From ffec24305c1e4bc234ee6306c7b93c8d53c40342 Mon Sep 17 00:00:00 2001 From: RemDelaporteMathurin Date: Thu, 21 Jul 2022 00:10:42 +0200 Subject: [PATCH 1/6] added remarks --- chapters/abstract.tex | 7 ++--- chapters/chapter1/intro.tex | 31 ++++++++++--------- .../analytical_verification.tex | 2 +- chapters/chapter3/monoblocks.tex | 5 +-- .../chapter3/monoblocks/parametric_study.tex | 2 +- chapters/chapter4/divertor.tex | 10 +++--- .../Influence_on_H_transport.tex | 4 +-- .../direct_implantation.tex | 4 +-- .../indirect_implantation.tex | 12 +++---- .../He_transport_in_PFCs/introduction.tex | 3 +- chapters/chapter5/he_transport_in_pfcs.tex | 2 +- chapters/conclusion.tex | 11 ++++--- chapters/demo_monoblock.tex | 2 +- chapters/introduction.tex | 8 ++--- glossary.tex | 12 +++---- 15 files changed, 59 insertions(+), 56 deletions(-) diff --git a/chapters/abstract.tex b/chapters/abstract.tex index 786e93e..3fbf10e 100644 --- a/chapters/abstract.tex +++ b/chapters/abstract.tex @@ -5,17 +5,16 @@ \chapter*{Abstract} As a radioactive isotope of hydrogen, tritium can represent a nuclear safety hazard and its inventory in the reactors materials must be controlled. In ITER, the tritium in-vessel safety limit is \SI{700}{g}. -The tritium inventory of the ITER divertor was numerically estimated. -To this end, the FESTIM code was developed to simulate hydrogen transport in tungsten monoblocks. +The tritium inventory of the ITER divertor was numerically estimated with the FESTIM code, which was developed to simulate hydrogen transport in tungsten monoblocks. A parametric study was performed varying the exposure conditions (surface temperature and surface hydrogen concentration) and a behaviour law was extracted. This behaviour law provided a rapid way of estimating a monoblock inventory for a given exposure time and for given surface concentration and temperature. This behaviour law was then used and interfaced with output data from the edge-plasma code SOLPS-ITER in order to estimate the hydrogen inventory of the whole ITER divertor. Under conservative assumptions, the total hydrogen inventory (deuterium and tritium) was found to be well below the ITER tritium safety limit, reaching $\approx \SI{14}{g}$ after 25 000 pulses of \SI{400}{s}. To investigate the influence of helium exposure on these results, a helium bubble growth model was developed. -The results of this helium growth model were in good aggreement to published numerical results and experimental observations. +The results of this helium growth model were in good aggreement with published numerical results and experimental observations. A parametric study was performed to investigate the influence of exposure conditions on the bubbles density and size. To investigate the influence of helium bubbles on hydrogen transport, deuterium TDS experiments of tungten pre-damaged with helium were then reproduced. The distribution of bubbles density and size was computed using this helium bubble growth model and the results were used in FESTIM simulations. -It was found that exposing tungsten to helium could potentially reduce the hydrogen inventory by saturating the defects. +It was found that exposing tungsten to helium could potentially reduce the hydrogen inventory by saturating defects, making it impossible for hydrogen to get trapped. Moreover, the effect of helium bubbles (creation of additional traps for hydrogen) is limited to the near surface region (small compared to the monoblock's scale) diff --git a/chapters/chapter1/intro.tex b/chapters/chapter1/intro.tex index 2260fa4..804d4b4 100644 --- a/chapters/chapter1/intro.tex +++ b/chapters/chapter1/intro.tex @@ -30,7 +30,7 @@ \section{Thermonuclear fusion} This Coulomb barrier increases with the charge of the nuclei (i.e.\ the number of protons). This means that the nuclei must collide with a high enough velocity. At the atomistic scale, the velocity $v_\mathrm{th}$ is a function of temperature (see \refeq{thermal velocity}). -This is one of the reasons why the probability of a fusion reaction (called cross-section) is temperature dependent. +This is one of the reasons why the probability of a fusion reaction is temperature dependent. \begin{equation} v_\mathrm{th} = \sqrt{\frac{k_B T}{m}} @@ -48,7 +48,7 @@ \section{Thermonuclear fusion} Hydrogen, as the lightest element, has the lowest fusion temperature. It is also the most abundant element on Earth (although bond to other elements). -Depending on which hydrogen \gls{isotope} is used, different fusion reactions are possible (see Equations \refeq{fusion reactions}) \cite{forrest_fendl-3_2012}. +Depending on which hydrogen \gls{isotope} is used, different fusion reactions are possible (see \refeq{fusion reactions}) \sidecite{forrest_fendl-3_2012}. \begin{subequations} \begin{equation} @@ -75,7 +75,7 @@ \section{Thermonuclear fusion} Each of these reactions has a different cross-section (measure of the reaction probability). The \gls{D}-\gls{T} reaction is the one with the highest cross-section at `low` temperature (see \reffig{fusion cross sections}). This is the reason why this reaction has been the focus of nuclear fusion for decades. -More recently, private companies have started experimenting with more exotic reactions like proton-boron (TAE Technologies) or $^2$H-$^3$He (Helion Energy). +More recently, private companies have started experimenting with more exotic reactions like proton-boron (TAE Technologies) or \gls{D}-$^3$He (Helion Energy). % \begin{figure} [h] % \centering @@ -332,7 +332,7 @@ \subsection{Breeding} Due to its radioactive nature, tritium is very rare on Earth. The current reserve of tritium in the world is a few dozens of kilograms. It is naturally produced by interaction of cosmic rays with the nitrogen in the atmosphere (\SI{0.2}{kg} per year). -Tritium is however produced in larger quantities in fission \gls{candu} reactors as a by-product (\SI{130}{g} per year per \gls{candu} reactor \sidecite{ni_tritium_2013}). +Tritium is however produced in larger