Nuclear Fusion: Overview of Challenges and Recent Progress

Abstract

This comprehensive review delves into nuclear fusion, elucidating its underlying principles, persistent challenges, and recent advancements. Exploring both magnetic confinement fusion and inertial confinement fusion, this study provides a detailed analysis of the complexities involved. In the realm of magnetic confinement, the article meticulously examines two leading configurations: tokamak and stellarator. By dissecting their operational mechanisms, energy hurdles, and computational intricacies, the review offers profound insights. Furthermore, the discussion extends to material challenges, focusing on the selection of suitable fusion materials crucial for the success of magnetic confinement fusion. In the field of inertial confinement fusion, we discuss direct drive inertial confinement. Computational challenges surrounding instabilities and ignition are discussed. Additionally, material challenges concerning diverse target materials are explored, illuminating the complexities in material science central to inertial confinement fusion success. The section culminates in the latest progress in inertial confinement fusion. The review illuminates the complexities of nuclear fusion and highlights the evolving strategies and innovations propelling fusion research into a promising future.

Introduction

Nuclear fusion is an option for meeting humanity’s long-term energy needs. This process involves the process of two light atomic nuclei combining into a singular, heavier nucleus, unleashing a tremendous amount of energy. To initiate this reaction, it is crucial to overcome the coulombic barrier, arising due to the positive charges of the nuclei involved. The release of energy, in the form of binding energy, occurs when particles combine to create larger entities. Notably, these fusion reactions transpire within a distinct state of matter called plasma—a high-temperature gas where positively and negatively charged particles coexist in equal numbers. Plasma is indispensable as it is the sole state in which thermonuclear reactions can autonomously sustain themselves.

The coulombic barrier is the energetic barrier that two nuclei must cross to be near enough to engage in a nuclear reaction. The potential energy of the coulombic barrier is given below:

   

where and are the charges of the interacting particles, is the permittivity of free space, and is the interaction radius. When the coulombic barrier is overcome, two atomic nuclei will collide with each other. Considering that hydrogen has the weakest charge, most experiments focus on the fusion reaction between deuterium and tritium , nuclear isotopes of hydrogen:

   

The D-T reaction has a Q-value of joule, where the Q-value is defined as:

   

where (B) is the binding energy. Binding energy is related to mass defect, which is given by:

   

where is the total mass of the protons, is the total mass of the neutrons, and is the mass of the nucleus. According to Einstein’s special theory of relativity, the formation of a nucleus from a system of isolated protons and neutrons releases energy. The energy emitted is the binding energy :

   

where (c) is the speed of light. Energy is released if the standard atomic weights of the final elements are lighter than iron, as shown in Fig. 1.

Nuclear fusion, despite its challenges, offers numerous benefits, driving ongoing scientific pursuit. Firstly, it generates abundant energy, releasing nearly four million times more energy than coal combustion and four times as much as nuclear fission at an equivalent mass. Secondly, fusion utilizes readily available elements: deuterium, extractable from various water sources, and tritium, producible during the fusion reaction itself. Thirdly, fusion stands out for its environmental friendliness, as it emits no greenhouse gases and primarily produces helium as a by-product. These advantages position fusion as a valuable contributor to addressing our resource challenges.

In the past few decades, nuclear fusion research has split into two main pathways: magnetic confinement fusion and inertial confinement fusion. Magnetic fusion plasmas are intricate systems with diverse spatial and temporal scales, necessitating advanced numerical techniques and algorithms. Inertial confinement employs high-power laser systems. Moreover, fusion occurs in an environment characterized by intense irradiation, plasma fluxes, and exceedingly high temperatures and pressures. Both pathways encounter computational science and materials science challenges, albeit with distinct advantages.

Magnetic Confinement Fusion

DT fusion can be realized at C. Such temperatures can be reached in the devices that confine heated fuel by magnetic fields. In such devices, charged particles in strong magnetic fields feel the Lorentz force and hence are confined to the magnetic field lines, following helical paths. According to the formula of the radius of gyration (also known as the Larmor radius): , where is the particle’s velocity perpendicular to the direction of the magnetic field, and is the angular cyclotron frequency ( is the particle’s charge, is the particle’s mass, and is the strength of the magnetic induction), the orbit of particles is affected by the strength of the magnetic field. An electron’s Larmor radius is of the order of . The nonuniform magnetic fields in space result in a phenomenon where the guiding center drifts from the field line, and it is bad for confinement. To deal with drift and other hydrodynamic instabilities, different configurations were tested.

