Figure of merit for the fusion gain for ITER extrapolations

1. Figure of merit for the fusion gainfor ITER extrapolations C. Angioni, A.G. Peeters A.G. Peeters, C. Angioni, A.C.C. Sips, submitted to Nuclear Fusion, ArXiv 0701185

2. Preamble • The point of this talk is not that high plasma beta is bad • High plasma beta leads to high fusion power • However for an experiment like ITER the fusion gain plays a central role • A figure of merit (or at least one of the figures of merit) should directly reflect this important quantity

3. Limitations • The results presented in this talk have implications for any reactor design • However we concentrate on ITER. • This means that we assume a fixed size and density • A reactor is not necessarily the same since one can optimise it in different ways (for instance through the size) • We also apologise if this talk appears trivial to you

4. The often used H bN/ q952 • This figure of merit does not reflect the fusion gain. • For instance, the following discharge reaches the ITER target • But extrapolates to a capital Q = 1 • A high value of H bN/ q952does guarantee neither a high fusion gain nor that such discharges might be run on ITER with the available heating power

5. Rough derivation • In the rough derivation one use nTt • And • To obtain • However, the confinement time is not independent of the heating power ( hence of beta)

6. Figure of Merit - definitions • Define (Only 20% of fusion power heats plasma) • Using the expression for the fusion power • One obtains for G (PHEAT = PLOSS = PFUS/5 +PAUX )

7. Figure of Merit - derivation • ll The Gain can be expressed in the engineering parameters using the scaling law

8. Figure of Merit – derivation (2) • Ratio of Gain with the Gain of the standard scenario

9. Figure of Merit • For the IPB98 at fixed Greenwald density • For the IPB98 at fixed density

10. Figure of Merit • Expression of the Figure of Merit for the Fusion Gain G is not universal, BUT depends on the exponents of the scaling law for the confinement time one applies • No beta dependence if alphaP = 0.5 (e.g. L-Mode 89 scaling) • if alphaP = 0 (no power degradation), and at fixed density

11. Dimensionless numbers • The Gain can then be expressed as Positive beta dependence ???

12. No contradiction • At fixed density and machine size the beta scaling is essentially a temperature scaling with affects also the normalised Larmor radius and collisionality • Scaling the temperature one can derive (for IPB98) Same exponent as in the expression with engeneering parameters

13. Example (ASDEX Upgrade) • Figure of merit as a function of the bootstrap fraction ( normalised to the Stand Scenario ) • Different colours correspond to different values of the safety factor • Even at the highest bootstrap fractions the ITER target can be reached

14. Figure of Merit describing the Fusion Gain • Same data with the figure of merit that directly reflects the Fusion Gain • Clearly, discharges with the highest bootstrap current fraction perform poorly

15. Proposed diagram • The diagram we propose to display the data • Figure of Merit versus the dimensionless scaling of the fusion power • The auxilary heating necessary to maintain the discharge is a curve in this diagram • Some discharges (high beta, moderate confinement) can not be sustained in ITER 2 10.8 H / ßN / q95 3

16. Conclusions • A figure of Merit has been derived that describes the fusion gain directly Its expression depends on the adopted scaling law for the confinement time • This figure shows that high beta discharges do not always reach sufficient fusion gain, and might not be sustainable with the fusion power available in ITER • The proposed diagram plots fusion gain versus fusion power. Constant auxiliary heating power is a curve in the diagram