Radioactive Waste

In fusion reactors, high-energy neutrons generated by the DT reaction activate the reactor structural materials. However, the radioactive waste produced from fusion reactors has fundamentally different characteristics from that of fission reactors. The ability to significantly reduce environmental impact through appropriate material selection and waste management is one of the key advantages of fusion energy.

This chapter provides a quantitative and systematic explanation of the physical and chemical characteristics unique to fusion reactor radioactive waste, activation mechanisms, development status of reduced-activation materials, waste management strategies, regulatory frameworks, and international initiatives.

Differences Between Fusion and Fission Waste

The nature of radioactive waste generated from fusion and fission reactors is fundamentally different. This difference originates from the essential differences in their respective nuclear reaction mechanisms.

Fission Reactor Waste

In fission reactors, the following radioactive materials are produced by the fission reaction of uranium or plutonium:

1. Fission products (cesium-137, strontium-90, etc.)
2. Transuranic elements (plutonium, americium, curium, etc.)

Some of these transuranic elements (actinides) have half-lives ranging from tens of thousands to hundreds of thousands of years, requiring long-term isolation through geological disposal. High-level radioactive waste from spent fuel reprocessing requires management for nearly one million years.

The radioactivity of fission products $A_{\text{FP}}(t)$ is composed of contributions from numerous nuclides:

$$A_{\text{FP}}(t) = \sum_i A_{i,0} \exp\left(-\frac{\ln 2}{T_{1/2,i}} t\right)$$

where $A_{i,0}$ is the initial radioactivity of nuclide $i$, and $T_{1/2,i}$ is its half-life. Due to the presence of long-lived nuclides (e.g., $^{239}$Pu with a half-life of 24,100 years), the overall radioactivity decay is extremely slow.

The production of transuranic elements proceeds through a chain of neutron capture reactions on uranium fuel:

$$^{238}\text{U} \xrightarrow{(n,\gamma)} ^{239}\text{U} \xrightarrow{\beta^-} ^{239}\text{Np} \xrightarrow{\beta^-} ^{239}\text{Pu}$$

Furthermore, additional neutron capture on $^{239}$Pu leads to transitions to $^{240}$Pu, $^{241}$Pu, and then to americium and curium. These reactions are unique to fission reactors and do not occur in fusion reactors.

Fusion Reactor Waste

In fusion reactors, fission reactions do not occur, so high-level radioactive waste is not generated. All radioactive waste produced originates from the activation of structural materials by neutron irradiation and is classified as low-level radioactive waste.

A characteristic feature of fusion reactor activation products is that the half-lives of the generated radioactive nuclides are relatively short. This can be controlled through material selection, and by using reduced-activation materials, the radioactivity decays to natural uranium ore levels within approximately 100 years after the end of operation.

The fusion reaction itself is:

$$^2\text{D} + ^3\text{T} \rightarrow ^4\text{He} (3.5 \, \text{MeV}) + n (14.1 \, \text{MeV})$$

and all products are stable nuclides or non-radioactive particles. Radioactive waste is produced secondarily when the 14.1 MeV neutrons interact with structural materials.

Fundamental Difference

It is important to understand from a physics perspective why transuranic elements are not produced in fusion reactors.

In fission reactors, elements heavier than uranium (atomic number 92) are produced through successive neutron capture. This is because uranium fuel, a “heavy seed,” is present.

On the other hand, fusion reactor fuels are deuterium (atomic number 1) and tritium (atomic number 1), and it is physically impossible to produce transuranic elements from these light elements. Fusion reactor structural materials also consist of elements lighter than uranium, such as iron (atomic number 26) and tungsten (atomic number 74).

The increase in mass number due to neutron capture is:

$$^A_Z\text{X} + n \rightarrow ^{A+1}_Z\text{X} + \gamma$$

and the atomic number Z does not change. Therefore, elements heavier than uranium cannot be produced from structural materials.

Quantitative Comparison

The main differences are shown below:

Item	Fission Reactor	Fusion Reactor
High-level waste	Yes (spent fuel)	None
Long-lived nuclides	Actinides (half-life tens of thousands of years or more)	None
Management period	Tens of thousands to hundreds of thousands of years	Approximately 100 years
Disposal method	Geological disposal required	Near-surface disposal possible
Toxicity decay	Very slow	Decays to one millionth in 100 years

Fusion reactor radioactive waste is more than two orders of magnitude less toxic than fission reactor waste even immediately after shutdown, and after 100 years it decreases to one millionth.

A quantitative comparison of radioactivity over time for a 1 GWe power plant:

Time Elapsed	Fission Reactor (relative value)	Fusion Reactor (relative value)
Immediately after shutdown	1.0	0.01
1 year later	0.1	0.001
10 years later	0.05	$10^{-4}$
100 years later	0.01	$10^{-6}$
1000 years later	0.005	$10^{-8}$

This difference is due to the fact that transuranic elements are not produced in fusion reactors.

Mathematical Description of Waste Characteristics

The radioactivity decay characteristics of both are determined by the half-life distribution of dominant nuclides. The long-term radioactivity of fission reactor waste is described by the actinide series:

$$A_{\text{fission}}(t) \approx A_{\text{Pu}} \exp\left(-\frac{t}{\tau_{\text{Pu}}}\right) + A_{\text{Am}} \exp\left(-\frac{t}{\tau_{\text{Am}}}\right) + \cdots$$

where $\tau = T_{1/2} / \ln 2$ is the mean lifetime. The $\tau$ of $^{239}$Pu is approximately 35,000 years, and that of $^{241}$Am is approximately 623 years, which dominate long-term radioactivity.

For fusion reactor waste:

$$A_{\text{fusion}}(t) \approx A_{\text{Mn-54}} e^{-t/\tau_{\text{Mn}}} + A_{\text{Fe-55}} e^{-t/\tau_{\text{Fe}}} + A_{\text{Co-60}} e^{-t/\tau_{\text{Co}}} + \cdots$$

Even Co-60, the longest-lived, has $\tau \approx 7.6$ years, and essentially all will have decayed after 100 years.

Activation Mechanisms

In DT fusion reactions, 14.1 MeV high-energy neutrons are generated. These neutrons interact with reactor structural materials, causing material activation.

Neutron Source Term

The neutron generation rate in DT fusion reactions is directly related to fusion power:

$$S_n = \frac{P_{\text{fusion}}}{E_{\text{fusion}}} = \frac{P_{\text{fusion}}}{17.6 \, \text{MeV}}$$

For 1 GW of fusion power:

$$S_n = \frac{10^9 \, \text{W}}{17.6 \times 1.602 \times 10^{-13} \, \text{J}} \approx 3.5 \times 10^{20} \, \text{n/s}$$

This enormous neutron flux continuously irradiates the structural materials.

Neutron Flux and Spectrum

The neutron flux $\phi(E)$ in fusion reactors is expressed as a function of energy $E$. Neutrons from the DT fusion neutron source have an initial energy of 14.1 MeV, but through moderation processes in materials, they form a broad energy spectrum.

Typical values of neutron flux at the first wall are:

$$\phi_{\text{wall}} \approx 10^{14} - 10^{15} \, \text{n/cm}^2\text{/s}$$

This is comparable to the flux near the core fuel in fission reactors, but the average energy is significantly higher.

The neutron spectrum $\phi(E)$ is obtained as a solution of the transport equation with the fusion source term $S(E)$:

$$\Omega \cdot \nabla \phi(\mathbf{r}, E, \Omega) + \Sigma_t(E) \phi = \int_0^\infty dE' \int_{4\pi} d\Omega' \, \Sigma_s(E' \to E, \Omega' \to \Omega) \phi + S(\mathbf{r}, E)$$

where $\Sigma_t$ is the total cross section and $\Sigma_s$ is the scattering cross section.

The spectrum with a 14 MeV peak unique to fusion reactors can be approximately described by group constants considering energy dependence:

$$\phi_g = \int_{E_g}^{E_{g-1}} \phi(E) dE$$

Generally, calculations are performed by dividing into tens to hundreds of energy groups. Libraries such as VITAMIN-J (175 groups) and FENDL (211 groups) are used.

Neutron-Material Interactions

The processes by which neutrons interact with atomic nuclei in materials are mainly classified into the following three types:

1. Elastic scattering: Neutron and nucleus collide and exchange kinetic energy
2. Inelastic scattering: Nucleus becomes excited and emits gamma rays
3. Nuclear reactions: Neutron is absorbed by nucleus and converted to another nuclide

In elastic scattering, the energy loss of neutrons in collision with a nucleus of mass number $A$ is:

$$\Delta E_{\text{max}} = E_n \cdot \frac{4A}{(1+A)^2}$$

This shows that lighter nuclides can moderate neutrons more efficiently.

The range of neutron energy $E'$ after scattering is:

$$\alpha E \leq E' \leq E$$

where $\alpha = \left(\frac{A-1}{A+1}\right)^2$.

The average logarithmic energy decrement (lethargy) is:

$$\xi = 1 + \frac{\alpha \ln \alpha}{1 - \alpha} \approx \frac{2}{A + 2/3}$$

For iron ($A = 56$), $\xi \approx 0.035$, and for hydrogen ($A = 1$), $\xi = 1$.

Displacement Damage

When fast neutrons collide with atomic nuclei in materials, atoms are knocked out of their normal lattice positions. This phenomenon is called “displacement damage.”

