Types of Fusion Reactions

The choice of which fusion reaction to use is a critical decision for realizing fusion power. Each reaction has different required temperatures, energy yields, and fuel availability, with respective advantages and challenges.

Physical Principles of Fusion Reactions

Coulomb Barrier

To fuse atomic nuclei together, one must first overcome the electrostatic repulsion (Coulomb force) between them. When two positively charged nuclei approach each other, the repulsive Coulomb potential increases rapidly.

The Coulomb potential between two nuclei (charges $Z_1 e$ and $Z_2 e$, nuclear radii $r_1$ and $r_2$) is given by:

$$V_C(r) = \frac{Z_1 Z_2 e^2}{4\pi\varepsilon_0 r}$$

At the distance where nuclear forces become effective (approximately $r_0 = r_1 + r_2 \approx 1.4 \times (A_1^{1/3} + A_2^{1/3})$ fm), the Coulomb barrier height is:

$$V_C(r_0) = \frac{Z_1 Z_2 e^2}{4\pi\varepsilon_0 r_0} \approx \frac{1.44 Z_1 Z_2}{r_0[\text{fm}]}\ \text{MeV}$$

For the D-T reaction, $Z_1 = Z_2 = 1$, and the nuclear radius is approximately 2.5 fm, so:

$$V_C \approx \frac{1.44 \times 1 \times 1}{2.5} \approx 0.58\ \text{MeV} \approx 580\ \text{keV}$$

This corresponds to a temperature of about 6.7 billion Kelvin. Classically, ions would need this energy to fuse, but actual fusion reactors only require temperatures of 100-200 million degrees (10-20 keV). This large discrepancy is explained by quantum tunneling.

Quantum Tunneling

According to quantum mechanics, particles can “tunnel” through regions that are classically forbidden in terms of energy. In fusion reactions, colliding nuclei can penetrate the barrier with a certain probability and undergo nuclear reactions even without reaching the top of the Coulomb barrier.

The tunneling probability (Gamow factor) is expressed as:

$$P_G = \exp(-2\pi\eta)$$

Here, $\eta$ is called the Sommerfeld parameter and is defined as:

$$\eta = \frac{Z_1 Z_2 e^2}{4\pi\varepsilon_0 \hbar v} = \frac{Z_1 Z_2 e^2}{\hbar} \sqrt{\frac{\mu}{2E}}$$

where $v$ is the relative velocity, $\mu$ is the reduced mass, and $E$ is the kinetic energy in the center-of-mass frame.

From this equation, the tunneling probability:

• Increases with larger energy $E$
• Increases with smaller $Z_1 Z_2$ (product of nuclear charges)
• Increases with smaller reduced mass $\mu$

This explains why light nuclei (hydrogen isotopes) are well-suited for fusion.

Gamow Peak and Reaction Probability

In a thermal equilibrium plasma, particles follow a Maxwell-Boltzmann distribution:

$$f(E) = \frac{2\pi n}{(\pi k_B T)^{3/2}} \sqrt{E} \exp\left(-\frac{E}{k_B T}\right)$$

The fusion reaction rate is determined by the product of this distribution and the reaction cross-section $\sigma(E)$. The cross-section is typically decomposed as:

$$\sigma(E) = \frac{S(E)}{E} \exp(-2\pi\eta)$$

Here, $S(E)$ is called the astrophysical S-factor and represents nuclear physics factors. Since the S-factor varies relatively slowly with energy, it is convenient for extrapolating experimental data.

The Maxwell distribution decreases exponentially at high energies, while the tunneling probability decreases exponentially at low energies. These two competing effects cause the reaction probability to peak at an intermediate energy range. This is called the Gamow peak (or Gamow window).

The Gamow peak energy is approximately:

$$E_G = \left(\frac{\pi^2 Z_1^2 Z_2^2 e^4 \mu k_B^2 T^2}{2\hbar^2}\right)^{1/3} = 1.22 (Z_1^2 Z_2^2 \mu T_{\text{keV}}^2)^{1/3}\ \text{keV}$$

For the D-T reaction at $T = 10$ keV, $E_G \approx 18$ keV. This is slightly higher than the thermal energy $k_B T = 10$ keV, but much lower than the Coulomb barrier of 580 keV.