Scientists have discovered that drift can be rectified by twisting the magnetic field line. In simple terms, a section of the field line is twisted outward while the other part remains inside the configuration. This twisting causes particles to drift in various directions along different parts of their trajectory, effectively nullifying the drift. In general, there are two machines employed to generate toroidal magnetic fields: the tokamak and the stellarator.

Tokamak

How It Works

The tokamak achieves magnetic field twisting by circulating a current around the plasma, creating an additional magnetic field component. Consequently, the tokamak requires a substantial current passing through the plasma. In its early stages, this phenomenon was understood through electromagnetic induction. To maintain a constant plasma current, the voltage of the loop must consistently maintain the same sign. This requires the primary current to be continually varied in the same direction, according to Faraday’s law of electromagnetic induction. Despite decades of development, the tokamak still faces various challenges.

Energy Challenges

For the tokamak, energy challenges have limited its development. Because , where (P) is the heating power, (R) is the electrical resistance of the plasma torus, and is the plasma current, must be increased to reach the fusion temperatures . Paradoxically, in a tokamak, there are some surfaces covered by the magnetic field lines. Each surface has a safety factor (q), which is related to the ratio , where (B) is a given magnetic induction that is limited by the design. Instabilities can destroy the magnetic confinement process whenever (q) gets close to or below two, so the maximum of cannot be very large². Moreover, the heating power provided by the current decreases when the electrical resistance of the plasma is reduced. It decreases with , where (T) is the plasma temperature. This will happen when the plasma is heated many times². In conclusion, operating a tokamak alone cannot reach the sufficiently high temperature that is needed for fusion.

Fortunately, there are some ways to generate additional heating. The first way is called neutral-beam injection heating. By injecting fast neutral particles, which are not confined by the Lorentz force, to transport energy into the plasma. The neutral particles collide with the plasma and get ionized, becoming part of the plasma. Injection heaters can supply 60 kW to the plasma per injector³. The second way is called auxiliary heating, which makes the transfer of power more efficient by injecting electromagnetic power. The electromagnetic waves are absorbed if they can match the frequency of the moving plasma particles in the orbit and resonate with the particles.

Four different systems are under consideration to provide additional thermal energy: electron cyclotron waves at a frequency of 170 GHz; fast waves operating in the range 40-70 MHz; lower hybrid waves at 5 GHz; and neutral beam injection using negative ion beam technology for operation at 1 MeV energy. Several of these systems might be used in parallel⁴. These heating methods are sufficient in providing extra heating, but this still proves difficult.

To generate fusion energy, the plasma must follow the Lawson criteria²,⁵:

   

where is the number density of the ions and is the energy-confinement time. The efficiency of the auxiliary method decreases with the increase of the injected power, failing to meet the expectation , where (P) is the amount of injected heating power⁶,⁷.

The improved concept is called High Confinement Mode (H-mode)⁸: when the input power is high enough, the plasma density rises at the edge of the plasma, and the density can reach a higher peak in the center, generating larger fusion power. However, instabilities like Edge Localized Mode (ELM) are the problems that hinder the development of H-mode. ELM is excited in an H-mode plasma and leads to the explosion of it, which damages the divertor (a configuration that separates the plasma from the material surface of the device in both tokamak and stellarator) and the first wall⁹. It is estimated that the heat flow density released by the ELM burst can reach 100 . In contrast, the maximum heat flow density that is known to be tolerated by the divertor is only 10 . H-mode is considered as the basic requirement to generate fusion power for future reactors, so minimizing the damage to the reactor from ELM is an essential task.

Computational Challenges

In a tokamak, toroidal plasma is contained within twisted magnetic field lines. These twisted lines serve to counteract particle drifts; otherwise, charge separation would lead to the emergence of a vertical electric field, resulting in the loss of plasma confinement. To maintain tokamak operation and plasma control, calculations involving equilibrium and microscopic stability are conducted within the Magnetohydrodynamics (MHD) model. This model employs a hydrodynamic description, treating the plasma as an ideal gas with infinite electrical conductivity. This is valid for plasma because the electrical conductivity increases with electron temperature (). Furthermore, the cross product of the ideal MHD force balance reads , and the magnetic equilibrium is well described by this relation², where is the plasma pressure, is the plasma current density, and is the magnetic induction. In conclusion, the stability of the system can be assessed using the MHD model.

Large-scale MHD instabilities pose significant limitations on tokamak operation. The macroscopic plasma equilibrium is threatened by pressure gradients and current density¹⁰. To simulate the maximum stable pressure under a given value of plasma current, Troyon -limit (the ratio of the plasma pressure and the magnetic-field energy density) is used in the design of devices. However, MHD instabilities can cause the sum of the ion and electron pressure to surpass the -limit¹¹. Operation at a high -value is crucial to the stable operation of the tokamak, emphasizing the importance of mitigating these instabilities.

