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| Fig. 1: Deuterium-Tritium nuclear fusion reaction used for energy generation purposes. (Source: Wikimedia Commons) |
Fusion is a nuclear reaction involving two light nuclei that combine to form a heavier nucleus accompanied by energy released mostly in the form of kinetic energy imbued to neutrons emitted during the process. Fusion reactions present an opportunity for renewable energy generation which does not produce radioactive waste at the same scale as fission reactors. The most feasible fusion reaction for energy generation is the deuterium-tritium reaction, shown in Fig. 1, which is given by
For a fusion reactor to sustain a stable plasma conducive for positive net energy gain, the plasma produced from the deuterium-tritium fuel must have sufficiently high temperature and pressure. An additional parameter used to describe plasmas is the energy loss time, τE, which indicates the time-scale over which the system loses energy to its environment. The figure of merit used to gauge fusion reactor design is the triple-product, a value derived from the product of the plasma particle density (n), temperature (T), and energy loss time (τE). [1] Lawson's Criterion establishes a minimum triple-product for DT ignition to be achieved, which is given by
Note that the Lawson Criteria shown above is calculated at the optimal temperature scale where the triple-product is minimized, but corresponds to an extremely high temperature that may be infeasible by real experiments. Given the coulomb barrier experienced by reactant nuclei and low probability of interaction, plasmas must be contained at sufficiently high temperatures and pressures for a sufficiently long time. Multiple strategies have been proposed to achieve ignition in fusion reactors, the most prominent being magnetic confinement fusion (MCF) and inertial confinement fusion (ICF). Inertial confinement fusion exploits high-energy pulsed lasers to achieve a targeted compressed fuel density of 1029 m-3 - 1031 m-3, but also show extremely low confinement time (< 10-8 s). [2] In contrast, MCF operates on much lower particle density (~1020 m-3) but is able to extend the confinement time on the order of seconds. [1,3] The most common MCF device is the tokamak, a torus-shaped structure using magnetic fields to contain plasma. These two confinement methods take very different approaches to achieve ignition, but their success relies on engineering of the reactor design. Here, we focus specifically on the use of superconductors for MCF.
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| Fig. 2: The toroidal geometry produces a magnetic field that moves along the circumference of the reactor radius. The charged particles within move helically, as shown by the current density J. [3,4] (Source: Wikimedia Commons) |
Magnetic confinement fusion is a reactor strategy that relies on strong magnetic fields to contain plasma and prevent contact with reactor walls. In the context of tokamaks, there are two separate magnetic fields to consider: the toroidal field and the poloidal field. The toroidal field, which is primarily responsible for plasma confinement, is constructed via a series of conducting coils arranged around the torus-shaped vessel comprising the tokamak. The resulting field lines run along the circumference of the torus, as demonstrated in Fig. 2. Consequently, the charged particles within the plasma follow a helical trajectory about the axis of the magnetic field lines. [3] The magnitude of the toroidal magnetic field produced by the toroidal coils is given by
Where μ is the magnetic permeability, N is the number of turns in the torus, I is the current running through the circuit, and R is the radius from the plasma axis to the center of the torus. [3,4] The strength of the magnetic field depends on how much current can be supplied to the coils.
The poloidal field is generated from the charged motion of plasma currents and wraps around the walls of the torus. The poloidal field provides stability to optimize plasma confinement.
A good candidate material must have a high current-carrying capacity. Superconductors are suitable candidates given its dissipationless current carrying capacity at high magnetic fields. Design criteria for future fusion reactors require superconducting coils to operate at 100 kA under 16-20 T magnetic fields. [5,6] We will discuss in depth the relevant superconducting parameters necessary to meet the design criteria for magnetic fusion reactors.
Superconductivity is a state of matter characterized by zero electrical resistance when cooled below its transition temperature, TC. In addition, superconductors expel magnetic fields from the materials interior, a phenomenon known as the Meissner Effect, which is demonstrated in Fig. 3. In type II superconductors, increasing the strength of an applied magnetic field allows for partial penetration of quantized flux lines, resulting in the suppression of the superconducting state. [7] The magnetic field strength that eliminates superconductivity is known as the upper critical field, HC2. The upper critical field is temperature-dependent and HC2 → 0 as T → TC. Additionally, the upper critical field varies with the field's orientation relative to the material's crystal axes (parallel H ∥ c or perpendicular H ⊥ c). Finally, superconductors can support a maximum critical current density, JC, before transitioning into the normal state. The critical current is also temperature dependent and varies with applied magnetic fields where JC → 0 as H → HC2. Hence, the relevant parameters we focus on are the transition temperature (TC), upper critical field (HC2), and the critical current density (JC).
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| Fig. 3: The Meissner Effect in Type II Superconductors. Magnetic flux lines begin to penetrate the material at the lower critical field, HC1. Superconductivity is killed at the upper critical field, HC2. [7] (Source: Wikimedia Commons) |
The International Tokamak Experimental Rector (ITER) is a magnetic confinement reactor whose construction includes superconducting coils to generate magnetic fields. The toroidal field (TF) coil system consists of Nb3Sn, an intermetallic compound that becomes superconducting at TC = 18 K (as seen in Fig. 4), and has upper-critical field > 20 T when cooled to 4K. [8] The coils are expected to operate at 4.5 K and carry a current of 68 kA to generate a peak field of 11.8 T. [9] We see that superconductors are being developed for magnetic confinement fusion, however further advances in superconducting technology can improve its use in such reactors.
