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14 декабря, 2021
An ITER TBM will experience not a constant heat load but a cyclic heat load behavior due to burn pulses of the plasma. Dalle Donne eta/.11 performed exploratory thermal cycling experiments with densified Li4SiO4 pebble beds in a horizontal tube (D = 20mm, L = 110mm). After about 500 cycles (350-600°C), fractions of 1.8% and 3.5 wt% of broken pebbles in two measurement campaigns were found. The pressure drop in the helium purge flow was found to saturate after some hundred cycles, indicating that no further pebble fragmentation occurred. Thermal shock is not considered an issue for ceramic breeder pebbles; the experiments showed that pebbles only fail for dT/dt>60°Cs~ that is, values much larger than expected in the blanket.
Cycles of UCTs up to 4 MPa at ambient temperatures lead to negligible plastic deformations in the Li4SiO4 and Li2TiO3 pebble beds. The residual compaction is likely to be due to pebble relocation or pebble cracking. Multiple 6 MPa compression cycles at 750 °C led to irreversible strains of ^3.5% and 4% for Li2TiO3 and Li4SiO4 pebble beds, respectively. When 4 MPa compression cycles are performed on an Li4SiO4 pebble bed at 840 °C, the creep strains reach values of 6%. In these last tests, the influence of thermal creep is clearly visible.110
Similar cyclic compression tests on Japanese Li2TiO3 pebble beds reveal a compression ‘equilibrium’ of ~1.5% only after several cycles of 10 MPa at 400 “C.1 2 Performing these tests at 600 °C gives lower strain values in the pebble bed, likely due to the increased compaction.1 This is in agreement
with the above-mentioned results.110
Several HCPB mock-up experiments have been performed in the HE-FUS3 facility at ENEA, Brasimone by Dell’Orco et a/.108,109,114 In the HELICHETTA and HELICA experiments, the thermomechanical behavior of Li4SiO4 or Li2TiO3 pebble beds under thermal cycling loads was investigated. The following larger HEXCALIBUR type experiments were characterized by two beryllium pebble beds and one ceramic breeder pebble bed in between. Nuclear heating was simulated by using electrically heated plates within the pebble beds.
In the HELICA mock-up tests, the thermal cycling of the pebble beds showed a saturation of the pebble-bed strains after ^30 cycles. The bed heights were then reduced by «4% and «1.5% for the Li4SiO4 and Li2TiO3 pebble beds, respectively. For constant power levels, the system did not change thermally with increasing cycle number. During demounting, submicron pulverized material was released, especially from the Li4SiO4 pebble beds, and pebble fragmentation was observed. An important objective of these experiments was the validation of pebble-bed thermomechanical models as outlined below.
To understand the effects of radiation on the performance of permeation barriers, we need to first examine how barriers work. For tritium to permeate through a material with or without a coating, the tritium must absorb on the surface, dissociate into atoms, dissolve into the material, diffuse through the material, and then recombine into molecules on the downstream side. In the simple case in which diffa — sion through the structural material is rate limiting, the permeation rate is controlled by the ratio of the permeability and the thickness of the pressure boundary (eqn [16]); as described earlier, the permeability is the product of the diffusivity and the solubility, which can be thought of as the velocity times capacity. These parameters are dependent on temperature, and should not be affected by radiation effects or nominal surface cracking. In the simple case of diffusion-limited permeation through the structural boundary, the experimental result determined in the laboratory cannot be extrapolated to the radiation environment.
Permeation barriers, by their basic nature, consist of a thin layer adhered to the structural material. The performance of barriers depends on the integrity of the barrier as well as the physical interaction of the barrier material with tritium. What is it about many barriers and how they operate that causes laboratory and reactor data to disagree? In their review, Hollenberg et al}15 considered these aspects of barriers and their performance in radiation, proposing three models that describe distinct physics of the interactions between tritium and the barrier material. The most basic model is the Composite Diffusion Model, in which hydrogen transport is diffusion — controlled in both the barrier and the base metal. The steady-state permeation rate (Q1) through a pressure boundary in this case is
Fb Fm
where A is the surface area of the boundary, and the subscripts B and M refer to the barrier and structural metal, respectively. Considering the intent of the barrier, the ratio tB/FB should be much larger than tM/FM, thus the permeation is controlled simply by the permeation through the barrier.
