First Wall

The first wall is the wall surface located closest to the core plasma in a fusion reactor. It directly receives radiation and particles from the plasma, protects the blanket, and plays a crucial role in recovering thermal energy. As one of the most challenging technical issues for practical fusion reactors, research and development spanning over half a century continues in this interdisciplinary field combining materials science, thermal engineering, and plasma physics.

Historical Background

The concept of the first wall dates back to the dawn of fusion research in the 1950s. Initially, it was expected that plasma-wall interactions could be minimized if plasma could be completely confined by magnetic fields, but as experiments progressed, the importance of plasma-wall interactions became recognized.

From the 1960s to the 1970s, as improved confinement performance achieved in Soviet tokamak experiments provided prospects for maintaining high-temperature plasma for extended periods, first wall design emerged as a serious engineering challenge. In particular, the plasma temperatures exceeding 10 million degrees achieved by the T-3 tokamak in 1968 made heat load issues on wall materials a reality.

In the 1980s, large tokamaks such as JET (Europe), TFTR (USA), and JT-60 (Japan) were constructed, and methodologies for first wall material selection and design were established. Carbon-based materials were widely used, but tritium retention issues became apparent, leading to a shift toward metallic materials (beryllium, tungsten) from the 1990s onward.

Through the ITER design process (1988-present), engineering design of the first wall has advanced dramatically, and design methodologies, material selection criteria, and testing/verification methods for plasma-facing components have been systematized.

Role and Position of the First Wall

The first wall is installed along the magnetic surfaces of the scrape-off layer and has the following functions:

• First to receive neutron energy (neutrons are not confined by magnetic fields and scatter in all directions)
• Receives electromagnetic radiation from plasma (bremsstrahlung, synchrotron radiation, etc.)
• Receives neutral particles generated by charge exchange reactions
• As the plasma-side surface of the blanket, minimizes impact on tritium breeding ratio
• Suppresses the amount of impurities entering the plasma

Approximately 20% of fusion output (alpha particle energy) ultimately flows into the first wall and divertor. Of this, line radiation from impurities in the plasma and bremsstrahlung from plasma electrons are mainly transported to the first wall surface.

Requirements and Design Constraints

The main requirements for first wall design are summarized below.

Category	Requirement	Typical Specification
Thermal Performance	Surface heat flux	0.25-0.5 MW/m²
	Neutron wall load	0.5-2.0 MW/m²
	Surface temperature limit	< 50% of material melting point
Mechanical Performance	Thermal stress limit	< 2/3 of allowable stress
	Fatigue life	> 10⁴ cycles
	Pressure resistance	> Coolant pressure × safety factor
Nuclear Properties	Neutron transmission	As high as possible
	Impact on TBR	< 0.05 reduction
	Activation suppression	Use of low-activation materials
Plasma Compatibility	Sputtering erosion	< Allowable erosion/operating time
	Impurity release	Prefer low-Z impurities
	Tritium retention	Below safety management limits

The total surface area of the first wall is approximately 680 m² for ITER and will exceed 1000 m² for future power reactors. Maintaining uniform cooling performance and mechanical integrity across this vast area is a major design challenge.

Position and Geometric Configuration

To understand the positional relationship of the first wall in a tokamak reactor, the following parameters are defined:

$$a_{\text{FW}} = a_p + \delta_{\text{SOL}} + \delta_{\text{gap}}$$

Here, $a_p$ is the plasma minor radius, $\delta_{\text{SOL}}$ is the scrape-off layer thickness (typically 3-10 cm), and $\delta_{\text{gap}}$ is the plasma-wall gap (5-10 cm). The distance between the first wall and the separatrix is determined by the balance between plasma control stability and plasma-wall interactions.

Heat Load and Particle Load

Because the first wall is separated from the outermost magnetic surface of the plasma, heat and particle loads are reduced compared to the divertor.

Design Conditions (ITER Example)

Parameter	Shielding Blanket	Test Blanket
Surface heat flux (average)	0.25 MW/m²	0.25 MW/m²
Surface heat flux (maximum)	0.5 MW/m²	0.5 MW/m²
Neutron wall load (average)	0.56 MW/m²	0.78 MW/m²

Considering that the heat load of a household boiler is approximately 0.1 MW/m², it is clear that the first wall receives very large amounts of heat. Although smaller than the heat load to the divertor (over 10 MW/m²), the first wall accounts for approximately 80% of the plasma-facing area, so the total heat received cannot be ignored.

Components of Surface Heat Flux

The surface heat flux $q_{\text{surf}}$ to the first wall consists of multiple components:

$$q_{\text{surf}} = q_{\text{rad}} + q_{\text{CX}} + q_{\text{conv}} + q_{\gamma}$$

The breakdown of each component is as follows.

Radiative Heat Flux

The radiative heat flux $q_{\text{rad}}$ from plasma is the sum of bremsstrahlung, line radiation, and synchrotron radiation:

$$q_{\text{rad}} = \frac{P_{\text{brem}} + P_{\text{line}} + P_{\text{sync}}}{A_{\text{FW}}}$$

The bremsstrahlung power density is:

$$P_{\text{brem}} = 5.35 \times 10^{-37} n_e^2 Z_{\text{eff}} T_e^{1/2} \quad [\text{W/m}^3]$$

Here, $n_e$ is electron density [m⁻³], $Z_{\text{eff}}$ is effective charge number, and $T_e$ is electron temperature [keV]. Under typical ITER conditions ($n_e = 10^{20}$ m⁻³, $T_e = 10$ keV, $Z_{\text{eff}} = 1.7$), the bremsstrahlung power density is approximately 0.03 MW/m³.

Line radiation power from impurities is:

$$P_{\text{line}} = n_e n_Z L_Z(T_e)$$

$L_Z(T_e)$ is the radiative cooling coefficient, which depends on impurity species and temperature. For tungsten impurities, there is a strong radiation peak with $L_W \sim 10^{-31}$ W·m³ in the electron temperature range of 1-5 keV.

Synchrotron radiation occurs when electrons move in the toroidal magnetic field:

$$P_{\text{sync}} = 6.21 \times 10^{-17} n_e B_T^2 T_e \frac{T_e}{m_e c^2} \quad [\text{W/m}^3]$$

Under high-temperature, high-field conditions this component cannot be ignored, but effective losses are reduced when wall reflectivity is high.