Primary Fusion Reactions

The following reactions are mainly considered as terrestrially achievable fusion reactions.

D-T Reaction (Deuterium-Tritium Reaction)

$$\text{D} + \text{T} \rightarrow {}^4\text{He}\ (3.52\ \text{MeV}) + n\ (14.06\ \text{MeV})$$

The D-T reaction is the most prominent reaction in current fusion research. It has a large cross-section and can occur at relatively low temperatures (about 10 keV, 120 million degrees). The Q-value (energy release) is 17.6 MeV, which is distributed between the alpha particle (3.52 MeV) and neutron (14.06 MeV).

The energy distribution is determined by momentum conservation. Assuming rest in the center-of-mass frame before the reaction, the products fly off with equal and opposite momenta:

$$m_\alpha v_\alpha = m_n v_n$$

The ratio of kinetic energies is the inverse ratio of masses:

$$\frac{E_\alpha}{E_n} = \frac{m_n}{m_\alpha} = \frac{1}{4}$$

Therefore, $E_\alpha = 17.6 \times \frac{1}{5} = 3.52$ MeV and $E_n = 17.6 \times \frac{4}{5} = 14.06$ MeV.

Most current fusion reactor plans, including ITER, adopt this D-T reaction.

D-D Reaction (Deuterium-Deuterium Reaction)

The D-D reaction has two branches, occurring with approximately equal probability (about 50% each):

$$\text{D} + \text{D} \rightarrow {}^3\text{He}\ (0.82\ \text{MeV}) + n\ (2.45\ \text{MeV})$$ $$\text{D} + \text{D} \rightarrow \text{T}\ (1.01\ \text{MeV}) + p\ (3.03\ \text{MeV})$$

The Q-value for the D-D reaction is 3.27 MeV for the first branch and 4.04 MeV for the second branch, smaller than the D-T reaction. Also, higher temperatures (about 100 keV or more) are required compared to the D-T reaction.

The advantage of the D-D reaction is that only deuterium is needed as fuel. The tritium produced in the second branch and the $^3$He produced in the first branch can be used as fuel for secondary reactions:

$$\text{D} + \text{T} \rightarrow {}^4\text{He} + n + 17.6\ \text{MeV}$$ $$\text{D} + {}^3\text{He} \rightarrow {}^4\text{He} + p + 18.3\ \text{MeV}$$

Including these chain reactions, even pure D-D plasma can achieve significantly improved effective energy yield.

D-$^3$He Reaction (Deuterium-Helium-3 Reaction)

$$\text{D} + {}^3\text{He} \rightarrow {}^4\text{He}\ (3.67\ \text{MeV}) + p\ (14.67\ \text{MeV})$$

The Q-value of the D-$^3$He reaction is 18.3 MeV, exceeding that of the D-T reaction. Its most significant feature is that the reaction products are only charged particles, producing no neutrons. This can significantly reduce neutron damage and activation of reactor wall materials.

However, the required temperature is several times higher than the D-T reaction (about 50 keV or more), making it difficult to achieve with current technology. Also, even in pure D-$^3$He plasma, D-D reactions occur as side reactions, inevitably producing neutrons.

p-$^{11}$B Reaction (Proton-Boron-11 Reaction)

$$p + {}^{11}\text{B} \rightarrow 3\,{}^4\text{He} + 8.68\ \text{MeV}$$

This reaction is notable as a representative example of “aneutronic fusion.” The reaction products are only three alpha particles, producing no neutrons as a primary reaction.

However, there are several significant challenges:

1. Extremely high required temperature (about 300 keV, 3.5 billion degrees)
2. The peak cross-section temperature and the temperature at which radiation losses balance are close, making ignition difficult
3. Large Bremsstrahlung losses due to boron with $Z = 5$

Bremsstrahlung power loss is proportional to $Z_{\text{eff}}^2$, making this a serious issue for fuels containing high-$Z$ elements.

p-$^6$Li Reaction

$$p + {}^6\text{Li} \rightarrow {}^4\text{He}\ (1.7\ \text{MeV}) + {}^3\text{He}\ (2.3\ \text{MeV})$$

The Q-value is about 4.0 MeV. The reaction products are charged particles only, but the cross-section is small, making it impractical.