quantities in fission \glspl{candu} as a by-product (\SI{130}{g} per year per \gls{candu} reactor \sidecite{ni_tritium_2013}). \acrshort{iter} itself will consume around \SI{18}{kg} of tritium over the duration of its operation \sidecite{glugla_iter_2007}, which represent a yearly consumption of \SI{0.9}{kg} for a 20-year lifetime. A \SI{800}{MWe} DEMO-type commercial fusion reactor would burn around \SI{300}{g} of tritium per day ($\approx \SI{100}{kg}$ a year). @@ -364,12 +364,12 @@ \subsection{Breeding} \text{n} + \text{\textsuperscript{7}Li} \ \ &\xrightarrow{} \ \ \text{\textsuperscript{3}H} + \alpha + \text{n}' - \SI{2.5}{MeV} \end{align} -Several \glspl{breeding blanket} designs have been proposed divided in three main categories: ceramic concepts, liquid metal concepts, and molten-salts concepts. +Several \glspl{breeding blanket} designs have been proposed and divided in three main categories: ceramic concepts, liquid metal concepts, and molten-salts concepts. All designs differ in the choice of tritium breeder, coolant and geometry. The European candidates for \glspl{breeding blanket} in DEMO are the \gls{wcll} \sidecite{aubert_design_2020, del_nevo_recent_2019}, the \gls{hcpb} \sidecite{hernandez_overview_2018, hernandez_new_2017,pereslavtsev_neutronic_2017}, the \gls{hcll} \sidecite{aubert_status_2018,jaboulay_nuclear_2017} and the \gls{dcll} \sidecite{urgorri_tritium_2017, palermo_neutronic_2015} \sidecite{federici_overview_2019}. -The \gls{tbr} is defined by the number of tritium atoms produced by generated neutrons. +The \gls{tbr} is defined as the number of tritium atoms produced per generated neutrons. In order to ensure tritium self-sufficiency, the \gls{tbr} of the blanket must be greater than or equal to one \sidecite{abdou_blanketfirst_2015}. A \gls{tbr} greater than one can only be obtained by neutron multiplication with lead or \gls{Be}. @@ -476,7 +476,7 @@ \subsubsection{Hydrogen} \labfig{helium3 neutron capture cross section} \end{figure} -Finally, interactions of lithium with neutrons represent a major source of hydrogen in tritium \glspl{breeding blanket} \sidecite{dark_influence_2021}. +Finally, interactions of lithium with neutrons represent a major source of tritium in tritium \glspl{breeding blanket} \sidecite{dark_influence_2021}. \subsubsection{Helium}\labsec{sources of helium} Helium is the product of the fusion reaction (see \refeq{fusion reactions}). @@ -515,7 +515,7 @@ \subsubsection{Diffusion} \begin{equation} D = D_0 \exp{(-E_D/k_B T)} \end{equation} -where $E_D$ is expressed in \si{eV}, $T$ is the temperature in \si{K}, $k_B$ is the Boltzmann constant in \si{eV.K^{-1}}. +where $E_D$ is expressed in \si{eV}, $T$ is the temperature in \si{K}, $k_B = \SI{8.617e-5}{eV.K^{-1}}$ is the Boltzmann constant. \Gls{diffusion} can also be assisted by temperature gradients (called the \emph{\gls{Soret effect}} or \emph{\gls{thermophoresis}}) \sidecite{martinez_thermal_2021, hodille_estimation_2017, longhurst_soret_1985} or hydrostatic pressure gradients. The tungsten property to simulate the \gls{Soret effect} (Soret coefficient or heat of transport) is currently missing from literature (for hydrogen). @@ -585,7 +585,7 @@ \subsubsection{Trapping at defects} where $E_k$ is the \gls{trapping} energy in \si{eV}, $k_B$ is the Boltzmann constant in \si{eV.K^{-1}}, $T$ is the temperature in \si{K}, $E_\mathrm{b}$ is the binding energy of the particle with the defect and $E_p = E_\mathrm{b} + E_k$ is the \gls{detrapping} energy. A common assumption is that $E_k = E_D$. -Each rate therefore has two parameters: the pre-activation factor and the activation energy. +Each rate therefore has two parameters: the pre-exponential factor and the activation energy. These parameters can be identified from fitting \gls{tds} experiments. \gls{tds} experiments consist in loading a metal sample with the studied species (e.g.\ \gls{H} or \gls{He}) and heat it at different temperatures with a well controlled temperature ramp (e.g.\ \SI{1}{K.s^{-1}}, \SI{10}{K.s^{-1}}...) while measuring the desorption flux. This results in a spectrum which typically has one or several desorption peaks corresponding to different traps (see \reffig{TDS example ialovega}). @@ -616,12 +616,12 @@ \subsubsection{Trapping at defects} \end{figure*} Defects can either be pre-existent in the material (sometimes called \textit{intrinsic} defects): impurities, grain boundaries, etc. -They can also be created from external factors (\textit{extrinsic} defects) like particle bombardment (ions, neutrons) \sidecite{ogorodnikova_deuterium_2003} or mechanical stress \sidecite{benannoune_multidimensional_2020}. +They can also be caused by external factors (\textit{extrinsic} defects) like particle bombardment (ions, neutrons) \sidecite{ogorodnikova_deuterium_2003} or mechanical stress \sidecite{benannoune_multidimensional_2020}. \subsubsection{Surface dissolution} When a surface is in contact with a gas, molecular species (e.g.\ $\text{H}_2$, $\text{T}_2$, $\text{HD}$...) can dissociate into mono-atomic species. -After their dissociation, the atomic particles can be adsorbed on the surface (on adsorption sites). +After their dissociation, the atomic particles can be adsorbed on the surface (on adsorption sites) \sidecite{hodille_modelling_2021-1}. This dissociation is described by a sticking probability usually associated with an Arrhenius law $s = s_0 \exp{(-E_s/k_B T)}$. \gls{dft} calculations can calculate energy barriers for adsorption and migration of solute species on surfaces \sidecite{heinola_first-principles_2010}. Studies have however shown that this process is not thermally activated (i.e.