FreeGS COCOS

[Lukáš Kripner]

To address the question, which COCOS is used by FreeGS I have prepared the attached PDF python notebook. There is discussion as well as cross-validation so I suppose it is right.

The consequence that FreeGS is using COCOS 3 or 7.

FreeGS-cocos.pdf

From the conclusion:

Both COCOS 3 and 7 are applicable for FreeGS; the difference is in the orientation of the poloidal angle (see PLEQUE figure for COCOS 7 and 3). However, poloidal angle $\theta$ is never used in FreeGS. The only practical consequence can be seen in the definition of safety factor $q$, which should be negative for COCOS 3 and positive for COCOS 7. That said COCOS 7 is favourable over 3. On the other hand, this notation is not always forced. For example, EFIT is COCOS 3 with $q$ value always positive.

Maintaining correct sign of $q$ may be important if poloidal angle is introduced. Esp. if streight fieldline $\theta^$ is used. Due to the the relationship of the $\theta^$ and toroidal angle $\phi$, since $\theta^_
\mathrm{end} = \theta^_\mathrm{start} + (1/q) \Delta \phi$.

To sum it up:

• COCOS = 3 - cnt-clockwise orientation of $\theta$, $q$ should be positive, is used by EFIT, and this orientation seems to be quite intuitive.
• COCOS = 7 - clockwise orientation of $\theta$, $q$ is positive as calculated by FreeGS, is generally used by the community.

[Ben Dudson]

Thank you @kripnerl this is very useful! I'm going to archive this repository but don't want this to be lost in the move to the new repository (https://github.com/freegs-plasma/freegs). Would you be willing to share this in LaTeX or RST or similar format, to be merged into the manual? Thanks!

[Lukáš Kripner]

Yop, if you do not see any mistake in the documents. I can formulate it into docs.