Fuel Cycle System

The fuel cycle system of a fusion reactor supplies deuterium (D) and tritium (T) fuel to the plasma, recovers unburned fuel, purifies it, and recycles it for reuse. In fusion reactors using the DT reaction, establishing a closed tritium cycle is essential to continue operation while producing tritium within the reactor itself.

Overview of the Fuel Cycle

Inner and Outer Loops

The fuel cycle system of a fusion reactor is classified into an inner loop and an outer loop based on processing speed and residence time.

Inner Loop

The inner loop is a high-speed circulation path from fuel injection to plasma, recovery of unburned fuel, and re-injection.

• Residence time: Several minutes to tens of minutes
• Processing target: Unburned D-T fuel, helium ash
• Main components: Fuel injection system, divertor exhaust system, cryopumps, roughing purification system
• Throughput: 50-100 times the burned tritium amount (depending on burn fraction)

The inner loop requires rapid fuel circulation, so the processing steps are simplified, focusing on rough impurity removal and quick fuel gas resupply.

Outer Loop

The outer loop is the path for precise processing of gas branched from the inner loop and tritium generated in the blanket.

• Residence time: Several hours to several days
• Processing target: Isotope gas mixture, tritiated water, blanket-recovered tritium
• Main components: Isotope separation system, tritiated water processing system, blanket recovery system, fuel storage system
• Throughput: Several to 10% of the inner loop

The outer loop performs precise isotope separation and high purification to produce D-T mixed gas meeting fuel specifications.

Material Balance of the Fuel Cycle System

The material balance of the fuel cycle system in steady-state operation is expressed by the following equation. Let the fuel injection rate be $\dot{N}_{in}$, burn fraction be $f_b$, exhaust recovery rate be $\eta_{ex}$, and purification recovery rate be $\eta_{pu}$:

$$\dot{N}_{in} = \dot{N}_{burn} + \dot{N}_{loss} = f_b \cdot \dot{N}_{in} + (1 - \eta_{ex} \cdot \eta_{pu})(1 - f_b) \cdot \dot{N}_{in}$$

Here, $\dot{N}_{burn}$ is consumption by burning, and $\dot{N}_{loss}$ is loss during the circulation process.

The fuel cycle efficiency $\eta_{cycle}$ is:

$$\eta_{cycle} = \eta_{ex} \cdot \eta_{pu} = \frac{\dot{N}_{recycle}}{\dot{N}_{exhaust}}$$

Commercial reactors require $\eta_{cycle} > 0.99$ to minimize tritium loss.

Components of the Fuel Cycle System

The fuel cycle system consists of multiple subsystems.

Subsystem	Function	Inner/Outer
Fuel injection system	Supply fuel particles to plasma	Inner
Vacuum exhaust system	Recover exhaust gas from plasma	Inner
Roughing purification system	Rapidly remove impurities from exhaust gas	Inner
Hydrogen isotope separation system	Separate and purify H, D, T	Outer
Blanket tritium recovery system	Recover bred tritium	Outer
Fuel storage system	Safely store tritium	Outer
Tritiated water processing system	Process and reuse tritiated water	Outer
Accountancy and monitoring system	Manage tritium inventory	Both

These systems work together to circulate tritium in a closed cycle.

D-T Fuel Supply and Recovery

Fuel Flow

The fuel flow within a fusion reactor is as follows:

1. Supply D-T mixed gas from fuel storage system to fuel injection system
2. Inject fuel from fuel injection system into plasma
3. Fusion reaction in plasma (burn fraction is several percent)
4. Exhaust unburned fuel through divertor
5. Recover exhaust gas with vacuum exhaust system
6. Remove impurities in fuel purification system
7. Separate and purify D, T in isotope separation system
8. Return to fuel storage system for reuse

Burn Fraction and Tritium Circulation Rate

The burn fraction $f_b$ of a fusion reaction is the fraction of injected fuel that actually undergoes fusion. In current designs, the burn fraction is only a few percent, and most fuel is exhausted unburned.

The burn fraction is defined by:

$$f_b = \frac{n_D n_T \langle \sigma v \rangle_{DT} \cdot V \cdot \tau_p}{\dot{N}_{in}}$$

Here, $n_D$, $n_T$ are deuterium and tritium densities, $\langle \sigma v \rangle_{DT}$ is the DT reaction rate coefficient, $V$ is the plasma volume, and $\tau_p$ is the particle confinement time.

The tritium consumption rate per unit time at fusion power $P_f$ is:

$$\dot{m}_T = \frac{M_T \cdot P_f}{E_f \cdot N_A} \approx 1.46 \times 10^{-6} \cdot P_f \text{ [kg/s]}$$

Here, $M_T = 3.016$ g/mol is the molar mass of tritium, $E_f = 17.6$ MeV is the DT reaction energy, and $N_A$ is Avogadro’s number.

