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

Drift surface solver for runaway electron current dominant equilibria
Di Hu1 and Lu Yuan1
1
School of Physics, Beihang University
e-mail (speaker): hudi2@buaa.edu.cn

Runaway electron current generated during theCurrent Quench phase of tokamak disruptions could
result in severe damage to future high-performancedevices [1]. In the most disastrous scenario,
significant portion of the original plasma current could
be converted into runaway electron current, and all of
their kinetic energy as well as a large portion of themagnetic energy it carries could be unleashed locally[2]. To control and mitigate such runaway electron
current, it is important to accurately describe therunaway electron current dominated equilibrium first,
based on which further stability analysis could becarried out. This could not be done with traditional
Grad-Shafranov equation, since the current carrier is
not following the magnetic field line and the current
no longer flow along the flux surfaces. Instead, thecurrent will follow the drift surface of the runawayelectrons, which is essentially the constant canonicalangular momentum surface in the axisymmetricgeometry [3,4].
To resolve this problem, we derive a GradShafranov-like equation solving for the axisymmetricdrift surfaces of the runaway electrons instead of themagnetic flux surfaces for the simple case that all
runaway electron shares the same parallel momentum
and is the dominant current carrier. This new
equilibrium equation is obtained by considering thetoroidal symmetry and the new force balance equationof the runaway electron fluid, which in turn isobtained from the Euler-Lagrangian equation of thestrongly passing runaway electrons [3]. This new
equilibrium equation is then numerically solved withgiven right hand side profiles as well as given
boundary conditions.
In this study, we look at simple rectangular wallcases with both ITER-like and MAST-like geometry
parameters. We first show that we obtain exact thesame equilibrium compared with the traditional GradShafranov solution in the negligible parallel runway
electron momentum limit. The deviation between thedrift surfaces and the flux surfaces is then readily
obtained in the finite runaway electron momentum
cases, and they are found to be well confined even inregions with open field lines. Any change of the
runaway electron parallel momentum, such as thosecaused by collision with background species [5],radiative drag [6], kinetic instabilities [7] or toroidal

electric field is found to result in a horizontal current
center displacement even without any changes in thetotal current or the external magnetic field. The
runaway current density profile is found to affect thesusceptibility of such displacement, with flatterprofiles result in more displacement by the same
momentum change. It is found that this effect is more
pronounced in smaller, compact device and weakerpoloidal field cases.
Another interesting finding is that, with up-down
asymmetry in the external poloidal field, theaforementioned horizontal displacement isaccompanied by a vertical displacement of runaway
electron current, which could contribute to the VDE ofthe runaway electron current during the current
quench phase.
The above results demonstrate the dynamics ofcurrent center displacement caused by the momentum
space change in the runaway electrons, and pave way
for future, more sophisticated runaway current
equilibrium theory with more realistic considerationon the runaway electron momentum distribution. This
new equilibrium theory also provides foundation forfuture stability analysis of the runaway electron
current.

References[1] Lehnen M, Aleynikova K, and Aleynikov P B et al.
2015 J. Nucl. Mater 463 39-48[2] Martín-Solís J R, Loarte A, and Lehnen M 2017
Nucl. Fusion 57 066025[3] Cary, John R, Brizard, and Alain J 2009 Rev. Mod.
Phys 81 693-738[4] Liu C, Qin H, Eero Hirvijoki,Wang Y L, and Liu J
2018 Nucl. Fusion 58 106018[5] Hesslow L, Embréus O, Stahl A , DuBois T C,Papp G, Newton S L, and Fülöp T 2017 Phys. Rev.
Lett 118 255001[6] Martín-Solís J R, and Sánchez R 2008 Phys.
Plasmas 15 112505[7] Liu C, Eero Hirvijoki, Fu G Y, Brennan Dylan P,
Bhattacharjee Amitava, Paz-Soldan Carlos 2018 Phys.
Rev. Lett 120 265001