Fast Ignition Scheme Research Articles

Formation of high areal density core using an efficient and robust implosion method for fast ignition

Abstract A new fuel compression method for a fast ignition scheme is discussed. To form a high areal density fuel plasma for the ignition condition, homogenous isentropic compression (HIC) with solid spherical target is effective. We improve a multi-step pulse shape method that uses progressive shockwaves and reflected shockwaves for the compression, where a precisely controlled step-pulse laser drives the shockwaves to compress the fuel and suppress entropy increase. Another advantage of this approach is the relatively smooth high dense fuel is distributed at maximum compression time, compared to our previous design based on Kidder’s HIC method. In addition, we insert a power dip as a preconditioning before the last pulse step to reduce the electron and ion temperature near critical density. As a result, an optimum implosion is designed using 245 kJ of implosion laser energy to meet the ignition condition.

Effects of Kelvin–Helmholtz instability on the material mixing in the double-cone ignition

The Kelvin–Helmholtz instability (KHI) occurs on the interface of gold cones and embedded fuels for fusion schemes with gold cones. The development of KHI on the inner surface of gold cones in the double-cone ignition scheme is investigated with two-dimensional radiation hydrodynamic simulations. It has been found that the colliding high-density fuel plasma between the tips of the two cones is spatiotemporally separated from the mixed gold ions from the inner surface of the gold cones due to the KHI. Furthermore, it is found that fuel layers coated on the inner surface of the cones can effectively mitigate the energy loss in the compression process. These results could provide a reference for fast ignition schemes with gold cones.

Formation of hot spots at end-on pre-compressed isochoric fuels for fast ignition

It is crucial to form a hot spot that can drive a self-heating nuclear burn propagation into the surrounding cold fuel in ignition process of laser fusion. In this paper, we discuss the formation of a hemispherical hot spot located at the edge of an end-on precompressed isochoric fuel instead of a central spherical hot spot surrounded by cold fuel in a corona plasma shell. This configuration leads to a new energy loss mechanism named hot spot collapse, which originates from mass loss of the hot spot through the interface with the vacuum. A semi-analytical model is proposed including α particle induced burning, hot spot collapse and other energy loss processes. Then a modified ignition criterion is derived. The results show that the competition between the hot spot collapse and the burn propagation is crucial in the formation of the hot spot. The formation of such a hot spot at end-on precompressed isochoric fuels would require a somewhat higher initial temperature of Th=9 keV for a hot spot with an initial areal density ρd=0.6gcm−2 . Simulations are performed with a 3D hybrid particle-in-cell/fluid code for the heating process by fast electrons and a 3D radiation hydrodynamics code for the burning process. Simulation results agree with the model. Our optimized result shows a 10 ps heating laser pulse with an energy as low as 39 kJ can lead to a fast ignition in the ideal case. This study provides an effective reference for design and evaluation of experiments planned for fast ignition schemes.

Optimization of target compression for high-gain fast ignition via machine learning

The hydrodynamic scaling relations are of great importance for the design and optimization of target compression in laser-driven fusion. In this paper, we propose an artificially intelligent method to construct the scaling relations of the implosion velocity and areal density for direct-drive fast ignition by combining one-dimensional hydrodynamic simulations and machine learning methods. It is found that a large fuel mass and a high areal density required for high-gain fusion can be obtained simultaneously by optimizing the implosion velocity with less compression laser energy, taking full advantage of the separation of the compression and ignition processes in the fast ignition scheme. The obtained scaling relations are applied to the implosion design for the double-cone ignition scheme [Zhang et al., “Double-cone ignition scheme for inertial confinement fusion,” Philos. Trans. R. Soc., A 378(2184), 20200015 (2020)]. An optimized implosion is proposed with an areal density of 1.30 g/cm2 and a fuel mass of 215.7 μg with a compression laser energy of 168 kJ. Two-dimensional hydrodynamic simulations are further employed to validate the results. Our methods and results may be useful for the optimization of fusion experiments toward high-gain fusion.