Calculating with specific values, for 1 GW of fusion power:

$$\dot{m}_T = \frac{3.016 \times 10^{-3} \times 10^9}{17.6 \times 1.602 \times 10^{-13} \times 6.022 \times 10^{23}} \approx 1.78 \times 10^{-3} \text{ g/s}$$

This corresponds to approximately 55.6 kg/year, or about 0.15 kg/day.

The relationship between burn fraction $f_b$ and circulating tritium rate $\dot{m}_{circ}$ is:

$$\dot{m}_{circ} = \frac{\dot{m}_T}{f_b}$$

With a burn fraction of 5%, for 0.15 kg/day consumption, 3 kg/day of tritium must be processed in circulation.

Fuel Injection Methods

Several methods exist for injecting fuel into plasma, each with different characteristics.

Gas Puffing

The simplest method of directly blowing fuel gas from a port in the vacuum vessel.

Operating Principle

Gas is injected in pulses or continuously from a high-pressure fuel tank through a piezoelectric valve or solenoid valve. The injected gas molecules ionize at the plasma periphery and are incorporated into the plasma.

The relationship between gas injection rate $\Gamma_{gas}$ [molecules/s] and valve opening:

$$\Gamma_{gas} = \frac{P_u \cdot A_{valve}}{\sqrt{2\pi m k_B T_u}} \cdot f(P_d/P_u)$$

Here, $P_u$ is upstream pressure, $A_{valve}$ is valve opening area, $m$ is molecular mass, $T_u$ is upstream temperature, and $f$ is the flow coefficient depending on pressure ratio.

Characteristics and Applications

• Simple structure with high reliability
• Suitable for fuel supply to plasma periphery
• Limited penetration to plasma core (penetration length $\lambda_{ion} \sim 1$ cm)
• Mainly used for fine adjustment of plasma density
• Response time: Several milliseconds

The fuel supply efficiency $\eta_{gas}$ by gas puffing strongly depends on edge plasma conditions:

$$\eta_{gas} = 1 - \exp\left(-\frac{a}{\lambda_{ion}}\right)$$

Here, $a$ is the plasma minor radius and $\lambda_{ion}$ is the ionization mean free path. In high-density plasmas, $\eta_{gas} \sim 0.3$-$0.5$.

Pellet Injection

A method of firing solid pellets (approximately 2-4 mm diameter) of fuel solidified at cryogenic temperatures (about 18 K) at high speed into the plasma.

Pellet Production

Deuterium-tritium mixed gas is cooled to cryogenic temperatures to form solid pellets. Pellet density is:

$$\rho_{pellet} = 0.255 \text{ g/cm}^3 \text{ (D}_2\text{)} \quad \text{or} \quad 0.32 \text{ g/cm}^3 \text{ (T}_2\text{)}$$

The number of atoms in one pellet (3 mm diameter):

$$N_{pellet} = \frac{4}{3}\pi r^3 \cdot \rho \cdot \frac{2 N_A}{M} \approx 6 \times 10^{20} \text{ atoms}$$

Acceleration Methods

Acceleration Method	Velocity	Features	Injection Frequency
Gas gun	300-1000 m/s	Pellet accelerated by helium gas	Single shot to several Hz
Centrifugal accelerator	300-600 m/s	Continuous injection possible with rotating arm	1-10 Hz
Two-stage light gas gun	1000-3000 m/s	High-speed injection possible	Single shot

The acceleration principle in gas gun method is described by the equation of motion of the pellet by high-pressure gas:

$$m_p \frac{dv}{dt} = P(t) \cdot A_p - \frac{1}{2} \rho_{gas} v^2 C_D A_p$$

Here, $m_p$ is pellet mass, $P(t)$ is propellant gas pressure, $A_p$ is pellet cross-sectional area, and $C_D$ is drag coefficient.

Plasma Penetration

When a pellet enters the plasma, it decelerates and disintegrates while its surface ablates (evaporates). The penetration depth $\lambda_p$ is predicted by the Neutral Gas Shielding (NGS) model:

$$\lambda_p \propto r_p^{1.64} \cdot v_p^{0.33} \cdot n_e^{-0.33} \cdot T_e^{-1.64}$$

Here, $r_p$ is pellet radius, $v_p$ is pellet velocity, $n_e$ is electron density, and $T_e$ is electron temperature.