In recent years, there has been a profound understanding of the limitations imposed on the tokamak by MHD stabilities. The heating and current-drive systems used to heat the plasma to the necessary temperatures can be used to optimize the limitations². Besides, using external coils and local current drive can neutralize the growth of MHD instabilities¹². However, whether these methods can effectively and stably mitigate the instabilities still require further evaluation.

Stellarator

How It Works

Research on stellarators started later than that on tokamaks. In contrast to tokamaks, stellarators employ helical coils around the plasma to twist the magnetic fields. This design eliminates the need for a plasma current that twists the magnetic field lines, reducing operational risks, while engineering these coils is a complex task. Optimized stellarators, such as quasi-helical and quasi-axisymmetric configurations, minimize plasma particle drift. The most recent optimized stellarator in Europe is Wendelstein 7-X¹³ in Germany.

Energy Challenges

The concepts mentioned in the previous section, including heating the plasma, the H-mode, and the divertor, can also be applied in stellarators with some differences. Due to the lack of axisymmetry, the plasma heat loss in a stellarator is larger than in a tokamak¹⁴. The instabilities caused by the plasma current only occur in tokamak because there is no plasma current in stellarators, which is a great advantage.

Computational Challenges

Stellarators require more intricate optimization techniques than tokamaks to achieve configurations with effective confinement of thermal particles, as well as favorable Magnetohydrodynamics (MHD) stability properties. The optimization of stellarators began in 1985, and one significant breakthrough¹⁵ pertained to the method for confining particles. As long as the magnetic field’s strength (B) has a near-symmetrical coordinate, particles can be confined in the absence of perfect axial symmetry of the magnetic field. This discovery led to the design of configurations like quasi-helical symmetric stellarators, or the quasi-axisymmetric stellarator.

A new method has been found to optimize a fixed-boundary stellarator equilibrium¹⁶. The first step is to minimize the deviation from quasi-axisymmetry on a single flux surface. The next step is maintaining the improved quasi-axisymmetry while minimizing the analytical quantity (). This work is performed at ( = 4.3%) (the volume-averaged ratio of plasma pressure to magnetic pressure), with collisional energy losses between (6.6%)–(7.4%). Although there are some flaws in the methods, for example, the choices of temperature and density profiles are better to be different, the method is still successful. Optimizing quantities like () is a promising way to realizing good confinement in the stellarator.

Another approach to optimization is to restrict particle drift motion across magnetic surfaces, which motivates the design of Wendelstein 7-X. It has a major radius of , a minor radius of , plasma volume of , and heating power for the plasma of (14 MW)¹⁷. With the biggest modular-superconducting-coils stellarator in the world, it has made plasma discharges lasting up to (30) minutes. By contrast, the world record made by a tokamak is (390) seconds. However, stellarators are not the short-term solution. The confinement time of stellarators is below that of tokamaks by a factor of (10), and the triple product of stellarators is inferior to tokamaks.

Material Challenges

Advanced structural materials will be needed to address the challenges posed by the environment. Typically, crystalline materials can satisfy the requirements. There are three kinds of Bravasis lattices: body-centered cubic (BCC), shown in Fig. 3, and face-centered cubic (FCC), and hexagonal closest packed (HCP), shown in Fig. 4. BCC and FCC metals are more widely used because the HCP lattice has anisotropy. FCC metals usually offer higher ductility and BCC metals offer higher strength¹⁸.

Over the decades, much work has been done to find the appropriate materials that are capable of resisting radiation damage, caused by phenomena like low-temperature embrittlement²⁰, radiation-induced segregation, and radiation-induced precipitation in different materials²¹,²², irradiation creep²³, volumetric swelling²⁴, and Helium embrittlement of grain boundaries²⁵,²⁶. When designing materials, it is crucial to account for these phenomena. Three kinds of materials have emerged: ferritic/martensitic steels (BCC), vanadium alloys (BCC), and SiC/SiC ceramic composites with multiple crystalline structures²⁷,²⁸,²⁹. Compared to conventional materials, the steels have better mechanical strength up to 500-550, alloys can provide higher thermodynamic efficiency up to 700-750, and silicon composites offer the possibility to operate at temperatures greater than ¹⁸. Experiments have proved that BCC conveys radiation resistance, which makes the steels and the alloys good candidates.