Beam-plasma interaction in fast ignition nuclear fusion: Hot-spot properties and gains for different initial plasma temperatures

The main objective of this work is to characterize relevant properties of the hot spots obtained in the interaction between ion beams of V23+ and a spherical pure precompressed deuterium–tritium plasmas in the field of ion fast ignition scheme. In particular, we focus our analysis on the determination of the length, average temperature and maximum temperature (and its location) achieved by the hot spot as a function of the ion beam parameters (particle density and initial energy). Special attention is paid to central hot spots with characteristic lengths in the range 20–40 μm. Furthermore, the self-heating and ignition curves associated to the hot spots generated as well as the burning gain of the precompressed deuterium–tritium fuel are determined. This study is made for a wide range of the beam parameters in which the ignition of the hot spot is achieved and for precompressed deuterium–tritium plasma at 500 g cm3 and temperatures of 0.5, 1 and 5 keV.

Effects of laser waveform on the generation of fast electrons in laser–solid interactions

In the scheme of fast ignition of inertial confinement fusion, the fuel temperature mainly relies on fast electrons, which act as an energy carrier, transferring the laser energy to the fuel. Both conversion efficiency from the laser to the fast electron and the energy spectrum of the fast electron are essentially important to achieve highly effective heating. In this study, a two-dimensional particle in cell simulation is applied to study the generation of fast electrons from solid-density plasmas with different laser waveforms. The results have shown that the slope of the rising edge has a significant effect on fast electron generation and energy absorption. For the negative skew pulse with a relatively slow rising edge, the J×B mechanism can most effectively accelerate the electrons. The overall absorption efficiency of the laser energy is optimized, and the fast electron yield in the middle- and low-energy range is also improved.

Magnetization of high-density plasma with a jet velocity of hundreds of km/s.

High magnetic fields at the kilotesla scale have been experimentally generated and finding methods to fully embed such fields into high-density plasma is interesting for magnetically assisted a fast ignition scheme of inertial confinement fusion, laboratory astrophysics, and magnetically guided fast electron beam for broad applications. We investigate diffusion and embedment of an external magnetic field inwards a high-density plasma by analysis and simulation. By introducing the magnetic Péclet number, dimensional analysis indicates that the magnetizing process is sensitive to the jet velocity, temperature, and size of the plasma and gives a phenomenological scaling law of the magnetic field embedment time with an arbitrary jet velocity. The analytical results are verified by magnetic field simulation and applied in 100-g/cm^{3},100-μm-radius plasmas with a jet velocity of 0-400 km/s and a temperature of 50-500eV, typically adopted in experiments. Attributed to an effective electric field from frame transformation, the magnetic field embedment time can be significantly reduced by one order of magnitude when a jetting plasma is adopted with a velocity of hundreds of kilometers per second, e.g., from 5.5ns in a static plasma to a 0.5ns timescale in a jetting plasma of 200 km/s. The promoted embedment process favors for various applications mentioned above.

Proton beam-driven instabilities in an inclined magnetic field

In this paper, the electrostatic and electromagnetic instabilities of a magnetized proton–DT plasma relevant to the fast ignition scheme of inertial fusion were examined. The magnetic field and proton beam define a plane and the magnetic field vector has the orientation angle of θ. The dispersion relation of two-stream and filamentation modes was first derived using the conservation, Euler, and Maxwell equations. Then, the more general case describing the wave propagation in an arbitrary direction in the two-dimensional case was derived symbolically. It is demonstrated that in a magnetized beam–plasma system, the two-stream instability depicts two separated growth curves, one larger than the other and there exists a stable frequency band between them. This zone will grow as the magnetic field inclination angle increases such that the smaller two-stream peak vanishes at the limiting angle of θ→π/2. The splitting in the growth rate curve becomes obvious at magnetic field parameter Ωe>0.5. The pure filamentation instability of the beam–plasma is about two orders of magnitude smaller than the two-stream instability and it just contributes to magnetic field orientation θ=0. In a two-dimensional case, the mixed electrostatic/electromagnetic instabilities contribute to the final growth rate curve producing an X-like shape. The interface point of two growth curves is characterized by coordinate (∼1.0, tan(θ)) in the zx-plane.