The degree of displacement damage is expressed in dpa (Displacement per Atom). This indicates how many times an atom is displaced. dpa is calculated by the following equation:

$$\text{dpa} = \int_0^t dt' \int_0^\infty dE \, \phi(E, t') \sigma_d(E)$$

where $\sigma_d(E)$ is the displacement cross section for neutrons of energy $E$.

The displacement cross section is evaluated by the Norgett-Robinson-Torrens (NRT) model:

$$\sigma_d(E) = \int_{E_d}^{T_{\text{max}}} \sigma(E, T) \nu(T) dT$$

where $E_d$ is the threshold displacement energy of lattice atoms (approximately 40 eV for iron), $T$ is the recoil atom energy, and $\nu(T)$ is the number of displacements produced by one recoil atom:

$$\nu(T) = \frac{0.8 T_{\text{dam}}}{2 E_d}$$

$T_{\text{dam}}$ is the damage energy after subtracting electronic excitation losses.

The separation of electronic stopping power and displacement stopping power is described by the Lindhard model:

$$T_{\text{dam}} = \frac{T}{1 + k_L g(\epsilon)}$$

where $k_L$ is the Lindhard constant and $g(\epsilon)$ is a function of reduced energy $\epsilon$.

Fusion reactor structural materials are expected to receive damage of about 150-200 dpa during operation. This is about 10 times that of ITER, at prototype reactor levels.

Displacement damage causes the following phenomena:

• Irradiation embrittlement: Material becomes brittle
• Irradiation creep: Deformation progresses under constant stress
• Swelling: Volume expansion due to vacancy accumulation

The volume change $\Delta V/V$ due to swelling is expressed as a function of vacancy concentration $C_v$ and void radius $r$:

$$\frac{\Delta V}{V} = \frac{4\pi}{3} N_v r^3$$

where $N_v$ is the void number density per unit volume.

The time evolution of swelling is described by the diffusion equations for vacancies and interstitials:

$$\frac{\partial C_v}{\partial t} = D_v \nabla^2 C_v + G_v - R_{iv} C_i C_v - k_v^2 D_v C_v$$ $$\frac{\partial C_i}{\partial t} = D_i \nabla^2 C_i + G_i - R_{iv} C_i C_v - k_i^2 D_i C_i$$

where $G$ is the production rate, $R_{iv}$ is the recombination coefficient, and $k^2$ is the sink strength.

Transmutation Damage

When neutrons are absorbed by atomic nuclei, transmutation occurs, changing them to different elements. Main reactions include:

• (n, p) reaction: Absorbs neutron and emits proton
• (n, α) reaction: Absorbs neutron and emits alpha particle (helium)
• (n, 2n) reaction: Absorbs neutron and emits two neutrons
• (n, γ) reaction: Gamma ray emission by neutron capture

Gas production rate by transmutation is an important parameter unique to fusion reactors. The helium production rate in iron by 14 MeV neutrons:

$$\dot{n}_{\text{He}} = \phi \cdot \sigma_{(n,\alpha)} \cdot N$$

where $\sigma_{(n,\alpha)}$ is the (n, α) reaction cross section and $N$ is the atomic number density.

Typical gas production rates in reduced-activation ferritic steel:

Gas	Production Rate (appm/dpa)
Helium	10 - 15
Hydrogen	40 - 50

Here, appm is atomic parts per million (number of produced atoms per million atoms).

Helium and hydrogen produced by these reactions accumulate in materials and cause degradation of mechanical properties. Helium in particular accumulates at grain boundaries, forming voids and causing embrittlement at high temperatures (helium embrittlement).

The mechanism of helium embrittlement is described by bubble growth at grain boundaries and grain boundary embrittlement:

$$r_{\text{bubble}} = \left( \frac{3 n_{\text{He}} k_B T}{4 \pi P_{\text{eq}}} \right)^{1/3}$$

where $n_{\text{He}}$ is the number of helium atoms in the bubble and $P_{\text{eq}}$ is the equilibrium pressure.

Physics of Induced Activation

Among the nuclides produced by transmutation, some are radioactive. When these radioactive nuclides emit beta and gamma rays, the material becomes radioactive. This phenomenon is called “activation,” and the resulting radioactivity is called “induced radioactivity.”

Basic Equation of Activation

The time evolution of the atomic number density $N_i$ of a nuclide $i$ is described by the Bateman equations:

$$\frac{dN_i}{dt} = \sum_j \phi \sigma_{j \to i} N_j + \sum_k \lambda_k f_{k \to i} N_k - \left( \phi \sigma_i + \lambda_i \right) N_i$$

where:

• $\sigma_{j \to i}$: Cross section for conversion from nuclide $j$ to $i$
• $\lambda_k$: Decay constant of nuclide $k$ ($\lambda = \ln 2 / T_{1/2}$)
• $f_{k \to i}$: Decay branching ratio from nuclide $k$ to $i$
• $\sigma_i$: Absorption cross section of nuclide $i$

By solving this system of coupled differential equations, the concentration of each nuclide at any time can be obtained.

In actual calculations, thousands to tens of thousands of nuclides must be handled simultaneously. Written in matrix form:

$$\frac{d\mathbf{N}}{dt} = \mathbf{A} \mathbf{N}$$

where $\mathbf{A}$ is the transition matrix. The solution is:

$$\mathbf{N}(t) = \exp(\mathbf{A} t) \mathbf{N}(0)$$

Various numerical methods are used to calculate the matrix exponential.

Description of Multi-Stage Reactions

In actual activation, there are nuclides produced through multiple pathways from parent nuclides. For example, the production pathway of Co-60:

$$^{59}\text{Co} \xrightarrow{(n,\gamma)} ^{60}\text{Co}$$

Also, the pathway from Ni-58:

$$^{58}\text{Ni} \xrightarrow{(n,p)} ^{58}\text{Co} \xrightarrow{\beta^+} ^{58}\text{Fe}$$

Analysis considering all these competing pathways is necessary.

Saturation Radioactivity

Under constant neutron flux with long-term irradiation, radioactivity approaches a saturation value. Considering simple one-stage production and decay:

$$A_{\text{sat}} = \phi \sigma N_{\text{target}}$$

The radioactivity at irradiation time $t$ is:

$$A(t) = A_{\text{sat}} \left( 1 - e^{-\lambda t} \right)$$

When irradiation time exceeds 5 times the half-life, radioactivity reaches more than 97% of the saturation value.

More generally, considering production and destruction:

$$\frac{dN}{dt} = \phi \sigma_{\text{prod}} N_{\text{parent}} - (\lambda + \phi \sigma_{\text{abs}}) N$$

The steady-state solution is:

$$N_{\text{sat}} = \frac{\phi \sigma_{\text{prod}} N_{\text{parent}}}{\lambda + \phi \sigma_{\text{abs}}}$$

In the high-flux environment of fusion reactors, the absorption term $\phi \sigma_{\text{abs}}$ may not be negligible.

Radioactivity Decay During Cooling

After reactor shutdown (end of irradiation), radioactivity decays. For a single nuclide:

$$A(t_c) = A_0 \exp\left( -\lambda t_c \right) = A_0 \exp\left( -\frac{\ln 2 \cdot t_c}{T_{1/2}} \right)$$

where $t_c$ is the cooling time and $A_0$ is the radioactivity at the end of irradiation.

In actual activated materials, numerous nuclides coexist, so the total radioactivity is:

$$A_{\text{total}}(t_c) = \sum_i A_{i,0} \exp\left( -\lambda_i t_c \right)$$

This shows a two-stage behavior where decay is rapid in the initial stage dominated by short half-life nuclides, and slow in the later stage when long half-life nuclides remain.

This behavior can be understood as a superposition of multiple components with different half-lives:

$$A(t) = A_{\text{short}} e^{-t/\tau_{\text{short}}} + A_{\text{medium}} e^{-t/\tau_{\text{medium}}} + A_{\text{long}} e^{-t/\tau_{\text{long}}}$$

The relative contribution of each component changes with time, with short-lived components dominating initially and long-lived components dominating later.

Decay Heat

Radioactive decay generates thermal energy. The decay heat $P(t)$ is:

$$P(t) = \sum_i \lambda_i N_i(t) \bar{E}_i$$

where $\bar{E}_i$ is the average energy release per decay of nuclide $i$.

Decay heat is calculated as the sum of beta ray, gamma ray, and alpha ray energies:

$$\bar{E}_i = \bar{E}_{\beta,i} + \bar{E}_{\gamma,i} + \bar{E}_{\alpha,i}$$

In beta decay, since some energy is carried away by neutrinos:

$$\bar{E}_{\beta} = \frac{1}{3} E_{\beta,\text{max}}$$

is approximated (assuming Fermi distribution).

For ITER, the decay heat immediately after shutdown is about 11 MW, but it decreases rapidly with time:

Cooling Time	Decay Heat
Immediately after shutdown	11 MW
1 hour later	2 MW
1 day later	0.6 MW
1 week later	0.2 MW
1 month later	0.1 MW

Fusion reactor decay heat is very small compared to fission reactors:

• Does not require emergency cooling systems
• Natural circulation cooling is sufficient
• Temperature rise is limited due to large heat capacity of large structures such as vacuum vessel

The decay heat density $q(t)$ is:

$$q(t) = \frac{P(t)}{V}$$

The temperature rise in the vacuum vessel (volume $V \approx 1000$ m³, mass $M \approx 5000$ tons) is:

$$\Delta T = \frac{P \cdot t}{M \cdot c_p}$$

Using the specific heat of iron $c_p \approx 500$ J/(kg·K), for 1 hour in adiabatic conditions:

$$\Delta T \approx \frac{2 \times 10^6 \times 3600}{5 \times 10^6 \times 500} \approx 2.9 \, \text{K}$$

This level of temperature rise does not affect structural integrity.