Advantages of Pellet Injection

• Direct fuel supply to plasma core is possible
• High fuel supply efficiency (several times that of gas puffing, $\eta_{pellet} \sim 0.8$-$0.95$)
• Effective for achieving high-density plasma
• Can also be used for ELM (Edge Localized Mode) control (pacing)
• Density profile control is possible

High Field Side (HFS) Injection

ITER plans pellet injection from the high field side (inside of the torus). Due to the curvature effect of magnetic field lines, the plasma cloud generated by ablation moves inward, increasing the effective penetration depth:

$$\Delta r_{HFS} \approx 1.5 \times \Delta r_{LFS}$$

Here, $\Delta r_{HFS}$ is the penetration depth for HFS injection and $\Delta r_{LFS}$ is the penetration depth for low field side injection.

Neutral Beam Injection (NBI)

While the main purpose is plasma heating, neutral deuterium beam injection also contributes to fuel supply.

NBI as Fuel Supply

The fuel supply rate by NBI is:

$$\dot{N}_{NBI} = \frac{P_{NBI}}{E_{beam}} \cdot \eta_{abs}$$

Here, $P_{NBI}$ is beam power, $E_{beam}$ is beam energy, and $\eta_{abs}$ is absorption efficiency.

For a 1 MW, 1 MeV deuterium beam:

$$\dot{N}_{NBI} = \frac{10^6}{10^6 \times 1.602 \times 10^{-19}} \times 0.9 \approx 5.6 \times 10^{18} \text{ D/s}$$

This corresponds to about 0.03 Pa·m³/s, and the contribution as fuel supply is limited compared to gas puffing or pellet injection.

Comparison of Fuel Injection Methods

Item	Gas Puffing	Pellet Injection	NBI
Reach position	Periphery	Core possible	Core
Supply efficiency	30-50%	80-95%	~100%
Controllability	High	Medium	Low
Continuous operation	Easy	Requires consideration	Easy
Equipment complexity	Low	High	Very high

Vacuum Exhaust System

Role of the Exhaust System

The vacuum exhaust system performs the following functions during plasma operation:

• Evacuate the vacuum vessel to ultra-high vacuum ($10^{-5}$ Pa or less) before operation
• Exhaust unburned fuel and helium ash during operation
• Exhaust impurity gases to maintain plasma purity
• Transfer exhaust gas to fuel purification system
• Control divertor neutral particle pressure

Physics of Divertor Exhaust

In the divertor region, plasma flowing through the scrape-off layer (SOL) is neutralized and exhausted through the pumping duct. The neutral particle pressure $p_n$ in the divertor is:

$$p_n = \frac{\Gamma_{SOL} \cdot k_B T_n}{S_{eff}} \cdot (1 - R_{recyc})$$

Here, $\Gamma_{SOL}$ is the particle flux from SOL, $T_n$ is neutral gas temperature, $S_{eff}$ is effective pumping speed, and $R_{recyc}$ is the recycling coefficient.

In the ITER divertor, approximately 200 Pa·m³/s of exhaust must be performed while maintaining a neutral particle pressure of 3-10 Pa.

Types of Exhaust Pumps

Pump Type	Operating Principle	Application Range	Pumping Speed
Scroll pump	Rotation of spiral vanes	Atmospheric → 1 Pa	100-500 m³/h
Roots pump	Rotation of figure-8 rotors	100 Pa → 0.1 Pa	500-5000 m³/h
Turbomolecular pump	Accelerate molecules with high-speed rotating blades	1 Pa → $10^{-7}$ Pa	100-3000 L/s
Cryopump	Gas condensation on cryogenic surfaces	1 Pa → $10^{-9}$ Pa	1000-100000 L/s

Operating Principle of Cryopumps

Cryopumps perform pumping by condensing and adsorbing gas molecules on cryogenic surfaces (4-80 K).

Pumping Speed

The theoretical pumping speed $S_i$ of a cryopump for gas species $i$ is:

$$S_i = \frac{A \cdot \alpha_i}{4} \sqrt{\frac{8 k_B T}{\pi m_i}}$$

Here, $A$ is the cooled surface area, $\alpha_i$ is the sticking coefficient, $T$ is gas temperature, and $m_i$ is molecular mass.

For hydrogen isotopes, $\alpha \approx 0.5$-$0.8$, and at 300 K temperature and 1 m² area:

$$S_{H_2} \approx 11 \text{ m}^3/\text{s} = 11000 \text{ L/s}$$

Challenges in Helium Pumping

The boiling point of helium is extremely low at 4.2 K, so it does not condense in conventional cryopumps (operating at 15-20 K). The following measures are necessary for helium pumping:

• Install activated carbon adsorbent on 4 K panels
• Regenerate when adsorption capacity is reached (desorption by heating)
• Alternate operation of multiple pumps

Cryopump Regeneration

Cryopumps have limited accumulation capacity and require periodic regeneration.

