of hot dense plasmas one often encounters the need to generate a list of detailed ionic configurations of bound states for each ion stage in the plasma. Here we present here a non-recursive algorithm for the efficient construction of such a list of states.
Laser-driven inertial confinement fusion creates a central hot-spot plasma by irradiating a spherical target containing a thermonuclear fuel layer of deuterium (D) and tritium (T) with temporally-shaped, high-intensity lasers or X rays. Inertial confinement fusion relies on the DT-fusion alpha particles depositing their energy in a hot-spot plasma, causing its temperature to rise sharply and a thermonuclear burn wave to propagate out through the surrounding cold, dense DT fuel, producing significantly more energy than was used to heat and compress the fuel. Alpha heating has been demonstrated and burning plasma (i.e., yield amplification due to alpha heating >3.5) is being explored with megajoule-scale lasers on the path to ignition (i.e., yield amplification due to alpha heating >20)
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Abstract Nonlinear coupling of cold and hot waves in a flowing magnetized plasma is analyzed with the Vlasov equation. An analytical solution is obtained for cold waves of a small amplitude (weak flow) and a long wavelength. The distribution function is obtained by integrating the kinetic equation along a perturbed phase-space trajectory for a time-varying plasma flow. The kinetic description presents a generalized dispersion relation that involves resonances depending on cold and hot wave dispersions. Coherent fluid motion leads to radiation peaks in addition to the cyclotron harmonics, where the wavenumber of the cold wave determines the peak frequencies. The peaks appear narrow when the wave propagates perpendicular to the time-averaged flow while they become broad due to the Doppler effect when the wave propagates parallel to the flow. Fully kinetic particle-in-cell simulations corroborate the theoretical predictions. The dispersion relation and resulting wave spectra provide information about plasma parameters and flow properties.
This topic describes the plasma and neutral particles in the transition boundary region between the hot core plasma and the surrounding material walls. A key geometrical transition that occurs in this region is where the equilibrium magnetic field changes topology from a set of closed, nested magnetic flux surfaces inside the magnetic separatrix to flux surfaces, and therefore magnetic field lines that intersect material walls. Because the plasma exhaust heat flows very rapidly along the field lines, these intersection locations can have heat fluxes much higher than the walls can withstand. The most promising strategy pursued here to avoid this problem is injection of moderate-Z impurities that radiate the exhaust power over a much larger surface area on the walls, thus keeping the peak heat flux at or below the goal of 10 MW/m 2 . Further, the intrusion of injected and wall-sputtered impurities into the core region must be kept below certain limits to prevent degradation of the fusion power generated in the core.
We study the effects of redistributing superthermal electrons on Bremsstrahlung radiation from hot relativistic plasma. We consider thermal and nonthermal distribution of electrons with an energy cutoff in the phase space and explore the impact of the energy cutoff on Bremsstrahlung losses. We discover that the redistribution of the superthermal electrons into lower energies reduces radiative losses, which is in contrast to nonrelativistic plasma. Lastly, we discuss the possible relevance of our results for open magnetic field line configurations and prospects of the aneutronic fusion based on proton-Boron11 (p-B11) fuel.
Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.
Abstract In magnetic fusion experiments, the cross sections for the D-T and D- 3 He fusion reactions are increased by as much as 50% if the fuel remains spin polarized parallel to the magnetic field. The goal of this study is to assess the feasibility of lifetime measurements of spin polarization, in magnetic fusion relevant conditions, on the DIII-D tokamak using relative changes in charged fusion product (CFP) loss measurements that depend upon the differential fusion cross section d σ /dΩ. Relative measurements that capture changes in the escaping CFP pitch, poloidal, and energy distributions are studied in two realistic TRANSP calculated plasma scenarios: (a) vector-polarized 3 He and D pellets are injected into a hot hydrogen plasma to produce thermonuclear reactions, and (b) a tensor-polarized deuterium pellet is injected into an L-mode hydrogen background plasma that includes unpolarized 3 He neutral beam injection. Ideal CFP signals in both scenarios show substantial pitch sensitivity to polarization for 14.7 MeV proton detection at a poloidal angle of − 56 ∘ (on the outer wall in the ion ∇ B direction), and strong sensitivity to polarization for 3.6 MeV alpha flux detection by an array of poloidal detectors. Energy-resolved measurements of 14.7 MeV protons are also sensitive to the degree of polarization for the − 56 ∘ port in the beam-plasma scenario. A realistic assessment of CFP signals in the thermonuclear scenario show count rates in the range of 2 × 10 4 cps for pitch-resolved proton detection and 2 × 10 5 cps for alpha flux measurements. Reduced chi-squared χ r 2 calculations show polarization lifetime measurements are feasible for either proton or alpha detection of both enhanced or suppressed polarization for the thermonuclear scenario. Measurements of gamma rays produced in the weak D + 3 He → γ + 5 Li branch complement the CFP measurements.