$^3$He-$^3$He Reaction

$${}^3\text{He} + {}^3\text{He} \rightarrow {}^4\text{He} + 2p + 12.86\ \text{MeV}$$

This reaction is known as the final stage of the solar pp chain. It is a completely aneutronic reaction, but extremely high temperatures are required for terrestrial realization, and the scarcity of $^3$He makes it impractical.

T-T Reaction

$$\text{T} + \text{T} \rightarrow {}^4\text{He} + 2n + 11.3\ \text{MeV}$$

Since two neutrons are produced, this is disadvantageous from the perspective of neutron shielding. Also, requiring large amounts of radioactive tritium presents challenges for the fuel cycle.

$^3$He-T Reaction

$${}^3\text{He} + \text{T} \rightarrow {}^4\text{He} + p + n + 12.1\ \text{MeV}\ (51\%)$$ $${}^3\text{He} + \text{T} \rightarrow {}^4\text{He}\ (4.8\ \text{MeV}) + \text{D}\ (9.5\ \text{MeV})\ (43\%)$$ $${}^3\text{He} + \text{T} \rightarrow {}^5\text{He} + p\ (\text{unstable})\ (6\%)$$

Multiple branches exist, forming a complex reaction system.

Cross-Sections and Astrophysical S-Factor

Definition and Measurement of Cross-Sections

The cross-section $\sigma$ is a physical quantity representing the likelihood of a fusion reaction occurring. Units are typically expressed in barns (1 barn = $10^{-28}$ m$^2$ = $10^{-24}$ cm$^2$).

Physically, the cross-section represents the “effective area for reactions when projectile nuclei are aimed at target nuclei.” Due to quantum mechanical effects, it can be larger or smaller than the actual geometric cross-section of nuclei (about 1 barn).

Fusion reaction cross-sections are measured using beam experiments with accelerators. However, in the low-energy region important for fusion reactors (several keV to tens of keV), cross-sections are extremely small, making direct measurement difficult.

Astrophysical S-Factor

To enable extrapolation of cross-sections to low energies, the astrophysical S-factor is introduced:

$$S(E) = E\sigma(E)\exp(2\pi\eta)$$

Here, $\exp(2\pi\eta)$ is the inverse of the Gamow factor, canceling out the exponential decrease due to tunneling. The S-factor reflects nuclear physics characteristics and varies relatively slowly with energy unless resonances are present.

The S-factor for many fusion reactions can be Taylor expanded in the low-energy region:

$$S(E) = S_0 + S_1 E + S_2 E^2 + \cdots$$

The S-factor parameters for major reactions are as follows:

Reaction	$S_0$ (keV b)	Notes
D-T	$1.1 \times 10^4$	Has resonance structure
D-D (n branch)	55
D-D (p branch)	57
D-$^3$He	$5.4 \times 10^3$
p-$^{11}$B	$2.0 \times 10^5$	Complex resonance structure

Comparison of Cross-Sections

Cross-sections depend strongly on temperature (ion energy) and peak at certain temperatures.

Reaction	Peak Cross-Section	Peak Energy
D-T	~5.0 barn	~64 keV
D-D	~0.096 barn	~1250 keV
D-$^3$He	~0.71 barn	~250 keV
p-$^{11}$B	~1.2 barn	~600 keV

The D-T reaction has a large cross-section at low energies, making it the most achievable reaction with current technology. This advantage is due to the $^5$He resonance level existing around 64 keV in the D-T system.

Reaction Rates and Temperature Dependence

Reaction Rate Density

In fusion reactor plasmas, particles move at various velocities and follow a Maxwell-Boltzmann distribution in thermal equilibrium. To calculate the fusion reaction rate, the cross-section must be averaged over the relative velocities of all particle pairs.

