Science & Technology of Controlled Fusion

Self-sustaining ignition requires that the fusion power deposited in α-particles exceed plasma losses. Lawson's triple product expresses this as:

where $n$ is ion density (m⁻³), $\tau_E$ the energy confinement time (s), and $T$ the ion temperature (keV). For D-T fuel at $T \approx 14\ \text{keV}$, ignition demands $n\tau_E \gtrsim 1.5 \times 10^{20}\ \text{m}^{-3}\,\text{s}$.

Magnetic confinement uses toroidal $\mathbf{B}$ fields to constrain charged particles along helical field lines, suppressing radial transport. The relevant pressure balance is governed by magnetic pressure:

The plasma beta — ratio of plasma to magnetic pressure — $\beta = \dfrac{2\mu_0 n k_B T}{B^2}$ — sets the economic ceiling of any magnetic device. High-temperature superconducting (HTS) REBCO tapes enable $B \approx 20\ \text{T}$, shrinking reactor volume by roughly $(B_0/B)^4$.

Inertial confinement fusion (ICF) compresses a cryogenic D-T pellet via $\sim\,\text{MJ}$-class laser pulses, achieving densities $\rho \sim 1000\ \text{g/cm}^3$. The relevant figure of merit is areal density:

NIF's December 2022 ignition shot at LLNL deposited 2.05 MJ of UV laser energy onto a hohlraum and produced 3.15 MJ of fusion yield — the first lab demonstration of target energy gain $G_\text{target} > 1$.

Field-reversed configurations (FRC) confine plasma in a self-organized compact toroid with zero toroidal field — pursued by TAE and Helion. Magnetized target fusion (MTF, General Fusion) and pulsed Z-pinch (Zap Energy) trade steady-state operation for pulsed compression cycles operating at 1–10 Hz.