\ $E_s=0$) \sidecite{alnot_adsorption_1989, tamm_interaction_1970} but rather depends on the ratio of the surface concentration of the species (hydrogen or helium) by the concentration of adsorption sites. @@ -732,7 +732,7 @@ \subsubsection{Clustering} \subsubsection{Bubble nucleation} -If its size is big enough the cluster pressure is sufficient to knock off a \gls{W} atom from the \gls{lattice}, creating a \gls{W} \gls{vacancy} and an interstitial \gls{W} atom (a \gls{Frenkel pair}). +If its size is big enough, the cluster pressure is sufficient to knock off a \gls{W} atom from the \gls{lattice}, creating a \gls{W} \gls{vacancy} and an interstitial \gls{W} atom (a \gls{Frenkel pair}). This process is called \gls{trap mutation} or \emph{\gls{self-trapping}} and the trapped clusters act as nuclei for bubble formation. \Gls{trap mutation} has been modelled in \gls{W} using \gls{dft} \sidecite{boisse_modelling_2014} and Monte Carlo computations \sidecite{de_backer_modeling_2015}. @@ -754,7 +754,7 @@ \subsubsection{Bubble growth} Condon and Schober \sidecite{condon_hydrogen_1993} reviewed the key mechanisms of bubble growth in metals. Each of these mechanisms can become dominant over another depending on the implantation and the metal conditions. -Bubbles can continue to grow by absorbing interstitial \gls{He} atoms or mobile \gls{He} clusters (i.e.\ that haven't self trapped). +Bubbles can continue to grow by absorbing interstitial \gls{He} atoms or mobile \gls{He} clusters (i.e.\ that have not self trapped). Considering that vacancies are mobile in the solid, the volume of a bubble could also increase if a \gls{vacancy} or a \gls{vacancy} cluster interacts with a \gls{He} bubble. The same is true for He-vacancies or H-vacancies clusters. @@ -847,10 +847,11 @@ \subsubsection{W tendrils or ``nano-fuzz''} In 2012, Wright et al.\ \sidecite{wright_tungsten_2012} observed the formation of nanostructures on the surfaces of the \gls{W} divertor of the reactor Alcator C-mod. These nanostructures are made of \gls{W} \glspl{tendril} (see \reffig{w fuzz wright}). -These structures are called \gls{W} \gls{fuzz}, nano-fuzz or even fuzzy W. +These structures are called \gls{W} \gls{fuzz}, nano-fuzz or even fuzzy \gls{W}. Because a small portion of the \gls{divertor} grew \gls{W} \gls{fuzz}, no conclusion was made regarding its influence on the \gls{plasma} operation. However, if these structures were to be removed during \gls{plasma} operation via erosion, \gls{W} atoms could be fed into the \gls{plasma}, affecting the \gls{tokamak} performances. -Moreover, this phenomenon could increase the \gls{W} dust formation in the reactor and lead to contamination and safety issues \sidecite{grisolia_tritium_2015}. +Moreover, this phenomenon could increase the \gls{W} dust formation in the reactor and lead to contamination and safety issues since the dust particles can be radioactive \sidecite{grisolia_tritium_2015}. +The formation of \gls{W} \gls{fuzz} also increases the specific surface area and therfore the potential intake of hydrogen. W \gls{fuzz} has been observed at high temperature (>1000K), high flux (>\SI{1e21}{He^+.m^{-2}.s^{-1}}) and long exposure (t>\SI{1e2}{s}) \sidecite{baldwin_formation_2010, nishijima_sputtering_2011}. diff --git a/chapters/chapter2/verification_and_validation/analytical_verification.tex b/chapters/chapter2/verification_and_validation/analytical_verification.tex index 0c1ad91..ab080da 100644 --- a/chapters/chapter2/verification_and_validation/analytical_verification.tex +++ b/chapters/chapter2/verification_and_validation/analytical_verification.tex @@ -12,7 +12,7 @@ These are then fed into the code and the computed solution is compared to the manufactured (exact) solution. This \gls{mms} is often used to unravel the complexity of governing equations \sidecite{dudson_verification_2016, roache_code_2002}. -This is particularly useful when dealing with complex geometries or to exercise non-trivial material propoerties. +This is particularly useful when dealing with complex geometries or to exercise non-trivial material properties. This section describes two verification cases of \gls{festim}. The first one uses the \gls{mes} and the second one the \gls{mms}. diff --git a/chapters/chapter3/monoblocks.tex b/chapters/chapter3/monoblocks.tex index 8447efe..a8aa094 100644 --- a/chapters/chapter3/monoblocks.tex +++ b/chapters/chapter3/monoblocks.tex @@ -19,6 +19,7 @@ \section{Model description}\labsec{model description} The materials properties (diffusivity, solubility, and thermal conductivity, density and heat capacity) are described in \reftab{materials properties monoblock} and plotted on \reffig{properties monoblock}. Finally, the traps properties are described in \reftab{traps monoblock}. +The traps for \gls{W} were taken from \sidecite{hodille_macroscopic_2015} and the trap created by ion implantation is neglected for it only affects the near surface of the monoblock. \begin{figure} \begin{overpic}[width=\linewidth]{Figures/Chapter3/monoblocks/interface_condition/iter case/monoblock_sketch.pdf} @@ -229,7 +230,7 @@ \subsection{Influence of dimensionality}\labsec{influence of dimensionality} Monoblocks simulations were run in 1D, 2D, and 3D and the inventory was computed for each case (see \reffig{monoblock inventories 1d 2d 3d}). Both the 1D and 2D approximations overestimate the inventory compared to the 3D reference, these approximations are therefore conservative. -It should however be noticed that, when neglecting the recombination on the poloidal gap (i.e.\ assuming hydrogen cannot desorb from this surface), the 2D approximation is strictly equivalent to the 3D reference (see \refch{DEMO monoblocks}). +It should however be noticed that, when neglecting the recombination on the poloidal gap (i.e.