The reaction rate density (reactions per unit volume per unit time) between two particle species (densities $n_1$, $n_2$) is:

$$R = n_1 n_2 \langle\sigma v\rangle$$

Here, $\langle\sigma v\rangle$ is called the Maxwell-averaged reactivity. For reactions between identical particles (such as D-D reactions):

$$R = \frac{1}{2} n^2 \langle\sigma v\rangle$$

The factor 1/2 prevents double-counting of the same particle pairs.

Maxwell-Averaged Reactivity

The reactivity assuming a Maxwell distribution is:

$$\langle\sigma v\rangle = \left(\frac{8}{\pi\mu}\right)^{1/2} \frac{1}{(k_B T)^{3/2}} \int_0^\infty E\sigma(E) \exp\left(-\frac{E}{k_B T}\right) dE$$

This integral generally cannot be solved analytically, and numerical integration or approximation formulas are used.

Low-temperature approximation (for non-resonant reactions):

$$\langle\sigma v\rangle \approx \sqrt{\frac{8}{\pi\mu(k_B T)^3}} S(E_G) \Delta E_G \exp\left(-3\frac{E_G}{k_B T}\right)$$

Here, $E_G$ is the Gamow energy and $\Delta E_G$ is the width of the Gamow peak. This formula shows that $\langle\sigma v\rangle$ has a strong exponential dependence on temperature.

Reactivity of Major Reactions

In practice, parameterized formulas for $\langle\sigma v\rangle$ as a function of temperature are used. The commonly used Bosch-Hale parameterization is:

$$\langle\sigma v\rangle = C_1 \theta \sqrt{\frac{\xi}{m_r c^2 T^3}} \exp(-3\xi)$$

where:

$$\theta = T \left/ \left(1 - \frac{T(C_2 + T(C_4 + TC_6))}{1 + T(C_3 + T(C_5 + TC_7))}\right)\right.$$ $$\xi = \left(\frac{B_G^2}{4\theta}\right)^{1/3}$$

$B_G$ is the Gamow constant, and $C_1$-$C_7$ are fitting parameters specific to each reaction.

Comparing the temperature dependence of $\langle\sigma v\rangle$ for each reaction:

Temperature (keV)	D-T	D-D	D-$^3$He	p-$^{11}$B
1	$6.3 \times 10^{-27}$	$1.5 \times 10^{-28}$	$1.0 \times 10^{-33}$	$< 10^{-40}$
10	$1.1 \times 10^{-22}$	$2.8 \times 10^{-25}$	$1.4 \times 10^{-26}$	$3.0 \times 10^{-33}$
20	$4.2 \times 10^{-22}$	$2.0 \times 10^{-24}$	$2.4 \times 10^{-25}$	$3.2 \times 10^{-29}$
50	$8.7 \times 10^{-22}$	$1.6 \times 10^{-23}$	$3.5 \times 10^{-24}$	$3.0 \times 10^{-25}$
100	$8.1 \times 10^{-22}$	$5.4 \times 10^{-23}$	$1.5 \times 10^{-23}$	$3.7 \times 10^{-24}$
200	$5.0 \times 10^{-22}$	$1.0 \times 10^{-22}$	$2.9 \times 10^{-23}$	$2.9 \times 10^{-23}$

Units are m$^3$/s. The D-T reaction maintains near-peak values over a wide temperature range of 10-20 keV, which is why this is preferred as the operating point for fusion reactors.

Optimal Reaction Temperature

From the balance of fusion output and radiation losses, each reaction has an optimal operating temperature:

Reaction	Optimal Temperature	$\langle\sigma v\rangle_{\max}$
D-T	13-15 keV	$\sim 9 \times 10^{-22}$ m$^3$/s
D-D	~100 keV	$\sim 5 \times 10^{-23}$ m$^3$/s
D-$^3$He	~60 keV	$\sim 5 \times 10^{-24}$ m$^3$/s
p-$^{11}$B	~300 keV	$\sim 5 \times 10^{-23}$ m$^3$/s

The $\langle\sigma v\rangle$ of the D-T reaction is about 20 times that of D-D and about 100 times that of D-$^3$He, and this difference manifests as differences in the confinement conditions required for achievement.

