Effect of Profiles and Shape on Ideal Stability of Advanced Tokamak Equilibria Page: 6 of 7
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
EFFECT OF PROFILES AND SHAPE ON IDEAL STABLITY
OF ADVANCED TOKAMAK EQUILIBRIA M.A. Makowski, et al.
if the lower $N values are ignored. In general, the n = 1 limit is dominated by profile effects,
whereas shape plays a more significant role with respect to the n = 2 limit, with the highest
ON values at a given peaking factor occurring for an optimal shape
Two ballooning unstable regions were often found to exist. The lower ballooning beta
limit was found to be uniformly in the range 2.7-3.0 except at the lowest peaking factor
where it increased abruptly to 5.5 for a restricted set of shapes.
As is evident in Fig. 1 there is a large variation in the data at any particular value of the
peaking factor. This results from the complicated dependence of the beta limit on the shape
factors, 6, K, and (o, as well as on the details of the pressure profile through bn as shown in
Fig. 2. Here the n = 1 and 2 limits are plotted versus 6 (at fixed K, (o, and peaking factor)
and versus (o (at fixed K, 8, and peaking factor). For the 8-scan of Fig. 2(a), the maximum
$N is limited everywhere by the n = 1 mode. In contrast, for the (o-scan of Fig. 2(b), the
$-limit is set everywhere by the n = 2 mode. The n = 1 8-scan shows an optimal intermediate
value of 6 - 0.6, whereas the n = 2 0-scan is monotone decreasing with (0. For the 8-scan,
an n = 1 internal mode actually sets the 1-limit at 8= 0.8.
4.5 .
(n =24.6
4.0
4.4
(n=1)
3.5 K=1.9 4.2 =1.90
o=0.0 a 4.0 o =0.65
3.0 3.8
2N(n=1) -
3.6
2.5
3.4 (n 2)
(a) ( (n =1, internal)-:.32 (b)
2.0 3.2
0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3
Fig. 2. Parameter scans of maximum $N VS S at fixed x and to (a) and vs , at fixed K and 5. The
peaking factor is -2.5 for both (a) and (b).
Figure 3 shows a parameter scan of 1-limit for the n = 1 and 2 modes versus K for
several values of (o at fixed 6 and peaking factor. The n = 2 mode always sets the 1-limit.
Again the parametric dependence is complicated. Increasing K leads to a higher 1-limit
except at the largest squareness. Considering all cases the 1-limit is 4.6 for a peaking factor
of -2.5 with K = 2.0, 6=0.65, and o =0, and results from an n = 2 mode.
The ideal stability code GATO was used to check some of the DCON results presented
here. For the six cases studied, corresponding to the (o parameter scan of Fig. 2(b), the
13-limits either agree exactly or differ by at most 10%, with DCON generally predicting a
slightly higher $-limit than GATO.
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Makowski, M. A.; Casper, T. A.; Ferron, J. R.; Taylor, T. S. & Turnbull, A. D. Effect of Profiles and Shape on Ideal Stability of Advanced Tokamak Equilibria, article, August 1, 2003; United States. (https://digital.library.unt.edu/ark:/67531/metadc784818/m1/6/: accessed April 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.