\ assuming hydrogen cannot desorb from this surface), the 2D approximation is strictly equivalent to the 3D reference (see \ref{DEMO monoblocks}). For these reasons, the 2D approximation will be employed in the following sections as it is the best compromise between accuracy and computational time. \begin{figure} @@ -302,7 +303,7 @@ \subsection{Influence of cycling}\labsec{influence of cycling} However, in the low flux case, the height of the spikes is greatly reduced. This is explained by the lower temperature difference between the resting phase and the plateau phase. -In both cases, the evolution trends are the same with or without cycling and the inventory evolution during the plateau phases nearly match the continuous case. +In both cases, the evolution trends are the same with or without cycling and the inventory evolution during the plateau phases match the continuous case. These results are consistent with the one observed in \sidecite{hodille_modelling_2021} with other trapping parameters. For a monoblock where the flux is even lower and the temperature difference is almost zero, no spikes will appear, and the cycled and continuous cases will match. diff --git a/chapters/chapter3/monoblocks/parametric_study.tex b/chapters/chapter3/monoblocks/parametric_study.tex index 238d27c..8649c8f 100644 --- a/chapters/chapter3/monoblocks/parametric_study.tex +++ b/chapters/chapter3/monoblocks/parametric_study.tex @@ -103,7 +103,7 @@ \subsection{Discussion} % ELMs It should be noted that specific scenarios like edge localised modes (ELMs) were also not taken into account in this work since their timescale is very short. -ELMs are transient plasma events releasing thermal energy and locally increasing the heat flux at the surface of the monoblock. +ELMs are transient plasma events releasing thermal energy and particles and locally increasing the heat flux at the surface of the monoblock. MRE simulations by Hu and Hassanein \sidecite{hu_predicting_2015} suggest that a \SI{400}{s} discharge with \SI{1}{Hz} or \SI{10}{Hz} ELMs significantly reduces (77 \%) the inventory in W materials. However, the modelling of the ELM is simulated by increasing the temperature for a very short time without changing the incident flux of particles that can also be much higher thus balancing the fuel retention reduction. Another study by Schmid et al.\ \sidecite{schmid_diffusion-trapping_2016} also simulated the effect of \SI{1}{Hz} ELMs on fuel retention in W. diff --git a/chapters/chapter4/divertor.tex b/chapters/chapter4/divertor.tex index a39972d..f6f8560 100644 --- a/chapters/chapter4/divertor.tex +++ b/chapters/chapter4/divertor.tex @@ -57,7 +57,7 @@ \subsubsection{\gls{soledge}-EIRENE runs} \\ Drifts & - \\ \\ - Transport coefficients & $D = \SI{0.3}{m^2.s^{-1}}$ \\ + Plasma transport coefficients & $D = \SI{0.3}{m^2.s^{-1}}$ \\ & $\nu = \SI{0.3}{m^2.s^{-1}}$ \\ & $\chi_e = \chi_i = \SI{1.0}{m^2.s^{-1}}$ \\ \end{tabular} @@ -157,11 +157,11 @@ \section{ITER results} \centering \begin{subfigure}{0.40\linewidth} \includegraphics[width=\linewidth]{Figures/Chapter4/ITER/inventory_along_inner_divertor.pdf} - \caption{Inner Vertical Target.} + \caption{\gls{ivt}.} \end{subfigure}% \begin{subfigure}{0.58\linewidth} \includegraphics[width=\linewidth]{Figures/Chapter4/ITER/inventory_along_outer_divertor.pdf} - \caption{Outer Vertical Target.} + \caption{\gls{ovt}.} \labfig{distrib outer target} \end{subfigure} \caption{Surface temperature, surface concentration and \gls{inventory} per unit thickness along the \gls{iter} \gls{divertor} with neutral pressures varying from \SI{2}{Pa} to \SI{11}{Pa}. The area corresponds to the 95\% confidence interval.} @@ -225,7 +225,7 @@ \section{ITER results} This was explained by the fact that the plasma is more detached at the inner target. Therefore the surface temperature reduction is more significant in the outer vertical target and the surface concentration is increased (see \reffig{distrib outer target}). -The maximum \gls{inventory} was found at around \SI{7}{Pa} and was approximately \SI{14}{g} of H, which is well below the \gls{iter} in-vessel safety limit of tritium (\SI{1}{kg}), especially considering only half of this quantity will be tritium. +The maximum \gls{inventory} was found at around \SI{7}{Pa} and was approximately \SI{14}{g} of H, which is well below the \gls{iter} in-vessel safety limit of tritium (\SI{700}{g}), especially considering only half of this quantity will be tritium. This is especially true considering that this was for a very long exposure time of \SI{e7}{s}, which corresponds to 25 000 pulses of \SI{400}{s}. @@ -378,7 +378,7 @@ \section{Summary} While \gls{west} operates at low input power, \gls{iter} operates at high input power with a high recycling \gls{divertor} . These differences in the operation regime can explain different trends. -The maximum hydrogen \gls{inventory} in the \gls{iter} \gls{divertor} was approximately \SI{14}{g} after \SI{e7}{s} of continuous plasma exposure (25 000 \gls{iter} discharges), which is well below the in-vessel safety limit (\SI{1}{kg} or \SI{700}{g} excluding the cryopumps). +The maximum hydrogen \gls{inventory} in the \gls{iter} \gls{divertor} was approximately \SI{14}{g} after \SI{e7}{s} of continuous plasma exposure (25 000 \gls{iter} discharges), which is well below the in-vessel safety limit of \SI{700}{g}. Note that the total number of discharges in \gls{iter} will be approximately 23 300 \cite{pitts_physics_2019}. Moreover, since the behaviour law is based on 2D \gls{monoblock} simulations, this value is an upper estimate (see \refsec{influence of dimensionality}). 2D simulations are indeed conservative in terms of \gls{inventory} (see \refsec{influence of dimensionality}). diff --git a/chapters/chapter5/He_transport_in_PFCs/Influence_on_H_transport.tex b/chapters/chapter5/He_transport_in_PFCs/Influence_on_H_transport.tex index 4544d50..d71a6ad 100644 --- a/chapters/chapter5/He_transport_in_PFCs/Influence_on_H_transport.tex +++ b/chapters/chapter5/He_transport_in_PFCs/Influence_on_H_transport.tex @@ -18,10 +18,10 @@ \subsection{Experiment}\labsec{helium hydrogen tds experiments} \subsection{Bubble growth simulation} The quantities $c_b$ and $\langle r_b \rangle$ have been computed from the helium bubble model described in \refsec{helium model description} (see \reffig{trap bubbles distribution}). -The helium implantation distritbuion is a Gaussian with a mean value of \SI{1.5}{nm} and a standard deviation of \SI{0.8}{nm} corresponding to a \SI{75}{eV} He exposure calculated with \gls{srim}. +The helium implantation distribution