Q-Value and Energy Balance

The Q-value represents the energy released in a fusion reaction. This energy is derived from the mass difference before and after the reaction ($E = \Delta m c^2$).

Mass Defect and Energy Release

The mass of an atomic nucleus is not simply the sum of the masses of its constituent protons and neutrons, but is lighter by the binding energy:

$$M(Z,A) = Zm_p + (A-Z)m_n - B(Z,A)/c^2$$

where $B(Z,A)$ is the binding energy.

The energy released in a fusion reaction (Q-value) is:

$$Q = (M_1 + M_2 - M_3 - M_4)c^2$$

where $M_1, M_2$ are the reactant masses and $M_3, M_4$ are the product masses.

Specific values:

Particle	Mass (u)	Mass (MeV/c$^2$)
p	1.007825	938.783
n	1.008665	939.565
D	2.014102	1876.124
T	3.016049	2809.432
$^3$He	3.016029	2809.413
$^4$He	4.002603	3727.379
$^{11}$B	11.009305	10252.548

For the D-T reaction:

$$Q = (2.014102 + 3.016049 - 4.002603 - 1.008665) \times 931.5\ \text{MeV} = 17.59\ \text{MeV}$$

Energy Distribution

Reaction	Q-Value	Charged Particle Energy	Neutron Energy
D-T	17.6 MeV	3.52 MeV (20%)	14.06 MeV (80%)
D-D (n branch)	3.27 MeV	0.82 MeV (25%)	2.45 MeV (75%)
D-D (p branch)	4.04 MeV	4.04 MeV (100%)	None
D-$^3$He	18.3 MeV	18.3 MeV (100%)	None
p-$^{11}$B	8.68 MeV	8.68 MeV (100%)	None
T-T	11.3 MeV	3.77 MeV (33%)	7.53 MeV (67%)

In the D-T reaction, about 80% of the energy is given to neutrons. This neutron energy is converted to heat in the blanket for power generation, but it also presents challenges for material activation.

On the other hand, in D-$^3$He and p-$^{11}$B reactions, all energy is given to charged particles, enabling the possibility of direct energy conversion.

Fusion Power Density

The fusion power density of plasma is:

$$P_{\text{fus}} = n_1 n_2 \langle\sigma v\rangle Q$$

For equimolar D-T plasma ($n_D = n_T = n/2$):

$$P_{\text{fus}} = \frac{n^2}{4} \langle\sigma v\rangle Q$$

At temperature $T = 15$ keV and density $n = 10^{20}$ m$^{-3}$, the power density is about 2.5 MW/m$^3$.

Relationship to the Lawson Criterion

To sustain fusion reactions, the fusion triple product (Lawson product) condition must be satisfied:

$$n \tau_E T > \text{critical value}$$

where $n$ is plasma density, $\tau_E$ is energy confinement time, and $T$ is ion temperature.

Derivation of Ignition Condition

For ignition (a state where fusion reactions are sustained without external heating), alpha particle heating must exceed plasma losses:

$$P_\alpha \geq P_{\text{loss}}$$

For the D-T reaction, the alpha particle heating power is:

$$P_\alpha = \frac{n^2}{4} \langle\sigma v\rangle E_\alpha$$

Energy loss is:

$$P_{\text{loss}} = \frac{3nk_B T}{\tau_E}$$

From these, the ignition condition is derived:

$$n\tau_E > \frac{12 k_B T}{E_\alpha \langle\sigma v\rangle}$$

Ignition Conditions for Each Reaction

The ignition conditions (conditions for sustained reactions without external heating) differ for each reaction:

Reaction	Optimal Temperature	Required $n\tau_E$	Required $n\tau_E T$
D-T	~10-20 keV	$\sim 1.5 \times 10^{20}$ s/m$^3$	$\sim 3 \times 10^{21}$ keV s/m$^3$
D-D	~50 keV	$\sim 5 \times 10^{21}$ s/m$^3$	$\sim 2.5 \times 10^{23}$ keV s/m$^3$
D-$^3$He	~50-100 keV	$\sim 2 \times 10^{21}$ s/m$^3$	$\sim 10^{23}$ keV s/m$^3$
p-$^{11}$B	~300 keV	$\sim 5 \times 10^{22}$ s/m$^3$	$\sim 1.5 \times 10^{25}$ keV s/m$^3$

The D-T reaction achieves ignition at the lowest conditions, making it the shortest path to realizing fusion power.