Charge Exchange Neutral Particle Heat Flux

The heat flux $q_{\text{CX}}$ transported to the first wall by neutral particles produced in charge exchange reactions is:

$$q_{\text{CX}} = \Gamma_{\text{CX}} \cdot \langle E_{\text{CX}} \rangle$$

The charge exchange flux $\Gamma_{\text{CX}}$ is:

$$\Gamma_{\text{CX}} = n_i n_0 \langle \sigma v \rangle_{\text{CX}} \cdot \lambda_{\text{CX}}$$

Here, $n_0$ is neutral particle density, $\langle \sigma v \rangle_{\text{CX}}$ is the charge exchange reaction rate coefficient, and $\lambda_{\text{CX}}$ is the mean free path of neutral particles. Typical charge exchange neutral particle energies range from 0.1-10 keV.

Volumetric Heating

Volumetric heating $\dot{q}_{\text{vol}}$ due to neutron irradiation decreases exponentially in the thickness direction of the first wall:

$$\dot{q}_{\text{vol}}(x) = \dot{q}_0 \exp\left(-\frac{x}{\lambda_n}\right)$$

Here, $\dot{q}_0$ is the volumetric heating rate at the surface, $x$ is the distance from the surface, and $\lambda_n$ is the neutron attenuation length. The attenuation length for 14.1 MeV neutrons varies by material:

Material	Attenuation length $\lambda_n$ [cm]	Surface heating rate (at 1 MW/m²) [MW/m³]
Beryllium	12	15
Steel	8	25
Tungsten	3	60

The total volumetric heating of the first wall is:

$$Q_{\text{vol}} = \int_0^{t_{\text{FW}}} \dot{q}_{\text{vol}}(x) \, dx = \dot{q}_0 \lambda_n \left[1 - \exp\left(-\frac{t_{\text{FW}}}{\lambda_n}\right)\right]$$

Here, $t_{\text{FW}}$ is the first wall thickness.

Temperature Distribution Analysis

The temperature distribution in the first wall under steady-state conditions is derived from the one-dimensional heat conduction equation. With surface heat flux $q_s$ and volumetric heating $\dot{q}$:

$$-k \frac{d^2 T}{dx^2} = \dot{q}(x)$$

Given boundary conditions of coolant-side temperature $T_c$ and surface heat flux $q_s$, the surface temperature $T_s$ is:

$$T_s = T_c + \frac{q_s \cdot t}{k} + \frac{\dot{q}_0 \lambda_n^2}{k} \left[1 - \exp\left(-\frac{t}{\lambda_n}\right) - \frac{t}{\lambda_n}\exp\left(-\frac{t}{\lambda_n}\right)\right]$$

In the typical temperature distribution for ITER’s first wall (beryllium surface, copper alloy structure), surface temperature is controlled within the range of 200-400°C.

Thermal Stress Analysis

Thermal stress due to temperature gradients directly affects the mechanical integrity of the first wall. The maximum thermal stress $\sigma_{\text{th}}$ in a flat plate approximation is:

$$\sigma_{\text{th}} = \frac{E \alpha \Delta T}{2(1-\nu)}$$

Here, $E$ is Young’s modulus, $\alpha$ is the coefficient of linear thermal expansion, $\nu$ is Poisson’s ratio, and $\Delta T$ is the temperature difference.

The temperature difference due to surface heat flux $q$ is:

$$\Delta T = \frac{q \cdot t}{k}$$

Therefore, to suppress thermal stress, the following are desirable:

• Thin first wall (small $t$)
• High thermal conductivity material (large $k$)
• Low thermal expansion material (small $\alpha$)
• Low Young’s modulus material (small $E$)

The thermal stress parameter $M$ combining these parameters is used as an indicator for material selection:

$$M = \frac{k \sigma_y (1-\nu)}{E \alpha}$$

Here, $\sigma_y$ is yield stress. Higher values of $M$ indicate tolerance to higher heat loads.

Sources of Particle Load

Charged particles in plasma normally move spiraling around magnetic field lines, but reach the first wall through the following processes:

1. Charge exchange reactions: Plasma ions collide with neutral particles and lose their charge, and the resulting neutral particles, no longer confined by magnetic fields, strike the first wall
2. Orbit loss of high-energy particles: High-energy ions such as alpha particles have large orbits and may directly collide with the first wall
3. Diffusive transport: Part of the edge plasma diffuses across magnetic field lines and reaches the first wall

The energy of neutral particles produced by charge exchange reaches several hundred eV to several keV, causing sputtering when they collide with the first wall.

Neutron Load

14.1 MeV DT neutrons are the first high-energy particles to reach the first wall. The neutron wall load $\Gamma_n$ is:

$$\Gamma_n = \frac{P_{\text{fusion}} \times 0.8}{A_{\text{FW}}}$$

Here, $P_{\text{fusion}}$ is fusion power, 0.8 is the fraction of energy carried by neutrons (14.1 MeV / 17.6 MeV), and $A_{\text{FW}}$ is the first wall area.

Neutron fluence $\Phi$ is defined as cumulative irradiation:

$$\Phi = \Gamma_n \cdot t_{\text{op}} \cdot f_{\text{avail}}$$

Here, $t_{\text{op}}$ is operating time and $f_{\text{avail}}$ is availability. Neutron fluence of 2-3 MW·year/m² per year is anticipated for power reactors.

Material Selection

Surface materials for the first wall require strong compatibility with plasma. To minimize impact when entering the plasma, low atomic number (low-Z) materials are primarily selected.

Beryllium (Be)

Adopted as the first wall surface material for ITER.

Parameter	Value
Atomic number	4
Melting point	1287 °C
Thermal conductivity	200 W/(m·K)
Density	1.85 g/cm³
Specific heat capacity	1825 J/(kg·K)
Coefficient of linear thermal expansion	11.3 × 10⁻⁶ /K
Young’s modulus	287 GPa
Poisson’s ratio	0.032

Advantages:

• Low atomic number: Small radiation loss when entering plasma
• Oxygen getter effect: Has property of reducing oxygen impurities
• Relatively low tritium retention
• High thermal conductivity and low density

Challenges:

• Low melting point: Not suitable for high heat load regions
• Toxicity: Handling requires caution
• Steam reaction: Reacts with steam at high temperatures to generate hydrogen

$$\text{Be} + \text{H}_2\text{O} \rightarrow \text{BeO} + \text{H}_2$$

This reaction becomes significant above approximately 600°C, and the reaction rate is:

$$R_{\text{Be-H}_2\text{O}} = A \exp\left(-\frac{E_a}{RT}\right) \cdot p_{\text{H}_2\text{O}}$$

Here, $A = 1.4 \times 10^8$ kg/(m²·s·Pa), $E_a = 108$ kJ/mol, and $p_{\text{H}_2\text{O}}$ is steam partial pressure.