is a Gaussian with a mean value of \SI{1.5}{nm} and a standard deviation of \SI{0.8}{nm} corresponding to a \SI{75}{eV} He exposure calculated with \gls{srim}. The other parameters are unchanged. -\subsection{\gls{festim} simulation} +\subsection{\gls{festim} simulations} Four traps are simulated with \gls{festim}: traps 1-3 are pre-existing defects and trap 4 represents the traps induced by \gls{He} bubbles. The detrapping energies and trap densities are set as free parameters, including the trap density $n_b$ (see \reftab{trap properties}). diff --git a/chapters/chapter5/He_transport_in_PFCs/direct_implantation.tex b/chapters/chapter5/He_transport_in_PFCs/direct_implantation.tex index ea4fe5f..a0d6eeb 100644 --- a/chapters/chapter5/He_transport_in_PFCs/direct_implantation.tex +++ b/chapters/chapter5/He_transport_in_PFCs/direct_implantation.tex @@ -18,7 +18,7 @@ \subsection{Half-slab case} \labsec{half slab} \SI{100}{eV} \gls{He} were implanted in the first \SI{1.5}{nm} as in \refsec{tendril case}. The implanted flux was \SI{1e22}{m^{-2} s^{-1}} and the temperature was \SI{1000}{K}. -At low \glspl{fluence}, \gls{He} diffused really quickly into the bulk (see \reffig{profiles half slab}) and the bubbles' concentration $c_b$ was found to be zero. +At low \glspl{fluence}, \gls{He} diffused quickly into the bulk (see \reffig{profiles half slab}) and the bubbles' concentration $c_b$ was found to be zero. As the \gls{fluence} increased, bubbles started to appear and acted as strong sinks for mobile \gls{He}. This lead to a great decrease in the mobile He concentration profile. @@ -70,7 +70,7 @@ \subsection{Half-slab case} \labsec{half slab} The average radius $\langle r \rangle$ cannot be easily compared to experimental observations for it includes contributions from very small mobile He$_x$ clusters which are not visible experimentally (only bubbles with a radius greater than 1-\SI{3}{nm} are observable depending on the observation technique). -\subsection{Influence of exposure parameters on He bubble growth} +\subsection{Influence of exposure parameters on helium bubble growth} The impact of He flux and temperature $T$ was studied on the case described in \refsec{half slab} in order to identify trends. Behaviour laws are identified and can be used to obtain information on He transport without needing to run any simulation. diff --git a/chapters/chapter5/He_transport_in_PFCs/indirect_implantation.tex b/chapters/chapter5/He_transport_in_PFCs/indirect_implantation.tex index 38dbfd7..db256b5 100644 --- a/chapters/chapter5/He_transport_in_PFCs/indirect_implantation.tex +++ b/chapters/chapter5/He_transport_in_PFCs/indirect_implantation.tex @@ -3,9 +3,9 @@ \subsection{Neutron induced transmutation} -In combination with the \gls{paramak} code \sidecite{shimwell_paramak_2021} used for creating the \gls{monoblock} geometry, a neutronics simulation was run to assess the total quantity of helium generation in a \gls{monoblock} under neutron irradiation with the \gls{openmc} code \sidecite{romano_openmc_2015}, a modern open-source Monte-Carlo neutron and photon transport code. +In combination with the \gls{paramak} code \sidecite{shimwell_paramak_2021} used for creating the \gls{monoblock} geometry, a neutronics simulation was run to assess helium generation in a \gls{monoblock} under neutron irradiation with the \gls{openmc} code \sidecite{romano_openmc_2015}, a modern open-source Monte-Carlo neutron and photon transport code. -\Gls{openmc} simulates the transport of neutroncs by modelling their paths from their birth until their deaths. +\Gls{openmc} simulates the transport of neutronics by modelling their paths from their birth until their deaths. Neutron interactions with matter (reflexion, absorption, fission...) are simulated using a probabilistic approach where each reaction has a corresponding cross-section (taken from the \gls{endf} \sidecite{brown_endfb-viii0_2018}). In this simulation, a neutron source was placed above the \gls{monoblock} and the total helium production was tallied via the $(n,X\alpha)$ reaction rate (MT reaction number 207). @@ -27,7 +27,7 @@ \subsection{Neutron induced transmutation} The production of helium was found to be more important close to the top surface and to the neutron source (see \reffig{transmutation helium in monoblock}). It evolves as linearly with the distance from the top surface. -The maximum generation rate is $\approx \SI{7e18}{m^{-3}.s^{-1}}$, which is well below the generation rate from direct implantation. +The maximum generation rate is $\approx \SI{7e18}{m^{-3}.s^{-1}}$, which is well below the generation rate from direct implantation in the near surface. \reffig{helium generation distribution} was obtained by averaging all the values by distance from the top surface. The error bars were computed by averaging the standard deviation provided by \gls{openmc}. @@ -77,12 +77,12 @@ \subsection{Tritium decay} \lambda_\mathrm{decay} = \frac{\ln 2}{\tau_{1/2}} \approx \SI{1.77e-9}{s^{-1}} \end{equation} -The generation rate of helium from tritium decay is directly proportional to the hydrogen (tritium) retention can therefore be expressed as $\lambda_\mathrm{decay} (c_\mathrm{m} + \sum c_{\mathrm{t}, i})$. +The generation rate of helium from tritium decay is directly proportional to the hydrogen (tritium) retention and can be expressed as $\lambda_\mathrm{decay} (c_\mathrm{m} + \sum c_{\mathrm{t}, i})$. In order to remain conservative, it was computed at steady state. The maximum generation rate of helium in the \gls{monoblock} was found to be \SI{6.5e12}{m^{-3}.s^{-1}} (see \reffig{he generation from t decay}). This value assumes all the implanted hydrogen is tritium and should be halved to consider a 50\%-50\% DT mixture. -This is order of magnitudes below the generation from direct implantation. +This is order of magnitudes below the generation from direct implantation in the near surface region. \begin{figure} \centering @@ -93,7 +93,7 @@ \subsection{Tritium decay} \subsection{Comparison