The second model proposed by Hollenberg et al. considers the barrier to be effectively impermeable to tritium and is called the Area Defect Model. In this case, hydrogen is transported through the metal, reaching the metal surface through a limited number of cracks or other defects in the barrier layer. The permeation rate for this case is
Qi = Ad— ppTT [23]
teff
where Ad is the area of the defects and teff is the effective distance the hydrogen isotope must traverse to reach the other side of the metal.
The third model proposed by Hollenberg et a/. is the Surface Desorption Model, in which case, permeation is controlled by the recombination rate of hydrogen isotope atoms into molecules on the back surface and the recombination-limited flux of tritium is described by eqn [19]. Surface desorption does not make sense by itself; as show, it is actually part of the Area Defect Model.
As reported by Hollenberg eta/.175 and as revealed by a review of the literature on barriers and oxides,196,223-225 the activation energy of permeation is generally not altered by the addition of the barrier layer onto the substrate. This means that, in practice, the permeation process itself is being controlled by the substrate, not the barrier, strongly supporting the Area Defect Model described earlier. In short, the barrier works simply by limiting the area of the metal exposed to the driving pressure.
Pisarev et a/.226 provide particularly intriguing insights into the effects of cracks on permeation barriers. Their report showed that permeation reduction for the Area Defect Model is difficult to achieve when the distance between defects is not larger than the combined thickness of the barrier and substrate. Inherent in this conclusion is the assumption that the dissociation rate at the defect is sufficiently fast to maintain the equilibrium concentration dictated by Sievert’s law. If this condition is not met, then the activation energy for the process would be that associated with the dissociation, and not that of permeation through the substrate. Thus, barriers that can provide a significant permeation reduction in the laboratory must be essentially defect free.
The physics of hydrogen transport in metals with permeation barriers can be further understood by examining the pressure dependence of permeation. As discussed earlier, diffusion-controlled permeation through metals is proportional to the square root of the hydrogen partial pressure. Perujo et a/.227 reported that the pressure dependence of permeation through MANET plasma sprayed with aluminum changed from the classic square root dependence to linear as the pressure was decreased below 20 000 Pa. Mcguire228 also noted the transition to near-linear pressure dependence in the pressure range from 200 to 1000 Pa. Linear pressure dependence is symptomatic of permeation limited by absorption or recombination. For example, if recombination limits permeation, the concentration of hydrogen in the metal will be almost constant and uniform, and it will be established by equilibrium at the upstream side of the pressure boundary. Thus, Sievert’s law (eqn [7]) can be substituted into eqn [24], leading to linear pressure dependence:
Jr = kTK2p tt [24]
While the same relationship will be found if the permeation is limited by absorption on the upstream surface, known values for the recombination-rate constant for MANET can explain the linear pressure dependence seen in permeation measurements.128 The conclusion is that a combination of the Area Defect Model and the Surface Desorption Model is needed to properly model permeation though barrier materials.
If barriers work by limiting the area available for the gas to contact the underlying metal surface, and possibly by creating low enough permeation to have recombination even further reduce the permeation, how does radiation affect this process? One possible answer is by increasing the porosity or cracking of the barrier. According to Arshak and Korostynska229 properties of metal oxide materials are directly or indirectly connected to the presence of defects, oxygen vacancies in particular. Oxygen vacancies are also known as color centers, and these color centers are stabilized by hydrogen trapped at the defects. The hydrogen can come from preexisting OH~ groups or from hydrogen isotopes migrating through the oxide, possibly increased by the enhanced electrical conductivity generated by the radiation damage and the oxygen vacancies. While cracking was not considered by Arshak and Korostynska, one can speculate that the radiation damage with increased oxygen vacancies and trapped hydrogen would lead to a more brittle oxide layer. In metals, lateral stress from hydrogen or helium trapping can lead to blisters.230 Without the required ductility to allow blistering, the oxide layer could experience significantly increased cracking. The cracking would then increase the area available for hydrogen to reach the metal surfaces.