Irradiation Behavior of Beryllium

Under neutron irradiation, beryllium generates helium through the following nuclear reactions:

$$^9\text{Be}(n, 2n)2 \,^4\text{He}$$ $$^9\text{Be}(n, \alpha)^6\text{He} \rightarrow ^6\text{Li} + \beta^-$$

The helium production rate is very high at approximately 500-1000 appm/dpa, causing swelling and embrittlement of the material. The swelling amount $\Delta V / V$ shows temperature dependence:

$$\frac{\Delta V}{V} = k_{\text{He}} \cdot c_{\text{He}} \cdot f(T)$$

Here, $k_{\text{He}}$ is the swelling coefficient per helium atom, $c_{\text{He}}$ is helium concentration, and $f(T)$ is a temperature-dependent function. Swelling is maximum in the 400-600°C range.

Tungsten (W)

Tungsten may be used in high heat load regions.

Parameter	Value
Atomic number	74
Melting point	3422 °C
Thermal conductivity	173 W/(m·K)
Density	19.3 g/cm³
Specific heat capacity	132 J/(kg·K)
Coefficient of linear thermal expansion	4.5 × 10⁻⁶ /K
Young’s modulus	411 GPa
Sputtering threshold (D incidence)	Approximately 300 eV
Recrystallization temperature	1100-1400 °C

Tungsten has the highest melting point among metals and has low sputtering erosion, making it an excellent material, but due to its high atomic number, radiation loss is large when it enters the plasma.

Plasma Impurity Effects of Tungsten

The radiation loss power for tungsten concentration $c_W$ in plasma is:

$$P_{\text{rad},W} = n_e^2 c_W L_W(T_e)$$

The radiative cooling coefficient $L_W$ of tungsten strongly depends on electron temperature, showing a peak of $10^{-31}$ W·m³ in the 1-5 keV range. To maintain burning plasma, tungsten concentration must be kept below $c_W < 10^{-5}$.

Irradiation Embrittlement of Tungsten

Tungsten has a high ductile-brittle transition temperature (DBTT) (approximately 200-400°C for unirradiated material), and irradiation further increases the DBTT:

$$\Delta T_{\text{DBTT}} = k_{\text{irr}} \cdot \phi^{1/2}$$

Here, $k_{\text{irr}}$ is the irradiation hardening coefficient and $\phi$ is neutron fluence. When operating temperature falls below DBTT, the risk of brittle fracture increases.

Detailed Comparison of Beryllium and Tungsten

Property	Beryllium	Tungsten	Notes
Plasma radiation loss	Low	High	Be advantage
Melting point	1287°C	3422°C	W advantage
Sputtering rate	High	Low	W advantage
Oxygen getter	Yes	No	Be advantage
Tritium retention	Low	Low	Equal
Neutron multiplication	Yes	No	Be advantage (TBR)
Toxicity	High	Low	W advantage
Machinability	Difficult	Difficult	Equal
Cost	High	Medium	W advantage

Structural Materials

The following materials are used for first wall structural materials:

• Chromium zirconium copper (CuCrZr): Excellent thermal conductivity and durability (ITER)
• Reduced activation ferritic steel (F82H, EUROFER97): Under development as structural material for prototype reactors
• Stainless steel (SS316LN): Proven with existing technology

Reduced Activation Ferritic/Martensitic Steel (RAFM Steel)

Properties of reduced activation ferritic/martensitic steel (RAFM steel) being developed as first wall structural material for power reactors:

Parameter	F82H	EUROFER97
Composition	Fe-8Cr-2W-V-Ta	Fe-9Cr-1W-V-Ta
Thermal conductivity	28 W/(m·K)	30 W/(m·K)
Coefficient of linear thermal expansion	11.3 × 10⁻⁶ /K	11.5 × 10⁻⁶ /K
Yield strength (RT)	530 MPa	550 MPa
Operating temperature range	350-550°C	350-550°C

These materials avoid elements that generate long-lived radioactive nuclides such as Mo and Nb, substituting them with low-activation elements such as W and Ta.

Cooling Methods

Water cooling is primarily adopted for first wall cooling.

Coolant

The following cooling conditions are set for ITER:

• Coolant: Water (3 MPa) or supercritical water (25 MPa)
• Inlet temperature: 100 °C (water) / 280 °C (supercritical water)
• Outlet temperature: 325 °C (water) / 510 °C (supercritical water)

Heat removal $Q$ is expressed by the following equation:

$$Q = S_c \cdot v \cdot \rho \cdot c_p \cdot \Delta T = \dot{m} \cdot c_p \cdot \Delta T$$

Here, $S_c$ is flow channel cross-sectional area, $v$ is flow velocity, $\rho$ is density, $c_p$ is specific heat at constant pressure, $\Delta T$ is temperature difference between inlet and outlet, and $\dot{m}$ is mass flow rate.

Heat Transfer Analysis

The heat transfer coefficient $h$ between coolant and wall surface depends on flow conditions. For forced convection, it is calculated from the Nusselt number $Nu$:

$$h = \frac{Nu \cdot k_f}{D_h}$$

Here, $k_f$ is the thermal conductivity of the coolant and $D_h$ is the hydraulic equivalent diameter.

Under turbulent conditions ($Re > 10^4$), the Dittus-Boelter correlation:

$$Nu = 0.023 \cdot Re^{0.8} \cdot Pr^{0.4}$$

Reynolds number $Re$ and Prandtl number $Pr$ are:

$$Re = \frac{\rho v D_h}{\mu}, \quad Pr = \frac{\mu c_p}{k_f}$$

ITER’s first wall cooling system operates under conditions of $Re \sim 10^5$, $h \sim 10^4$ W/(m²·K).

