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Figure of merit for the fusion gain for 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 - PowerPoint PPT Presentation
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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 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