Regeneration Cycle

1. Exhaust operation: Accumulate gas on cooled surfaces (several hours to tens of hours)
2. Valve closure: Disconnect from vacuum vessel
3. Warm-up: Heat cooled surfaces to 80-300 K
4. Gas recovery: Transfer released gas to fuel purification system
5. Cool-down: Cool again to cryogenic temperature
6. Resume exhaust operation

ITER installs 8 cryopumps and uses a batch system alternately regenerating 2 units at a time.

Effective Pumping Speed

The effective pumping speed $S_{eff}$ as seen from the vacuum vessel, from the pump body pumping speed $S_p$ and exhaust duct conductance $C$:

$$\frac{1}{S_{eff}} = \frac{1}{S_p} + \frac{1}{C}$$

Duct conductance in the molecular flow regime (mean free path > duct diameter):

$$C = \frac{\pi d^3}{12 L} \sqrt{\frac{8 k_B T}{\pi m}}$$

Here, $d$ is duct diameter and $L$ is duct length. Shorter and thicker exhaust ducts have higher conductance and can secure effective pumping speed.

Doubling the duct diameter increases conductance by 8 times, but space constraints around the divertor require optimized design in practice.

Tritium Purification and Recovery System

Front-end Processing

The exhaust gas recovered from the vacuum exhaust system contains, in addition to fuel (D, T), impurities such as helium, water vapor, hydrocarbons, and nitrogen oxides. The fuel purification system selectively separates hydrogen isotopes from these.

Exhaust Gas Composition (Typical Values)

Component	Concentration	Origin
D₂, DT, T₂	70-90%	Unburned fuel
He	5-20%	Fusion reaction product
H₂O, HDO, HTO	0.1-1%	Desorption from wall materials
CH₄, CD₄, CT₄	0.1-1%	Reaction with carbon wall
CO, CO₂	0.01-0.1%	Reaction with oxygen
N₂	0.001-0.01%	Air leak

Palladium Diffuser

Palladium (Pd) membranes have the property of selectively permeating only hydrogen isotopes.

The permeation flux $J$ follows Sieverts’ law:

$$J = \frac{\Phi}{d} \left( \sqrt{P_1} - \sqrt{P_2} \right)$$

Here, $\Phi$ is permeability, $d$ is membrane thickness, and $P_1$, $P_2$ are hydrogen partial pressures on the high and low pressure sides.

Temperature dependence of permeability:

$$\Phi = \Phi_0 \exp\left(-\frac{E_a}{RT}\right)$$

The activation energy $E_a \approx 15$ kJ/mol, and operation is at 400-600°C.

Characteristics of palladium diffusers:

• Hydrogen isotope purity > 99.99%
• Complete separation of helium
• Membrane material degradation from tritium permeation (helium accumulation)
• Membrane life: Several years (periodic replacement required)

Catalytic Oxidation + Moisture Adsorption

Processing of organic tritium compounds (CT₄, C₂T₆, etc.):

$$\text{CT}_4 + 2\text{O}_2 \xrightarrow{\text{Pt catalyst}} \text{CO}_2 + 2\text{T}_2\text{O}$$

The generated tritiated water is adsorbed and recovered with molecular sieves (zeolites). Adsorption capacity is about 20 wt% at room temperature.

Hydrogen Isotope Separation Technologies

D and T for fuel use are separated and concentrated from purified hydrogen isotope gas.

Cryogenic Distillation

A separation method using the boiling point differences of hydrogen isotopes.

Isotope	Boiling Point (101.3 kPa)	Triple Point
H₂	20.39 K	13.96 K
HD	22.14 K	16.60 K
D₂	23.67 K	18.73 K
HT	22.92 K	17.63 K
DT	24.38 K	19.79 K
T₂	25.04 K	20.62 K

In distillation column design, the relationship between theoretical stages $N$ and separation factor $\alpha$ is given by the Fenske equation:

$$N_{min} = \frac{\ln\left[\frac{x_D}{1-x_D} \cdot \frac{1-x_B}{x_B}\right]}{\ln \alpha}$$

Here, $x_D$ is the top composition and $x_B$ is the bottom composition.

For H₂/D₂ separation ($\alpha \approx 1.5$), approximately 100 stages are needed to obtain 99% purity D₂.

Characteristics of cryogenic distillation:

• Suitable for large-scale processing (kg/h order)
• Continuous operation is possible
• Energy consumption: About 1 kW/(g-T/h)
• Operating temperature: 20-25 K

TCAP (Thermal Cycling Absorption Process)

Hydrogen isotope separation by temperature swing adsorption. Uses the hydrogen absorption characteristics of palladium alloys (Pd-Ag, etc.).

Operating principle:

1. Preferentially absorb light isotope (H) at low temperature (room temperature to 150°C)
2. Desorb at high temperature (300-400°C), heavy isotope (T) is concentrated
3. Repeat thermal cycles to increase concentration

The separation factor is $\alpha \approx 1.3$-$1.5$ for a single cycle, but high purity can be achieved with multi-stage cascades.

