Merge pull request #63 from RemDelaporteMathurin/christians_remarks

Christian's remarks + typo fixes

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)
+    - [5.5 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)

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)

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}).
@@ -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]
@@ -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.
@@ -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}
 
@@ -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}.
 

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}.

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.