In fusion reactors, the choice of first-wall materials holds immense importance (the first wall is a barrier between the plasma and the magnets, safeguarding outer components from radiation damage). Carbon was historically employed in numerous fusion experiments due to its relatively high sublimation temperature. However, a drawback arises when carbon atoms cool at the plasma’s edge, leading to the formation of hydrocarbon compounds that redeposit in various areas. This situation poses significant safety concerns³⁰. Tungsten is now regarded as a candidate material and is used in the Axially Symmetric Divertor Experiment—Upgrade tokamak. Many fusion studies assume tungsten as the material for the divertor³¹. It is necessary to conduct further experiments to assess the properties of tungsten.

Inertial Confinement Fusion

How It Works

Inertial confinement fusion (ICF) is another scheme that might realize controlled nuclear fusion. ICF is different from magnetic confinement fusion due to that the fusion fuel is compressed and maintained at fusion densities and temperatures by its own inertia. At present, the focus of international ICF research is laser driven ICF(LICF). Basically, there are two approaches to LICF: direct drive and indirect drive. In direct drive the target is irradiated by the laser beams directly and in indirect drive the laser beams do not irradiate the target directly. The differences between indirect drive and direct drive ICF are shown in Fig. 5. The review below is mainly focused on direct drive ICF.

Compared to indirect drive, direct drive can use the energy of the laser beam more effectively and the structure of the target is easier. The disadvantage is that the laser beam must irradiate the target uniformly to reduce the possibility of hydrodynamic instabilities. The target is a sphere a few millimeters in diameter, containing DT fusion fuel. The implosion of the fusion particles should be symmetrical, and the instabilities, which can form turbulence, interrupt the condensed plasma, resulting in bad confinement.

The physical process of implosion in direct-drive LICF can be summarized into four steps: absorbing the laser beam, condensing the target, fusion ignition, and fusion burning³². After condensing, the laser pulse intensity increases, resulting in shock towards the target. At shock stage, the target evolves as the result of Richtmyer Meshkov-like instabilities. The interactions between laser and plasma can generate hot electrons that lead to preheat. These factors should be considered while designing the target, ignition plan, and conducting experiments.

Computational Challenges

Direct-drive implosions require extremely uniform irradiation to minimize the impact of hydrodynamic instabilities. It is generally considered that the overall level of nonuniformity should be 1% root mean square³². Schmitt shows the possibility of obtaining a high level of uniformity with a small number of beams³⁴. He indicated that uniform illumination is possible with as few as six beams, as long as the absorption profile of each beam is proportional to , where is the angle between an incident ray and the target normal at the aim point of the ray on the target surface. In addition, implementation of phase plates at the end of each beamline and adding bandwidth to the laser can lead to smooth drive.

The Inertial Confinement Fusion (ICF) target must remain spherically symmetric because even small deviations from symmetry are amplified by instabilities. The instabilities include Richtmyer-Meshkov (RM) instability³⁵ caused by the rippled outer surface, Rayleigh-Taylor (RT) instability³⁶ caused by the acceleration field, and Kelvin-Helmholtz (KH) instability³⁷ caused by the rate of shear. RM instability is when shock waves impact the interface of different substances, forming complex wave systems and vortices, which in turn leads to interface instability and turbulent mixing. This instability significantly affects parameters like energy convergence, eventually causing “ignition” failure. Therefore, suppressing the occurrence of interface instability is the key to successful “ignition.” The initial situation of the surface is essential to the formation of RM instability, but the generation of the three-dimensional initial surface is complex, and convergent shock waves are difficult to produce in the laboratory³⁸. RT instability occurs in the acceleration field when two fluids of different densities meet each other. The effect of RT instability is shown in Fig. 6. KH instability occurs when there is a velocity difference across the interface of two different fluids or a velocity shear in a continuous fluid. It causes the fluid to flow from one side to the other side. In inertial confinement fusion, the fuels in different layers can be mixed up because of it, resulting in energy loss.

In an Inertial Confinement Fusion (ICF) implosion, ignition is extremely important. There are three different types of ignitions: conventional hot-spot ignition, shock ignition, and fast ignition. Compared to the conventional way of hot-spot ignition, these new concepts are likely to provide higher fusion gain³². The background and history of fast ignition are in the passage written by Tabak et al.⁴⁰. There are three steps in fast ignition. First, the DT capsule is imploded. Second, a short-pulse laser is injected to form a channel through the plasma. Third, the fast electron produced by the laser would ignite the fuel³². When the fusion fuel is uniformly compressed to the maximum density, an ultrashort pulse intense laser is focused on the surface of the target. The ignition starts in the small region at the core. Because the two processes, condensing and ignition, are separated in fast ignition, the requirements of symmetrical implosion and energy input are remarkably reduced. The minimum ignition energy that must be coupled into the DT fuel to initiate a burn wave is 10 kJ for an idealized target design³². The potential available high gain is shown in Figure 7.