TCAP characteristics:

• Suitable for small-scale processing (g/h order)
• Batch operation
• High reliability with no mechanical moving parts
• Proven track record in tritium recovery (TSTA, STP)

Liquid Phase Catalytic Exchange (LPCE)

An effective method for processing tritiated water.

$$\text{HTO}_{(l)} + \text{D}_2 \leftrightarrow \text{DTO}_{(l)} + \text{HD}$$

The equilibrium constant (separation factor) depends on temperature:

$$K = \exp\left(\frac{\Delta G}{RT}\right) \approx 2.0-2.5 \text{ (25°C)}$$

Efficient tritium transfer is possible through countercurrent contact.

Tritium Storage System

Storage in Metal Hydrides

Tritium is stored in the form of metal hydrides (metal beds). Compared to high-pressure gaseous storage, the hydrogen density per volume is higher and safety is superior.

Hydride Formation Reaction

$$M + \frac{x}{2} T_2 \leftrightarrow MT_x + \Delta H$$

Absorption is an exothermic reaction ($\Delta H < 0$), and release is endothermic.

PCT Curve (Pressure-Composition-Temperature)

Relationship between equilibrium hydrogen pressure $P_{eq}$ and temperature $T$ (van’t Hoff equation):

$$\ln P_{eq} = -\frac{\Delta H}{RT} + \frac{\Delta S}{R}$$

From this relationship, hydrogen absorption and release can be controlled by temperature control.

Representative Storage Materials

Material	Hydride	Storage Capacity (wt%)	Equilibrium Pressure (25°C)	Features
U	UT₃	1.3	0.1 Pa	High capacity, radioactive
Zr	ZrT₂	2.2	$<10^{-10}$ Pa	Very low pressure, difficult recovery
ZrCo	ZrCoT₃	1.5	0.01 Pa	Moderate pressure
LaNi₅	LaNi₅T₆	1.4	200 kPa	High pressure, room temperature operation
ZrNi	ZrNiT₃	1.8	0.1 Pa	Adopted for ITER

ITER Tritium Storage System

ITER primarily uses ZrCo alloy, designed with the following specifications:

• Storage per bed: ≤ 70 g (safety standard)
• Number of beds: About 100
• Total storage capacity: About 4 kg
• Operating temperature: Room temperature to 500°C
• Helium-3 accumulation countermeasure: Periodic regeneration treatment

Helium-3 Accumulation Problem

Beta decay of tritium causes ³He to accumulate, leading to hydride degradation:

$$T \rightarrow {}^3\text{He} + e^- + \bar{\nu}_e \quad (t_{1/2} = 12.3 \text{ yr})$$

About 5.5% of stored tritium is converted to helium-3 per year. Periodic heat regeneration is necessary to remove ³He.

Gaseous Storage

Gaseous storage is also used as a short-term operational buffer.

• Pressure vessel: Several to tens of atmospheres
• Material: Stainless steel (hydrogen embrittlement countermeasure)
• Capacity: Several liters to tens of liters
• Application: Piping buffer, emergency discharge receiver

Tritium Recovery from Blanket

Tritium Breeding Reactions

In the blanket, tritium is produced by reactions between lithium and neutrons.

$$^6\text{Li} + n \rightarrow \text{T} + {}^4\text{He} + 4.78 \text{ MeV}$$ $$^7\text{Li} + n \rightarrow \text{T} + {}^4\text{He} + n' - 2.47 \text{ MeV}$$

The ⁶Li reaction occurs efficiently with thermal neutrons, while the ⁷Li reaction is an endothermic reaction that occurs with fast neutrons (> 2.5 MeV).

The tritium breeding ratio (TBR) is:

$$\text{TBR} = \frac{\text{Tritium production rate}}{\text{Tritium consumption rate}} > 1.0$$

Self-sustaining operation requires TBR > 1.05 (accounting for losses).

Recovery Methods

Sweep Gas Method

Sweep gas with helium containing a small amount of hydrogen (0.1-1%) flows through the blanket to recover generated tritium.

Tritium exists in the following forms:

$$\text{T}_2, \text{HT}, \text{DT}, \text{T}_2\text{O}, \text{HTO}$$

The recovery system captures tritium using a combination of catalytic oxidation and moisture adsorption.

Recovery from Lithium-Lead Eutectic (LiPb)

In liquid blankets, lithium-lead eutectic (Li₁₇Pb₈₃) may be used.

Tritium solubility (Sieverts’ law):

$$c_T = K_S \sqrt{P_{T_2}}$$

Since the solubility constant $K_S$ is low (10⁻⁵-10⁻⁴ mol/(m³·Pa^0.5)), permeation recovery or vacuum degassing is effective.