to direct implantation} -The volumetric source of helium $\Gamma$ due to direct implantation can be calculated by: +The volumetric source of helium $\Gamma$ due to direct implantation from the plasma can be calculated by: \begin{equation} \Gamma = \varphi_\mathrm{imp} \, f(x) \end{equation} diff --git a/chapters/chapter5/He_transport_in_PFCs/introduction.tex b/chapters/chapter5/He_transport_in_PFCs/introduction.tex index 7f55bfc..05b9cee 100644 --- a/chapters/chapter5/He_transport_in_PFCs/introduction.tex +++ b/chapters/chapter5/He_transport_in_PFCs/introduction.tex @@ -1,7 +1,8 @@ \refch{Chapter4} focussed on the estimation of the tritium inventory in the \gls{iter} \gls{divertor}, taking into account only hydrogen implantation. However, the \gls{divertor} of a \gls{tokamak} will not only be exposed to hydrogen: it will also be bombarded by helium ions with a high enough energy to penetrate the tungsten lattice. +Helium will also be generated from neutron transmutation and tritium decay. -This Chapter will thererfore focus on determining the effect of helium on hydrogen transport and its impact on the conclusions made in \refch{Chapter4}. +This Chapter will therefore focus on determining the effect of helium on hydrogen transport and its impact on the conclusions made in \refch{Chapter4}. It will first assess the different sources of helium in a tungsten \gls{divertor}, which are the direct implantation of helium ions, the production of helium from tritium decay, and the production of helium from \gls{transmutation}. diff --git a/chapters/chapter5/he_transport_in_pfcs.tex b/chapters/chapter5/he_transport_in_pfcs.tex index a0fdacb..0d64fc1 100644 --- a/chapters/chapter5/he_transport_in_pfcs.tex +++ b/chapters/chapter5/he_transport_in_pfcs.tex @@ -38,7 +38,7 @@ \section{Summary} \end{itemize} From these results, several experimental suggestions can be made. -Running the \gls{tds} only up to \SI{750}{K} would limit helium desorption. +Running the \gls{tds} only up to \SI{750}{K} would limit helium desorption from defects. Indeed, the authors \cite{ialovega_hydrogen_2020} showed that there was no helium desorption below this temperature after the initial cleaning \gls{tds}. If helium does not desorb and remains in the pre-existing defects, the deuterium \gls{tds} spectra should not be affected and only the desorption from bubbles should be observed. This would confirm or infirm the interpretation of the results presented herein. diff --git a/chapters/conclusion.tex b/chapters/conclusion.tex index 6319e39..390ef79 100644 --- a/chapters/conclusion.tex +++ b/chapters/conclusion.tex @@ -16,7 +16,7 @@ \section*{Contributions to the field} One of the main contribution of this research is the development of the \gls{festim} code: a hydrogen transport code that has been developed to answer the main questions of the study. The first article introducing \gls{festim} was published during the master project preceding this PhD research \cite{delaporte-mathurin_finite_2019}. At the time of writing, \gls{festim} is used by a handful of researchers, engineers and students and applied on other cases. -Making \gls{festim} available to other researchers (by making it open-source) would greatly benefit the broader community. +\gls{festim} was recently open-sourced and will hopefully greatly benefit the broader community. The parametric optimisation method used in \refch{Chapter2} now provides an efficient way of automatically fitting experimental data without manually tweaking parameters, saving precious time in the process. This method was published in a proceedings article \cite{delaporte-mathurin_parametric_2021}. @@ -33,6 +33,11 @@ \section*{Contributions to the field} \section*{Limitations} +This study has physical limitations inherent to the assumptions that have been made. +While some of these assumptions are conservative (i.e.\ represent a worst-case scenario) and do not jeopardise the key findings, others were made as a response to uncertainties. +For instance, no desorption was assumed on the monoblocks gaps. +The value of the recombination coefficient at the interface between the coolant and the monoblock also has a high uncertainty as it was measured in vacuum. + Many of the technical limitations of this research lie with the development issues of \gls{festim}. Since the code was built from scratch, features were added gradually. For instance, at the time the simulations in \refsec{influence of exposure conditions} were run, the surface concentration could not be inhomogeneous \emph{and} directly dependent on the inhomogeneous surface temperature due to the heat flux. @@ -40,10 +45,6 @@ \section*{Limitations} Even though the required feature was added a few months later, re-running all the \gls{festim} simulations was too much time-consuming given the time constraints. % Many of these development drawbacks could have been alleviated if \gls{festim} had been open-sourced, as external community experts such as \gls{fenics} developers could have more easily contributed to its development or bug fixes. -This study also has physical limitations inherent to the assumptions that have been made. -While some of these assumptions are conservative (i.e.