Water Cooling Design

Advantages of water cooling include high heat transfer coefficient and proven existing technology. However, the following challenges exist:

• Tritium permeation: Tritium permeation management to water is necessary
• Corrosion: Corrosion due to radiolysis of water in radiation environment
• Pressure constraints: Mechanical constraints from high-pressure operation

Radiolysis of cooling water produces the following reactions:

$$\text{H}_2\text{O} \xrightarrow{\gamma, n} \text{H}^{\bullet} + \text{OH}^{\bullet} \rightarrow \text{H}_2 + \text{H}_2\text{O}_2 + \text{O}_2$$

The generated hydrogen peroxide $\text{H}_2\text{O}_2$ and dissolved oxygen promote corrosion of piping materials. Water chemistry management is required to control dissolved oxygen concentration at ppb levels.

Helium Gas Cooling

For power reactors, helium gas cooling is being considered for improved thermal efficiency through high-temperature operation:

Parameter	Water cooling (ITER)	Helium cooling (future reactors)
Coolant pressure	3-4 MPa	8-10 MPa
Inlet temperature	100°C	300°C
Outlet temperature	150°C	500°C
Thermal efficiency	30-33%	40-45%

The heat transfer coefficient of helium cooling is about 1/10 that of water, so extended heat transfer surfaces and turbulence-promoting structures are required. The following design methods are used for heat transfer enhancement:

$$h_{\text{enhanced}} = h_{\text{smooth}} \cdot \eta_{\text{fin}} \cdot \frac{A_{\text{fin}}}{A_{\text{base}}}$$

Here, $\eta_{\text{fin}}$ is fin efficiency and $A_{\text{fin}}/A_{\text{base}}$ is surface area expansion ratio.

Flow Channel Structures

The following types of flow channel cross-sections are available for the first wall:

1. Tube type: Structure with many circular tubes joined together. Circular cross-section is ideal for coolant internal pressure
2. Rib type: Integrated structure with rectangular cross-section channels. Can reduce coolant equivalent thickness, improving tritium breeding performance
3. Corrugated type: Structure with corrugated plates joined to flat plates. Can reduce coolant equivalent thickness but has manufacturability challenges

Classification of First Wall Structures

Item	Integrated type	Separate type
Structure	First wall and blanket are integrated	Can be exchanged independently
TBR	Thin plate thickness with small impact	Thick plate thickness with large impact
Maintenance	Simultaneous exchange required	Can be exchanged separately

The integrated type is currently mainstream from the perspectives of structural simplicity and tritium breeding ratio.

Sputtering and Erosion

Sputtering

When plasma particles collide with the first wall, surface atoms are ejected through momentum transfer.

Physical Sputtering

This depends on incident ion energy and material atomic number. The sputtering yield (number of atoms released per incident ion) has an energy threshold, and for high-Z materials like tungsten, the threshold is high so sputtering does not occur with low-energy ions.

Physical sputtering yield $Y$ is described by a semi-empirical model:

$$Y(E) = Q \cdot s_n(\varepsilon) \cdot \left[1 - \left(\frac{E_{\text{th}}}{E}\right)^{2/3}\right] \cdot \left(1 - \frac{E_{\text{th}}}{E}\right)^2$$

Here, $Q$ is a material constant, $s_n(\varepsilon)$ is reduced nuclear stopping power, $E_{\text{th}}$ is threshold energy, and $E$ is incident energy.

The threshold energy is approximated by:

$$E_{\text{th}} = \frac{E_s}{g(1-g)}$$

Here, $E_s$ is surface binding energy and $g = 4M_1 M_2 / (M_1 + M_2)^2$ is the kinematic factor ($M_1$: incident particle mass, $M_2$: target atom mass).

For beryllium, the sputtering threshold is approximately 10 eV, which is low, but for tungsten it increases to approximately 300 eV.

Incident particle	Beryllium threshold [eV]	Tungsten threshold [eV]
H	12	450
D	9	220
T	8	150
He	20	120

Chemical Sputtering

This is a phenomenon specific to carbon materials, where hydrogen isotope ions react chemically to produce hydrocarbons such as methane (CH₄) and ethylene (C₂H₄), causing material erosion. The sputtering rate is maximum around 500 °C, and erosion can be about 10 times that of physical sputtering.

Temperature dependence of chemical sputtering rate:

$$Y_{\text{chem}}(T) = Y_0 \cdot \exp\left[-\frac{E_a}{k_B}\left(\frac{1}{T} - \frac{1}{T_{\text{max}}}\right)^2 / \sigma^2\right]$$

Hydrocarbons generated by this reaction dissociate in the plasma and form co-deposited layers containing tritium. Tritium accumulation in these layers poses a major safety management challenge, so carbon material use is restricted in ITER.

Erosion Rate Due to Sputtering

Annual erosion amount $\Delta t$ is:

$$\Delta t = \frac{Y \cdot \Gamma \cdot M}{\rho \cdot N_A} \cdot t_{\text{year}}$$

Here, $\Gamma$ is particle flux [m⁻²s⁻¹], $M$ is atomic mass, $\rho$ is density, $N_A$ is Avogadro’s number, and $t_{\text{year}}$ is annual operating seconds.

Under ITER conditions, annual sputtering erosion of the beryllium first wall is estimated at approximately 0.1-1 mm/year.

Redeposition and Plasma-Wall Interaction

Atoms released by sputtering are ionized in the plasma, transported along magnetic field lines, and then redeposited elsewhere. This redeposition process significantly affects the surface condition and lifetime of the first wall.

Formation of Redeposited Layers

The growth rate of redeposited layers $R_{\text{dep}}$ is:

$$R_{\text{dep}} = \frac{\Gamma_{\text{dep}} \cdot M}{\rho \cdot N_A}$$

Here, $\Gamma_{\text{dep}}$ is deposited particle flux. Redeposited layers often have porous structures and show different properties from bulk materials:

Property	Bulk material	Redeposited layer
Density	100% of theoretical density	50-80%
Thermal conductivity	Standard value	1/5-1/10
Mechanical strength	Standard value	Significantly reduced
Tritium retention	Low	High

The reduced thermal conductivity of redeposited layers creates local overheating risks and causes layer delamination and particle generation.