Recovery from Solid Breeding Materials

Tritium recovery from lithium ceramics (Li₂O, Li₄SiO₄, Li₂TiO₃, etc.):

1. Tritium diffuses along grain boundaries at high temperature (400-900°C)
2. Desorbs from surface with sweep gas (He + H₂)
3. Transferred to recovery system in HTO/T₂O form

Recovery efficiency depends on the tritium retention rate of the material, and reducing residual inventory is a challenge.

Tritium Accountancy and Measurement

Legal Requirements for Accountancy

Tritium is legally required to be accounted for as nuclear fuel material.

• Compliance with IAEA Safeguards
• Domestic regulations (Japan: Act on the Regulation of Nuclear Source Material, Nuclear Fuel Material and Reactors)
• Accountancy reporting as a facility license condition

Measurement Technologies

Gaseous Tritium Measurement

Method	Target	Detection Limit	Features
Ionization chamber	T₂, HT	10⁻³ Bq/cm³	Real-time continuous measurement
Proportional counter	T₂, HT	10⁻⁴ Bq/cm³	High sensitivity
Mass spectrometry	H₂, HD, D₂, HT, DT, T₂	ppm order	Isotope ratio measurement
Calorimetry	Total tritium	mg order	Absolute measurement, used for calibration

Calorimetry (Heat Measurement)

An absolute measurement method that measures the beta decay heat of tritium:

$$Q = \lambda \cdot N_T \cdot \bar{E}_\beta = 0.324 \text{ W/g-T}$$

Here, $\lambda$ is the decay constant, $N_T$ is the number of tritium atoms, and $\bar{E}_\beta = 5.7$ keV is the average beta energy.

1 g of tritium generates approximately 0.324 W of decay heat. With high-precision calorimeters, tritium above several mg can be absolutely measured.

PVT Method (Pressure-Volume-Temperature Method)

Gas is sealed in a container of known volume, and the amount of substance is calculated from pressure and temperature:

$$n = \frac{PV}{ZRT}$$

Here, $Z$ is the compressibility factor. The isotope ratio is measured by mass spectrometry to determine the tritium amount.

Inventory Monitoring System

Real-time Monitoring

Data from sensors installed at various process points are integrated to continuously monitor tritium inventory:

• Pressure and temperature measurement of piping and containers
• Online mass spectrometry
• Ionization chamber monitors
• Inventory evaluation by process calculation

Material Balance Verification

Periodic inventories verify calculated inventory against measured inventory:

$$\Delta I = I_{in} - I_{out} - I_{decay} - I_{measured}$$

Acceptable error (MUF: Material Unaccounted For) is set according to facility scale.

Tritium Inventory Management

Definition and Classification of Inventory

Tritium inventory is the total amount of tritium present within a fusion reactor plant.

Category Classification

Category	Definition	Management Method
Operating inventory	Circulation amount needed for steady operation	Process monitoring
Storage inventory	Amount held in storage systems	Physical inventory
Retained inventory	Amount accumulated in structures and walls	Evaluation calculation
Decay loss	Decrease due to beta decay	Calculation

Main Tritium Locations (ITER Design Values)

Location	Form	Typical Amount	Residence Time
Fuel storage system	Metal hydride	500-700 g	Long-term
Blanket	In breeding material	~100 g	Hours
Plasma-facing wall	Material surface/interior	300-700 g	Long-term
Fuel cycle piping	Gas/liquid	50-100 g	Minutes to hours
Vacuum vessel	Gas/adsorbed	10-50 g	Minutes

Wall Retention Inventory

Tritium accumulation in plasma-facing materials is a major safety concern.

Accumulation Mechanisms

1. Ion implantation: Penetration of plasma ions into material
2. Diffusion/dissolution: Diffusion into material interior
3. Trapping: Capture by lattice defects and impurities
4. Co-deposition: Formation of C-T co-deposited layers on carbon walls

Evaluation of Accumulation Amount

Surface concentration $C_s$ by ion implantation:

$$C_s = \frac{\Gamma_{ion}}{D/\lambda + k_r}$$

Here, $\Gamma_{ion}$ is ion flux, $D$ is diffusion coefficient, $\lambda$ is implantation depth, and $k_r$ is recombination coefficient.

Retention amount over the entire wall $I_{wall}$:

$$I_{wall} = \int_A C(x) \cdot d \cdot dA$$

Here, $C(x)$ is concentration distribution, $d$ is penetration depth, and $A$ is wall area.

ITER Limits

ITER limits the tritium amount in the vacuum vessel to 700 g or less. This limit is set to keep the release amount within acceptable limits in the event of a design basis accident (DBA).