4.18.2.1 Plasma Impurities and the Need for Graphite Materials
The fusion plasma is maintained through a combination of internal heating, (i. e., the 3.5 MeV helium nucleus from the D+T reaction) and externally, by means ofinduction, radio frequency waves, or neutral particle injection. Plasma heating is balanced by plasma-cooling mechanisms among which electromagnetic radiation dominates. In fully ionized plasma, the radiative cooling comes from the Bremsstrahlung that occurs when the energetic ions interact with the plasma electrons. A fraction of the electromagnetic radiation released from this interaction is lost from the plasma. The energy lost in this manner is significantly increased by low concentrations of impurities. The plasma power loss in the Bremsstrahlung channel, Pbrem, is determined through:
Pbrem(MWm~3) « 4.8 x 10-43 Z2NiNe TlJ2 / Z? N [2]
where Zi, Ni, Ne, and Tare the atomic number of the radiating species, their density, the electron density, and the plasma temperature, respectively. Clearly, from the linear dependence on the plasma impurity concentration, and the square dependence on the atomic mass of the impurity, the ideal PFMs comprise light elements that have a low tendency to erode and migrate into the plasma. Carbon and beryllium are two low atomic number elements commonly used in tokamaks. The next suitable element is aluminum, which would have almost a factor of five higher radiative loss on an atom-per-atom basis compared to carbon. On the same basis, molybdenum, which has been used in many tokamak experiments, has a radiative loss 49 times that of carbon, and tungsten 150 times the radiative loss of carbon. However,
this is based on the assumption that the same number of impurity atoms find their way into the plasma (i. e., Ni), which, as discussed later, is not the case.
Several authors have reviewed the properties of neutron-irradiated beryllium for fusion applications in the past.139-141 Neutron irradiation leads to complex changes in the microstructure, such as the radiation-induced change of volume in beryllium, which is dominated by the nucleation and growth of He bubbles.
There are two important pathways for gas production. One is the (n, 2n) reaction in which the 9Be is reduced to 8Be, which then splits into two 4He atoms. The second is the (n, a) reaction where the 9Be absorbs a neutron and then splits to form a 4He and a 6He. The 6He rapidly undergoes a p decay to become 6Li. The 6Li then reacts with a thermal neutron to produce 4He and 3H. These processes have been incorporated into the inventory code FISPACT,142 which is used (see, e. g., Forty et a/.143) to estimate the generation rates of gas and other reaction products in a tokamak.
Helium generation has significant effects on the properties of materials, especially at elevated temperatures. Helium is initially trapped within the beryllium lattice in submicroscopic clusters. At higher neutron fluence massive helium-bubble-induced swelling occurs, especially at elevated irradiation or postanneal temperatures. Because of the atomistic nature of the helium bubble nucleation and growth, porous beryllium microstructures, such as from powder metallurgy or plasma spray technology, were not found to be effective in releasing significant amounts of helium under fusion reactor conditions.2
The maximum neutron-induced damage and helium production expected in Be for ITER first — wall applications (fluence of 0.5MWam~) are ~1.4-1.7dpa and ~1500appm, respectively and the expected irradiation temperatures are in the range of 200-600 °C. The maximum temperature is on the surface of beryllium tile and depends on thickness and heat flux. Tritium production in beryllium is expected to be about 16 appm. Recently, Barabash et a/.144 have analyzed the specific effects of neutron — induced material property changes on ITER PFCs foreseen during ITER operation.
Typically, property changes induced by neutron irradiation are investigated by exposing samples/ mock-ups in fission reactors. However, the differences between the fission and fusion neutron spectra are important to interpret and predict the effects. The key difference is transmutation production, which needs to be considered for the correct prediction of the material performance.145 During irradiation in fission reactors, for example, the typical value of the ratio (appm He per dpa) is 100-250, whereas for a fusion neutron spectrum this value is ~1000. Depending on operational temperature, the dpa or He transmutation must be used as a reference neutron damage parameter. For beryllium, during low — temperature irradiation (<~300 °C) the dpa value must be considered. For high-temperature irradiation (more than ~500 °C), the He generation must be taken as the reference parameter.
A detailed discussion on this subject is beyond the scope ofthis review. We summarize only some ofthe main findings with emphasis on results for ITER relevant grades. Considerations of the effects of neutron irradiation of duplex Be/Cu alloy mock-ups are provided in Section 4.19.5.
