In extrapolating from current experience to unprecedented domains, there are unavoidable uncertainties. To assess the probability of achieving a fusion gain of Q > 10 in ITER, an analysis has been made based on the estimated uncertainty in the confinement scaling.

It is assumed that the energy confinement time (or, in practice, the H_H factor) for a given set of plasma parameters can be described by a Gaussian distribution having a standard deviation of either 10% or 20% about the mean value. (In fact, for similar discharge conditions, the actual distribution of H_H in the database has a smaller spread, ~ 5%.)

Using conservative operating conditions, it is possible to identify the operation space for various values of auxiliary heating, and then fold in the assumed probability density function for H_H to quantify the probability that Q exceeds a given Q₀ value.

This analysis is illustrated below for two different values of plasma current. The "total probability" shown is the probability that Q>Q₀ in ELMY H-mode

The probability of achieving Q > 10 in this regime is high at 15 MA. However, if Q > 10 were not achieved under nominal operating conditions, raising the plasma current to 17.4 MA would significantly increase the probability of achieving the required Q.

This calculation is not a complete evaluation of the true probability of achieving Q > 10. It is a model calculation carried out in only one dimension of the multi-dimensional operating space which describes a burning plasma. It neither fully reflects the complexity of the behaviour close to operating limits, nor the degree to which experimental optimization of plasma parameters can improve plasma performance. Furthermore, the energy confinement time scaling law used for deriving ITER parameters excludes explicit reference, for example, to the effect of magnetic shear on confinement in high density discharges, and the effect of saw-teeth on low edge safety factor discharges at higher elongation and triangularity.

To overcome these difficulties, a deterministic procedure has been followed. Each discharge from the experimental database is used to size, by means of a system code (in accordance with the ITER engineering criteria), a Q=10 machine with the same geometry and parameter values for plasma elongation, triangularity, aspect ratio, helicity safety factor, and density relative to the Greenwald limit as in the experimental case. The energy confinement time is therefore scaled from the experimental values only by the remaining parameters of the scaling, i.e. power, toroidal field, major radius, and atomic mass.

From the more than 1000 discharges in the ELMy H-mode database, half of them turn out to extrapolate to a Q=10 machine of major radius smaller than 8m, but only 70 to a radius smaller than 6.2 m and only a few to radius smaller than 6 m, the smallest value being 5.6 m with q₉₅=3.0.

As a second check, avoiding completely the use of empirical scaling formulas, device size was extrapolated to obtain the required fusion power (and not the Q value) from experimental discharges, keeping a fixed value for b_N.

The following figure shows the result plotted as major radius versus the helicity safety factor q₉₅ for all machines extrapolated to 500 MW of fusion power. A good number of discharges can be extrapolated to 500MW devices with radius between 6 and 6.2 m.

Further information on confidence levels for ITER operation can be found in the ITER Plant Description.