Dose Rate

The dose rate $\dot{D}$ from activated material is, in point source approximation at distance $r$:

$$\dot{D}(r) = \frac{A \cdot \Gamma}{r^2} \cdot B(E, r) \cdot e^{-\mu r}$$

where $\Gamma$ is the gamma-ray constant, $B$ is the buildup factor, and $\mu$ is the attenuation coefficient.

The buildup factor represents the contribution of scattered radiation, and in Taylor approximation:

$$B(\mu r) = A_1 e^{-\alpha_1 \mu r} + (1 - A_1) e^{-\alpha_2 \mu r}$$

where $A_1$, $\alpha_1$, $\alpha_2$ are parameters that depend on material and energy.

In actual evaluations, Monte Carlo calculation codes (MCNP, Serpent, etc.) are used to calculate dose distributions in complex geometries.

Major Radioactive Nuclides

We explain in detail the major radioactive nuclides produced by activation of fusion reactor materials.

Activation Products of Iron-Based Alloys

Nuclides produced from iron, chromium, and tungsten, which are the main constituent elements of reduced-activation ferritic steels (such as F82H):

Fe-55 (Iron-55)

• Half-life: 2.737 years
• Decay mode: Electron capture (EC)
• Production reaction: $^{56}$Fe(n, 2n)$^{55}$Fe
• Threshold energy: 11.2 MeV
• Characteristics: Emits only low-energy X-rays (5.9 keV), small contribution to external exposure

The production cross section is about 460 mb (millibarns) for 14 MeV neutrons, making it one of the dominant activated nuclides in the fusion reactor environment.

The cross section for threshold reactions depends strongly on energy:

$$\sigma(E) = \begin{cases} 0 & (E < E_{\text{th}}) \\ \sigma_0 \left(1 - \frac{E_{\text{th}}}{E}\right)^n & (E \geq E_{\text{th}}) \end{cases}$$

where $n$ is a reaction-dependent parameter, typically $n \approx 1-2$ for (n, 2n) reactions.

Mn-54 (Manganese-54)

• Half-life: 312.2 days
• Decay mode: Electron capture
• Gamma-ray energy: 835 keV
• Production reactions: $^{54}$Fe(n, p)$^{54}$Mn, $^{55}$Mn(n, 2n)$^{54}$Mn
• Characteristics: Emits relatively high-energy gamma rays, important for dose evaluation

Mn-54 is the nuclide that dominates dose rate for several years after shutdown and is important in maintenance work planning.

The contribution to dose is:

$$\dot{D}_{\text{Mn-54}} = A_{\text{Mn-54}} \cdot \Gamma_{\text{Mn-54}} = A_{\text{Mn-54}} \cdot 1.18 \times 10^{-3} \, \text{(mSv/h)/(MBq at 1 m)}$$

Co-60 (Cobalt-60)

• Half-life: 5.27 years
• Decay mode: Beta decay
• Gamma-ray energies: 1.17 MeV, 1.33 MeV
• Production reaction: $^{59}$Co(n, γ)$^{60}$Co
• Characteristics: High-energy gamma rays, large contribution to dose rate

Cobalt exists as an impurity in reduced-activation materials, and its concentration management is extremely important. By keeping impurity concentration below 10 ppm, Co-60 production can be minimized.

The relationship between Co-60 production and impurity concentration:

$$A_{\text{Co-60}} = \phi \cdot \sigma_{\gamma} \cdot N_{\text{Co}} = \phi \cdot \sigma_{\gamma} \cdot \frac{\rho}{M_{\text{Co}}} \cdot c_{\text{Co}}$$

where $c_{\text{Co}}$ is the mass concentration of cobalt (ppm).

With impurity concentrations of 10 ppm versus 100 ppm, the dose rate from Co-60 differs by a factor of 10.

Activation of Chromium and Tungsten

Cr-51 (Chromium-51)

• Half-life: 27.7 days
• Production reactions: $^{52}$Cr(n, 2n)$^{51}$Cr, $^{50}$Cr(n, γ)$^{51}$Cr
• Characteristics: Short half-life, disappears during initial cooling stage

W-181 (Tungsten-181)

• Half-life: 121.2 days
• Production reaction: $^{182}$W(n, 2n)$^{181}$W
• Characteristics: Contributes to initial radioactivity of tungsten alloys

W-185 (Tungsten-185)

• Half-life: 75.1 days
• Production reaction: $^{184}$W(n, γ)$^{185}$W
• Decay mode: Beta decay

W-187 (Tungsten-187)

• Half-life: 23.7 hours
• Production reaction: $^{186}$W(n, γ)$^{187}$W
• Characteristics: Dominant nuclide immediately after shutdown, decays rapidly

The activation characteristics of tungsten vary greatly depending on isotope composition. Isotope composition of natural tungsten:

Isotope	Natural Abundance	Main Activation Reaction
$^{180}$W	0.12%	(n, γ) → $^{181}$W
$^{182}$W	26.50%	(n, 2n) → $^{181}$W
$^{183}$W	14.31%	(n, γ) → $^{184}$W (stable)
$^{184}$W	30.64%	(n, γ) → $^{185}$W
$^{186}$W	28.43%	(n, γ) → $^{187}$W

Long-Term Important Nuclides

Nb-94 (Niobium-94)

• Half-life: 20,300 years
• Production reaction: $^{93}$Nb(n, γ)$^{94}$Nb
• Characteristics: Extremely long half-life, reason for excluding niobium from reduced-activation materials

The presence of niobium has a significant impact on long-term management of fusion reactor waste. In F82H, niobium concentration is controlled to below 1 ppm.

The reason why Nb-94 is problematic is shown quantitatively. The residual radioactivity after 100 years of cooling is:

$$A_{\text{Nb-94}}(100 \, \text{yr}) = A_0 \cdot e^{-\ln 2 \cdot 100/20300} \approx 0.997 \cdot A_0$$

That is, it hardly decays even after 100 years. On the other hand, Mn-54:

$$A_{\text{Mn-54}}(100 \, \text{yr}) = A_0 \cdot e^{-\ln 2 \cdot 100 \cdot 365/312} \approx 10^{-35} \cdot A_0 \approx 0$$

It completely disappears.

Mo-93 (Molybdenum-93)

• Half-life: 4,000 years
• Production reaction: $^{92}$Mo(n, γ)$^{93}$Mo
• Characteristics: Problematic in molybdenum-containing materials, reduced-activation steels replace molybdenum with tungsten

Ni-59 (Nickel-59)

• Half-life: 76,000 years
• Production reaction: $^{58}$Ni(n, γ)$^{59}$Ni
• Characteristics: Cause of long-term radioactivity in nickel-based alloys

Ni-63 (Nickel-63)

• Half-life: 100.1 years
• Production reaction: $^{62}$Ni(n, γ)$^{63}$Ni
• Decay mode: Pure beta (66.9 keV)
• Characteristics: Contributes to medium-term radioactivity

In nickel-containing materials (316SS, etc.), Ni-59 and Ni-63 dominate long-term radioactivity.

Activation of Aluminum

In aluminum alloys being considered as lightweight structural materials, there are special problems:

Al-26 (Aluminum-26)

• Half-life: 717,000 years
• Production reaction: $^{27}$Al(n, 2n)$^{26}$Al
• Threshold energy: 13.5 MeV
• Characteristics: Extremely long half-life, produced by 14 MeV neutrons

This reaction is a problem unique to fusion. Since the threshold is 13.5 MeV, it does not occur in fission reactors, but it becomes a problem in fusion reactors with 14 MeV neutrons.

Calculation of Radioactive Nuclide Production

The atomic number density of nuclide $i$ at the end of irradiation is, in a simplified model:

$$N_i = \frac{\phi \sigma_{\text{prod}}}{\lambda_i} N_{\text{parent}} \left( 1 - e^{-\lambda_i t_{\text{irr}}} \right)$$

where $\sigma_{\text{prod}}$ is the production cross section and $t_{\text{irr}}$ is the irradiation time.

In actual calculations, activation calculation codes such as FISPACT-II, ACAB, and ORIGEN are used, considering complete decay chains and cross-section libraries.

Activation Calculation Codes and Evaluation Methods

Dedicated calculation codes and nuclear data libraries are used for activation evaluation of fusion reactors.

Major Activation Calculation Codes

FISPACT-II

Activation calculation code developed by UK Atomic Energy Authority (UKAEA), a standard tool for fusion applications.

Features:

• Matrix exponential solution of Bateman equations
• Uncertainty propagation analysis capability
• Sensitivity analysis capability
• Support for multiple nuclear data libraries

The calculation flow is:

1. Input neutron spectrum
2. Calculate group-averaged cross sections
3. Build transition matrix
4. Calculate time evolution
5. Output radioactivity, decay heat, dose rate

Group-averaged cross section:

$$\bar{\sigma}_g = \frac{\int_{E_g}^{E_{g-1}} \sigma(E) \phi(E) dE}{\int_{E_g}^{E_{g-1}} \phi(E) dE}$$

ORIGEN-S

Code developed by Oak Ridge National Laboratory (ORNL), provided as part of the SCALE package.