DEUTERON INDUCED FUSION REACTION TARGET FOR INERTIAL CONFINEMENT FUSION (ICF)

Objective: Energy efficiency enhancement is one of the most effective ways to achieve Fast ignition (FI) in inertial confinement fusion ICF. High energy output gain is essential for ICF reactors and greater energy efficiency can reduce energy costs. The injection of Ion beam is one method used to achieve FI fusion reaction in ICF. A fusion of deuteron with lithium-6 isotope, DLi6 is reviewed in this work alongside the fusion of Deuterium – Tritium (DT), Deuterium – Deuterium (DD), Deuterium – Helium-3 (DHe3) and Proton – Boron-11 (PB11).
 Materials and Methods: In this work, it is proposed the projection of laser-driven deuteron beam in the FI scheme for ICF in the DLi6 plasma. Fusion occurs as the projected deuteron ion beam hits the lithium-6 target in the thermonuclear fusion reaction.
 Results: The results show that the fusion reactions of DD, DHe3 and PB11 all require high input kinetic energy (Mega-electronvolts) for the fusion process to occur because of higher Coulomb barrier and the probability of fusion increases by increasing the input energy drive with low output energy gain. DT fusion which require low input kinetic energy of about 400 KeV with high cross section and generated considerable high output energy gain of about 17.59 MeV, However this fusion reaction require large tritium inventory and tritium does not occur naturally, therefore the need for tritium breeding. When the energy of deuteron beam is projected at 200 keV to lithium-6 isotope target, although D + Li6 has a low total cross section of about 19.409 mbarn, the stopping power of the electrons would be more than ions, nuclear stopping power is considerable at very low deuterons energies, the Coulomb interaction of deuteron and lithium-6 occurs with output energy gain of about 22.373 MeV.
 Conclusion: The investigations indicate that fusion target energy gain efficiency is independent of lithium-6 numerical density. The highest value of energy efficiency gain occurs with lower input kinetic energy of deuteron beam of about 200 KeV to lithium-target.
 Recommendation: This findings contribute to the core mission of NIF in achieving fast ignition with low ignition energy input to achieve Lawson break-even or "ignition" point of the fusion fuel pellet, where it gives off 100% or more energy than it absorbs. However the simulation results were based on programmed model of Geant4 Hadr03. This results can be validated with the appropriate experimental design of the Hadr03 process.

Improvement of ignition and burning target design for fast ignition scheme

For the fast ignition scheme of laser fusion, a highly compressed fuel core is necessary using a cone-inserted spherical solid target. We design an optimal compression method with a multistep laser pulse shape using a 2D radiation hydrodynamics simulation. In the design, the maximum areal density is ρR max = 0.46 g cm−2 with 8 kJ of implosion laser. Considering the scaling law of hydrodynamic, we obtained 82 kJ and 1.3 MJ for the ignition-scale-target (ρR max = 1.1 g cm−2) and burning-scale-target (ρR max = 2.5 g cm−2), respectively. In a preliminary study of hydrodynamic instability in the optimized cone-inserted implosion, there is no significant growth of the instabilities that affect the implosion performance. A parameter search to investigate the feasibility and robustness of a high areal density design for changes in the laser pulse shape is performed. As a result, a delay of several tens of pico-second of the rising laser pulse is acceptable.