Inventory Reduction Measures

Baking (Thermal Desorption)

Wall materials are heated to 150-350°C to thermally desorb accumulated tritium:

$$\tau_{release} \propto \exp\left(\frac{E_a}{k_B T}\right)$$

Periodic baking maintains retained inventory at manageable levels.

Plasma Cleaning

Deposited layers are removed by glow discharge with oxygen or nitrogen introduction:

$$C + O^* \rightarrow CO \uparrow$$

This allows recovery of tritium trapped in co-deposited layers.

Material Selection

Tungsten has less tritium accumulation compared to carbon and is adopted as the divertor material for ITER:

• Tungsten: Low solubility, no co-deposition
• Carbon (CFC): Large accumulation by co-deposition (discontinued)

Tritium Safety

Radiation Characteristics of Tritium

Characteristic	Value
Half-life	12.32 years
Decay mode	β⁻ decay
Maximum beta energy	18.6 keV
Average beta energy	5.7 keV
Specific activity	3.59 × 10¹⁴ Bq/g

Tritium beta rays are very low energy and do not penetrate skin (range < 6 μm in tissue).

Exposure Pathways and Dose Assessment

Internal Exposure

The main exposure pathways for tritium are inhalation and percutaneous absorption.

Biological half-life of tritiated water (HTO):

$$T_{bio} \approx 10 \text{ days (metabolism of body water)}$$

Organically bound tritium (OBT) stays in tissues longer, with biological half-life of 40-450 days.

Effective dose coefficients (ICRP):

Form	Dose Coefficient (Sv/Bq)
HTO (inhalation/percutaneous)	1.8 × 10⁻¹¹
OBT (oral)	4.2 × 10⁻¹¹
HT (inhalation)	1.8 × 10⁻¹⁵

Exposure Assessment Example

If 1 g of tritium (3.59 × 10¹⁴ Bq) leaks as HTO, the effective dose when the entire amount is inhaled:

$$E = 3.59 \times 10^{14} \times 1.8 \times 10^{-11} = 6.5 \text{ Sv}$$

In practice, exposure is significantly reduced by dilution and protection, but protective design against large-scale leakage is necessary.

Confinement Design

Tritium facilities apply the concept of multiple barriers.

Confinement Hierarchy

Level	Barrier	Function
1st	Process piping/vessels	Primary confinement
2nd	Glove boxes/cells	Secondary confinement
3rd	Building	Tertiary confinement

Negative Pressure Maintenance

Negative pressure is maintained at each level to restrict diffusion inward during leakage:

$$P_{external} > P_{building} > P_{cell} > P_{glovebox}$$

Typical differential pressures:

• Building vs outside air: -50 to -100 Pa
• Cell vs building: -100 to -200 Pa
• Glovebox vs cell: -100 to -300 Pa

Atmosphere Detritiation System

Tritium leaked into facility air is recovered by catalytic oxidation.

$$\text{HT} + \frac{1}{2}\text{O}_2 \xrightarrow[\text{room temperature}]{\text{Pt/Pd catalyst}} \text{HTO}$$

Processing system configuration:

1. Pre-filter: Dust removal
2. Catalytic reactor: HT → HTO conversion (efficiency > 99.9%)
3. Drying tower (molecular sieve): HTO adsorption
4. HEPA filter: Particle removal
5. Exhaust fan: Negative pressure maintenance

Removal efficiency (decontamination factor DF):

$$DF = \frac{C_{in}}{C_{out}} > 1000$$

Accident Countermeasures

Design Basis Accidents (DBA)

Analysis and countermeasures are required for the following scenarios:

• Vacuum vessel coolant leakage (LOCA)
• Plasma disruption
• Fuel processing system pipe rupture
• Release from storage system

Beyond Design Basis Accidents

Design is required to keep public exposure within acceptable limits even for combined events or accidents exceeding design assumptions.

Burn Efficiency and Fuel Economics

Definition of Burn Efficiency

Burn efficiency of a fusion reactor is evaluated by multiple indicators.

Fractional Burn-up (Single Pass)

$$f_b = \frac{\text{Tritium burned}}{\text{Tritium injected}}$$

In current designs, $f_b \approx 0.02$-$0.1$ (2-10%).

Overall Fuel Efficiency

Overall efficiency including circulation losses:

$$\eta_{fuel} = \frac{\text{Burned tritium}}{\text{Externally supplied tritium}} = \frac{f_b}{f_b + (1-f_b)(1-\eta_{cycle})}$$

With $\eta_{cycle} = 0.99$, $f_b = 0.05$:

$$\eta_{fuel} = \frac{0.05}{0.05 + 0.95 \times 0.01} = 0.84$$

16% of tritium is lost in the circulation system. Commercial reactors target $\eta_{fuel} > 0.95$.