Spatial Distribution of Erosion/Redeposition

The first wall surface is divided into erosion-dominated and redeposition-dominated regions depending on local plasma conditions. Net erosion rate $E_{\text{net}}$ is:

$$E_{\text{net}} = E_{\text{gross}} - R_{\text{dep}} = Y \cdot \Gamma_{\text{ion}} - S_{\text{dep}} \cdot \Gamma_{\text{neutral}}$$

In tokamaks, generally:

• Near the outer midplane: Erosion-dominated
• Upper and lower poloidal regions: Redeposition-dominated
• Near divertor: Mixed region

Mixed Material Effects

In ITER, which uses both beryllium and tungsten, mixed layers form on surfaces through sputtering and redeposition. In Be-W mixed layers:

$$\text{Be}_x\text{W}_{1-x} \quad (x = 0.2 \sim 0.8)$$

Intermetallic compounds (Be₂W, Be₁₂W, etc.) form in this composition range, reducing the melting point below that of bulk materials. The melting point of Be₂W is approximately 2200°C, significantly lower than tungsten (3422°C). This phenomenon increases the risk of local melting under high heat loads.

Surface Morphology Changes

Plasma irradiation causes characteristic morphological changes on first wall surfaces:

1. Nanostructure formation: “Fuzz” structures formed on tungsten surfaces

   • Generated by helium ion irradiation
   • Highly porous nanofibrous structure
   • Significant reduction in thermal conductivity

2. Surface roughening: Irregularity formation from ion irradiation

   • Due to angular dependence of sputtering yield
   • Increased gas retention due to surface area increase

3. Bubbles and blisters: Surface bulging from gas accumulation

Tungsten fuzz formation conditions:

• Helium ion energy > 20 eV
• Surface temperature 1000-2000 K
• Helium fluence > 10²⁴ m⁻²

Blistering

Incident gas atoms precipitate as bubbles near the material surface and grow with irradiation dose. Eventually, surface blisters rupture, causing surface delamination and flaking.

Erosion thickness $\epsilon$ due to blistering is:

$$\epsilon = \frac{R}{\phi_c} \cdot \phi$$

Here, $R$ is blister skin thickness, $\phi_c$ is critical irradiation dose, and $\phi$ is irradiation dose. The critical dose decreases as material temperature increases.

The critical condition for blister formation is from the balance between bubble internal pressure and surface tension:

$$p_{\text{bubble}} = \frac{2 \gamma}{r} + \sigma_y$$

Here, $\gamma$ is surface energy, $r$ is bubble radius, and $\sigma_y$ is yield stress.

Erosion During Disruptions

During plasma disruptions, large amounts of energy are deposited on the first wall in short times of 1-10 ms during the thermal quench phase. Heat loads reach 1-10 MJ/m², causing surface melting and evaporation.

Erosion due to evaporation is:

$$\Delta m = \frac{Q_{\text{dep}} - Q_{\text{melt}}}{L_v}$$

Here, $Q_{\text{dep}}$ is deposited energy density, $Q_{\text{melt}}$ is energy required for melting, and $L_v$ is latent heat of vaporization.

For beryllium, evaporation erosion of approximately 10 μm is predicted for a heat load of 1 MJ/m². Considering the number of disruptions expected during ITER’s operating period (several hundred), cumulative erosion may reach several mm.

Radiation Damage

Displacement Damage (dpa)

Neutron irradiation displaces material atoms from lattice positions. Damage is expressed in dpa (displacements per atom):

$$\text{dpa} = \int_0^{t} \int_{E_{\min}}^{E_{\max}} \phi(E) \cdot \sigma_d(E) \cdot \nu(E) \, dE \, dt$$

Here, $\phi(E)$ is neutron flux, $\sigma_d(E)$ is displacement cross-section, and $\nu(E)$ is cascade multiplication factor.

The dpa accumulation rate in the first wall is:

Material	dpa rate (at 1 MW/m²) [dpa/year]
Beryllium	10
Steel	8
Tungsten	5

For power reactors, 20-30 dpa/year and 100-300 dpa over lifetime (5-10 years) of damage is predicted.

Generation of Irradiation Defects

Neutron irradiation generates the following defects:

1. Frenkel pairs: Pairs of interstitial atoms and vacancies
2. Dislocation loops: Structures from defect agglomeration
3. Voids/bubbles: Vacancy agglomeration or gas atom precipitation
4. Precipitates: Agglomeration of transmutation products

The time evolution of defect concentration is described by rate equations:

$$\frac{dc_v}{dt} = G_v - R_{iv} c_i c_v - k_v^2 D_v c_v$$ $$\frac{dc_i}{dt} = G_i - R_{iv} c_i c_v - k_i^2 D_i c_i$$

Here, $c_v$, $c_i$ are vacancy and interstitial concentrations, $G$ is generation rate, $R_{iv}$ is recombination coefficient, $k^2$ is sink strength, and $D$ is diffusion coefficient.

Helium Generation

Nuclear reactions between fusion neutrons and materials generate helium and hydrogen. Helium generation rate by (n, α) reactions:

Material	He generation rate (at 1 MW/m²) [appm/dpa]
Beryllium	500-1000
Steel	10-15
Tungsten	0.5-1

Main reactions for helium generation in steel:

$$^{56}\text{Fe}(n, \alpha)^{53}\text{Cr}$$ $$^{58}\text{Ni}(n, \alpha)^{55}\text{Fe}$$

Helium accumulates in materials and segregates to grain boundaries, causing high-temperature grain boundary embrittlement. When critical helium concentration is exceeded, grain boundary strength decreases rapidly:

$$\sigma_{\text{GB}} = \sigma_{\text{GB},0} \exp\left(-\frac{c_{\text{He}}}{c_{\text{He}}^*}\right)$$

Irradiation Hardening and Embrittlement

Irradiation defects act as obstacles to dislocation motion, causing material hardening. The increase in yield stress $\Delta \sigma_y$ is:

$$\Delta \sigma_y = M \mu b \sqrt{\sum_j N_j d_j}$$

Here, $M$ is Taylor factor, $\mu$ is shear modulus, $b$ is Burgers vector, and $N_j$, $d_j$ are number density and diameter of various defects.