However, fast ignition encounters several challenges. Firstly, the varying intensities and pulses of laser beams have different effects on the target, making it unclear which choice is the most suitable. Secondly, the transportation of fast electrons through the plasma when creating a channel remains unknown⁴¹. Thirdly, in the cone-in-shell variation of fast ignition, where a cone guides the short-pulse laser and fast electrons are generated closer to the core, preventing electron divergence is a challenge. Although the concept of fast ignition has been tested theoretically, further experiments are necessary to confirm its feasibility.

In shock ignition, an intensity spike pulse is added to the compression pulse. By reducing the power of the drive pulse, the fuel implodes slower than conventional ignition. In conventional hot-spot design, targets implode with velocities at . By contrast, shock ignition targets implode at a velocity of ³². After reaching a low enough velocity, the intense laser spike launches a spherically symmetric converging shock wave into the target. The shock ignition target can be more massive compared to the conventional hot-spot ignition driven by the same input laser energy, so it can generate higher gain at low laser energy. Besides, the massive target is more stable to hydrodynamic instabilities³².

However, there are also problems with shock ignition. The hot electrons generated by the laser-plasma instabilities (LPI) were thought to be used to generate a strong shock, but some experiments have shown that if the electrons are not properly utilized, they may also destroy the ignition. Simulations have shown that hot electrons enter the target faster than the main shock wave and preheat the fuel, resulting in low reaction efficiency. The effect of the electrons might be determined by the design of the target and the laser. Further experiments and simulations are needed to fully understand shock ignition⁴².

Material Challenges

The material challenges in Inertial Confinement Fusion (ICF) focus on the selection of target materials. To achieve better spherical implosion, the requirements for the target include several aspects. First, the shell material should be mainly composed of atoms with low atomic number, such as hydrogen, beryllium, boron, and carbon. Second, the dimensions and surface smoothness of the shell. Third, the impurity content, deponent element content, and distribution within the shell.

With these requirements, the following targets show great potential.

Glow discharge polymer (GDP) target is one of the first-used concepts. The GDP shell is mainly made of carbon and hydrogen, which can resist erosion in the environment. It also has high surface smoothness and abundant experimental data. Be (Cu) target (beryllium doped with copper) has a defect volume below , and its surface smoothness can achieve nm⁴³. It can be used at lower radiation drive temperatures. The main drawback of this target is the high level of difficulty in preparation because beryllium is poisonous.

Other alternative concepts include the polyimide (PI) target (surface smoothness of nm⁴³, high-density carbon target (surface smoothness of nm⁴³, and boron-carbide target with high hardness, all require further discussion to ensure their feasibility.

Latest Progress

Although many people consider Magnetic Confinement Fusion (MCF) as a better scheme than Inertial Confinement Fusion (ICF), the recent experiments done at the Lawrence Livermore National Laboratory (LLNL) are such a monumental achievement that proves the worth of ICF and greatly promotes the development of fusion physics. On Dec. 5, 2022, a team at LLNL conducted the first controlled fusion experiment in history. This is the first time that humanity has produced more energy from fusion than what was required to start the fusion. In December 2022, the reported energy input is about 2.05 million joules while the energy output is about 3.15 million joules⁴⁴. It is reported that the researchers at LLNL achieved fusion gain for the second time on July 30, 2023, and the energy generated this time is higher than the one in December.

Conclusion

Nuclear fusion, as explored in this review article, poses a significant challenge due to the formidable Coulomb barrier. Over the years, two primary approaches have been pursued to realize nuclear fusion: magnetic confinement and inertial confinement. Within magnetic confinement, the tokamak and stellarator configurations have emerged as the most successful. Each configuration comes with unique advantages and faces distinct challenges, particularly in the fields of energy production, computational science, and material science. This article focuses on direct drive inertial confinement. In the pursuit of ICF, challenges in computational modeling and material science have been pivotal. Overcoming these difficulties is crucial for advancing the feasibility of inertial confinement fusion as a viable energy source. A noteworthy milestone is the achievement of net energy gain in inertial confinement fusion in LLNL. This is the beginning of a new era for nuclear fusion research and shows a bright energy future for humanity. In summary, the review underscores the ongoing efforts and notable achievement in the realm of nuclear fusion. There is a famous saying that nuclear fusion is 30 years away and always will be, but it seems like nuclear fusion will be realized sooner than we think.

Acknowledgements

I would like to acknowledge the support from Mr. Andrew Wildridge and thank him for the stimulating discussions we have had on nuclear fusion.

