7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Density Limits as Disruption Forecasters for Spherical Tokamaks

Jack Berkery1, S.A. Sabbagh2, C.J. Ham3, M. Giacomin4, V. Zamkovska2, J. Butt5, J. Riquezes2,M. Tobin2, S. Henderson3, L. Kogan3, B.S. Patel3, R. Scannell3, E. Trier3
and B. LeBlanc1
123
PPPL, Columbia University, UKAEA, 4University of York, 5Princeton University
e-mail (speaker): jberkery@pppl.gov
Fusion power output from spherical tokamaks would
benefit from increased confined plasma density, but there
exists a limit on the density before confinement is lost andthe plasma current is disrupted. Understanding the physics
of the density limit in spherical tokamaks (STs) by testing
multiple theories and determining their utility fordisruption forecasting is vital work to be carried out on
present machines to have confidence in designs of stably
operating future ST fusion pilot plants. This density limit
has long been characterized by a simple, global
Greenwald limit proportional to the plasma current andinversely proportional to the cross sectional area of theplasma. It is shown that in the database of discharges fromthe NSTX and MAST spherical tokamaks, the likelihoodof disruption does increase above the Greenwald limit,
and especially in the plasma current rampdown phase.
The physics of the density limit has been recently
theoretically explored through local criteria. Several ofthese are now tested for STs [1] using the disruption event
characterization and forecasting (DECAFTM) code [2] for
their potential effectiveness as disruption warning signals.
The framework of the DECAF code, and its large databaseof discharge data from many machines, including these,represents an opportunity to test the density limit theories.
For a limited set of NSTX discharges, a local island power
balance criteria [3] was found to be less reliable, presently,
than the Greenwald limit. An empirical critical edge line
density (Bernert) [4] and a first-principles boundary
turbulent transport limit (Giacomin) [5] have found somesuccess in various conventional tokamaks. The Giacominlimit was derived from turbulent transport considerations
at the separatrix, by balancing heat source and cross-field
turbulent heat flux, derived from a quasi-linear non-local
theory. In particular, turbulent transport is found toincrease with edge collisionality, which increases withdensity. At high density, turbulent transport iscatastrophically large, therefore causing a collapse of theedge pressure gradient, which is followed by the onset of
MHD instabilities and the subsequent plasma disruption.
These limits were tested for MAST-U, which has adetailed electron density profile measurement. Both werefound to have similar dependencies. MAST-U has mostly
operated under the Greenwald limit so far [6], but in alimited set of MAST-U discharges that appear to disrupt
due to rising density at values under the Greenwald limit,
crossing of the Giacomin limit (ne,edge,crit) occurred close
to the time of disruption. Figure 1 shows the trajectories
of MAST-U plasmas in the space of ne/ne,edge,crit vs. ne/nGW,
showing that many of the discharges cross the edge limit

and disrupt before the Greenwald limit.
Finally, these limits were evaluated for their potential use
in real-time, and it was found that with the necessary realtime inputs and with refinement through further testing,these limits could be implemented in a real-time
disruption forecasting system.

Figure 1: Plots of ne/ne,edge,crit vs. ne/nGW for (top) four
MAST-U Ohmic ∼ 600 kA discharges, and (bottom) fivebeam heated ∼750 kA discharges. Stars indicate
disruptions.

References[1] J.W. Berkery, et al., Plasma Phys. Control. Fusion 65,095003 (2023)[2] S. A. Sabbagh, J.W. Berkery, et al., Phys. Plasmas 30,032506 (2023)[3] D. A. Gates and L. Delgado-Aparicio, Phys. Rev.
Lett. 108, 165004 (2012)[4] M. Bernert et al., Plasma Phys. Control. Fusion 57,014038 (2015)[5] M. Giacomin et al., Phys. Rev. Lett. 128, 185003(2022)[6] J.W. Berkery et al., Plasma Phys. Control. Fusion 65,045001 (2023)