Elongation and Triangularity in STs #1087

Closed jonmaddock closed 1 year ago

In GitLab by @stuartmuldrew on Aug 10, 2020, 10:03

The x-point to 95% conversion values for elongation and triangularity come from the ITER Physics Design guidelines. These may not hold at the higher elongations in spherical tokamaks.

shape

Initial comparison with FIESTA shows there is an offset in the elongation. Solid line is the ITER design guidelines, currently used, and dashed is the relation proposed by Peng, Galambos & Shipe (1992). The triangularity is more scattered, loosely correlated with the major radius due to the simple coil set being used. This requires further investigation.

The aim is to add new relations to ishape.

In GitLab by @mkovari on Aug 25, 2020, 09:27

Can you attach details of the Fiesta equilibria?

Were they single or double null?

Do you think we should move to using upper and lower triangularity values for single null cases?

Can you colour code the triagularity plot by the different parameter that determines the lines visible in the plot?

Existential night thought: has anyone ever made single null tight aspect ratio plasmas?

In GitLab by @stuartmuldrew on Aug 28, 2020, 16:57

created branch issue-1086-kd to address this issue

In GitLab by @stuartmuldrew on Sep 8, 2020, 12:12

Similar plot comparing to MAST data: mast Top left: X-point vs 95% Elongation
Top right: X-point vs 95% Upper Triangularity
Bottom left: X-point vs 95% Lower Triangularity
Bottom right: Upper vs Lower Triangularity

The grid-like triangularity is due to rounding, with only two decimal places being reported in the table I have.

In GitLab by @stuartmuldrew on Sep 9, 2020, 08:41

Geof Cunningham comment on triangularity in FIESTA:

After a bit of thought - this relationship is purely geometric, so the delta one is purely the major radius, not the field, as you suggest. Is it expected? Well it's not unexpected, but it's also probably not a unique relationship. The way I did the scan, using a very simple coil set, means the shape varies quite a bit with major radius. If you had a more fancy coil set which allowed the shape to remain quasi-constant then I would hope for more more consistent output. You could try a multiple regression with kappa as well as delta, but I wouldn't be surprised if you need to introduce a higher order shape parameter (normally called squareness, but I'm not sure of the definition).

or we could use a fixed boundary solver which would indeed fix the shape but could easily create shapes which are not physically achievable.

In the end you have to decide what you are trying to achieve.

Geof

In GitLab by @stuartmuldrew on Sep 9, 2020, 14:11

The best fits to the above data are:

MAST:

\kappa = 0.91 \kappa_{95} + 0.39

\delta = 0.77 \delta_{95} + 0.19

FIESTA:

\kappa = 0.91 \kappa_{95} + 0.39

\delta = 1.38 \delta_{95} + 0.05

This is not constraining the relation to go through the origin like the existing ones do.

The elongation relations are near identical however there is some difference in the triangularity. This is probably influenced by the coil set/overall plasma shape. If we add the equilibrium solver, that will remove the need to use these equations (ref: @jmorris-uk)

In GitLab by @stuartmuldrew on Sep 9, 2020, 14:35

Red line is MAST fit, blue line is FIESTA:

fiesta

mast

In GitLab by @stuartmuldrew on Sep 9, 2020, 16:53

mentioned in commit c83083d0cba46a38ea6ccf63e1b4df5ae931f3a4

In GitLab by @stuartmuldrew on Sep 10, 2020, 10:21

mentioned in commit 5d0f691080b1009423b5440807ff77a7dfe2bceb

In GitLab by @stuartmuldrew on Sep 10, 2020, 11:51

mentioned in commit cd4120ad8754689d94a6d53cc0706fa7b17295f3

In GitLab by @stuartmuldrew on Sep 11, 2020, 16:42

closed

ukaea / PROCESS

Elongation and Triangularity in STs #1087