References

1. Book: University Physics (OpenStax). (2022, September 12). Physics LibreTexts. https://phys.libretexts.org/@go/page/4340. [↩]
2. Ongena, J., Koch, R., Wolf, R., & Zohm, H. (2016). Magnetic-confinement fusion. Nature Physics, 12(5), 398–410. https://doi.org/10.1038/nphys3745 [↩] [↩] [↩] [↩] [↩] [↩]
3. Kelley, G. G., Morgan, O. B., Stewart, L. D., Stirling, W. L., & Forsen, H. K. (1972). Neutral-beam-injection heating of toroidal plasmas for fusion research. Nuclear Fusion, 12(2), 169–176. https://doi.org/10.1088/0029-5515/12/2/004 [↩]
4. Drive, I. P., & Editors, I. P. (1999). Chapter 6: Plasma Auxiliary Heating and current drive. Nuclear Fusion, 39(12), 2495–2539. https://doi.org/10.1088/0029-5515/39/12/306 [↩]
5. Hurricane, O. (2022). Lawson criterion for ignition exceeded in an inertial fusion experiment. 2022 IEEE International Conference on Plasma Science (ICOPS). https://doi.org/10.1109/icops45751.2022.9813006 [↩]
6. Goldston, R. J. (1984). Energy confinement scaling in Tokamaks: Some implications of recent experiments with ohmic and strong auxiliary heating. Plasma Physics and Controlled Fusion, 26(1A), 87–103. https://doi.org/10.1088/0741-3335/26/1a/308 [↩]
7. Kaye, S. M., & Goldston, R. J. (1985). Global energy confinement scaling for neutral-beam-heated tokamaks. Nuclear Fusion, 25(1), 65–69. https://doi.org/10.1088/0029-5515/25/1/006 [↩]
8. Andrew Yasmin and Kim Eun-jin 2023H-mode transition and pedestal studies Phil. Trans. R. Soc. A.3812021024120210241. http://doi.org/10.1098/rsta.2021.0241 [↩]
9. A. W. Leonard; Edge-localized-modes in tokamaks. Physics of Plasmas 1 September 2014; 21 (9): 090501. https://doi.org/10.1063/1.4894742 [↩]
10. Fasoli, A., Brunner, S., Cooper, W. A., Graves, J. P., Ricci, P., Sauter, O., & Villard, L. (2016). Computational challenges in magnetic-confinement fusion physics. Nature Physics, 12(5), 411–423. https://doi.org/10.1038/nphys3744 [↩]
11. Troyon, F., Gruber, R., Saurenmann, H., Semenzato, S., & Succi, S. (1984). MHD-Limits to plasma confinement. Plasma Physics and Controlled Fusion, 26(1A), 209–215. https://doi.org/10.1088/0741-3335/26/1a/319 [↩]
12. Igochine, V. (2015). Active control of magneto-hydrodynamic instabilities in hot plasmas. In Springer series on atomic, optical, and plasma physics. https://doi.org/10.1007/978-3-662-44222-7 [↩]
13. Dinklage, A., Beidler, C.D., Helander, P. et al. Magnetic configuration effects on the Wendelstein 7-X stellarator. Nature Phys 14, 855–860 (2018). https://doi.org/10.1038/s41567-018-0141-9 [↩]
14. Helander, P. (2014). Theory of plasma confinement in non-axisymmetric magnetic fields. Reports on Progress in Physics, 77(8), 087001. https://doi.org/10.1088/0034-4885/77/8/087001 [↩]
15. Grieger, G., Lotz, W., Merkel, P., Nührenberg, J., Sapper, J., Strumberger, E., Wobig, H., Burhenn, R., Erckmann, V., Gasparino, U., Giannone, L., Hartfuß, H. J., Jaenicke, R., Kühner, G., Ringler, H., Weller, A., & Wagner, F. (1992). Physics optimization of stellarators. Physics of Fluids. B, Plasma Physics, 4(7), 2081–2091. https://doi.org/10.1063/1.860481 [↩]
16. LeViness, A., Schmitt, J. C., Lazerson, S. A., Bader, A., Faber, B. J., Hammond, K. C., & Gates, D. A. (2022). Energetic particle optimization of quasi-axisymmetric stellarator equilibria. Nuclear Fusion, 63(1), 016018. https://doi.org/10.1088/1741-4326/aca4e3 [↩]
17. Klinger, T., Andreeva, T., Bozhenkov, S., Brandt, C., Burhenn, R., Buttenschön, B., Fuchert, G., Geiger, B., Grulke, O., Laqua, H. P., Pablant, N., Rahbarnia, K., Stange, T., Von Stechow, A., Tamura, N., Thomsen, H., Turkin, Y., Wegner, T., Abramovic, I., . . . Zuin, M. (2019). Overview of first Wendelstein 7-X high-performance operation. Nuclear Fusion, 59(11), 112004. https://doi.org/10.1088/1741-4326/ab03a7 [↩]
