Review. The path to fusion power 1097 6. Performance measures—what plasma performance has been achieved? In this section we deﬁne the three key plasma performance measures—the energy conﬁnement time, τE; the usage of the magnetic ﬁeld, β; and the current drive efﬁciency—and review the performance that has been achieved. It is necessarily technical and can be omitted by the reader focused on fusion policy. The power balance in the plasma is critical to fusion performance. One-ﬁfth of the fusion power is produced as kinetic energy of helium nuclei (alpha particles). The alpha particles heat the plasma. Let us denote the external heating power density from microwaves or beams as PHeat. The heat losses are almost entirely from turbulent transport of heat across the magnetic ﬁeld—the leakage. We parameterize these losses by the ‘energy conﬁnement time’ (τE) deﬁned by energy in plasma τE = power supplied to heat plasma . τE measures how well the magnetic ﬁeld insulates the plasma. It is obvious that the larger τE, the more effective a fusion reactor will be as a net source of power. In steady state the power balance per unit volume is PFusion 5 + PHeat ∼ 0.15 P τE , (6.1) where, as before, we express power density in MW m−3 and pressure in atmospheres. The energy gain is deﬁned by Q = PFusion/PHeat. At sufﬁcient pressure the plasma is entirely self-heated and PHeat = 0 and Q → ∞; this is termed ignition. High gain is essential for commercial fusion as supplying PHeat reduces the net output and complicates reactor design. The ‘fusion product’, PτE, and the temperature, T , determine the energy gain of the fusion device. In the temperature range 100–200 million degrees Celsius (where equation (3.4) applies) ignition occurs when PτE > 20 (P in atmospheres and τE in seconds). The ‘fusion performance plot’ (ﬁgure 3) of PiτE versus T (Pi = P/2 is the ion pressure) shows the breakeven point (Q = 1) and data points from different tokamaks, and indicates the substantial progress towards power station conditions that has been achieved in recent decades. Much of this progress in tokamak performance over 40 years has been achieved by suppressing the turbulent convection of heat and thereby increasing τE. The turbulent ‘eddies’ are a few ion larmor radii (ρi) across (typically a centimetre) and they are highly elongated along the magnetic ﬁeld lines (typically with a length the size of the tokamak, L(m)). These eddies turn over in a time L/vi, where vi is a typical ion velocity. The theory of this turbulence is complicated and just beginning to be understood. Progress has been greatly helped by high performance computations. However, the rough scaling of the conﬁnement can be estimated by considering the turbulent motion to be a random walk of step size ρi and correlation time L/vi—this yields τE ∼ (L/vi)(L/ρi)2 ∝ L3B2T −3/2. The experimental/empirical conﬁnement scaling differs a little from this simple estimate. Nonetheless, strong dependence on size and magnetic ﬁeld is observed. In 1982 the serendipitous discovery (in a fusion experiment at Garching in Germany (Wagner et al. 1982)) of a ‘high-conﬁnement’ plasma mode (H mode) revealed the important role played by plasma rotation. In these plasmas a narrow Phil. Trans. R. Soc. A (2010)