The cuprates are a family of copper-based high-temperature superconductors (HTS) that are promising candidates for use in magnetic fusion reactors. These materials have been touted for their high transition temperatures and current-carrying capacity despite large external magnetic fields. Notably, REBCO (rare-earth barium copper oxide) superconductors are known to have superconducting transition temperatures exceeding the boiling point of liquid nitrogen (77°K) and expected critical current densities on the order of kA/mm2 when exposed to 15-20 T magnetic field. [1,3] Fig. 4 shows a timeline of discovered superconductors and their associated transition temperatures, with the cuprates labelled in light blue diamonds. Given the brittleness of REBCO materials, manufacturing wires is exceedingly difficult. However, REBCO tapes synthesized via various thin film deposition methods onto metallic substrates have presented a pathway towards greater commercialization of HTS. These superconducting tapes have become commercially available from companies including American Superconductor Corporation (ASMC) and SuperPower. [6] Hence, we are interested in whether these superconducting tapes are able to retain their electrical transport properties against a fusion environment for a sufficiently long lifetime. Specifically, we wish to determine whether its superconducting properties remain robust against the effects of high-energy neutron fluence.
We will explore the effects of high-energy neutron fluence on the superconducting properties of REBCO. Note that fluence is a measure of the total number of neutrons passing through a given area, and can be thought of as the total neutron flux integrated over some exposure time. The neutron irradiation studies presented here make use of TRIGA Mark II reactor in Vienna, whose distribution of neutron energies have been determined in previous studies. [10] The neutron energy spectrum can be categorized between thermal neutrons, whose kinetic energy is on the order of eV, and fast neutrons, whose kinetic energy is on the order of MeV. The TRIGA Mark II offers a fast neutron flux density of ~7.6 × 1016 m-2 s-1, and a total flux density of ~2.1 × 1017 m-2 s-1.
We first consider the effects of high energy neutrons on the zero-field superconducting transition temperature, TC (H = 0). Experimental studies have consistently shown a negative linear relationship between the transition temperature and the fast-neutron fluence; indicating a steady degradation of superconductivity with greater neutron irradiation. [11] The reduction in transition temperature is attributed to greater impurity scattering from greater defect densities. [12] In the case of YBCO (Yttria-based), which has unirradiated TC (H = 0) = 92°K, the transition temperature has been shown to degrade by approximately 2-3°K per 1022 m-2 of fast neutron fluence. Given that future MCF reactors will operate with fast-neutron fluence on the order of 1022 m-2, the superconducting temperature remains reasonably high for potential applications in energy generation.
We now consider the effect of fast-neutron fluence on the critical current density, specifically within the expected magnetic field strength produced within fusion reactors at 15-20 T. The effect of neutron irradiation on the critical current is not monotonic; rather the critical current initially increases with neutron fluence, reaches a maximal value and subsequently begins to degrade. [13] The initial rise in critical current is attributed to a phenomenon known as flux pinning where microstructural defects prevent the movement of quantized flux lines, helping to preserve the superconducting state. This phenomenon has been shown in both YBCO and GdBCO tapes where the critical current is maximized with a fast-neutron fluence of ~ 2 x 1022 m-2. When tested at 30°K with a perpendicular magnetic field of 15 T, these tapes have shown a critical current density as high as a few 10 kA/mm2. [13] These tapes demonstrate a large current carrying capacity at sufficiently large magnetic fields, given that the superconductor is cooled to a low enough temperature. To make superconductivity more robust to the reactor environment, defect engineering has capitalized on the flux pinning phenomenon to further enhance the critical current. For example, researchers have introduced BaZrO3 (BZO) nanoparticles to enhance the critical current in REBCO tapes. [14]
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| Fig. 4: Plot of discovered superconductors since 1900, along with their respective transition temperatures. The HTS cuprates are labelled in light blue diamonds. [18] (Source: Wikimedia Commons) |
Another complication is the effect of mechanical strain on the performance of REBCO tapes. Mechanical strain may originate during the construction of coil windings in tokamaks and stellarators. REBCO tapes tested at 4.2°K and experiencing a field of 15 T have shown minimal change in its critical current under both tensile and compressive strain. Specifically, it has been shown that REBCO tapes under 0.7% of tensile/compressive strain lose a maximum of 5% of their unstrained critical current. [15] The loss in critical current was also shown to be reversible. While we don't expect REBCO tapes to experience extreme levels of strain, it is important to verify that their use in various MCF reactor designs will not significantly impact their performance.
Superconducting magnets using REBCO tapes have been under development for the past decade. In 2016, Brookhaven National Lab (BNL) demonstrated a 15 T HTS coil using REBCO tapes. This magnet operated with an operational current of 285 A at 4.2°K. [16] While REBCO tapes show promise in MCF reactors, there remain obstacles to greater use. While REBCO superconductors all have a transition temperature above the boiling point of liquid nitrogen, these materials must still be cooled down below 30°K to obtain sufficient critical current at high magnetic fields. The cryogenic cooling cost remains an obstacle for all uses of superconductors in MCF reactors. Additionally, REBCO superconductors are quaternary complex oxides with non-trivial synthesis processes. One challenge includes non-uniformity in critical current over extended lengths of REBCO tapes of several hundred meters. [6] REBCO superconductors are also significantly more expensive to synthesize compared with traditional semiconductor and metallic structures. The cost of running current through REBCO is > $100 per kA m, large in comparison to low-temperature superconductors including NbSn which costs > $10 per kA m. [17] In conclusion, while REBCO has been studied for use in MCF reactors, further development in their synthesis and refinement in their properties are needed for their use in future fusion reactors.
© Martin Gonzalez. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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