Irradiation causes large changes in tensile properties of copper and copper alloys. Copper and copper alloys can be hardened or softened by irradiation, depending on the irradiation temperature and the amount of the cold work prior to irradiation. Irradiation hardening of copper and copper alloys due to defect cluster formation is significant at irradiation temperatures <300 °C. Irradiation softening occurs at irradiation temperatures >300 °C because of radiation-enhanced recrystallization and precipitate coarsening in PH copper alloys.
Low-temperature neutron irradiation of pure copper leads to development of a yield drop and significant hardening. Typical stress-strain behavior of pure copper and copper alloys irradiated to low doses at low temperatures is illustrated in Figure 8. The data of irradiated copper are from the work of Edwards eta/.,64 and the data of irradiated CuCrZr from Li et a/.14 Irradiation significantly changes the work hardening behavior of pure copper. Work hardening capability is progressively reduced with increasing doses. Appreciable work hardening still exists at the dose of 0.1 dpa. The effect of irradiation on the tensile behavior of copper alloys can be quite different. A complete loss of work hardening capability and
uniform elongation occurs at 0.14 dpa in neutron — irradiated CuCrZr in the prime-aged condition. Irradiation to 1.5 dpa further reduces the yield strength, and recovers some total elongation in CuCrZr.
The dose dependence of radiation hardening in copper at irradiation temperatures of 30-200 °C is summarized by Zinkle et a/., and shown in Figure 9.65’66 Radiation hardening in copper can be observed at a dose as low as 0.0001 dpa. The yield stress increases dramatically with increasing dose and saturates at ^0.1 dpa. Significant radiation hardening is accompanied by loss of strain hardening capabilities, resulting in prompt necking upon yielding.
The temperature dependence of radiation hardening ofpure copper at different irradiation temperatures was summarized and discussed by Fabritsiev and Pokrovsky.67 The radiation hardening decreases with increasing irradiation temperature in copper. The magnitude of radiation hardening is ^200 MPa at 80 °C, while only ^40 MPa at 300 °C at a dose of 0.1 dpa. Annealing at temperatures higher than 0.4 Tm can effectively reduce the defect cluster density in copper. Annealing at 300 °C for 50 h after irradiation of copper to 0.01-0.3 dpa at 100 °C and annealing at 350 °C for 10 h after irradiation of CuCrZr IG and GlidCop Al25 IG to 0.4 dpa at 150 °C can essentially recover the ductility of the copper and copper alloys.68,69 However, postirradiation
Figure 9 Radiation hardening in copper. Reproduced from Zinkle, S. J.; Gibson, L. T. Fusion Materials Semi-annual Progress Report; DOE/ER-0313/27; Oak Ridge National Laboratory, 1999; p 163.
annealing also reduces the critical stress for flow localization in pure copper.70
Irradiation creates a large increase in strength and decrease in ductility in copper alloys for irradiation temperatures below 300 °C. The strengthening effect decreases with increasing temperature. The crossover to radiation softening occurs at approximately 300 °C. The radiation softening effect in CuAl25 alloy is not as strong as for CuCrZr alloy where precipitate stability may be an issue. Neutron-irradiated copper alloys exhibit low uniform elongation after low-dose, low-temperature irradiation. The uniform elongation is recovered to near unirradiated values at 300 °C. Figure 10 compiles the yield strength data for PH CuCrZr and DS copper alloys (CuAl 25, CuAl15, MAGT 0.2) as a function of dose for the irradiation temperature of ^100 °C.14,71 Both alloys show significant radiation hardening at low doses and an apparent saturation at ~0.1 dpa. Irradiation-induced hardening is accompanied by the loss of strain hardening capability and a complete loss of uniform elongation, while the total elongation remains on the level of ~10% for doses up to 2.5 dpa for CuCrZr.
The strain rate dependence of tensile properties in neutron-irradiated CuCrZr was investigated at room temperature by Li eta/.14 The strain rate sensitivity is small at room temperature in unirradiated CuCrZr. The measured strain rate sensitivity parameter, m, is <0.01 for CuCrZr. The strain rate sensitivity parameter increased to ^0.02 in CuCrZr after neutron irradiation to 1.5 dpa. Zinkle eta/.65 observed a small strain rate dependence of tensile strength in GlidCop Al15 and MAGT 0.2 neutron irradiated to ^13 dpa at 200 °C with m ~ 0.02 for GlidCop
Al15 and m < 0.01 for MAGT 0.2. In general, the strain rate and temperature dependence of flow stresses is small in fcc metals.