Irradiation embrittlement increases the ductile-brittle transition temperature (DBTT):

$$\Delta T_{\text{DBTT}} \propto \Delta \sigma_y$$

For reduced activation ferritic steel, a DBTT increase of 100-200°C has been reported at 10 dpa irradiation.

Swelling

Void formation from vacancy agglomeration causes volumetric expansion of materials. Swelling amount is:

$$\frac{\Delta V}{V} = \frac{4\pi}{3} \sum_i N_i r_i^3$$

Austenitic stainless steel shows high swelling rates (several %/dpa), making its use difficult in fusion reactors after ITER. Ferritic/martensitic steel has excellent swelling resistance (< 0.1 %/dpa) and is expected as structural material for power reactors.

Tritium Retention and Permeation

Tritium Retention Mechanisms

Tritium (T) retention in first wall materials occurs through the following processes:

1. Implantation retention: Direct implantation by ion incidence
2. Diffusion penetration: Absorption and diffusion from gas phase
3. Defect trapping: Trapping at irradiation defects
4. Co-deposition: Incorporation into sputtering redeposition layers

Total tritium retention $I_T$ is:

$$I_T = I_{\text{implant}} + I_{\text{diffusion}} + I_{\text{trap}} + I_{\text{codeposit}}$$

Diffusion and Solubility

Tritium diffusion into materials follows Fick’s law:

$$\frac{\partial C}{\partial t} = D \nabla^2 C - \sum_j k_j C (N_j - C_j^T) + \sum_j p_j C_j^T$$

Here, $C$ is dissolved concentration, $D$ is diffusion coefficient, $k_j$, $p_j$ are trapping/detrapping rates for various traps, $N_j$ is trap density, and $C_j^T$ is trapped concentration.

Temperature dependence of diffusion coefficient:

$$D = D_0 \exp\left(-\frac{E_D}{k_B T}\right)$$

Solubility:

$$S = S_0 \exp\left(-\frac{E_S}{k_B T}\right)$$

Diffusion and solubility parameters for representative materials:

Material	$D_0$ [m²/s]	$E_D$ [eV]	$S_0$ [mol/(m³·Pa^0.5)]	$E_S$ [eV]
Be	3×10⁻⁹	0.28	2×10⁻²	0.9
W	4×10⁻⁷	0.39	10⁻³	1.0
Steel	2×10⁻⁷	0.14	0.3	0.1

Permeation and Permeation Barriers

Tritium permeation flux through the wall $J_T$ is:

$$J_T = \frac{D \cdot S}{t} \cdot \sqrt{p_T}$$

Here, $t$ is wall thickness and $p_T$ is tritium partial pressure. It is characterized by permeability $\Phi = D \cdot S$.

Oxide coatings (Al₂O₃, Er₂O₃, etc.) are being considered for permeation prevention. The permeation reduction factor (PRF) by coating is:

$$\text{PRF} = \frac{J_{\text{bare}}}{J_{\text{coated}}} = 1 + \frac{\Phi_{\text{base}} \cdot t_{\text{coat}}}{\Phi_{\text{coat}} \cdot t_{\text{base}}}$$

Under ideal conditions, PRF > 1000 is achieved, but maintaining performance in real environments (irradiation, thermal cycling) is a challenge.

Tritium Management in ITER

A safety management limit of 700 g is set for tritium inventory in ITER. To meet this limit:

• Adoption of low tritium retention material (beryllium)
• Restrictions on carbon material use
• Periodic tritium removal operations
• Online monitoring

are implemented.

ITER First Wall Design

Design Overview

ITER’s first wall is designed as part of the shielding blanket. Main specifications are as follows:

Parameter	Value
Total surface area	680 m²
Number of blanket modules	440
Number of first wall panels	Approximately 1800
Surface material	Beryllium
Structural material	CuCrZr / 316L(N)-IG
Coolant	Water (4 MPa, 70°C→120°C)

First Wall Panel Structure

ITER’s first wall panel has the following layered structure:

1. Beryllium armor (8-10 mm)
2. CuCrZr heat sink (10 mm)
3. 316L(N) stainless steel structure (20 mm)

HIP (Hot Isostatic Pressing) bonding is used for joining beryllium and copper alloy. The integrity of the bonding interface must be maintained against thermal cycling and neutron irradiation during operation.

Residual stress $\sigma_{\text{res}}$ at the bonding interface from thermal expansion coefficient difference:

$$\sigma_{\text{res}} = \frac{E_{\text{eff}} (\alpha_{\text{Be}} - \alpha_{\text{Cu}}) \Delta T}{1 + E_{\text{Be}} t_{\text{Be}} / E_{\text{Cu}} t_{\text{Cu}}}$$

Standard and Enhanced Panels

Two types of panels are used for ITER first wall depending on heat load conditions:

Type	Surface heat flux	Beryllium thickness	Installation location
Standard (NHF)	2 MW/m²	8 mm	Most areas
Enhanced (EHF)	4.7 MW/m²	10 mm	High heat load regions

Enhanced panels employ a finger structure to improve heat transfer performance.

Cooling System

The first wall cooling system operates under the following design conditions:

• Coolant: Deionized water
• Pressure: 4 MPa
• Inlet temperature: 70°C
• Outlet temperature: 120°C
• Total flow rate: Approximately 1000 kg/s

Independent cooling loops are configured for each blanket module, minimizing impact on other modules in case of cooling loss in one module.

Remote Maintenance

ITER’s first wall/blanket is exchanged using a remote handling (RH) system. Since the interior of the fusion reactor is strongly activated after DT operation, direct human access is impossible, and all maintenance work is performed by remote operation.

