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Concepts & Physics

Energy Confinement Time

The characteristic duration over which a fusion plasma retains its thermal energy—one of the three factors in the triple product that determine whether a device can achieve net energy gain.

Reviewed Last reviewed: 9 Aug 2026 · Category: Concepts & Physics

Definition

The energy confinement time, denoted τE, is defined as the ratio of the total stored thermal energy in the plasma (W) to the total power loss (Ploss):[1]

Definition: τE = W / Ploss

where W = (3/2) ∫ n(r) kBT(r) dV is the total plasma stored energy.

τE represents how quickly a plasma would cool if all heating were suddenly removed. A longer confinement time means less external heating is needed to maintain fusion-relevant temperatures.[4]

Scaling Laws

The most widely used scaling is IPB98(y,2) for H-mode tokamak plasmas:[1]

IPB98(y,2) scaling:
τEIp0.93 · BT0.15 · P−0.69 · n0.41 · M0.19 · R1.97 · ε0.58 · κ0.78

This scaling was derived from a multi-machine database and forms the primary basis for predicting ITER’s confinement performance.[3]

H-Mode and Confinement Enhancement

The discovery of H-mode at the ASDEX tokamak in 1982 by Friedrich Wagner approximately doubled τE compared with L-mode. This is a verified result reproduced on virtually every divertor tokamak worldwide. ITER’s baseline design assumes standard H-mode confinement (H98(y,2) = 1.0).[2]

Typical Values

τE ranges from tens of milliseconds in smaller devices to 1–3 seconds in large machines such as JET. ITER is projected to achieve τE ≈ 3.7 seconds at its nominal 15 MA operating point. Wendelstein 7-X has demonstrated values consistent with design predictions.[3]

Sources

  1. ITER Physics Expert Group on Confinement and Transport. "Chapter 2: Plasma confinement and transport." Nuclear Fusion, vol. 39, no. 12, 1999, pp. 2175–2249.
  2. Wagner, F. et al. "Regime of Improved Confinement and High Beta in Neutral-Beam-Heated Divertor Discharges of the ASDEX Tokamak." Physical Review Letters, vol. 49, no. 19, 1982, pp. 1408–1412.
  3. Doyle, E.J. et al. "Chapter 2: Plasma confinement and transport." Nuclear Fusion, vol. 47, no. 6, 2007, pp. S18–S127.
  4. Wesson, J. Tokamaks. 4th edition, Oxford University Press, 2011.

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