Oak Ridge National Laboratory (ORNL) performed several PTS tests as part of the HSST program. One test (TSE-7) was performed in the 1980s on a pressure vessel (steel A508 Cl. 2) with 152-mm wall thick — ness.31 The initial crack shape was semielliptic, but the form changed in the test to something very irregular, which complicated the analysis of this test. The material was characterized by Kjc tests made in the transition region with 25.4 mm C(T) specimens. In the PTS test, neither KI nor temperature was constant along the crack length. Due to subsequent inaccuracies in the original KI data, the Master Curve reanal — ysis30 was performed using the apparent maximum
Kj and the local temperature of the crack tip area. The crack length 2 c = 37 mm was used as the effective crack length. Due to the crack shape changes in the test, only the first initiation was included in the Master Curve analysis. The estimated stress intensity in the first initiation is shown together with the fracture toughness data adjusted to a crack length of 37mm in Figure 25. Despite the inaccuracies, the result of the test is also consistent with the measured fracture toughness data.
Only a few types of microstructures have been studied until today, preventing clear conclusions regarding their suitability for reactor application. Both for pebble-bed and pellet/block type designs, significant opportunities still exist to tailor stoichiometric composition, grain size, and porosity shape and size as well as surface treatments, coatings, and other pre-conditioning treatments.
Though some high lithium burnup samples have been achieved in experimental programs, the findings are not yet conclusive as to whether the
ceramic still functions adequately under normal operation, and whether interaction with the blanket structure satisfies, for example, future power plant safety requirements.
Few data were obtained in fast breeder experiments; the influence of fast neutron damage on the integrity and functionality of the breeder ceramics is yet to be addressed, in particular for the newly developed pebble types and compositions.
The effect of long-term exposure in a high radiation environment, causing damage, induced swelling, with increasing burnup, may also affect the vaporization behavior and even induce lithium transport within the breeder area.
4.15.8.4 Effects of Transients and Off-Normal Conditions
Though work has been done already on thermal cycling of pebble beds, there is uncertainty with regard to the effects of disruption and electromagnetic (EM) loads on, for example, pebble relocation, fragment relocation, and ratcheting in case of inclined or vertical beds. Specific attention is required on the change of heat transfer properties and free flow of purge gas.
4.17.4.1 Thermal Shock Resistance
Tungsten-armored PFCs will be subjected to different types of heat fluxes dependent on their field of application (see Section 4.17.2). Among others, this includes thermal transient loads (e. g., ELMs and disruptions). The behavior of the material under these conditions, that is, the combination of cyclic steady state and transient heat loads, is a key factor that has to be considered for the selection of a suitable grade of W.
The machines simulating these operational conditions are electron and ion beam facilities, quasistationary plasma accelerators, plasma guns, and high-energy lasers. A most critical issue is the comparability of such simulations. Therefore, a round robin test involving some representative facilities was made for investigating the influence of the different time regimes and different power density levels. The results showed that when compared on the basis of a heat flux parameter P (MW m~2 s1/2), which is directly proportional to the temperature increase, the cracking and melting thresholds are almost identical. This permits a direct transfer of the qualitative results obtained in any of these facilities.161 In contrast, quantitative results representative of the operational conditions in large fusion devices can only be obtained when the loads are applied in the desired time range. The reason for this is the heat penetration depth and the related stress field that is produced, which influences crack and melting depth.
There are several parameters influencing the thermal shock behavior of tungsten that will be discussed in the following sections for the different materials under disruption and ELM-like loads.