Features:

• Extensive decay data library
• Consideration of spontaneous fission, (α, n) reactions
• Neutron source term calculation
• Processing of multi-stage irradiation history

ACT-4

Activation calculation code developed by Japan Atomic Energy Agency (JAEA).

Features:

• Compatible with JENDL (Japanese Evaluated Nuclear Data Library)
• Optimized for Japanese fusion research
• Used in ITER TBM evaluation

EASY-II

Standard activation analysis system used by EUROfusion.

Components:

• FISPACT-II (inventory calculation)
• EAF (European Activation File)
• TENDL (nuclear data library)

Nuclear Data Libraries

The accuracy of activation calculations depends greatly on the quality of nuclear data.

EAF (European Activation File)

Activation-specific nuclear data library developed in Europe:

• 816 target nuclides
• Approximately 62,000 reactions
• Optimized for 14 MeV neutrons

TENDL

Evaluated nuclear data library based on the TALYS nuclear reaction code:

• Systematic evaluation based on theoretical models
• Includes uncertainty information
• Updated annually

JENDL/AD

Japanese nuclear data library for activation:

• Added activation reactions based on JENDL-4.0
• Approximately 770 target nuclides
• Standard use in Japanese fusion research

FENDL (Fusion Evaluated Nuclear Data Library)

Library maintained by IAEA for fusion applications:

• International standard
• Applicable to both transport and activation calculations
• Used in ITER design

Uncertainty Evaluation of Calculations

Activation calculations have various uncertainty sources:

1. Nuclear data uncertainty

   • Cross section measurement errors
   • Covariance data

2. Neutron spectrum uncertainty

   • Transport calculation errors
   • Geometric model approximations

3. Material composition uncertainty

   • Impurity concentration variations
   • Variability between manufacturing lots

Uncertainty propagation is:

$$\sigma_A^2 = \sum_i \left( \frac{\partial A}{\partial \sigma_i} \right)^2 \sigma_{\sigma_i}^2 + \sum_i \left( \frac{\partial A}{\partial N_i} \right)^2 \sigma_{N_i}^2$$

In FISPACT-II, uncertainty analysis by Monte Carlo sampling is possible:

1. Set probability distributions for input parameters
2. Multiple sampling calculations
3. Statistical analysis of outputs

Experimental Verification

The validity of activation calculations is verified by comparison with experimental data.

FNS (Fusion Neutron Source)

Accelerator neutron source of Japan Atomic Energy Agency:

• 14 MeV neutron beam
• Sample irradiation and activation measurement
• Comparison verification with calculations (C/E values)

Representative verification results:

Nuclide	C/E Value	Uncertainty
Mn-54	0.95	±10%
Fe-55	1.02	±15%
Co-60	1.10	±12%

The closer the C/E (Calculation/Experiment) value is to 1.0, the higher the calculation accuracy.

IFMIF-DONES

High-intensity neutron irradiation facility under construction:

• Neutron spectrum equivalent to fusion
• High irradiation dose of 40 dpa/year
• Acquisition of material irradiation data

Calculation Example

Activation calculation example of F82H steel (1 MW/m² wall load, 5-year irradiation):

Input conditions:

• Material: F82H (Fe-8Cr-2W-0.2V-0.04Ta)
• Neutron flux: $5 \times 10^{14}$ n/cm²/s
• Neutron spectrum: ITER first wall conditions
• Irradiation time: 5 years
• Cooling time: 0-100 years

Calculation results (specific radioactivity):

Cooling Time	Specific Radioactivity (Bq/kg)	Major Nuclides
0 (immediately after shutdown)	$3 \times 10^{12}$	Mn-56, W-187
1 day	$1 \times 10^{12}$	Mn-54, Fe-55
1 year	$5 \times 10^{11}$	Mn-54, Fe-55
10 years	$1 \times 10^{11}$	Fe-55, Co-60
100 years	$1 \times 10^{8}$	Nb-94, Mo-93

Waste Categories and Classification

Radioactive waste from fusion reactors is classified based on radioactivity concentration and half-life.

International Waste Classification

IAEA (International Atomic Energy Agency) classification system:

1. Exempt Waste (EW)

   • Below clearance levels
   • Can be processed as non-regulated

2. Very Short Lived Waste (VSLW)

   • Dominated by short half-life nuclides
   • Decays with several years of storage

3. Very Low Level Waste (VLLW)

   • Near-surface disposal possible
   • Management period: Several decades

4. Low Level Waste (LLW)

   • Near-surface disposal
   • Management period: Several hundred years

5. Intermediate Level Waste (ILW)

   • Requires deeper disposal
   • Low heat generation

6. High Level Waste (HLW)

   • Requires deep geological disposal
   • Not generated in fusion reactors

IAEA classification and disposal method correspondence:

Category	Radioactivity Level	Heat	Disposal Method
EW	Below clearance	None	General waste
VSLW	Very low	None	Decay storage
VLLW	Very low	None	Near-surface disposal
LLW	Low	Negligible	Near-surface disposal
ILW	Intermediate	Low	Intermediate depth disposal
HLW	High	High	Deep geological disposal

Japanese Classification System

Disposal categories for low-level radioactive waste defined by the Atomic Energy Commission:

Category	Radioactivity Concentration	Disposal Method	Management Period
L3	Very low level	Trench disposal	Several decades
L2	Low level	Near-surface pit disposal	300 years
L1	Relatively high	Intermediate depth disposal	Several thousand years

Activated materials from fusion reactors are classified as L2 or L3 after appropriate cooling periods.

Concentration upper limits for each category (representative nuclides):

Nuclide	L3 Upper Limit (Bq/t)	L2 Upper Limit (Bq/t)	L1 Upper Limit (Bq/t)
Co-60	$10^{10}$	$10^{12}$	$10^{14}$
Ni-63	$10^{11}$	$10^{13}$	$10^{15}$
Nb-94	$10^{7}$	$10^{9}$	$10^{11}$

US Classification System

Classification by NRC (Nuclear Regulatory Commission) 10 CFR 61:

Class A

• Lowest level
• No stabilization required
• Decays in 100 years

Class B

• Structural stabilization required
• Decays in 300 years
• Intrusion prevention design

Class C

• Highest level of LLW
• Burial at depth of 5 m or more
• Intrusion prevention barriers

Greater Than Class C (GTCC)

• Level exceeding Class C
• Special disposal required
• Fusion reactor waste does not fall into this category

Class C concentration upper limits:

Nuclide	Concentration Upper Limit
Ni-63	700 Ci/m³
Nb-94	0.2 Ci/m³
Co-60	Unlimited
C-14	8 Ci/m³

Fusion Reactor-Specific Waste Classification

Practical classification considering characteristics of fusion reactor waste:

Class C Equivalent

The highest level for near-surface disposal under US NRC classification. Highly activated components of fusion reactors (first wall, divertor, etc.) fall within this level after cooling.

Nuclide concentration upper limits for determination:

Nuclide	Concentration Upper Limit (Ci/m³)
Ni-63	700
Nb-94	0.2
Co-60	Unlimited

Recyclable Materials

Radioactivity level that allows remote-operated recycling. Defined by dose rate:

$$\dot{D} < 10 \, \text{mSv/h at 1 m}$$

Hands-On Materials

Low radioactivity materials allowing direct work:

$$\dot{D} < 10 \, \mu\text{Sv/h at 1 m}$$

Waste Generation Estimates

Estimated waste generation from a 1 GWe fusion power plant:

Component	Replacement Cycle	Weight (tons/year)	Major Nuclides
First wall	2-3 years	50-100	Mn-54, Fe-55
Blanket	4-5 years	200-400	W isotopes, Cr-51
Divertor	2 years	20-50	W-181, W-185
Vacuum vessel	Plant lifetime	1000-2000	Co-60, Ni-63

After 40 years of operation, total waste volume is estimated at about 10,000 tons. This is comparable to a fission reactor of the same output (including spent fuel), but the radioactivity and toxicity are much lower.

Time evolution of waste volume:

$$V_{\text{waste}}(t) = \sum_{\text{components}} \frac{M_{\text{component}}}{t_{\text{cycle}}} \cdot t$$

Estimated waste amounts by category after 40 years of operation:

Category	Mass (tons)	Volume (m³)	Proportion
L1 equivalent	2,000	400	20%
L2 equivalent	5,000	1,000	50%
L3 equivalent	2,000	400	20%
Clearance	1,000	200	10%

Transition between categories is possible with cooling periods.

Reduced-Activation Materials

To reduce radioactive waste from fusion reactors, development of “reduced-activation materials” that do not readily produce long-lived radioactive nuclides under neutron irradiation is being advanced.

Principles of Reduced Activation

The basic principle of reduced-activation material design is to exclude elements that produce long half-life nuclides.

The activation characteristics of elements are determined by the following factors:

1. Abundance ratios of stable isotopes
2. Neutron reaction cross sections
3. Half-lives of produced nuclides
4. Decay modes (gamma-ray energies)

Definition of Activation Potential (AP):

$$\text{AP} = \sum_i \sigma_i \cdot f_i \cdot \frac{A_i}{\text{MPC}_i} \cdot T_{1/2,i}$$

where $f_i$ is the production branching ratio and MPC is the Maximum Permissible Concentration.