We report on the status of Fast Ion Regulated Enhancement (FIRE) mode experiments in the Korea Superconducting Tokamak Advanced Research. This regime is being developed for high-performance, steady-state operation which features a stationary ion internal transport barrier, enabling a central ion temperature approaching 10 keV to be sustained for up to 50 s, without the need for delicate profile control and with no significant impurity accumulation. As its key novelty lies in the significant contribution of fast ions that stabilize core turbulence, the regime has been named FIRE mode. To achieve this regime, neutral beam injection is applied at moderate power levels near the L–H power threshold, while maintaining low plasma density to avoid the L–H transition. The scenario is typically established in diverted magnetic configurations. The core features of FIRE mode were investigated through power balance analysis and fluctuation measurements, revealing a clear transport bifurcation in the ion channel. At the plasma edge, FIRE mode occasionally exhibits I-mode characteristics, particularly in unfavorable magnetic null configurations with q 95 ∼ 4, including the presence of weakly coherent modes. In terms of MHD activity, sawtooth oscillations are observed but appear to be stabilized during the high-performance phase. Fast ion-driven Alfvénic eigenmodes (AEs), indicated by strong frequency chirping near 200 kHz, are also observed. Additionally, lower-frequency MHD activities, distinct from the fast ion-driven AEs, are present and have some influence on plasma performance. The enhancement of core confinement is primarily attributed to fast ion effects, which were evaluated with respect to dilution, alpha stabilization, and resonant interactions with turbulence using gyrokinetic analyses. Among these, the dilution effect was found to be the most dominant. The characteristics of FIRE mode were compared with those of other hot ion plasma scenarios, such as supershot and hot ion mode. While they share many similarities, FIRE mode is distinguished by the accessibility to conditions with T i ≈ T e , presence of I-mode edge features, and its long-duration sustainment. Predictive simulations of FIRE mode were performed using integrated transport modeling with TRIASSIC, employing the TGLF anomalous transport model. These simulations confirmed the critical role of fast ions in achieving this regime. The future prospect of FIRE mode for application in fusion reactors is discussed, with an emphasis on possibly extending the regime to higher density operation.
The instability that was previously identified as a fast-ion driven beta-induced Alfv´en-acoustic eigenmode (BAAE) in DIII-D was misidentified. In a dedicated experiment, low frequency modes (LFM) with characteristic “Christmas light” patterns of brief instability linked to the safety factor evolution occur in plasmas with electron temperature T e ≳ 2.1 keV but modest beta. To isolate the importance of different driving gradients on these modes, the electron cyclotron heating power and 80 keV, sub-Alfv´enic neutral beams are altered for 50-100 ms durations in reproducible discharges. Although beta-induced Alfv´en eigenmodes and reversed-shear Alfv´en eigenmodes stabilize when beam injection ceases (as expected for a fast-ion driven instability), the low frequency modes that were called BAAEs persist. Data mining reveals that characteristic LFM instabilities can occur in discharges with no beam heating but strong electron cyclotron heating. A large database of over 1000 discharges shows that LFMs are only unstable in plasmas with hot electrons but modest overall beta. The experimental LFMs have low frequencies (comparable to diamagnetic drift frequencies) in the plasma frame, occur near the minimum of the safety factor q min , and appear when q min is close to rational values. In conclusion, theoretical analysis suggests that the LFMs are a low frequency reactive instability of predominately Alfv´enic polarization.
High energy density plasmas generated in laser-driven inertial confinement fusion implosions provide unparalleled laboratory conditions for studying stellar-relevant nuclear reactions: plasma environment; hot and dense; uniquely high achievable neutron flux. These experiments have the potential to address long-standing questions about plasma effects on nuclear reactions hitherto experimentally inaccessible, including nuclear rates with thermally distributed reactants, plasma screening, and reactions involving nuclei in excited states. The National Ignition Facility (NIF) and OMEGA lasers are two primary facilities for executing experiments of this type. Existing and future nuclear diagnostics, along with supporting diagnostics to characterize the platform, enable exploitation of these plasmas for such nuclear astrophysics-relevant experiments. Here, this review describes the nuclear diagnostic capabilities currently available for these types of experiments at the NIF and OMEGA, including neutron time-of-flight spectrometers, charged-particle detectors, gamma detectors and radiochemistry diagnostics, and briefly summarizes other available diagnostic capabilities used for platform characterization. Enabling tools not yet available are also identified, including a rapid radioactive sample retrieval system, a low-energy neutron spectrometer and a high-efficiency gamma spectrometer.
Several mm-wave diagnostics on the DIII-D tokamak provide multi-scale and multi-dimensional measurements of plasma profile evolution and turbulence fluctuations. Mm-wave fusion plasma diagnostics that adopt system-on-chip integrated circuit technology can provide better space utilization, flexible installation, and improved sensitivity. In order to further extend this technology for additional fusion facilities with a higher toroidal magnetic field, V-band (55–75 GHz) and F-band (90–140 GHz) chips for Microwave Imaging Reflectometer (MIR) and Electron Cyclotron Emission Imaging (ECEI) instruments are developed and tested in the Davis Millimeter Wave Research Center (DMRC). Current measurement data show that correlation between these SoC-based diagnostic instruments with other state-of-the-art diagnostics enables co-located multi-field turbulence fluctuation measurement.