\ represent a worst-case scenario) and do not jeopardise the key findings, others were made as a response to uncertainties. -For instance, no desorption was assumed on the monoblocks gaps. -The value of the recombination coefficient at the interface between the coolant and the monoblock also has a high uncertainty as it was measured in vacuum. \section*{Recommendations for future work} diff --git a/chapters/demo_monoblock.tex b/chapters/demo_monoblock.tex index b59f748..d378d71 100644 --- a/chapters/demo_monoblock.tex +++ b/chapters/demo_monoblock.tex @@ -1,6 +1,6 @@ \setchapterstyle{lines} \labpage{DEMO monoblocks} -\chapter{DEMO monoblocks}\labch{DEMO monoblocks} +\chapter{DEMO monoblocks}\labch{DEMO monoblocks}\label{DEMO monoblocks} So far, only 2D monoblocks simulations were run, assuming an infinite thickness (or assuming no desorption from the poloidal gaps). The goal of this section is to assess the influence of 3D edge effects on the monoblocks simulation results. It will be shown that the error induced by 2D assumption decreases for thick monoblocks. diff --git a/chapters/introduction.tex b/chapters/introduction.tex index 640f90d..2c4483b 100644 --- a/chapters/introduction.tex +++ b/chapters/introduction.tex @@ -6,7 +6,7 @@ \chapter*{Introduction} However, their intensive use led to astronomical carbon dioxide (CO$_2$) emissions. Since Edison died in 1931, 1500 billion tonnes of CO$_2$ have been emitted on Earth from burning fossil fuels and about 33 billion tonnes of CO$_2$ are still being released every year \cite{friedlingstein_global_2021}. The consequence of these emissions is global warming and these CO$_2$ emissions must stop in order to limit it to an ``acceptable'' level - regardless of the remaining oil and coal reserves. -Reducing the CO$_2$ emissions implies reducing the world's energy consumption while developing clean sources of energy. +Reducing the CO$_2$ emissions implies reducing the world's energy consumption while developing low-carbon sources of energy. It is very unlikely that these new sources will be able to completely replace fossil fuels. They would however act as a shock absorber in the energy crisis mankind is facing. @@ -37,7 +37,7 @@ \chapter*{Introduction} This would make the tritium fuel cycle even more challenging: how to inject tritium in the reactor if a large portion of the fuel is trapped in the materials? Moreover, as time goes by, the components of a reactor would build up an inventory of tritium, which would increase their radioactivity, making the decommissioning of a power plant more challenging. Contaminated components would indeed have to be handled as radioactive waste. -Other issues like material embrittlement are impacted by hydrogen retention. +Other issues like material embrittlement are also impacted by hydrogen retention. \emph{Are we able to predict tritium retention in fusion reactors?}\newline \emph{Will the tritium inventory remain within the safety limits over their lifespan?}\newline @@ -49,7 +49,7 @@ \chapter*{Introduction} FESTIM, which stands for Finite Element Simulation of Tritium In Materials, is able to simulate hydrogen transport in complex geometries encountered in tokamaks components. This PhD work focusses on the \textit{divertor}, a component of fusion reactors made of tungsten exposed to very intense particle (hydrogen and helium) and heat fluxes. The divertor is made of multiple unit bricks called \textit{monoblocks}. -The first Chapter of this manuscript will provide a general introduction to the research and a litterature review of the main phenomena at stake. -A method has been developed to make use of monoblock-level FESTIM simulations data and scale it up to divertor-level to have an estimate of the hydrogen inventory in the entire component. +The first Chapter of this manuscript will provide a general introduction to the research and a literature review of the main phenomena at stake. +A method has been developed to make use of monoblock-level FESTIM simulations data and scale it up to divertor-level to have an estimate of the hydrogen inventory in the entire divertor. Finally, a separate model has been developed to study the behaviour of helium in tungsten. This model has then been coupled to hydrogen simulations to investigate the potential effect of helium on the previously calculated hydrogen inventory. diff --git a/glossary.tex b/glossary.tex index 1818b5c..2284e5f 100644 --- a/glossary.tex +++ b/glossary.tex @@ -169,8 +169,8 @@ \newacronym{wcll}{WCLL}{Water-Cooled-Lithium-Lead} \newacronym{hcll}{HCLL}{Helium-Cooled-Liquid-Lead} \newacronym{dcll}{DCLL}{Dual-Coolant-Lithium-Lead} -\newacronym{tbr}{TBR}{Tritium breeding ratio} -\newacronym{fpy}{FPY}{Full Power Year} +\newacronym{tbr}{TBR}{tritium breeding ratio} +\newacronym{fpy}{FPY}{full power year} \newglossaryentry{tokamak}{ @@ -206,17 +206,17 @@ \newacronym{vv}{V\&V}{Verification and Validation} \newglossaryentry{p1}{ name=P1, - description={Lagrange finite element of order 1, also called piecewise linear elements.} + description={Lagrange finite element of order 1, also called piecewise linear elements} } \newglossaryentry{p2}{ name=P2, - description={Lagrange finite element of order 2.} + description={Lagrange finite element of order 2} } \newglossaryentry{p3}{ name=P3, - description={Lagrange finite element of order 3.} + description={Lagrange finite element of order 3} } -\newacronym{bcc}{bcc}{Body-Centered Cubic (type of metallic lattice)} +\newacronym[description={type of metallic lattice}]{bcc}{bcc}{body-centered cubic} \newglossaryentry{lattice}{ name=lattice, description={Three-dimensional crystalline structure of metals. The lattice is how the atoms are ordered within a metal} From bd6dcc94785d2c7fad7b934f94d5b8313377a1b8 Mon Sep 17 00:00:00 2001 From: RemDelaporteMathurin Date: Thu, 21 Jul 2022 00:25:41 +0200 Subject: [PATCH 2/6] fixed bcc --- glossary.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/glossary.tex b/glossary.tex index 2284e5f..8f94bcb 100644 --- a/glossary.tex +++ b/glossary.tex @@ -216,7 +216,7 @@ name=P3, description={Lagrange finite element of order 3} } -\newacronym[description={type of metallic lattice}]{bcc}{bcc}{body-centered cubic} +\newacronym[description={body-centered cubic. Type of metallic lattice}]{bcc}{bcc}{body-centered cubic} \newglossaryentry{lattice}{ name=lattice, description={Three-dimensional crystalline structure of metals. The lattice is how the atoms are ordered within a metal} From 0592e401474633bb70135687d9c5b63693b21639 Mon Sep 17 00:00:00 2001 From: RemDelaporteMathurin Date: Thu, 21 Jul 2022 12:34:14 +0200 Subject: [PATCH 3/6] a few more changes --- chapters/chapter1/intro.tex | 4 ++-- chapters/chapter5/he_transport_in_pfcs.tex | 2 +- images/monoblocks3.jpeg | Bin 0 -> 21256 bytes 3 files changed, 3 insertions(+), 3 deletions(-) create mode 100644 images/monoblocks3.jpeg diff --git a/chapters/chapter1/intro.tex b/chapters/chapter1/intro.tex index 804d4b4..0caa81a 100644 --- a/chapters/chapter1/intro.tex +++ b/chapters/chapter1/intro.tex @@ -674,8 +674,8 @@ \subsubsection{Surface dissolution} \begin{figure} \centering - \includegraphics[width=0.75\linewidth]{Figures/Chapter1/materials_solubility_review_comparison.pdf} - \caption{Solubitity values for tungsten, copper and CuCrZr. Data from \cite{delaporte-mathurin_remdelaportemathurinh-transport-materials_2022}.