Material Selection Criteria

Elements suitable as reduced-activation materials, when irradiated with 14 MeV neutrons:

• Do not produce long half-life radioactive nuclides
• Produced radioactive nuclides decay relatively quickly

As a quantitative evaluation index, Contact Dose Rate (CDR) is used:

$$\text{CDR}(t) = \sum_i A_i(t) \cdot \Gamma_i$$

where $\Gamma_i$ is the gamma-ray constant of nuclide $i$.

The target for reduced-activation materials is to achieve after 100 years of cooling:

$$\text{CDR}(100 \, \text{yr}) < 10 \, \mu\text{Sv/h}$$

This corresponds to a level allowing direct hands-on work.

Activation Classification of Elements

Elements can be classified into 3 groups by activation characteristics:

Group I: Reduced-Activation Elements

Decay to near clearance levels after 100 years of cooling:

• C, Si, Ti, V, Cr, Mn, Fe, Ta, W

Group II: Intermediate Elements

LLW level with several hundred years of cooling:

• Cu, Y, Zr

Group III: High-Activation Elements

Produce long-lived nuclides, elements that should be excluded:

• Nb, Mo, Ni, Co, Al, Ag

Elements to Exclude

The following elements are excluded from reduced-activation materials because they produce long-lived radioactive nuclides:

Element	Produced Nuclide	Half-life	Production Reaction
Nb	Nb-94	20,300 years	(n, γ)
Mo	Mo-93	4,000 years	(n, γ)
Ni	Ni-59	76,000 years	(n, γ)
Co	Co-60	5.27 years	(n, γ)
Al	Al-26	717,000 years	(n, 2n)

These elements also require management when present as impurities.

Relationship between impurity concentration and long-term radioactivity:

$$A_{\text{long}}(t) \propto c_{\text{impurity}} \cdot \phi \cdot \sigma \cdot (1 - e^{-\lambda t})$$

Reduced-Activation Ferritic/Martensitic Steel (RAFM Steel)

RAFM (Reduced Activation Ferritic/Martensitic) steel is the primary candidate for fusion reactor structural materials.

Development History

Development of RAFM steel began in the 1980s:

• 1985: Start of conceptual design
• 1990s: Laboratory-scale manufacturing
• 2000s: Establishment of industrial-scale manufacturing
• 2010s: Adoption for ITER TBM

F82H (Japan)

F82H, developed by Japan Atomic Energy Research Institute (now National Institutes for Quantum Science and Technology), is a representative reduced-activation ferritic steel.

Basic composition:

Element	Content	Role
Fe	Balance	Base material
Cr	7.5-8.5%	Corrosion resistance
W	1.5-2.5%	Solid solution strengthening
V	0.15-0.25%	Precipitation strengthening
Ta	0.02-0.08%	Precipitation strengthening
C	0.08-0.12%	Carbide formation
Mn	0.1-0.5%	Deoxidation

Impurity management upper limits:

Impurity	Upper Limit	Reason
Nb	< 1 ppm	Suppress Nb-94 production
Mo	< 50 ppm	Suppress Mo-93 production
Ni	< 200 ppm	Suppress Ni-59/63 production
Co	< 10 ppm	Suppress Co-60 production
Cu	< 100 ppm	Suppress irradiation embrittlement

Mechanical properties of F82H:

Property	Value	Condition
Tensile strength	550 MPa	Room temperature
Yield strength	450 MPa	Room temperature
Elongation	20%	Room temperature
Impact transition temperature	-70°C	DBTT
Creep rupture time	10⁵ h	550°C, 120 MPa

Features of F82H:

• Replaced molybdenum with tungsten from conventional chrome-molybdenum steel
• Manufacturing experience of 5-ton scale through IEA (International Energy Agency) international joint research
• Adopted as structural material for ITER Test Blanket Module
• Primary candidate material for prototype reactor

The upper limit of operating temperature is about 550°C, used in combination with water-cooled blankets.

EUROFER97 (Europe)

RAFM steel developed in Europe with a composition similar to F82H.

Composition: Fe-9Cr-1.1W-0.2V-0.12Ta-0.11C

Main differences:

• Slightly higher tungsten content (1.1%)
• Higher vanadium content (0.2%)
• Reference material for DEMO design

Industrial-scale manufacturing of EUROFER97 was established through cooperation of 15 European countries.

9Cr-2WVTa Series (USA)

Groups of reduced-activation steels developed in the United States. Various variations are being studied.

ODS Steel (Oxide Dispersion Strengthened Steel)

To overcome the operating temperature limit of conventional RAFM steel (550°C), development of oxide dispersion strengthened (ODS) steel is being advanced.

Strengthening Mechanism

By dispersing fine oxide particles (Y₂O₃, etc.) in steel, high-temperature strength is improved:

$$\sigma_y = \sigma_0 + \sigma_{\text{Orowan}}$$

Orowan strengthening:

$$\sigma_{\text{Orowan}} = \frac{0.8 M G b}{2\pi\sqrt{1-\nu}} \cdot \frac{\ln(d/b)}{\lambda}$$

where $M$ is the Taylor factor, $G$ is the shear modulus, $b$ is the Burgers vector, $d$ is the particle diameter, and $\lambda$ is the particle spacing.

9Cr-ODS Steel

Composition: Fe-9Cr-2W-0.2V-0.35Y₂O₃

Properties:

• Operating temperature: Up to 650°C
• Excellent high-temperature creep strength
• Stable oxide dispersion under irradiation

Manufacturing process:

1. Mechanical alloying
2. Sintering and hot working
3. Heat treatment

Challenges:

• High cost
• Anisotropy
• Joining technology

Vanadium Alloys

Features of V-4Cr-4Ti (vanadium-4% chromium-4% titanium) alloy:

• Extremely low induced radioactivity
• Excellent compatibility with liquid lithium
• High-temperature strength
• Challenges: Irradiation embrittlement, workability

Comparison of radioactivity decay (100 years after irradiation):

Material	Relative Radioactivity
316SS (conventional material)	1.0
F82H	0.01
V-4Cr-4Ti	0.001

Main produced nuclides in vanadium alloys:

Nuclide	Half-life	Production Reaction
Ti-45	3.1 h	Ti-46(n, 2n)
V-52	3.8 min	V-51(n, γ)
Cr-51	27.7 d	Cr-52(n, 2n)
Ca-45	163 d	Ti-48(n, α)

Short-lived nuclides are dominant, and radioactivity after 100 years of cooling is very low.

SiC/SiC Composite Materials

Silicon carbide fiber-reinforced silicon carbide matrix composites:

• Inherently reduced activation (Si, C are difficult to activate)
• Ultra-high temperature capability (above 1400°C)
• High thermal efficiency (> 50%)
• Challenges: Property changes under irradiation, joining technology

Structure and Manufacturing

Structure of SiC/SiC composite materials:

1. SiC fibers (diameter 10-15 μm)
2. Interface layer (PyC or BN, thickness 0.1-1 μm)
3. SiC matrix

Manufacturing methods:

• CVI (Chemical Vapor Infiltration)
• PIP (Polymer Infiltration and Pyrolysis)
• MI (Melt Infiltration)

Activation Characteristics

Main nuclides produced:

Nuclide	Half-life	Production Reaction
C-14	5,730 years	N-14(n, p) impurity origin
Si-32	172 years	Si-30(n, γ)Si-31(β)Si-32
H-3	12.3 years	Li-6(n, α) impurity origin

C-14 production depends on nitrogen impurities:

$$A_{\text{C-14}} = \phi \cdot \sigma_{(n,p)} \cdot N_{\text{N}}$$

By controlling nitrogen impurities below 10 ppm, C-14 production can be minimized.

Tungsten and Beryllium

Activation characteristics of tungsten and beryllium used as plasma-facing materials:

Tungsten

• High melting point, low sputtering rate, ideal for divertor
• Activation: W-181, W-185, W-187, etc.
• Long-lived nuclides are not readily produced
• Low-level waste after 100 years of cooling

Tungsten activation calculation example (divertor conditions):

Cooling Time	Specific Radioactivity (Bq/kg)	Major Nuclides
0	$10^{13}$	W-187
1 day	$10^{12}$	W-185, W-181
1 year	$10^{10}$	W-181, Ta-182
100 years	$10^{7}$	Ta-182, Hf-178m

Beryllium

• Neutron multiplier, first wall coating material
• Activation: Be-10 (half-life 1.6 million years)
• Production amount is small but long half-life
• Also issues with tritium accumulation

Be-10 production reaction:

$$^9\text{Be} + n \rightarrow ^{10}\text{Be} + \gamma$$ $$^9\text{Be}(n, 2n)^8\text{Be} \rightarrow 2\alpha$$

Helium is produced by (n, 2n) reactions, affecting material properties.

Clearance and Recycling

Clearance systems and recycling are being considered for volume reduction of radioactive waste.

Clearance System

Clearance is a system that excludes materials with radioactivity concentrations below a certain level (clearance level) from regulation as radioactive waste. Materials below clearance levels can be processed and disposed of as general waste.