When a relatively high-energy impacting particle transfers energy to a near-surface carbon atom in an amount sufficient to overcome the lattice bond energy or surface binding energy, some carbon atoms may be displaced and these may move in a direction defined by the angle between their path and the initial path of the impacting atom. Analogous to striking a billiard ball, this angle must be between 0° and 90°. The energy imparted to the displaced atom follows that given in eqn [6]. For a relatively high-energy atom striking a surface normally, the recoiling atom cannot be sputtered from the surface. However, in off-normal impact or displacement cascade events from fusion neutrons that occur near the surface, some fraction of atoms will be emitted (physically sputtered) from the graphite surface. The amount of material lost from the surface is defined by the sputtering yield (Y), which is the number of target PFM atoms emitted per plasma ion impacting the surface. From eqn [6], the energy transferred to a target PFM atom, which is directly
related to the erosion yield, is a strong function of the impacting particle mass and the mass of the material being sputtered. The impact angle also has a large effect on the number of atoms that receive adequate kinetic energy normal to the PFM surface to be physically sputtered. The plasma ions travel along the magnetic field lines that are at a shallow (grazing) angle with the PFM, typically 1-5°, though the ion impact angle will be modified by surface potentials and collisional processes.81
The quantitative effect of the mass, energy, and angle of impact on the sputter yield of impacting deuterium ions is shown in Figure 26(a) and 26(b). As the kinetic energy of deuterium increases, the total amount of energy transferred to the target atoms increases, and the average amount of energy per collision results in greater erosion. From Figure 26(a), it may be seen that the physical sputtering yield of light target atoms is considerably greater than that for the heavy atoms, primarily due to the reduced impact energy required to overcome the displacement energy of the higher target atoms. For example, in purely kinetic terms, approximately 20eVis required to displace an atom of carbon from the surface, while 220 eV is required for an atom of tungsten. In the sub-keV energy range of plasma fuels, the high yield materials are therefore carbon and beryllium. As the impacting ion energy increases, the sputtering yield for all materials decreases as the depth of interaction of
Figure 26 Sputtering yields for plasma-facing material atoms of various candidate materials (a); and as a function of angle of incidence for various graphite materials. |
the impacting ion becomes too great for displaced atoms to back scatter to the surface. In the case of graphite, the majority of the sputtered material comes from the top few atomic layers.82
With the correct combination of incident energy and target mass, it is possible for the sputtering yield to exceed unity, that is, more than one atom leaves the surface for every impacting particle. This quickly leads to what is called the catastrophic ‘carbon bloom,’ that is, the self-accelerating sputtering of carbon. As can be seen in Figure 26(b), this problem is the worst for carbon self-impacts at grazing angles to the surface.
4.19.6.2.1 Safety issues in ITER
4.19.6.2.1.1 In-vessel tritium inventory
Estimates of the tritium inventory and of permeation in the PFCs of a magnetic fusion device are important for assessing the radiological hazards from routine operation and from potential accidents, for the design of the water detritiation system, and for predicting the tritium supply requirements. In addition, these estimates have contributed to the decisions involving the choice of different armor materials in ITER options, which have a strong impact on tritium retention. In spite of the experimental and modeling progress which has taken place in the recent past, understanding of the subject of tritium-wall interactions is still far from complete and quantification of the tritium inventory in ITER is highly uncertain. The retention and permeation of implanted tritium in ITER PFCs have been widely studied in the past (see Section 4.19.3 and the example of calculations found elsewhere).9,187-189 On the basis of the results of these calculations, it can be concluded that the inventory of tritium in the beryllium first wall of a device like ITER, due to implantation, diffusion, trapping, and neutron-induced transmutation, will be on the order of 100 g rather than the kilogram quantities estimated previously70,100 and most of that will come from neutron-induced transmutations in the Be itself.
The dominant process for long-term retention of tritium in beryllium for ITER is expected to be
codeposition (see Section 4.19.3.2.2) with eroded wall material (i. e., the incorporation of tritium in the deposited layers where impurity atoms or molecules are deposited together with eroded material and a flux of energetic or thermal atoms). The inventory of this potentially volatile tritium must be kept as low as reasonably achievable (~ 1 kg tritium), in order to minimize the impact on the environment in case of an accidental release, in particular to avoid the evacuation of the neighboring population.
The rate of formation of the codeposited material depends on the energy of the incident particles and on the substrate temperature during the deposition. In ITER, the total amount of tritium trapped in the codeposited layers will strongly depend on whether carbon is retained in the divertor during DT operation. But even in a full metal ITER configuration (e. g., with Be wall and W divertor) there is evidence for potential tritium accumulation for ITER in deposited Be layers.9 In contrast to carbon, tritium codeposition in beryllium layers is expected to be released at relatively low temperature and there are provisions to periodically bake the divertor in ITER at 350 °C to release tritium trapped in the codeposited Be layers (see Section 4.19.3.2.2).