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Glossary

Energy Balance in Fusion Plasmas

The global power bookkeeping that determines whether a magnetically confined plasma heats itself, cools down, or ignites.

Reviewed Last reviewed: 9 Aug 2026 · Category: Glossary

The Fundamental Equation

A fusion plasma is a thermodynamic system with well-defined energy inputs and losses. In steady state the global energy balance requires that the total heating power equals the total loss power:1

Pheat = Paux + Pα = Ploss = W / τE + Prad
where Paux is externally applied heating (NBI, ICRH, ECRH), Pα is alpha-particle self-heating (one-fifth of fusion power), W is the plasma stored energy, τE is the energy confinement time, and Prad is radiated power from impurities and bremsstrahlung.

Heating Channels

Ohmic heating provides the initial energy input from resistive dissipation of the plasma current. However, ohmic power decreases as Te−3/2, making it negligible above a few keV. Auxiliary heating—neutral beam injection, ion and electron cyclotron resonance heating, and lower hybrid current drive—raises the plasma into the thermonuclear-relevant regime of 10–25 keV.2

In a burning D-T plasma, alpha particles born at 3.52 MeV slow down on electrons and ions, depositing their energy in the core. When Pα dominates over Paux, the plasma is said to be self-heated. The fusion gain parameter Q = Pfus/Paux quantifies how far along this path the plasma has progressed: Q = 1 is breakeven, Q = 10 is ITER's goal, and Q → ∞ is ignition.1

Loss Channels

Energy escapes the confined plasma through three main routes. Transport losses (conduction and convection through turbulent and neoclassical channels) are characterized by τE. Radiation losses—bremsstrahlung, cyclotron emission, and line radiation from impurities—can be volumetric or concentrated at the edge. Particle losses carry kinetic energy with escaping ions and electrons, including ELM-driven bursts in H-mode.3

The Lawson criterion, n τE T > a threshold, is simply the energy balance equation rearranged to state the minimum plasma conditions for self-sustaining burn. For D-T at optimal temperature (~14 keV), the triple product must exceed roughly 3 × 1021 keV·s·m−3.4

Understanding and closing the energy balance is the central challenge of fusion science. Every advance in confinement, density, or impurity control shifts the ledger toward net energy gain.

Sources

  1. Wesson, J., Tokamaks, 4th ed., Oxford University Press (2011), Chapter 1: Fusion and Chapter 14: Power balance
  2. Stacey, W.M., Fusion Plasma Physics, 2nd ed., Wiley-VCH (2012), Chapter 5: Energy balance
  3. Lawson, J.D., 'Some criteria for a power producing thermonuclear reactor,' Proceedings of the Physical Society B 70 (1957) 6-10
  4. Freidberg, J.P., Plasma Physics and Fusion Energy, Cambridge University Press (2007), Chapter 2: Fusion energy

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