Correlation of the Tokamak H-Mode Density Limit with Ballooning Stability at the Separatrix

In GitLab by @mkovari on Aug 30, 2017, 13:41

See Correlation of the tokamak H-Mode density limit with ballooning stability at the separatrix, T. Eich et al.

the measured value of the ballooning-scaled dimensionless pressure gradient, $\alpha$, rises about linearly with the separatrix (edge) density normalized to the Greenwald value, until it reaches the ideal stability limit of $\alpha = 2 - 2.5$, where confinement degrades and H-Mode characteristics are terminated. This generally occurs at about 0.8 - 0.9 of the line-averaged Greenwald density limit for conventional L-Mode and Ohmically-heated plasmas.

The formula for the ballooning parameter for the separatrix position, $\alpha_{sep}$, is given in equation 1. An equation for the critical value of this parameter is given as

which has been implemented in PROCESS. Alternatives given, but not implemented are fixed at $\alpha_{crit}=2.2$ for $\kappa=2$, and $\alpha_{crit}=2.5$. Chat with Chris Ham leant towards using the equation, as these fixed values may be machine dependent, and do not reflect the equation calculated number (~3.6 with current DEMO baseline inputs).

Eich has given a usable formula for the critical separatrix density in terms of fundamental plasma parameters:
,
which has been implemented. There is also an alternative form (equation 6) that uses $<\lambda_q>$, the poloidal average of $\lambda_q$, which is needed for the divertor model but this has not been implemented.

But note,

Our results indicate that if shallow pellet injection, as planned for ITER, increases the ratio of $n_{e,av}/n_{e,sep}$ compared with gas fueling, it would allow higher average normalized density operation, and so higher performance, in ITER.

No consideration of this has been made in PROCESS as yet.

Questions

If we implement this limit, should it be
instead of the regular density limit,
instead of the LH power threshold, or
a third independent limit, which replaces the current option of setting the separatrix density in terms of the Greenwald density? (see iscdens)
If we implement this limit, how do we handle the possible improvements due to pellet fuelling?

Implementation notes (KE):
Added new constraint 76 with f-value fnesep. Made nesep an iteration variable. Both nesep_crit and alpha_crit are made global variables. Added output which looks like this when nesep is being constrained:

Critical ballooning parameter value (alpha_crit) 3.657E+00
Critical electron density at separatrix (/m3) (nesep_crit) 3.017E+19
Electron density at separatrix (/m3) (nesep) 3.017E+19 ITV

Test case: useConstraint75_copy.7z
Additional test material:
K:\Power Plant Physics and Technology\PROCESS\Katy Ellis\EichDensityLimit

@Hlux @rkemp @msiccini

In GitLab by @msiccini on Aug 30, 2017, 15:52

Hallo everybody.

Personally, I would implement the nsep/nGW limit instead of the regular density limit.

Incidentally, I think this is more or less the message of the paper of Thomas and especially of the last sentence you quoted, i.e. it is possible to vary the density profile - and therefore n_line averaged / n_GW - without affecting the discharge stability, provided that we are fulfilling the constraint on n_sep/n_GW, which is what actually dominates the H-L transition physics (from an MHD point of view, at least).

Which is the same as: if we are able to peak a lot our density profile in the centre, we can tolerate n_line,av >> n_GW, which is what Hartmut has assumed for Flexi-DEMO.

Once the limit is set on n_sep, other profile effects (e.g. due the use of pellet fuelling) can be introduced by changing the shape of the density profiles, or somehow taken into account in the transport model of Emiliano. I think the user should be to some extent left free to shape the profile as he wishes (more/less peaked), with n_peak being indirectly constrained by the limit on n_sep once the profile shape is set. Or this is something you might want to make more automatic, something like I want to have pellet -> I must have this profile shape?

On the contrary, I would say that the P_LH threshold is connected to completely different physical mechanisms (e.g. you could have a H -> L transition by turning off the auxiliary power even if n_sep < 0.5 n_GW). Thus, the criteria on Psep > P_LH and n_sep < some fraction of n_GW have to be enforced at the same time and independently one from another.

Mattia

In GitLab by @kellis on Feb 2, 2018, 14:44

Committed changes to git for the new constraint on nesep, using the equation definition for alpha_crit. Discuss with @mkovari whether this issue can be closed.

In GitLab by @kellis on Feb 2, 2018, 17:31

Edited this issue to reflect what has been implemented. Added the new 'critical' variables to the PROCESS output.

In GitLab by @mkovari on Feb 5, 2018, 13:09

I notice that

Tag No. : "1.0.12-51-g61012f1 Code used contains Untracked Changes"

This should probably be fixed. The code should be committed and then pushed to the relevant branch, then rerunning will generate an output file that shows the correct tag number.

In GitLab by @mkovari on Sep 7, 2018, 16:33

Ideally this should be documented where the users and collaborators can see it!

In GitLab by @mkovari on Sep 7, 2018, 16:33

closed