Historical Background

Development of clearance systems:

• 1988: IAEA proposes concept
• 1996: IAEA Safety Guide RS-G-1.7
• 2004: Institutionalized in Japan (amendment of Reactor Regulation Act)
• 2005: EU Directive

Determination of Clearance Levels

Based on IAEA Safety Guide RS-G-1.7, determined under the following conditions:

• Individual dose: 10 μSv/year or less
• Collective dose: 1 man·Sv/year or less

Dose evaluation considers various exposure pathways:

1. External exposure

   • Direct gamma rays
   • Exposure from surface contamination

2. Internal exposure

   • Inhalation intake
   • Ingestion

The most restrictive pathway is identified through scenario analysis:

• Metal recycling scenario
• Landfill disposal scenario
• Reuse scenario

The clearance level $C_L$ is determined from the most restrictive pathway:

$$C_L = \frac{D_{\text{limit}}}{\text{DCF} \cdot \text{intake} \cdot \text{factor}}$$

where DCF (Dose Conversion Factor) is the dose conversion factor.

Clearance Levels for Major Nuclides

Nuclide	Clearance Level (Bq/g)
Fe-55	1000
Mn-54	0.1
Co-60	0.1
Ni-63	100
Nb-94	0.1

Nuclide-specific clearance levels in Japanese nuclear regulation (Reactor Regulation Act):

Nuclide	Radioactivity Concentration (Bq/g)
H-3	100
C-14	1
Fe-55	1000
Co-60	0.1
Ni-63	100

Estimation of Clearable Amounts

Clearable rate of fusion reactor components after cooling:

Component	10 Years Cooling	50 Years Cooling	100 Years Cooling
Outer blanket	30%	60%	80%
Vacuum vessel	40%	70%	90%
Shield	60%	85%	95%
Support structure	80%	95%	99%

By providing appropriate cooling periods, waste amounts can be significantly reduced.

Calculation of clearance achievement time:

For each nuclide, the clearance achievement time $t_c$ is obtained:

$$A_i(t_c) = A_{i,0} \exp(-\lambda_i t_c) = C_{L,i}$$ $$t_c = \frac{1}{\lambda_i} \ln\left(\frac{A_{i,0}}{C_{L,i}}\right) = \frac{T_{1/2,i}}{\ln 2} \ln\left(\frac{A_{i,0}}{C_{L,i}}\right)$$

Time when all nuclides satisfy the condition:

$$t_{\text{clearance}} = \max_i \{ t_{c,i} \}$$

Recycling Possibilities

Even materials processed as radioactive waste have recycling possibilities.

Hierarchy of Recycling

1. Unrestricted reuse

   • Below clearance level
   • Reuse as general materials

2. Restricted reuse

   • Reuse within nuclear facilities
   • Processing into new fusion reactor components

3. Remote-operated recycling

   • High radioactivity materials
   • Processing in hot cells

Economics of Recycling

Comparison of recycling cost $C_R$ and disposal cost $C_D$:

$$C_R = C_{\text{separation}} + C_{\text{processing}} + C_{\text{fabrication}}$$ $$C_D = C_{\text{conditioning}} + C_{\text{transport}} + C_{\text{disposal}}$$

Economic decision criterion:

$$\text{Recycling advantageous} \Leftrightarrow C_R + V_{\text{material}} < C_D$$

where $V_{\text{material}}$ is the market value of recycled materials.

Rare metals such as tungsten and vanadium have high economic value for recycling.

Recycling value by material:

Material	Price ($/kg)	Annual Generation (tons)	Potential Value ($/year)
Tungsten	30	50	1.5M
Vanadium	20	20	0.4M
Beryllium	500	5	2.5M
Steel	1	500	0.5M

Technical Challenges

• Separation by material type
• Processing technology under residual radioactivity
• Quality assurance (management of impurity accumulation)
• Development of regulatory framework

Recycling process for radioactive materials:

1. Dismantling and cutting
2. Decontamination
3. Separation (material type, radioactivity level)
4. Melting and refining
5. Processing into new materials
6. Quality inspection

Waste Management Strategy

Waste management of fusion reactors requires a consistent strategy from design stage through operation to decommissioning.

Lifecycle Management

Design Stage

1. Selection of reduced-activation materials
2. Formulation of impurity management specifications
3. Consideration of ease of dismantling
4. Design for waste minimization

Waste impact assessment formula in design:

$$I_{\text{waste}} = \sum_i m_i \cdot f_i(C_i, t_{\text{cool}})$$

where $m_i$ is the component mass and $f_i$ is a waste coefficient depending on cooling time $t_{\text{cool}}$ and composition $C_i$.

Objective function for design optimization:

$$\min_{design} \left[ C_{\text{construction}} + C_{\text{operation}} + C_{\text{decommissioning}} \right]$$

With constraints:

• Safety requirements
• Performance requirements
• Waste limitations

Manufacturing Stage

1. Verification of material purity
2. Obtaining impurity certificates
3. Ensuring traceability
4. Storage of manufacturing records

Quality assurance program for impurity management:

• Analysis certification of raw materials
• Control of manufacturing processes
• Inspection of final products
• Long-term storage of records

Operational Stage

1. Activation monitoring
2. Management of replacement components
3. Operation of interim storage facilities
4. Management of cooling periods

Tracking of activation inventory during operation:

$$\frac{dA}{dt} = \phi(t) \sigma N - \lambda A$$

Calculations considering time-varying neutron flux $\phi(t)$ are necessary.

Decommissioning Stage

1. Formulation of dismantling plan
2. Implementation of decontamination work
3. Separation and classification
4. Final disposal

Decommissioning cost model:

$$C_{\text{D\&D}} = C_{\text{prep}} + C_{\text{removal}} + C_{\text{processing}} + C_{\text{disposal}}$$

Interim Storage

Replacement components and decommissioning waste require interim storage for cooling.

Storage Facility Requirements

• Shielding capability
• Cooling capability (initial stage)
• Environmental monitoring
• Safety management system

Shielding thickness design:

$$\dot{D}(d) = \dot{D}_0 \cdot B(d) \cdot e^{-\mu d} < \dot{D}_{\text{limit}}$$

For concrete shielding, $\mu \approx 0.1$ cm⁻¹ (1 MeV gamma rays).

Optimization of Storage Period

The optimal storage period $t_{\text{opt}}$ minimizes the sum of storage cost $C_S(t)$ and disposal cost $C_D(t)$:

$$t_{\text{opt}} = \arg\min_t \left[ C_S(t) + C_D(t) \right]$$

Extending the storage period:

• Lowers disposal category (reduces disposal cost)
• Increases storage cost
• Increases land use cost

Generally, a cooling period of 50-100 years is the economic optimum.

Detailed economic model:

$$C_{\text{total}}(t) = C_S \cdot t + C_D(A(t))$$

where $C_D(A)$ is the disposal cost depending on radioactivity level $A$.

Waste Minimization

Measures to minimize waste generation:

1. Optimization of material selection

   • Use of reduced-activation materials
   • Thorough impurity management

2. Design optimization

   • Ingenious shielding arrangement
   • Localization of activated regions

3. Operational management

   • Uniformization of neutron fluence distribution
   • Efficient use of materials

4. Dismantling strategy

   • Effective separation
   • Utilization of clearance

The waste volume reduction factor $R$ is:

$$R = \frac{V_{\text{disposed}}}{V_{\text{total}}} = 1 - f_{\text{clearance}} - f_{\text{recycle}}$$

The target is $R < 0.3$ (70% or more to clearance or recycling).

Dismantling and Decontamination Technology

Decommissioning of fusion reactors requires specialized dismantling and decontamination technologies.

Dismantling Technology

Remote Dismantling Systems

Remote operation technology is essential for dismantling highly activated components.

Main technologies:

• Master-slave manipulators
• Program-controlled robots
• Remote cutting devices

Comparison of cutting methods:

Method	Cutting Speed	Secondary Waste	Application Range
Plasma cutting	High	Medium	Thick plates
Laser cutting	Medium	Low	Precision machining
Mechanical cutting	Low	Low	Thin plates
Abrasive water jet	Medium	Medium	Complex shapes

Physics of each cutting method:

Plasma cutting:

$$P = \frac{1}{2} \rho v^3 A + \rho v \Delta H$$

where $\rho$ is material density, $v$ is cutting speed, $A$ is cutting area, and $\Delta H$ is melting enthalpy.

Laser cutting:

$$v_{\text{cut}} = \frac{\alpha I}{\rho (c_p \Delta T + L_m)}$$

where $I$ is laser intensity, $\alpha$ is absorptivity, and $L_m$ is latent heat of melting.

Dismantling of Large Structures

Dismantling strategies for large structures such as vacuum vessels:

1. Segmentation approach

   • Divisible structure from design stage
   • No large on-site cutting required

2. On-site dismantling approach

   • Use of large cutting equipment
   • Securing of removal routes

3. One-piece removal

   • Remove entire structure
   • Dismantling at dedicated facility

Decontamination Technology

Surface contamination removal aims to reduce waste volume and improve working environment.

Chemical Decontamination

Surface contamination removal using acids and chelating agents:

$$M + nH^+ + mL^{n-} \rightarrow ML_m^{(n-mn)+} + \frac{n}{2}H_2$$

Main decontaminants:

• Acids (nitric acid, sulfuric acid, phosphoric acid)
• Chelating agents (EDTA, citric acid)
• Redox agents (potassium permanganate)

Decontamination Factor (DF):

$$\text{DF} = \frac{A_{\text{before}}}{A_{\text{after}}}$$

Typical DF for chemical decontamination is about 10-100.

Electrochemical Decontamination

Surface layer removal by electrolytic polishing:

$$M \rightarrow M^{n+} + ne^-$$

According to Faraday’s law, the removal amount is:

$$m = \frac{M \cdot I \cdot t}{n \cdot F}$$

where $M$ is atomic weight, $I$ is current, $t$ is time, and $F$ is Faraday constant.

