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

Intrinsic toroidal rotation in tokamaks from global total-f gyrokinetic
simulations
Hongxuan Zhu, T. Stoltzfus-Dueck, R. Hager, S. Ku, and C. S. Chang
Princeton Plasma Physics Laboratory
e-mail (speaker): hzhu@pppl.gov

Tokamak plasmas can rotate toroidally without external
momentum input. Understanding the physics behindsuch intrinsic toroidal rotation is important for the safe
operation of future reactors. Core rotation is dominantly
determined by the turbulent momentum flux, and muchtheoretical and computational research effort has been
based on the delta-f gyrokinetic formulation in simplified
local flux-tube geometry. However, a symmetry incoordinate transformation then prevented net turbulent
momentum flux to the lowest order in ρ𝑖𝑖 /𝑎𝑎, where ρ𝑖𝑖
is the ion gyroradius and 𝑎𝑎 is the tokamak minor radius.
This led to a long debate over symmetry-breaking
mechanisms, as well as the accuracy of the gyrokinetic
equation. Edge rotation is affected by complicatedfactors such as realistic geometry across the last-closedflux surface, flows in the scrape-off layer, interactions
with neutrals, and ion orbit loss. With the advance incomputing power, global gyrokinetic simulations withrealistic geometry and more physical ingredients are
expected to provide new understanding for this topic.
Here, we use the global total-f particle-in-cellgyrokinetic code XGC1 and its axisymmetric version
XGCa to study toroidal rotation driven by turbulent andneoclassical processes. We simulate a DIII-D H-mode
plasma with gyrokinetic ions and drift-kinetic electrons.
Core and edge rotation are studied together through thewhole-volume plasma simulation. In a gyrokinetic
plasma, the toroidal-angular-momentum density is driven
by the divergence of the radial momentum flux of ion
gyrocenters, including the parallel-momentum flux fromthe grad-B and curvature drift (denoted Π∥𝐷𝐷 ), theparallel-momentum flux from the 𝐸𝐸 × 𝐵𝐵 drift (denotedΠ∥𝐸𝐸 ), and the 𝐸𝐸 × 𝐵𝐵-momentum flux from the 𝐸𝐸 × 𝐵𝐵drift (denoted Π𝐸𝐸× 𝐵𝐵 ). Most theoretical research on corerotation has focused on Π∥𝐸𝐸 while assuming Π𝐸𝐸× 𝐵𝐵 issmaller by a factor 𝑘𝑘𝑟𝑟 ρ𝑖𝑖 𝐵𝐵θ /𝐵𝐵 and Π∥𝐷𝐷 is at a small
neoclassical level. However, our simulation results
showed that in the core, Π∥𝐷𝐷 is not at neoclassical levelin the presence of turbulence, and it tends to balance Π∥𝐸𝐸
due to interactions between turbulence and zonal flows(Figure 1). Due to this balance, Π𝐸𝐸×𝐵𝐵 could makesignificant contribution to toroidal rotation. These results
are consistent with other global gyrokinetic codes such
as GYSELA and GT5D. We also compare with atheoretical explanation of nonzero Π∥𝐷𝐷 in Ref. [1].
In the edge, turbulence is suppressed in the deep 𝐸𝐸𝑟𝑟
well, which is formed due to the H-mode density
pedestal. Therefore, edge toroidal rotation is mainly
driven by Π∥𝐷𝐷 . However, the edge Π∥𝐷𝐷 is different fromits value in a neoclassical plasma, which is due tononlocal interactions between finite ion orbit width andturbulence at the pedestal top (Figure 2) [2,3]. We
developed an orbit-flux formulation to identify different
physical processes that contribute to Π∥𝐷𝐷 , including
collisions, turbulence, heating, and neutral ionization[4,5]. In particular, through this formulation we identify
the contribution from collisional and turbulent ion orbit
loss in edge toroidal rotation [6,7].
References[1] Garbet et al., New J. Phys. 19, 015011 (2017).
[2] Müller et al., Phys. Rev. Lett. 106, 115001 (2011).
[3] Seo et al., Phys. Plasmas 21, 092501 (2014).
[4] Stoltzfus-Dueck, Nucl. Fusion 60, 016031 (2020).
[5] Stoltzfus-Dueck and Zhu, Plasma Phys. Control.
Fusion 63, 115001 (2021).
[6] Zhu et al., Nucl. Fusion, 62, 066012 (2022).
[7] Zhu et al., Nucl. Fusion, 63, 066009 (2023).

Figure 1 In the core, turbulent mode structures are distorted
according to the local zonal-flow velocity indicated by 𝐸𝐸𝑟𝑟 . The
corresponding gyrocenter radial currents 𝐽𝐽 (A) and momentum
fluxes Π (N⋅m) also correlate with the zonal-flow velocity.

Figure 2 In the edge, turbulence is suppressed in the deep 𝐸𝐸𝑟𝑟
well so Π∥𝐸𝐸 ≈ 0. However, due to nonlocal interactions withturbulence, Π∥𝐷𝐷 in a turbulent plasma from XGC1 is different
from a neoclassical plasma from XGCa.