Excitation of electrostatic standing wave in the superposition of two counter propagating relativistic whistler waves

The problem of standing wave formation by superposing two counter-propagating whistler waves in an overdense plasma, studied recently by Sano et al (2019 Phys. Rev. E 100, 053 205 and 2020 Phys. Rev. E 101, 013 206), has been revisited in the relativistic limit. A detailed theory along with simulation has been performed to study the standing wave formation in the interaction of two counter propagating relativistically intense whistler waves. The relativistic theory explains such interaction process more precisely and predicts correct field amplitudes of the standing wave for a much wider range of physical parameters of the problem as compared to its non-relativistic counterpart. The analytical results are compared with 1-D Particle-in-Cell (PIC) simulation results, performed using OSIRIS 4.0. The results are of relevance to ion heating and fast ignition scheme of inertial confinement fusion.

A study of the effect of self‐generated pressure gradient sources on the resistive filamentation instability

AbstractIn the field of fast ignition scheme, self‐generated magnetic fields via beam resistive filamentation have a significant role in the angular divergence of the relativistic electron beam, which can be affected by the intensity of other self‐generated magnetic fields. In this context, the effects of pressure gradient sources arising from temperature and density gradient of the pellet along the beam flow direction are investigated. The results showed that the resistive filamentation instability can be strongly amplified compared to the fully homogeneous plasma. In this respect, for the distance away from the critical surface, the instability is protected for a longer wave number. Also, the beam and plasma properties such as the beam relativistic factor, the beam number density, and the degree of the plasma temperature anisotropy might be effective.

The effect of deuteron beam injection on the efficiency of energy production in the D6Li plasma

One of the major problems for attaining fusion is to heat the plasma particles to very high temperatures.High gain is essential for a fusion reactor and greater energy efficiency can reduce energy costs. Ion beam injection is one method used to heat plasma inside a fusion reactor. A fusion of deuteron with the isotope lithium-6, D6Li is more difficult than a fusion of deuterium and tritium,DT. In this paper, it is proposed to inject laser-driven deuteron beam in the fast ignition (FI) scheme for inertial confinement fusion (ICF) in the D6Li plasma. Fusion occurs as injected high-energy deuteron ions slow down in the plasma. The results show that the reaction probability increases by increasing electron temperature. The stopping power of electrons and ions decrease with the increase of temperature. When the energy of deuteron beam is achieved at a few hundred keV, stopping power of the electrons would be more than ions. Nuclear stopping power is considerable at very low deuterons energies. The deuteron beam range reduces as incident energy decreases. At low hot spot temperatures, deuterons can be deposited immediately within a very little range. The contribution of the released energy due to the deuteron beam interaction with ions into D6Li plasma provides the additional heating, which generally increases the energy efficiency. The investigations indicate that fusion energy efficiency is independent of lithium-6 numerical density, initial deuteron beam range and increases with electron temperature. The highest value of energy efficiency occurs with lower energy deuteron beam around the 2.5-MeV range from deuteron beam-target fusion.

An investigation of the effects of plasma-heating on the resistive-driven filamentation modes

In the field of fast ignition schemes, it is possible to heat the plasma during the injection of the relativistic electron beams. This might be strongly effective in the self-generated magnetic fields and divergence of the relativistic electron beams in the transport process. In this paper, the effects of plasma heating, J×B pinching, and Nernst (arising from the hot electrons flux) on the resistive filamentation modes in a magnetized anisotropic plasma were investigated. Results showed a significant reduction of the instability growth rate. Findings suggested that the reconnection and convection of the magnetic field lines could change the intensity of the collimation coefficient of the electron beams. In addition, the instability could exist in a safe mode even when the plasma entered an isotropic condition, compared to the temperature anisotropy-driven instabilities, where this could be affected by the relativistic electrons mean velocity.