Features:

• Uniform surface removal
• Applicable to complex shapes
• Secondary effluent treatment required

Mechanical Decontamination

Physical surface removal:

• Blast treatment
• Grinding
• Ultra-high pressure water washing

Relationship between surface removal thickness $d$ and decontamination effect (when contamination is limited to surface layer):

$$A(d) = A_0 \exp\left(-\frac{d}{\lambda}\right)$$

where $\lambda$ is the contamination penetration depth.

Pressure and removal effect of ultra-high pressure water washing:

$$\dot{m}_{\text{removal}} \propto P^{0.5} \cdot Q$$

where $P$ is pressure and $Q$ is flow rate.

Target Decontamination Levels

Use	Target Surface Contamination Density
Unrestricted release	< 0.4 Bq/cm² (β, γ)
Restricted reuse	< 4 Bq/cm² (β, γ)
Within controlled area	Below regulatory limits

ITER Decommissioning Plan

ITER decommissioning will be a model case for fusion reactor decommissioning.

Decommissioning Phases

1. End of operation and transition period (5 years)

   • Tritium removal
   • System decontamination
   • Initial dismantling preparation

2. Dismantling period (10 years)

   • Removal of highly activated components
   • Remote dismantling work
   • Waste processing and packaging

3. Site restoration (5 years)

   • Building demolition
   • Environmental restoration
   • Final measurement and release

Waste Generation Estimates

Category	Generated Amount (tons)
High activation (L1 equivalent)	4,000
Medium activation (L2 equivalent)	8,000
Low activation (L3 equivalent)	12,000
Clearance target	6,000

Main challenges for ITER decommissioning:

1. Management of beryllium dust
2. Processing of tritium-contaminated components
3. Dismantling of large superconducting coils
4. Remote removal of highly activated divertor

Disposal Concepts

Final disposal of fusion reactor waste applies methods according to radioactivity levels.

Near-Surface Disposal

The majority of fusion reactor waste can be disposed of by near-surface disposal.

Trench Disposal

Applied to very low level waste (L3):

• Burial in trenches near the surface
• Shielding by natural soil
• Management period: About 50 years

Trench design criteria:

• Depth: 3-5 m
• Width: 10-20 m
• Cover thickness: 1-2 m

Dose calculation in safety assessment:

$$D = C \cdot V \cdot f_{\text{release}} \cdot f_{\text{dilution}} \cdot \text{DCF}$$

where $C$ is the waste package concentration, $V$ is the volume, $f_{\text{release}}$ is the release factor, and $f_{\text{dilution}}$ is the dilution factor.

Pit Disposal

Applied to low level waste (L2):

• Storage in concrete pits
• Containment by artificial barriers
• Management period: 300-400 years

Multi-barrier system:

1. Waste form (solidified body)
2. Container (metal drum)
3. Filling material (mortar)
4. Concrete pit
5. Cover soil

Functions of each barrier:

Barrier	Main Function	Design Life
Waste form	Fixation of radionuclides	300 years
Container	Physical containment	50 years
Filling material	Void filling, pH buffering	300 years
Concrete	Structure, water barrier	300 years
Cover soil	Intrusion prevention, water barrier	Permanent

Intermediate Depth Disposal

Applied to relatively high radioactivity waste (L1):

• Underground 50-100 m
• More robust barrier system
• Management period: Several thousand years

Highly activated components of fusion reactors (first wall, divertor, etc.) can be disposed of in this category after appropriate cooling periods.

Design requirements for intermediate depth disposal:

• Rock permeability coefficient: $< 10^{-7}$ m/s
• Groundwater flow velocity: $< 1$ m/year
• Depth: 50-100 m

Comparison with Deep Geological Disposal

High-level waste (HLW) from fission reactors requires deep geological disposal.

Item	Near-Surface Disposal	Deep Geological Disposal
Depth	Several m to 100 m	300 m or more
Target	LLW, ILW	HLW
Management period	Several hundred years	Tens of thousands of years or more
Cost	Low	Extremely high
Social acceptance	Relatively easy	Difficult

Fusion reactors do not generate waste requiring deep geological disposal.

Reasons why deep geological disposal is not needed:

1. Actinides are not produced
2. Production of long-lived nuclides can be suppressed by material selection
3. Radioactivity decays significantly with about 100 years of cooling

Disposal Cost Comparison

Estimated waste disposal costs for 1 GWe power plants:

Reactor Type	Disposal Cost	Notes
Fission (PWR)	100-200 billion yen	Including HLW disposal
Fusion	20-40 billion yen	Near-surface disposal only

Fusion reactors have a significant advantage in disposal costs.

Breakdown of disposal costs (fusion reactor):

Item	Cost (billion yen)	Proportion
Interim storage	5	15%
Processing and packaging	8	25%
Transport	2	6%
Disposal facility construction	10	31%
Disposal operation	5	15%
Post-closure management	2.5	8%

Disposal Site Requirements

Geological Conditions

• Stable ground
• Low groundwater flow velocity
• Appropriate depth

Groundwater migration assessment (1D advection-dispersion model):

$$C(x, t) = \frac{C_0}{2} \left[ \text{erfc}\left( \frac{x - vt}{2\sqrt{Dt}} \right) + \exp\left(\frac{vx}{D}\right) \text{erfc}\left( \frac{x + vt}{2\sqrt{Dt}} \right) \right] \exp(-\lambda t)$$

where $v$ is groundwater flow velocity, $D$ is dispersion coefficient, and $\lambda$ is decay constant.

Nuclide retardation factor (depends on distribution coefficient $K_d$):

$$R = 1 + \frac{\rho_b}{\epsilon} K_d$$

where $\rho_b$ is soil bulk density and $\epsilon$ is porosity.

Social Conditions

• Local community agreement
• Accessibility
• Long-term management system

Site selection process:

1. Literature survey (national screening)
2. Preliminary investigation (investigation from ground surface)
3. Detailed investigation (boring survey)
4. Safety review
5. Construction and operation

Regulation and Standards

Both international standards and national regulations apply to radioactive waste management of fusion reactors.

International Regulatory Framework

IAEA Safety Standards

IAEA has established a safety standards framework for radioactive waste management:

1. Safety Fundamentals (SF-1)

   • Basic principles of radiation protection
   • Intergenerational equity

2. Safety Requirements (GSR Part 5)

   • Predisposal management of radioactive waste
   • Safety assessment requirements

3. Safety Guides

   • Specific technical standards
   • Clearance levels (RS-G-1.7)

Three Principles of Radiation Protection

1. Justification: Benefits must outweigh risks
2. Optimization: ALARA (As Low As Reasonably Achievable)
3. Dose limits: Limitation of individual doses

Mathematical expression (optimization):

$$\min \left[ S + \alpha X + \beta Y \right]$$

where $S$ is protection cost, $X$ is collective dose, $Y$ is individual dose, and $\alpha$, $\beta$ are cost coefficients.

National Regulations

Japan

Regulated by the Nuclear Regulation Authority:

1. Act on the Regulation of Nuclear Source Material, Nuclear Fuel Material and Reactors (Reactor Regulation Act)
2. Act on the Regulation of Radioisotopes, etc. (RI Act)
3. Specified Radioactive Waste Final Disposal Act

Application to fusion reactors:

• ITER: Regulated as nuclear material use facility
• From prototype reactor onwards: Regulation equivalent to power reactor is expected

Clearance system (Article 61-2 of Reactor Regulation Act):

• Radioactivity concentration confirmation system
• Concentration standards by nuclide
• Confirmation by third-party organization

European Union

Regulation under the EURATOM Treaty:

1. Basic Safety Standards Directive (BSS Directive 2013/59/EURATOM)
2. Radioactive Waste Directive (2011/70/EURATOM)

Member states implement through national law.

United States

Regulated by NRC (Nuclear Regulatory Commission):

1. 10 CFR 20: Radiation protection standards
2. 10 CFR 61: Low-level waste disposal
3. 10 CFR 30: Use of radioactive materials

Fusion reactor-specific regulations have not yet been developed; NRC is studying.

Fusion Reactor-Specific Regulatory Issues

Current regulatory systems are based on fission reactors, and there are issues in applying them to fusion reactors:

1. Waste classification criteria

   • Classification assuming fission products
   • Application to activation products

2. Tritium regulation

   • Large-scale tritium use unique to fusion
   • Setting of release and management standards

3. Clearance standards

   • Response to fusion-specific nuclides
   • Evaluation of W isotopes, etc.

4. Licensing procedures

   • Applicability of existing procedures
   • Fusion-specific review requirements

Technical Basis for Standards

Regulatory values are set based on risk assessment.

Annual Dose Limits

General public: 1 mSv/year Occupational exposure: 20 mSv/year (5-year average)

These values are derived from acceptable risk levels:

$$\text{Risk} = D \times \text{Risk coefficient} < \text{Acceptable risk}$$

ICRP risk coefficient: $5 \times 10^{-2}$ Sv⁻¹ (fatal cancer)

For 1 mSv/year:

$$\text{Risk} = 10^{-3} \times 5 \times 10^{-2} = 5 \times 10^{-5} \, \text{/year}$$

This is comparable to other social risks (traffic accidents, etc.).

