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 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 q95

2does 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 nT

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

Dimensionless numbers

The Gain can then be expressed as

Positive beta dependence ???

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

10.

8 H

/ ß

N /

q95

32

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