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Figure of merit for the fusion gain for ITER extrapolations PowerPoint Presentation

Figure of merit for the fusion gain for ITER extrapolations

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### 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

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

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

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

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)

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 )

Figure of Merit - derivation

- ll

The Gain can be expressed in the engineering parameters using the

scaling law

Figure of Merit – derivation (2)

- Ratio of Gain with the Gain of the standard scenario

Figure of Merit

- For the IPB98 at fixed Greenwald density
- For the IPB98 at fixed density

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

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

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

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

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

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

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