Clearance Level

Derivation of clearance level (10 μSv/year):

1. Set scenarios (metal recycling, landfill, etc.)
2. Identify exposure pathways
3. Build dose assessment model
4. Derive levels by back-calculation

$$C_L = \frac{10 \, \mu\text{Sv/year}}{\text{DCF} \times \text{intake} \times \text{utilization factor}}$$

Quantitative Evaluation

We quantitatively evaluate the characteristics of fusion reactor waste.

Radioactivity Inventory

Radioactivity at end of operation for a 1 GWe fusion reactor (structural materials only):

$$A_{\text{total}} \approx 10^{18} - 10^{19} \, \text{Bq}$$

This is about 1/100 of a fission reactor of the same output.

Contribution of major nuclides (immediately after shutdown):

Nuclide	Radioactivity Fraction
Mn-54	20%
Fe-55	35%
W isotopes	15%
Cr-51	10%
Others	20%

Time evolution of radioactivity:

$$A(t) = A_0 \sum_i f_i e^{-\lambda_i t}$$

where $f_i$ is the initial fraction of each nuclide.

Toxicity Index

Radiotoxicity is evaluated by VDT (Volume Dilution for Toxicity):

$$\text{VDT} = \sum_i \frac{A_i}{\text{MPC}_i}$$

where MPC (Maximum Permissible Concentration) is the maximum permissible concentration.

The VDT of fusion reactor waste decreases to 10⁻⁶ times that of fission reactors after 100 years.

Comparison (per 1 GWe·year):

Time	Fusion Reactor VDT (m³)	Fission Reactor VDT (m³)
0	$10^{13}$	$10^{15}$
100 years	$10^{9}$	$10^{15}$
1000 years	$10^{6}$	$10^{14}$

Potential Hazard

Long-term potential hazard (RI: Radiotoxicity Index):

$$\text{RI}(t) = \sum_i A_i(t) \cdot e_{\text{ing},i}$$

where $e_{\text{ing},i}$ is the dose coefficient for ingestion.

Comparison (after 1 GWe operation):

Time	Fusion Reactor RI (Sv)	Fission Reactor RI (Sv)	Ratio
1 year	$10^7$	$10^9$	$10^{-2}$
100 years	$10^3$	$10^8$	$10^{-5}$
1000 years	$10^1$	$10^7$	$10^{-6}$

Material-Specific Activation Comparison

Contact dose rate at 100 years after irradiation for each material (1 MW/m² wall load, 5-year irradiation):

Material	CDR (μSv/h)	Evaluation
316SS	10⁵	Remote operation required
F82H	10²	Limited access possible
V-4Cr-4Ti	10	Direct access possible
SiC/SiC	1	Near clearance

The effect of reduced-activation materials is clearly demonstrated.

Uncertainty Evaluation

Uncertainty in activation evaluation is mainly due to the following factors:

1. Nuclear data uncertainty

   • Cross sections: 5-30%
   • Decay data: 1-5%

2. Neutron spectrum uncertainty

   • Transport calculation: 10-20%
   • Geometry approximation: 5-10%

3. Material composition uncertainty

   • Main components: 1-2%
   • Impurities: 50-100%

Propagation of total uncertainty:

$$\sigma_A^2 = \sum_i \left(\frac{\partial A}{\partial p_i}\right)^2 \sigma_{p_i}^2 + 2\sum_{i<j} \frac{\partial A}{\partial p_i} \frac{\partial A}{\partial p_j} \text{cov}(p_i, p_j)$$

Typical total uncertainty is about 20-50%.

International Research and Development

International research and development activities on fusion reactor waste management are being advanced.

Waste Management at ITER

ITER will be a pioneering case for fusion reactor waste management:

1. Activation evaluation

   • Detailed calculations with FISPACT-II
   • Implementation of uncertainty evaluation

2. Waste classification

   • Compliance with French regulations
   • Harmonization with international standards

3. Decommissioning planning

   • Lifecycle cost evaluation
   • Development of dismantling technology

ITER activation inventory (at end of operation):

Component	Radioactivity (Bq)	Major Nuclides
First wall	$5 \times 10^{17}$	Fe-55, Mn-54
Blanket	$2 \times 10^{18}$	W isotopes
Vacuum vessel	$3 \times 10^{17}$	Co-60, Ni-63
Divertor	$1 \times 10^{17}$	W isotopes

EUROfusion Initiatives

European fusion development is conducting waste research in coordination with DEMO design:

1. Development of reduced-activation materials

   • Improvement of EUROFER97
   • Development of ODS steel

2. Recycling technology

   • Remote recycling process
   • Quality assurance methods

3. Development of regulatory framework

   • Formulation of EU unified standards
   • Harmonization of clearance systems

Japanese Research and Development

Activities centered on QST (National Institutes for Quantum Science and Technology):

1. Reduced-activation materials

   • Advancement of F82H
   • Impurity management technology

2. Activation evaluation

   • Development of ACT-4 code
   • Maintenance of JENDL/AD

3. Neutron irradiation testing

   • Participation in IFMIF-DONES
   • Testing at domestic facilities

US Initiatives

DOE (Department of Energy)-led programs:

1. Material development

   • 9Cr RAFM steels
   • SiC/SiC composites

2. Activation database

   • ENDF/B nuclear data
   • Activation calculation codes

3. Regulatory research

   • Collaboration with NRC
   • Study of fusion-specific regulation

Tritium-Containing Waste

A problem unique to fusion reactors is the management of waste contaminated with tritium.

Characteristics of Tritium Contamination

Tritium is:

• Half-life: 12.3 years
• Decay mode: Pure beta (maximum 18.6 keV)
• Chemical behavior: Identical to hydrogen

Tritium permeation into materials:

$$C(x, t) = C_0 \left[1 - \text{erf}\left(\frac{x}{2\sqrt{Dt}}\right)\right]$$

$D$ is the diffusion coefficient, and its temperature dependence is:

$$D = D_0 \exp\left(-\frac{E_a}{RT}\right)$$

Tritium diffusion coefficient in iron: $D_0 \approx 10^{-4}$ m²/s, $E_a \approx 10$ kJ/mol

Classification of Tritium-Contaminated Waste

Contamination Level	Tritium Concentration	Management Method
Low	< 10⁶ Bq/g	Managed as normal LLW
Medium	10⁶ - 10⁹ Bq/g	Special containment
High	> 10⁹ Bq/g	Consider recovery and reuse

Tritium Removal Technology

Tritium removal from tritium-contaminated waste:

1. Thermal desorption

   • Degassing at high temperature (300-500°C)
   • In vacuum or inert gas

2. Oxidative detritiation

   • Heating in presence of oxygen
   • Recovery as HTO

3. Isotope exchange

   • Isotope exchange with hydrogen
   • Catalyst use

Detritiation efficiency:

$$\eta = 1 - \exp\left(-\frac{D t}{L^2}\right)$$

where $L$ is the characteristic length of the material.

Future Outlook

The following initiatives are important in radioactive waste management of fusion reactors.

Technology Development Challenges

1. Advancement of reduced-activation materials

   • Stricter impurity management
   • Development of new materials
   • Establishment of manufacturing processes

2. Activation evaluation technology

   • High-precision cross-section data
   • Verification of calculation codes
   • Uncertainty evaluation

3. Dismantling and decontamination technology

   • Advancement of remote technology
   • Efficient decontamination methods
   • Waste processing technology

4. Disposal technology

   • Optimization of disposal concepts
   • Establishment of safety assessment methods
   • Long-term stability evaluation

Development of Regulatory Framework

A regulatory framework specific to fusion reactor waste is needed:

1. Establishment of clearance standards

   • Evaluation of fusion-specific nuclides
   • International harmonization

2. Formulation of recycling standards

   • Reuse standards for radioactive materials
   • Quality assurance requirements

3. Development of disposal standards

   • Classification of fusion waste
   • Requirements for disposal facilities

4. Rationalization of licensing procedures

   • Fusion-specific review requirements
   • Phased approach

Social Challenges

1. Promotion of public understanding

   • Explanation of differences from fission reactors
   • Risk communication

2. Securing disposal sites

   • Site selection process
   • Consensus building with local communities

3. International cooperation

   • Formulation of common standards
   • Sharing of experience and knowledge

Long-Term Vision

Toward practical use of fusion power generation after 2050:

1. First generation (2050-2070)

   • Use of RAFM steel
   • Response by near-surface disposal
   • Clearance rate 50%

2. Second generation (2070-2100)

   • Introduction of ODS steel, SiC/SiC
   • Improved recycling rate
   • Clearance rate 70%

3. Third generation (after 2100)

   • Complete reduced-activation materials
   • Nearly complete recycling
   • Clearance rate 90%

Expected Outcomes

Through these initiatives, fusion energy is expected to contribute to the realization of a sustainable society as an energy source with low environmental impact.

Advantages of fusion reactor waste management:

1. No high-level waste
2. Short management period (approximately 100 years)
3. Can be handled by near-surface disposal
4. Low disposal costs
5. High social acceptability

These characteristics will be significant advantages in the social implementation of fusion energy.

Radioactive waste from fusion reactors can minimize the burden on the environment and future generations through appropriate material selection and management strategies. This demonstrates the important role that fusion will play in building a sustainable energy system.

Related Topics

• Tritium Management - Safe management of tritium
• Structural Materials - Blanket structural materials
• Plasma-Facing Materials - First wall and divertor materials
• ITER Project - World’s first burning plasma experiment