In this study, physics models and design codes for hot dense plasmas undergoing thermonuclear burn are evaluated objectively using statistical metrics that compare the difference between calculations and data relative to the experimental uncertainties. The analysis is applied to the National Ignition Campaign (NIC) because it is relevant, comprehensive, and well documented. The statistics confirm that a key process afflicting NIC performance is mix driven by hydrodynamic instabilities as approximated here using the KL model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)]. New physics models are also presented for instability-driven magnetic fields [B. Srinivasan et al., Phys. Rev. Lett. 108, 165002 (2012)] and the Coulomb logarithm for electron–ion thermal relaxation [G. Dimonte and J. Daligault, Phys. Rev. Lett. 101, 135001 (2008)]. The plasma-generated magnetic fields improve the agreement between code and data in a statistically significant manner by reducing the electron thermal conduction in the hot-spot via the Hall term. The Coulomb logarithm is presented in a numerically practical form that incorporates recent theoretical advances. However, it does not improve the agreement between the code and data because the thermal relaxation is so fast in non-ignited NIC plasmas that the typical 20% error does not change the tight coupling between electrons and ions. Even with these improved physics models, the one-dimensional simulations presented here are not able to describe the high-convergence NIC implosions in a statistically acceptable manner. Of the heroic multi-dimensional simulations of Clark et al. [Phys. Plasmas 23, 056302 (2016)], only those in three-dimensions satisfy the statistical acceptance criterion.
The notch filter plays a crucial role as a protective component in microwave diagnostics, primarily by addressing issues related to catastrophic interference. Designed for millimeter-wave diagnostics on the stellarator Wendelstein 7-X (W7-X), a WR-6 waveguide-based notch filter has been successfully developed to effectively isolate leakage from auxiliary heating gyrotrons operating at 140 GHz. The filter incorporates cylindrical cavities resonating at 140 GHz for the TE11p mode, with coupling structures that are designed and optimized for high-efficiency coupling. This configuration simplifies fabrication, thereby ensuring high-yield production. Experimental fabrication and in-house characterization confirm the notch filter's exceptional performance, with over 60 dB rejection in the vicinity of 140 GHz and low insertion loss (< 2 dB) above and below the notch frequency across a broad frequency bandwidth (121–138 GHz, 142–163 GHz). Furthermore, the utilization of this high-frequency structure fabrication technology can be applied to millimeter-wave diagnostics on other machines. In addition to the design elements of the notch filter, this paper also provides a detailed discussion of the fabrication process and methodology.
We performed two-dimensional simulations of turbulent laser-plasma instabilities in the presence and absence of external magnetic fields using the Laser Plasma Simulation Environment (LPSE) code. The results demonstrate that, in the presence of a magnetic field, the transition from ballistic to gyrating electron motion enhances the energy transfer from electron plasma waves to the electron population. Although stronger magnetic fields produce a larger population of hot electrons, these electrons tend to remain confined near the quarter-critical density, where the instabilities also localize, thereby reducing the potential for hot electron transport deeper into the target. Additionally, we present a scaling analysis that quantifies hot electron generation as a function of plasma electron temperature, density scale length, and applied magnetic field strength. These findings may have important applications for controlling hot electron flux and mitigating preheat in inertial confinement fusion targets.
Three-dimensional effects play a crucial role during the hot-spot formation in inertial confinement fusion (ICF) implosions. A data analysis technique for 3D hot-spot reconstruction from experimental observables has been developed to characterize the effects of low modes on 3D hot-spot formations. In nuclear measurements, the effective flow direction, governed by the maximum eigenvalue in the velocity variance of apparent ion temperatures, has been found to agree with the measured hot-spot flows for implosions dominated by mode ℓ = 1. Asymmetries in areal-density (ρR) measurements were found to be characterized by a unique cosine variation along the hot-spot flow axis. In x-ray images, a 3D hot-spot x-ray emission tomography method was developed to reconstruct the 3D hot-spot plasma emissivity using a generalized spherical-harmonic Gaussian function. The gradient-descent algorithm was used to optimize the mapping between the projections from the 3D hot-spot emission model and the measured x-ray images along multiple views. Furthermore, this work establishes a platform to analyze 3D low-mode core asymmetries in ICF.
A series of 2D in-plane plane wave particle-in-cell simulations find distinctive paths of laser-plasma instability evolution in OMEGA-scale implosions, depending on the initial electron temperature. At low temperatures, two-plasmon decay (TPD) dominates in both initial growth and the steady state. At high temperatures, the initial dominant modes switch to stimulated Raman scattering, but TPD still dominates a steady state characterized by cavitation and Langmuir turbulence. A hot electron scaling is also obtained from the simulations that, when combined with laser/plasma conditions from hydro simulations, can predict hot electron generation in implosions that do not employ smoothing-by-spectral-dispersion (SSD). It also shows that under the same laser/plasma conditions, SSD can reduce hot electron generation.