Transverse beam envelope structures in strongly coupled stimulated Brillouin scattering

We use a newly developed code to investigate cross beam energy transfer via Brillouin scattering in the strong coupling limit. The code couples a single fluid model of the plasma to the complete set of Maxwell's equations. The code can describe beam interaction at arbitrary angles. We observe that the formation of a transverse structure on both beams is caused when the pump beam is fully depleted within the width of the beam. We present a simplified envelope model that confirms the results of the simulation. This transverse beam structure formation has implications for short pulse amplification. The results may also be relevant for fast ignition schemes for inertial confinement fusion.

Enhanced energy coupling for indirect-drive fast-ignition fusion targets

One of the most promising approaches to reach a high gain in inertial confinement fusion is the fast ignition scheme. In this scheme, a relativistic electron beam is generated; this passes through the imploded plasma and deposits parts of its energy in the core. However, the large angular spread of the relativistic electron beam and the poorly controlled compression of the target affect realization of the fast ignition technique. Here, we demonstrate that indirectly driven (that is, driven by X-rays generated inside a gold hohlraum) implosions with a ‘high-foot’ and a short-coast time of less than 200 ps allow us to tightly compress the shell. Furthermore, we show the ability to optimize the symmetry of the imploding shell by changing the hohlraum length, successfully tuning a suitable tube-shaped shell to compensate for the large angular spread of the relativistic electron beam and to enhance the electron-to-core coupling efficiency via resistive magnetic fields. Benefiting from those experimental techniques, a significant enhancement in neutron yield was achieved in our indirectly driven fast ignition experiments. These results pave the way towards high-coupling fast ignition experiments with indirectly driven targets similar to those at the National Ignition Facility. Experiments realizing the indirect-drive fast ignition scheme for inertial confinement fusion are reported. Enabled by a tightly compressed target, an increase of neutron yield is observed.

Collisional shock waves induced by laser radiation pressure

AbstractThe formation of a collisional shock wave by the light pressure of a short-laser pulse at intensities in the range of 1018–1023 W/cm2 is considered. In this regime the thermodynamic parameters of the equilibrium states, before and after the shock transition, are related to the relativistic Rankine–Hugoniot equations. The electron and ion temperatures associated with these shock waves are calculated. It is shown that if the time scale of energy dissipation is shorter than the laser pulse duration a collisional shock is formed. The electrons and the ions in the shock-heated layer may have equal or different temperatures, depending on the laser pulse duration, the material density and the laser intensity. This shock wave may serve as a heating mechanism in a fast ignition scheme.

Self-consistent feedback mechanism for the sudden viscous dissipation of finite-Mach-number compressing turbulence.

Previous work [Davidovits and Fisch, Phys. Rev. Lett. 116, 105004 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.105004] demonstrated that the compression of a turbulent field can lead to a sudden viscous dissipation of turbulent kinetic energy (TKE), and that paper suggested this mechanism could potentially be used to design new fast-ignition schemes for inertial confinement fusion (ICF). We expand on previous work by accounting for finite Mach numbers, rather than relying on a zero-Mach-limit assumption as previously done. The finite-Mach-number formulation is necessary to capture a self-consistent feedback mechanism in which dissipated TKE increases the temperature of the system, which in turn modifies the viscosity and thus the TKE dissipation itself. Direct numerical simulations with a tenth-order accurate Padé scheme were carried out to analyze this self-consistent feedback loop for compressing turbulence. Results show that, for finite Mach numbers, the sudden viscous dissipation of TKE still occurs, for both the solenoidal and dilatational turbulent fields. As the domain is compressed, oscillations in dilatational TKE are encountered due to the highly oscillatory nature of the pressure dilatation. An analysis of the source terms for the internal energy shows that the mechanical-work term dominates the viscous turbulent dissipation. As a result, the effect of the suddenly dissipated TKE on temperature is minimal for the Mach numbers tested. Moreover, an analytical expression is derived that confirms the dissipated TKE does not significantly alter the temperature evolution for low Mach numbers, regardless of compression speed. The self-consistent feedback mechanism is thus quite weak for subsonic turbulence, which could limit its applicability for ICF.