} + \includegraphics[width=0.8\linewidth]{Figures/Chapter1/materials_solubility_review_comparison.pdf} + \caption{Solubility values for tungsten, copper and CuCrZr. Data from \cite{delaporte-mathurin_remdelaportemathurinh-transport-materials_2022}.} \labfig{solubility materials} \end{figure} diff --git a/chapters/chapter5/he_transport_in_pfcs.tex b/chapters/chapter5/he_transport_in_pfcs.tex index 0d64fc1..c5a2c52 100644 --- a/chapters/chapter5/he_transport_in_pfcs.tex +++ b/chapters/chapter5/he_transport_in_pfcs.tex @@ -46,4 +46,4 @@ \section{Summary} Moreover, if this interpretation was confirmed, it could have implications for hydrogen retention. Indeed, one could imagine reducing the tritium inventory of components by exposing them to helium first. 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zDQ|?mF;NSzNGlf(jvx)Kr^MrLJmYILOt)Hufaxl5j63|f7ZUP*-&)Zn4eoD|`2sl# zXQ7Ae(`_p!K|NoP{8+(Se7-YaTAK-P?o_4*~tpujIx^{WH?zK2wpN=ZSmHyue*U|1Y8O;#Ks zQA45ESgTs;ENPb+?<>MzIMs5S%8kB|v8}`)@P>*;CK#h^O;D2c*^B=Gkg1uk+J5qe zEXS_!e8y7yC+7OqwAN1>e-SJZylB#C{8e91j&yl~l&s%Qy%-TioYpIoD9ZSQs32=~ zD3z+e6OPEHZe+vWQS^?tj4(RD7`6$kRkh3W0~uPgMN=<>K+qkrga?YuS@?{FHQYI$TD^8_ zk1kGVia`;`{0g{fm#4~$xh|c*&*LOPPg5Qjk#8xCW}H;{c$lDA4h{fdKj3wBF?D=K zuMTsZDgwf>SAZBC#%O+;e80QD@Y+{!iN^Tov&v%`rxiY4CMXsIgMb(h_%Msk#@KC- zIyNaU?{o$$23t8=#)r%MyZr3^*|NUN?L6ve=o&)z2i4jfFen0m{{V!&2q+dO39WG@ zdfl Date: Thu, 21 Jul 2022 12:39:07 +0200 Subject: [PATCH 4/6] added label --- chapters/chapter1/intro.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/chapters/chapter1/intro.tex b/chapters/chapter1/intro.tex index 0caa81a..e3f345e 100644 --- a/chapters/chapter1/intro.tex +++ b/chapters/chapter1/intro.tex @@ -490,7 +490,7 @@ \subsubsection{Helium}\labsec{sources of helium} Depending on the position in the DEMO \gls{divertor}, cumulative helium production over the course of three \glspl{fpy} could reach more than \SI{400}{appm}. -\subsection{H/W \& He/W interactions} +\subsection{H/W \& He/W interactions} \labsec{hydrogen and helium interactions with tungsten} \begin{figure} [h] From 62d345357d9675c835942021ceb20d76bf77dfff Mon Sep 17 00:00:00 2001 From: RemDelaporteMathurin Date: Thu, 21 Jul 2022 12:39:14 +0200 Subject: [PATCH 5/6] fixed TOC --- README.md | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/README.md b/README.md index 260ce0d..1292e60 100644 --- a/README.md +++ b/README.md @@ -19,8 +19,8 @@ Find the repositories to reproduce the results shown in this manuscript: - **Chapter 2 Model description**: - 2.5.1 Analytical verification: - [Case 1: H transport MES](https://github.com/RemDelaporteMathurin/PhDthesis/blob/main/scripts/mes_simple_diffusion.py) - - Case 2a: 1D H transport MMS: need to find the repo - - Case 2b: 2D H transport MMS: need to find the repo + - Case 2a: 1D H transport MMS + - Case 2b: 2D H transport MMS - [2.5.2 Experimental validation](https://github.com/RemDelaporteMathurin/tds_optimisation) - [2.5.3 Comparison with TMAP7](https://github.com/RemDelaporteMathurin/interface_conditions_paper) @@ -32,12 +32,12 @@ Find the repositories to reproduce the results shown in this manuscript: - [3.2.4 Influence of cycling](https://github.com/RemDelaporteMathurin/monoblock_cycling) - [3.3 Monoblock behaviour law](https://github.com/RemDelaporteMathurin/monoblock_parametric) - [**Chapter 4 Divertor inventory estimation**](https://github.com/RemDelaporteMathurin/divHretention-Nucl.Fusion-2021) -- **Chapter 5 He transport in PFCs**: - - [5.2 Direct implantation](https://github.com/RemDelaporteMathurin/he_fenics) - - 5.3 Indirect sources: - - [5.3.1 Neutron induced transmutation](https://github.com/RemDelaporteMathurin/monoblock_neutronics) - - [5.3.2 Tritium Decay](https://github.com/RemDelaporteMathurin/t_decay_in_monoblocks) - - [5.4 Influence on H transport](https://github.com/RemDelaporteMathurin/he_h_coupling) +- **Chapter 5 Influence of helium on hydrogen transport**: + - 5.1 Sources of helium: + - [5.1.1 Neutron induced transmutation](https://github.com/RemDelaporteMathurin/monoblock_neutronics) + - [5.1.2 Tritium Decay](https://github.com/RemDelaporteMathurin/t_decay_in_monoblocks) + - [5.3 to 5.4 Bubble growth results](https://github.com/RemDelaporteMathurin/he_fenics) + - [5.4 Influence on hydrogen transport](https://github.com/RemDelaporteMathurin/he_h_coupling) - **Appendix**: - A. FESTIM verification: - [A.1 Conservation of chemical potential (MES)](https://github.com/RemDelaporteMathurin/interface_conditions_paper) From a82e777d5edd59ae84dbfd38aeb86c6f522077c1 Mon Sep 17 00:00:00 2001 From: RemDelaporteMathurin Date: Thu, 21 Jul 2022 12:40:22 +0200 Subject: [PATCH 6/6] fixed toc again --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 1292e60..14acae8 100644 --- a/README.md +++ b/README.md @@ -37,7 +37,7 @@ Find the repositories to reproduce the results shown in this manuscript: - [5.1.1 Neutron induced transmutation](https://github.com/RemDelaporteMathurin/monoblock_neutronics) - [5.1.2 Tritium Decay](https://github.com/RemDelaporteMathurin/t_decay_in_monoblocks) - [5.3 to 5.4 Bubble growth results](https://github.com/RemDelaporteMathurin/he_fenics) - - [5.4 Influence on hydrogen transport](https://github.com/RemDelaporteMathurin/he_h_coupling) + - [5.5 Influence on hydrogen transport](https://github.com/RemDelaporteMathurin/he_h_coupling) - **Appendix**: - A. FESTIM verification: - [A.1 Conservation of chemical potential (MES)](https://github.com/RemDelaporteMathurin/interface_conditions_paper)