18. Steven J. Zinkle; Fusion materials science: Overview of challenges and recent progress. Physics of Plasmas 1 May 2005; 12 (5): 058101. https://doi.org/10.1063/1.1880013 [↩] [↩]
19. Structure & Reactivity in Organic, Biological and Inorganic Chemistry (Worksheets). (2021, June 11). Chemistry LibreTexts. https://chem.libretexts.org/@go/page/136239 [↩] [↩]
20. V.M. Chernov, B.K. Kardashev, K.A. Moroz, Low-temperature embrittlement and fracture of metals with different crystal lattices – Dislocation mechanisms, Nuclear Materials and Energy, Volume 9,2016, Pages 496501, ISSN23521791. https://doi.org/10.1016/j.nme.2016.02.002 [↩]
21. Wang, X., Zhang, H., Baba, T. et al. Radiation-induced segregation in a ceramic. Nat. Mater. 19, 992–998 (2020). https://doi.org/10.1038/s41563-020-0683-y [↩]
22. Z. Jiao, G.S. Was, Novel features of radiation-induced segregation and radiation-induced precipitation in austenitic stainless steels, Acta Materialia, Volume 59, Issue 3,2011,Pages 1220-1238,ISSN 1359-6454. https://doi.org/10.1016/j.actamat.2010.10.055 [↩]
23. Fabien Onimus, Thomas Jourdan, Cheng Xu, Anne A. Campbell, Malcolm Griffiths,1.10 – Irradiation Creep in Materials, Editor(s): Rudy J.M. Konings, Roger E. Stoller, Comprehensive Nuclear Materials (Second Edition), Elsevier, 2020, Pages 310-366, ISBN 9780081028667. https://doi.org/10.1016/B978-0-12-803581-8.11645-5 [↩]
24. Hyosim Kim, Jonathan G. Gigax, Connor J. Rietema, Osman El Atwani, Matthew R. Chancey, Jon K. Baldwin, Yongqiang Wang, Stuart A. Maloy, Void swelling of conventional and composition engineered HT9 alloys after high-dose self-ion irradiation, Journal of Nuclear Materials, Volume 560, 2022, 153492, ISSN00223115. https://doi.org/10.1016/j.jnucmat.2021.153492 [↩]
25. Tomoaki Suzudo, Masatake Yamaguchi, Simulation of He embrittlement at grain boundaries in bcc transition metals, Journal of Nuclear Materials, Volume 465, 2015, Pages 695701, ISSN00223115. https://doi.org/10.1016/j.jnucmat.2015.07.002 [↩]
26. Ullmaier, H. (1984). The influence of helium on the bulk properties of fusion reactor structural materials. Nuclear Fusion, 24(8), 1039–1083. https://doi.org/10.1088/0029-5515/24/8/009 [↩]
27. Bloom, E., Zinkle, S., & Wiffen, F. (2004). Materials to deliver the promise of fusion power – progress and challenges. Journal of Nuclear Materials, 329–333, 12–19. https://doi.org/10.1016/j.jnucmat.2004.04.141 [↩]
28. Muroga, T., Nagasaka, T., Abe, K., Chernov, V. M., Matsui, H., Smith, D., Xu, Z., & Zinkle, S. (2002). Vanadium alloys – overview and recent results. Journal of Nuclear Materials, 307–311, 547–554. https://doi.org/10.1016/s0022-3115(02)01253-9 [↩]
29. Bloom, E. (1998). The challenge of developing structural materials for fusion power systems. Journal of Nuclear Materials, 258–263, 7–17. https://doi.org/10.1016/s0022-3115(98)00352-3 [↩]
30. Federici, G., Skinner, C., Brooks, J., Coad, J., Grisolia, C., Haasz, A., Hassanein, A., Philipps, V., Pitcher, C., Roth, J., Wampler, W., & Whyte, D. (2001). Plasma-material interactions in current tokamaks and their implications for next step fusion reactors. Nuclear Fusion, 41(12), 1967–2137. https://doi.org/10.1088/0029-5515/41/12/218 [↩]
31. Maisonnier, D., Campbell, D., Cook, I., Di Pace, L., Giancarli, L., Hayward, J., Puma, A. L., Medrano, M., Norajitra, P., Roccella, M., Sardain, P., Tran, M., & Ward, D. (2007). Power plant conceptual studies in Europe. Nuclear Fusion, 47(11), 1524–1532. https://doi.org/10.1088/0029-5515/47/11/014 [↩]