Proton imaging of relativistic laser-produced near-critical-density plasma

When ultrashort pulse laser interacts with near-critical-density plasma, extremely strong transient electromagnetic field will generate a great variety of nonlinear phenomena, such as efficient pulse absorption, magnetic self-channeling, nonlinear coherent structure, and electron and ion acceleration. It is of great significance to make a profound study of these physical processes for studying the laser-plasma interaction. Here in this work, we investigate the near-critical-density plasma structure and its temporal evolution by using proton radiography. The plasma is generated by the interaction of ultra-intense femtosecond laser (<i>I</i> <inline-formula><tex-math id="Z-20190727124236-1">\begin{document}$\sim $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190610_Z-20190727124236-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190610_Z-20190727124236-1.png"/></alternatives></inline-formula> 3.6 × 10<sup>18</sup> W/cm<sup>2</sup>) with high-density gas-jet target, which can produce plasma with electron density <i>n</i><sub>e</sub> <inline-formula><tex-math id="Z-20190727124238-2">\begin{document}$ \sim$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190610_Z-20190727124238-2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190610_Z-20190727124238-2.png"/></alternatives></inline-formula> 0.7<i>n</i><sub>c</sub> (here, <i>n</i><sub>c</sub> is the near-critical-density) for 800 nm laser. The proton beam is produced by the interaction of another ultra-intense femtosecond laser with stainless steel foil target. In the experiment, the proton beam is split into two asymmetric spots. On the one hand, the distance between two spots first increases rapidly and decreases slowly as time goes by. On the other hand, the size of proton beam spot on the right side is obviously lager than the one on the left side. The modification of proton beam profile indicates that a transient electric field with a maximum amplitude of 10<sup>9</sup> V/m is produced when ultrashort laser pulse interacts with the plasma. Besides, the electric field in the direction of laser propagation axis is stronger than that in the opposite direction. When the proton beam goes through the laser-plasma interaction area, most of the protons enter into the electric field in the direction of laser propagation axis, only a small number of protons enter into the electric field in the opposite direction, resulting in the fact that the proton beam is split into two asymmetric spots. The space-charge field in the plasma is induced by the laser ponderomotive force which expels the electrons piled up into a step-like profile. This field can be sustained for a long time, as the ions expand slowly because of the coulomb repulsion between ions, and the hot electrons continue to move forward with energy of a few MeV. At the end, these expanded ions gradually recombine with the reflowed electrons, causing the space-charge field to weaken until it disappears eventually. As a result, the deflection of the proton beam by the electric field in the plasma is also weakened, so the distance between proton beam splitting spots is correspondingly reduced. The hypothesis is justified by the particle-in-cell simulations. The results may have important implications in laser wake-field electron acceleration, ion acceleration and fast ignition scheme to inertial confinement fusion.

Numerical analysis of pulsed magnetic field diffusion dynamics in gold cone target

Strong magnetic fields from a few hundred to a thousand tesla have been produced in a laboratory by using high-intensity laser beams. This strong magnetic field in a laboratory becomes a powerful tool to perform experiments in the fields such as laboratory astrophysics and nuclear fusion research. The diffusion dynamics of a pulsed magnetic field in a target is a key phenomenon for experiments with the laser-produced magnetic field. Here, we have developed a two-dimensional (2D) electromagnetic dynamics simulation code with consideration of inductive heating to simulate spatiotemporally resolved 2D profiles of the applied magnetic field in a target. The application of an external kilo-tesla-level magnetic field to a gold-cone-attached target is a promising scheme for the enhancement of heating efficiency of the fast-ignition inertial confinement fusion scheme. Our simulation revealed that the magnetic field heats the gold cone due to the inductive heating and penetrates the gold cone during its pulse duration. The developed simulation code is generally useful for designing and analyzing experiments using a strong magnetic field.