Fusion Reactions in the Sun and Stars

pp Chain (Proton-Proton Chain Reaction)

In stars with masses similar to the Sun, the pp chain is the main energy source. This is a series of reactions that produce one helium-4 from four protons:

First stage (pp-I, about 83%):

$$p + p \rightarrow \text{D} + e^+ + \nu_e + 0.42\ \text{MeV}$$ $$\text{D} + p \rightarrow {}^3\text{He} + \gamma + 5.49\ \text{MeV}$$ $${}^3\text{He} + {}^3\text{He} \rightarrow {}^4\text{He} + 2p + 12.86\ \text{MeV}$$

The first p + p reaction involves the weak interaction (beta decay), so its cross-section is extremely small ($\sigma \sim 10^{-47}$ cm$^2$), becoming the bottleneck of the reaction. Therefore, even at the density and temperature of the solar core ($n \sim 10^{32}$ /m$^3$, $T \sim 1.5 \times 10^7$ K), the average proton lifetime is about 10 billion years.

pp-II branch (about 17%):

$${}^3\text{He} + {}^4\text{He} \rightarrow {}^7\text{Be} + \gamma$$ $${}^7\text{Be} + e^- \rightarrow {}^7\text{Li} + \nu_e$$ $${}^7\text{Li} + p \rightarrow 2\,{}^4\text{He}$$

pp-III branch (about 0.02%):

$${}^7\text{Be} + p \rightarrow {}^8\text{B} + \gamma$$ $${}^8\text{B} \rightarrow {}^8\text{Be}^* + e^+ + \nu_e$$ $${}^8\text{Be}^* \rightarrow 2\,{}^4\text{He}$$

This branch is rare but plays an important role in solar neutrino detection experiments because it emits high-energy neutrinos.

Overall, the net reaction of the pp chain is:

$$4p \rightarrow {}^4\text{He} + 2e^+ + 2\nu_e + 26.73\ \text{MeV}$$

Of this, about 0.5 MeV is carried away by neutrinos, and the rest becomes heat.

CNO Cycle

In stars heavier than the Sun (about 1.3 solar masses or more), the CNO cycle becomes dominant. Carbon, nitrogen, and oxygen act as catalysts to produce helium-4 from four protons:

CNO-I (main cycle):

$${}^{12}\text{C} + p \rightarrow {}^{13}\text{N} + \gamma$$ $${}^{13}\text{N} \rightarrow {}^{13}\text{C} + e^+ + \nu_e$$ $${}^{13}\text{C} + p \rightarrow {}^{14}\text{N} + \gamma$$ $${}^{14}\text{N} + p \rightarrow {}^{15}\text{O} + \gamma$$ $${}^{15}\text{O} \rightarrow {}^{15}\text{N} + e^+ + \nu_e$$ $${}^{15}\text{N} + p \rightarrow {}^{12}\text{C} + {}^4\text{He}$$

In the CNO cycle, the $^{14}$N + p reaction is the slowest and becomes the bottleneck. The temperature dependence is very strong ($\propto T^{16-20}$), and it rapidly becomes dominant at higher temperatures than the pp chain ($\propto T^4$).

In the Sun, the CNO cycle accounts for about 1.5% of total energy generation.