32. R. S. Craxton, K. S. Anderson, T. R. Boehly, V. N. Goncharov, D. R. Harding, J. P. Knauer, R. L. McCrory, P. W. McKenty, D. D. Meyerhofer, J. F. Myatt, A. J. Schmitt, J. D. Sethian, R. W. Short, S. Skupsky, W. Theobald, W. L. Kruer, K. Tanaka, R. Betti, T. J. B. Collins, J. A. Delettrez, S. X. Hu, J. A. Marozas, A. V. Maximov, D. T. Michel, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, A. A. Solodov, J. M. Soures, C. Stoeckl, J. D. Zuegel; Direct-drive inertial confinement fusion: A review. Physics of Plasmas 1 November 2015; 22 (11): 110501. https://doi.org/10.1063/1.4934714 [↩] [↩] [↩] [↩] [↩] [↩] [↩] [↩]
33. Ditmire, T., Roth, M., Patel, P.K. et al. Focused Energy, A New Approach Towards Inertial Fusion Energy. J Fusion Energ 42, 27 (2023). https://doi.org/10.1007/s10894-023-00363-x [↩]
34. Schmitt, A. J. (1984b). Absolutely uniform illumination of laser fusion pellets. Applied Physics Letters, 44(4), 399–401. https://doi.org/10.1063/1.94788 [↩]
35. The richtmyer-meshkov instability | annual Review of Fluid Mechanics. https://www.annualreviews.org/doi/10.1146/annurev.fluid.34.090101.162238 [↩]
36. Ye Zhou, Robin J.R. Williams, Praveen Ramaprabhu, Michael Groom, Ben Thornber, Andrew Hillier, Wouter Mostert, Bertrand Rollin, S. Balachandar, Phillip D. Powell, Alex Mahalov, N. Attal, Rayleigh–Taylor and Richtmyer–Meshkov instabilities: A journey through scales, Physica D: Nonlinear Phenomena, Volume 423, 2021, 132838, ISSN 0167-2789. https://doi.org/10.1016/j.physd.2020.132838 [↩]
37. Kumar, K., Bandyopadhyay, P., Singh, S., Dharodi, V. S., & Sen, A. (2023, March 9). Kelvin-Helmholtz instability in a compressible dust fluid flow. Nature News. https://www.nature.com/articles/s41598-023-30992-3 [↩]
38. Xisheng LUO, Zhigang ZHAI, Ting SI, Jiming YANG. Experimental study on the interfacial instability induced by shock waves[J]. Advances in Mechanics, 2014, 44(1): 201407. doi: 10.6052/1000-0992-14-028 [↩]
39. Remington, B. A., Park, H.-S., Casey, D. T., Cavallo, R. M., Clark, D. S., Huntington, C. M., Kalantar, D. H., Kuranz, C. C., Miles, A. R., Nagel, S. R., Raman, K. S., Wehrenberg, C. E., & Smalyuk, V. A. (2018). Rayleigh–Taylor instabilities in high-energy density settings on the National Ignition Facility. Proceedings of the National Academy of Sciences, 116(37), 18233–18238. https://doi.org/10.1073/pnas.1717236115 [↩]
40. Tabak, M., Hinkel, D., Atzeni, S., Campbell, E. M., & Tanaka, K. (2006). Fast ignition: Overview and background. Fusion Science and Technology, 49(3), 254–277. https://doi.org/10.13182/fst49-3-254 [↩]
41. Tabak, M., Hammer, J., Glinsky, M. E., Kruer, W. L., Wilks, S. C., Woodworth, J., Campbell, E. M., Perry, M. D., & Mason, R. J. (1994). Ignition and high gain with ultrapowerful lasers*. Physics of Plasmas, 1(5), 1626–1634. https://doi.org/10.1063/1.870664 [↩]
42. Barlow, D., Goffrey, T., Bennett, K., Scott, R. H., Glize, K., Theobald, W., Anderson, K., Solodov, A. A., Rosenberg, M. J., Hohenberger, M., Woolsey, N. C., Bradford, P., Khan, M., & Arber, T. D. (2022). Role of hot electrons in shock ignition constrained by experiment at the National Ignition Facility. Physics of Plasmas, 29(8). https://doi.org/10.1063/5.0097080 [↩]
43. Zhang Zhan-Wen, Qi Xiao-Bo, & Li Bo. (2012). Properties and fabrication status of capsules for ignition targets in inertial confinement fusion experiments. Acta Physica Sinica, 61(14), 145204. https://doi.org/10.7498/aps.61.145204 [↩] [↩] [↩]
44. Lawrence Livermore National Laboratory achieves fusion ignition. LLNL. https://www.llnl.gov/archive/news/lawrence-livermore-national-laboratory-achieves-fusion-ignition [↩]