Remote Maintenance System Configuration

ITER’s in-vessel remote maintenance system consists of the following elements:

1. Blanket Remote Handling System (BRHS)

   • Multi-jointed manipulator inserted through vacuum vessel ports
   • Maximum payload: 5 tons
   • Positioning accuracy: ±2 mm
   • Working range: Entire vacuum vessel interior

2. Divertor Remote Handling System (DRHS)

   • Access from lower ports
   • Designed exclusively for cassette exchange

3. In-vessel inspection system

   • Cameras and lighting for visual inspection
   • Surface erosion evaluation by laser measurement
   • Thermal integrity confirmation by infrared camera

Blanket Module Exchange Procedure

1. Vacuum vessel evacuation and purge (1-2 days)
2. Port plug removal (1 day per port)
3. Cooling pipe cutting and capping
4. Module fixing bolt removal
5. Module gripping and removal by manipulator
6. New module insertion and positioning
7. Fixing bolt fastening
8. Cooling pipe reconnection and leak testing
9. Port plug restoration

Main parameters of blanket modules:

• Total number: 440 modules
• Weight: Approximately 4-4.5 tons/module
• Exchange time: Approximately 2-3 weeks/module
• Full exchange: Approximately 6-12 months

Challenges in Radiation Environment

Remote maintenance systems must operate in the following radiation environment:

Parameter	Immediately after shutdown	After 2 weeks	After 1 year
γ dose rate	10⁴ Gy/h	10³ Gy/h	10² Gy/h
Contact dose rate	10⁵ mSv/h	10⁴ mSv/h	10³ mSv/h

In this environment:

• Radiation degradation countermeasures for electronics (radiation-resistant design)
• Prevention of optical system browning (special glass, periodic replacement)
• Countermeasures for lubricant radiolysis (solid lubrication, special grease)
• Cable insulation material degradation management

are necessary. Remote maintenance equipment is designed for a cumulative dose target of 10⁶ Gy (lifetime).

Exchange Decision Criteria

First wall replacement timing is determined from the following indicators:

1. Surface erosion amount

$$t_{\text{remain}} = t_{\text{initial}} - \int_0^{t} \dot{t}_{\text{erosion}}(t') \, dt' > t_{\text{min}}$$

2. Neutron damage amount

$$\text{dpa}_{\text{accumulated}} < \text{dpa}_{\text{limit}}$$

3. Tritium retention amount

$$I_T < I_{T,\text{limit}}$$

4. Thermal fatigue damage

$$D_{\text{fatigue}} = \sum_j \frac{n_j}{N_{f,j}} < 1 \quad (\text{Miner's rule})$$

One to two full replacements are planned during ITER’s DT operation period.

Challenges for Future Reactors

Design Requirements for Power Reactors

For power reactors (DEMO and beyond), the following points become more demanding compared to ITER:

Parameter	ITER	DEMO	Commercial reactor
Neutron wall load	0.56 MW/m²	2-3 MW/m²	3-5 MW/m²
Annual availability	10%	50%	80%
Lifetime dpa	3	50-100	150-200
Operating time	1000 seconds	Steady-state	Steady-state

Response to High Neutron Wall Load

To address the high neutron wall load (2-5 MW/m²) of power reactors:

1. Development of high thermal conductivity materials
2. Advanced cooling structures (microchannels, porous bodies)
3. Application of composite materials
4. Functionally graded materials

are being considered. The allowable range when surface heat flux increases:

$$q_{\text{max}} = \frac{k \cdot (T_{\text{melt}} - T_{\text{coolant}})}{t_{\text{armor}}} \cdot \eta_{\text{safety}}$$

Expansion of Irradiation Materials Database

Current material irradiation data extends only to about 100 dpa at most, and there is uncertainty in predicting behavior under power reactor conditions (150-200 dpa). In particular:

• Helium accumulation and grain boundary embrittlement
• Effects of transmutation products
• Combined damage (irradiation + thermal cycling)

require data expansion. Material irradiation testing at 14 MeV neutron source facilities (IFMIF-DONES, etc.) is planned.

Development of Advanced Materials

The following advanced materials are under development for future reactors:

1. ODS steel (Oxide Dispersion Strengthened steel)

   • Strengthening by nano-sized oxide particles (Y₂O₃-Ti-O)
   • Improved creep strength and irradiation resistance
   • Upper temperature limit extended to 650°C or higher

2. SiC/SiC composite materials

   • Low activation characteristics
   • High-temperature strength
   • Operating temperatures above 1000°C
   • Challenges: Gas-tightness, joining technology

3. Tungsten alloys

   • Recrystallization suppression (K-doped, La₂O₃ dispersed)
   • Toughness improvement (ReW alloy)
   • Irradiation embrittlement suppression

Economics and Reliability

For power reactors, long lifetime of the first wall/blanket is required from an economic perspective:

$$\text{COE} \propto \frac{C_{\text{FW/BLK}}}{t_{\text{life}} \cdot f_{\text{avail}}}$$

Here, COE is cost of electricity, $C_{\text{FW/BLK}}$ is first wall/blanket cost, $t_{\text{life}}$ is lifetime, and $f_{\text{avail}}$ is availability.

Target values:

• Lifetime 5 years or more
• Exchange time within 3 months
• Availability 80% or more

are set. Achieving these requires both improved material durability and more efficient maintenance operations.

Advanced First Wall Concepts

Various advanced first wall concepts are being researched for future fusion power reactors. These aim to develop the technology demonstrated in ITER toward higher performance and reliability.

Self-Healing First Wall

A concept for replenishing plasma-facing surface erosion during operation.

Liquid Metal First Wall

A method using liquid metals such as lithium (Li) or tin (Sn) flowing over the first wall surface as the plasma-facing surface instead of solid materials:

Advantages:

• Self-replenishment of sputtering erosion
• Response to high heat loads (evaporative cooling effect)
• Tritium capture (for Li)
• Self-recovery from radiation damage

Challenges:

• Impurity contamination into plasma
• MHD effects in magnetic fields
• Liquid metal circulation and recovery systems
• Material compatibility at high temperatures

The plasma impurity effect of liquid lithium is evaluated by evaporation flux $\Gamma_{\text{evap}}$:

$$\Gamma_{\text{evap}} = \frac{p_{\text{Li}}(T)}{\sqrt{2\pi m_{\text{Li}} k_B T}}$$

At surface temperatures below 450°C, impurity contamination from evaporation can be kept within acceptable limits.

Redeposition Replenishment Type

A method of supplying material lost in erosion-dominated regions from elsewhere. Periodic surface restoration by plasma spraying of tungsten powder is being considered.

Functionally Graded Materials (FGM)

Materials with continuously varying composition or structure from surface to substrate. Relaxes interface stress from thermal expansion coefficient mismatch and improves joint reliability.

W/Cu Functionally Graded Materials

By continuous composition change from tungsten (surface) to copper (substrate):

$$\alpha_{\text{FGM}}(x) = \alpha_W + (\alpha_{Cu} - \alpha_W) \cdot f(x)$$

Mitigates sharp thermal stress concentration at interfaces. Manufacturing methods include powder metallurgy, thermal spraying, and PVD/CVD methods.