Differences Between Solar and Terrestrial Fusion

Characteristic	Sun	Terrestrial Fusion Reactor
Temperature	15 million K (1.3 keV)	100-200 million K (10-20 keV)
Density	$1.5 \times 10^{32}$ /m$^3$	$10^{20}$ /m$^3$
Confinement	Gravity	Magnetic/Inertial
Primary Reaction	p + p	D + T
Power Density	~300 W/m$^3$	~10$^6$ W/m$^3$

The Sun compensates for low power density with enormous volume and long confinement time (by gravity). Terrestrial fusion reactors need to achieve high power density in limited volumes, which is why the high-reactivity D-T reaction is chosen.

Fuel Availability

Deuterium (D)

Deuterium is a stable isotope of hydrogen, present in seawater at about 0.015% (1 in 6,500). Separation technology from seawater is established, making it virtually an inexhaustible resource.

The following methods are used for deuterium separation:

1. Distillation: Uses the boiling point difference between heavy water (D$_2$O) and light water (H$_2$O)
2. Electrolysis: Uses the property that light water is preferentially decomposed during electrolysis
3. Girdler-Sulfide process: Uses isotope exchange reaction between water and hydrogen sulfide
4. Adsorption: Isotope exchange on catalysts

The fusion energy contained in deuterium in 1 liter of seawater is equivalent to about 300 liters of gasoline. The total amount of deuterium in seawater is about $4 \times 10^{13}$ tons, sustainable for over 1 billion years at current world energy consumption.

Tritium (T)

Tritium (triton) is a radioactive isotope of hydrogen with a half-life of about 12.3 years. It barely exists in nature (trace amounts are produced by cosmic ray interactions with the atmosphere) and must be produced artificially.

Current tritium supply sources are mainly heavy water reactors (such as CANDU reactors), with annual production of several kg. The world’s tritium inventory is estimated at about 25 kg, sufficient for ITER operation but entirely inadequate for future commercial reactors.

In fusion reactors, tritium is produced by reactions between lithium and neutrons in the blanket:

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

The $^6$Li reaction is exothermic with a large cross-section for thermal neutrons (about 940 barn). The $^7$Li reaction is endothermic but contributes to improving the tritium breeding ratio (TBR) by consuming fast neutrons while generating new neutrons.

For self-sustaining fusion reactors, TBR > 1 (producing more tritium than consumed) is required. Using neutron multipliers such as beryllium (Be) or lead (Pb), TBR of 1.1-1.15 is expected to be achievable.

Lithium is abundant in the Earth’s crust (about 20 ppm) and seawater (about 0.17 ppm), with reserves equivalent to tens of thousands of years of fusion power generation.

Helium-3 ($^3$He)

Helium-3 is an extremely rare isotope on Earth. The helium concentration in Earth’s atmosphere is about 5 ppm, of which $^3$He is only about 1.4 ppm (0.000137% of the total).

Earth’s $^3$He supply sources:

1. Beta decay of tritium (from nuclear weapons/reactors)
2. Trace components in natural gas (mantle-derived)
3. $^6$Li(n,$\alpha$)T → $^3$He pathway in fission reactors

Annual production is only tens of kg, far from sufficient for commercial D-$^3$He power plant operation.

However, the lunar regolith has accumulated $^3$He carried by the solar wind, attracting attention as a future resource. An estimated $10^6$ to $10^9$ tons of $^3$He exist on the Moon, and 1 ton is estimated to be capable of generating about 1 GW-year.

Mars and Jupiter’s atmosphere are also considered as $^3$He resource candidates, but mining and transportation costs are currently unpredictable.

Possibilities and Challenges of Advanced Fuel Fusion

Fusion reactions other than D-T (D-D, D-$^3$He, p-$^{11}$B, etc.) are called “advanced fuels.” These have the advantage of producing few or no neutrons, but significant technical challenges exist for their realization.

Challenges of D-$^3$He Fuel

1. Achieving and maintaining high reaction temperatures (50-100 keV)
2. Suppressing neutron production from side reactions (D-D reactions)
3. Securing $^3$He fuel (lunar mining, etc.)
4. Increased synchrotron radiation losses

In D-$^3$He plasma, T and $^3$He produced in D-D reaction branches react further, forming a complex nuclear reaction network. Completely aneutronic reactions are difficult to achieve.