Approaches to Improve Burn Fraction

Improving Confinement Performance

Extending particle confinement time $\tau_p$ improves burn fraction:

$$f_b \propto n \langle \sigma v \rangle \tau_p$$

However, balance is needed as helium ash accumulation also increases.

Optimizing Fuel Supply Position

Fuel supply to the plasma core extends residence time in the high-temperature region with high reaction rates. High field side pellet injection is effective for this purpose.

Optimizing Divertor Design

Recycling control in the divertor improves effective particle confinement:

$$\tau_p^{eff} = \frac{\tau_p}{1 - R_{recyc}}$$

Here, $R_{recyc}$ is the recycling coefficient (0.9-0.99).

Fuel Economics

Initial Tritium Loading

Starting a fusion reactor requires external tritium supply. The required amount is:

$$I_0 = I_{operating} + I_{storage} + I_{margin}$$

ITER: About 4 kg DEMO: 10-20 kg (design dependent) Commercial reactor: 5-30 kg

Tritium Doubling Time

Under TBR > 1 conditions, the time for excess tritium to equal the initial loading:

$$T_D = \frac{I_0}{(\text{TBR} - 1) \cdot \dot{m}_T \cdot C_F}$$

Here, $C_F$ is the capacity factor.

Example: With $I_0 = 10$ kg, TBR = 1.1, $\dot{m}_T = 0.15$ kg/day, $C_F = 0.5$:

$$T_D = \frac{10}{0.1 \times 0.15 \times 0.5} = 1333 \text{ days} \approx 3.7 \text{ years}$$

Shortening the doubling time is important for commercial reactor deployment.

World Tritium Supply

The current tritium supply source is mainly recovery from Canadian CANDU reactors (heavy water reactors).

World Tritium Inventory (Estimated)

• Canada (OPG): About 20 kg
• South Korea (KSTAR/K-DEMO use): Accumulating
• Others: Several kg

This is sufficient for ITER DT operation (around 2035), but insufficient to simultaneously start multiple DEMO reactors. Self-sustaining operation of fusion reactors and tritium supply to multiple reactors are future challenges.

ITER Fuel Cycle System

The ITER fuel cycle system is designed to meet the requirements of an experimental reactor.

Main Specifications

Parameter	Value
Tritium throughput	Maximum 0.5 kg/day
Fuel injection method	Pellet injection + Gas puffing + NBI
Pellet injection frequency	Maximum 10 Hz
Vacuum exhaust	8 cryopumps (batch operation)
Exhaust speed	200 Pa·m³/s (D₂ equivalent)
Isotope separation	Cryogenic distillation
Fuel storage	Metal hydride beds (divided storage)
Site tritium limit	4 kg (regulatory value)
Vacuum vessel tritium limit	700 g

Tritium Plant Layout

The ITER tritium plant is installed in the Tritium Building, located approximately 100 m from the vacuum vessel. Main systems:

• Storage and Delivery System (SDS): Fuel storage and supply
• Tokamak Exhaust Processing (TEP): Exhaust gas processing
• Isotope Separation System (ISS): Isotope separation
• Water Detritiation System (WDS): Tritiated water processing
• Atmosphere Detritiation System (ADS): Air tritium processing

ITER Demonstrations and Challenges

The following technology demonstrations are planned at ITER:

• Integrated operation of large-scale D-T fuel cycle
• Central fuel supply by pellet injection
• Batch operation of cryopumps
• Continuous isotope separation by cryogenic distillation
• Long-term tritium storage by metal hydrides
• Real-time inventory monitoring

Following demonstration at ITER, larger and more efficient fuel cycle systems will be needed for future prototype and commercial reactors.

Future Reactor Outlook

DEMO Reactor Requirements

DEMO (demonstration reactor) will have the following additional requirements:

Item	ITER	DEMO
Tritium throughput	0.5 kg/day	Several kg/day
Continuous operation time	~1 hour	Several weeks to continuous
TBR	Testing only	> 1.05
Target burn fraction	Several %	> 10%
Inventory limit	4 kg	1-2 kg (target)

Technology Development Challenges

High Burn Fraction Operation

Research is ongoing to achieve burn fractions of 30% or higher through Advanced Tokamak scenarios.

Compact Fuel Cycle System

Retained inventory is reduced by improving processing speed and miniaturizing equipment.

Advanced Tritium Breeding Blanket

Blanket designs that achieve both high TBR (> 1.15) and efficient tritium recovery are needed.

Direct Tritium Recovery

Concepts to minimize external circulation through direct recycling technology from plasma are also being considered.

Related Topics

• Tritium Management - Tritium safety management and exposure countermeasures
• Blanket - Tritium breeding blanket design
• ITER Project - Overview of the International Thermonuclear Experimental Reactor
• Tokamak - Tokamak principles and configuration
• Plasma-Facing Materials - First wall and divertor materials