W/RAFM Functionally Graded Materials

Combination of tungsten and reduced activation ferritic steel ensures structural material compatibility for power reactors.

Nanostructured Materials

A concept for improving material properties through nanoscale microstructures.

Nanocrystalline Tungsten

By refining grain size to below 100 nm:

• Lowering of ductile-brittle transition temperature
• Increase of recrystallization temperature
• Promotion of irradiation defect annihilation at grain boundaries

are expected. From the Hall-Petch equation:

$$\sigma_y = \sigma_0 + k_y d^{-1/2}$$

strength also improves with grain size $d$ refinement.

Nanocomposite Materials

Materials with nano-sized oxide particles (Y₂O₃, La₂O₃, etc.) dispersed in a tungsten matrix. Dispersed particles function as sinks for irradiation defects, suppressing irradiation embrittlement.

Self-Healing Materials

A concept where materials themselves repair irradiation damage.

MAX Phase Ceramics

Ceramics with layered structures such as Ti₃SiC₂ and Ti₂AlC, showing special defect recovery mechanisms:

• Stress relaxation through easy interlayer slip
• Promotion of defect annihilation at high temperatures
• Metallic thermal and electrical conductivity

High Entropy Alloys

Alloys mixing five or more elements in equimolar ratios, showing properties not found in conventional materials:

• Improved radiation damage resistance (lattice strain effect)
• Maintenance of high-temperature strength
• Excellent corrosion resistance

WTaCrVTi-based high entropy alloys are being researched for fusion applications.

Advanced Cooling Structures

High-performance cooling structures to replace conventional tubular cooling channels.

Microchannel Cooling

Arranges many microchannels on the order of several hundred μm to expand heat transfer area. Heat transfer coefficient improvement:

$$h_{\text{micro}} = h_{\text{macro}} \cdot \left(\frac{D_{\text{macro}}}{D_{\text{micro}}}\right)^{0.2}$$

achieves 2-5 times heat removal performance with the same flow rate.

Porous Body Cooling

Flows coolant through porous structures of metal foam or sintered bodies, achieving high-efficiency cooling utilizing internal surface area.

Heat Pipe Integrated Type

Incorporates high thermal conductivity heat pipe structures into the first wall to distribute localized high heat loads.

Design Optimization by Computational Materials Science

Efforts are advancing to optimize material design from the atomic level using first-principles calculations and molecular dynamics simulations.

Multiscale Modeling

Continuously models irradiation damage evolution at multiple scales:

1. First-principles calculations (electronic states, interatomic potentials)
2. Molecular dynamics (cascade damage, defect formation)
3. Kinetic Monte Carlo (defect diffusion, aggregation)
4. Rate theory models (microstructure evolution)
5. Finite element method (mechanical property changes)

This hierarchical approach predicts material behavior in high-irradiation regimes where experiments are difficult.

Materials Discovery by Machine Learning

Research combining large-scale materials databases with machine learning algorithms to efficiently search for optimal material compositions and structures is beginning.

Safety and Regulations

The first wall is critical equipment directly related to fusion reactor safety, requiring strict regulations and safety evaluation.

Safety Functions

Safety functions performed by the first wall:

1. Confinement of radioactive materials

   • Tritium retention within vacuum vessel
   • Prevention of activated product dispersion

2. Decay heat removal

   • Residual heat removal after shutdown
   • Coordination with passive safety systems

3. Contribution to reactivity control

   • Natural shutdown through plasma impurities

Design Basis Events

Events to be considered in first wall design:

Event category	Specific examples	Expected frequency
Normal operation	Steady-state heat load, pulse operation	Continuous
Anticipated operational occurrences	ELMs, small-scale disruptions	10³-10⁵ times/lifetime
Design basis accidents	Large-scale disruptions	10-10² times/lifetime
Design extension conditions	Loss of coolant, vacuum breach	< 10⁻² /year

Loss of Coolant Accident (LOCA)

Temperature rise is evaluated when first wall cooling is lost. Temperature rise rate under adiabatic conditions:

$$\frac{dT}{dt} = \frac{\dot{q}_{\text{decay}}}{\rho c_p}$$

Here, $\dot{q}_{\text{decay}}$ is decay heat generation rate. For ITER’s first wall, decay heat immediately after shutdown is approximately 1% of normal operation, and passive heat removal by natural convection and radiation maintains temperatures below material melting points.

Hydrogen Generation Evaluation

Hydrogen generation from beryllium-steam reactions and radiolysis is important from an explosion risk perspective:

$$\dot{m}_{H_2} = A_{\text{Be}} \cdot R_{\text{Be-H}_2\text{O}}(T) \cdot x_{\text{exposed}}$$

Here, $A_{\text{Be}}$ is beryllium exposed area and $x_{\text{exposed}}$ is the fraction of reactable surface.

The following countermeasures are taken to prevent hydrogen concentration from reaching explosive limits (4-75 vol%):

• Dilution through vacuum vessel internal volume
• Inert gas purge system
• Catalytic recombiners

Tritium Safety Management

Tritium retained in the first wall is evaluated as a release source term in accidents. Release amount is:

$$R_T = I_T \cdot f_{\text{release}}(T, t)$$

Here, $f_{\text{release}}$ is a temperature and time-dependent release fraction. ITER’s tritium inventory limit (700 g) is set based on this evaluation.

Low Activation and Waste Management

Activation of first wall materials affects waste classification at decommissioning. Achieving clearance levels after 100 years is an important design goal in material selection:

$$A(t) = A_0 \sum_i f_i \exp\left(-\frac{\ln 2}{T_{1/2,i}} t\right)$$

Low activation materials (RAFM steel, SiC/SiC, V alloys) exclude elements that produce long-lived nuclides such as Mo, Nb, and Ni, aiming to achieve clearance levels in about 100 years.

Related Topics

• Plasma-Facing Materials - Details on beryllium, tungsten, etc.
• Blanket - Breeding blanket integrated with first wall
• Divertor - Plasma-facing component receiving higher heat loads
• Superconducting Coils - Coil system for magnetic confinement
• ITER Project - ITER first wall design
• Tokamak Configuration - Core plasma and scrape-off layer structure