However, there is potential to reduce neutron production rates to about 1/100 compared to D-T reactions, offering significant mitigation of material problems.

Challenges of p-$^{11}$B Fuel

1. Extremely high required reaction temperature (~300 keV)
2. Large Bremsstrahlung losses ($Z_{\text{eff}} = 2.5$)
3. Difficulty in decoupling electron and ion temperatures
4. Low reactivity density

In p-$^{11}$B reactions, Bremsstrahlung losses may equal or exceed fusion output. Approaches to overcome this include:

1. Use of non-Maxwellian distribution plasmas
2. Promoting reactions under non-thermal equilibrium conditions such as laser-driven
3. Suppressing hot electron confinement

These are being researched but are far from realization.

Advantages of Advanced Fuels

If advanced fuels are realized, the advantages are substantial:

1. Neutron shielding and activation problems are eliminated or greatly reduced
2. Direct energy conversion by charged particles becomes possible
3. Tritium handling problems are eliminated
4. Blanket simplification
5. Significantly extended material lifetimes

These advantages could greatly improve the economics of commercial fusion power.

Current Research Trends

Private companies targeting advanced fuels have also emerged:

1. TAE Technologies (FRC approach targeting D-$^3$He)
2. Helion Energy (D-D + D-$^3$He hybrid)
3. HB11 Energy (laser-driven p-$^{11}$B)

All of these are in early stages but are attracting attention as different approaches from the D-T pathway.

Comprehensive Comparison of Each Reaction

Detailed Advantages and Disadvantages

Reaction	Advantages	Disadvantages
D-T	Most reactive, high reaction rate at low temperature, technically achievable	Activation by neutrons (80% of energy is neutrons), special facilities needed for tritium handling, TBR > 1 required
D-D	Abundant fuel (inexhaustible supply from seawater), no tritium breeding blanket needed	High reaction temperature required (~5x D-T), reaction rate ~1/100 of D-T, neutron production unavoidable
D-$^3$He	No neutrons in primary reaction, high Q-value (18.3 MeV), direct conversion possible	Extremely high temperature required, $^3$He scarcity, neutron production from D-D side reactions
p-$^{11}$B	Completely aneutronic reaction, relatively abundant fuel, optimal for direct conversion	Extremely high required temperature, large Bremsstrahlung losses, infeasible with current technology

Comparison of Technical Achievement

Reaction	Required $n\tau_E T$	Current Achievement	Realization Outlook
D-T	$3 \times 10^{21}$ keV s/m$^3$	JET: $\sim 10^{21}$	Ignition target at ITER
D-D	$2.5 \times 10^{23}$ keV s/m$^3$	~1% of D-T	Long-term challenge
D-$^3$He	$10^{23}$ keV s/m$^3$	Extremely insufficient	Long-term challenge
p-$^{11}$B	$1.5 \times 10^{25}$ keV s/m$^3$	Extremely insufficient	Difficult to achieve

Summary

The choice of fusion reaction is a fundamental factor determining the feasibility and characteristics of fusion power.

Current fusion development is focused on the D-T reaction, which has the lowest technical barriers. The D-T reaction achieves high reaction rates at relatively low temperatures (10-20 keV) and is adopted by ITER and future DEMO reactors.

However, the D-T reaction has challenges with material activation from 14 MeV fast neutrons and tritium handling. Research on advanced fuels (D-$^3$He, p-$^{11}$B, etc.) that address these issues is ongoing, but the required temperature and confinement conditions are far more stringent than D-T, requiring technical breakthroughs for realization.

In the long-term development of fusion power, the D-T reaction is the first step, with future realization of advanced fusion reactors using D-D and D-$^3$He reactions also anticipated.

Related Topics

• What is Fusion - Basic principles of fusion reactions
• Lawson Criterion - Conditions for fusion ignition
• Tokamak Confinement - Mainstream confinement method using D-T reaction
• Confinement Methods: Overview - Overview of confinement methods
• ITER Project - International cooperation project aiming for D-T burning experiments
• Plasma Heating Principles - Heating methods for achieving fusion temperatures