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

Study of ion kinetic effects on plasma distributions
by anisotropic-ion-pressure plasma fluid simulation

Keishi Homma1, Satoshi Togo1, Tomonori Takizuka2, Yuki Homma3,
Kenzo Ibano2, Kazuma Emoto1, Mizuki Sakamoto1
1
Plasma Research Center, University of Tsukuba, 2 Graduate School of Engineering,Osaka University, 3 National Institutes for Quantum Science and Technology
e-mail (speaker): honma_keishi@prc.tsukuba.ac.jp
Currently, efforts are being made to improve edge
plasma transport simulations to establish methods forcontrolling the heat load on the divertor.
In plasma fluid models primarily used for scrape-off
layer (SOL) plasma, the conductive heat flux along
magnetic field lines is represented by the Spitzer-Härm(SH) heat flux 𝑞 || [1]. However, the actual heat flux
becomes smaller than the SH heat flux when themean-free path is longer than the SOL characteristic
length. This is referred to as the kinetic effect. In theSONIC code [2,3], a free streaming energy (FSE)limited model is employed for the kinetic effect.
According to the SONIC simulation of JA DEMO [4],the kinetic effect of ion heat flux leads to remarkablechanges in the SOL plasma profiles [3]. In thesesimulations, however, the anisotropy between the ion
temperature parallel and perpendicular to the magnetic
field direction, denoted as 𝑇 || , 𝑇 , which might besignificant in the low-collisionality regime [5], have notbeen considered.
In this study, we aim to study the ion kinetic effects inthe presence of anisotropic ion pressure. A plasma fluid
model based on the anisotropic ion pressure (AIP model)[6,7] is applied to a tandem mirror device GAMMA
10/PDX which exhibits significant ion pressure
anisotropy [8]. In the AIP model, the ion conductive heat
flux is evaluated based on a simple FSE-limited model[6].
||𝑞𝑞||||

= 1+
= −𝜅
||||𝑞
𝛼 𝑞

(𝜕𝑇 /𝜕𝑠),𝑞||𝑞(𝜎 ∈ {i||, i ⊥})(1)

||(2)

=𝑝

𝑇 || /𝑚Here, 𝜅represents the SH thermal conductivity, 𝑇is the temperature, 𝑝 is the pressure, 𝑚 is the ion mass,and 𝑠 is the coordinate in the magnetic field direction.
Equation (1) describes the FSE-limited model using the||||||
harmonic mean of 𝑞
and 𝑞 , where 𝑞
is thefree-streaming heat flux as a collisionless limit. The
kinetic effects occur depending on collisionality, and thedegree of these effects is defined by the heat flux limitercoefficients ( 𝛼 ). Note that, in the AIP model, theparallel ion conductive heat flux is divided into two||||components 𝑞 || and 𝑞 which transport the paralleland perpendicular energy components in the parallel
direction, respectively. In this study, we vary the value of
𝛼 and change the kinetic effects in each component.
Figure 1 shows the spatial distribution of ion
temperature anisotropy ( 𝑇 /𝑇 || ) in the GAMMA

Figure 1. Spatial distributions of magnetic field intensity
𝐵 in GAMMA 10/PDX and ion temperature anisotropy
𝑇 /𝑇 || for various 𝛼 || values. The center (𝑠 = 0) is asymmetric point.
10/PDX device for various 𝛼 || values with fixed 𝛼 =0.5. By the increase of 𝛼 || , both 𝑇 || and 𝑇 in thecentral region (|𝑠| < 2.8 m) are decreased. On the otherhand, it is found that the anisotropy is unchanged(𝑇 /𝑇 || ≈ 2.5). Simulations are conducted in a uniform
magnetic field system with the same collisionality. By
increasing 𝛼 || , an increase in 𝑇 /𝑇 || is observed
clearly. As a common phenomenon in both systems,||
increasing 𝛼 || leads to an increase in 𝑞 || (> 0) and a
resultant decrease in 𝑇 || . Moreover, the nonlinear||changes in the plasma distribution also affect 𝑞 . In thecase of GAMMA 10/PDX, particle flow is hindered due
to mirror confinement, and the conductive heat flux iscomparable in magnitude to the convective heat flux. As||a result, the decrease in 𝑞 ( < 0 ) brings about adecrease in 𝑇 . That is why the change in 𝑇 /𝑇 || isminimal in GAMMA 10/PDX. In the presentation, theeffect of 𝛼on the plasma distribution is also
discussed.
References[1] S.I. Braginskii, Reviews of Plasma Physics, vol.1(Consultants Bureau, New York, 1965), 205.
[2] K. Shimizu et al., Nucl. Fusion 49 (2009) 065028.
[3] Y. Homma, Plasma Phys. Control. Fusion 64 (2022)
045020.
[4] Y. Sakamoto et al., DEMO concept development andassessment of relevant technologies [FIP/3-4Rb], 25th IAEA
Int. Conf. on Fusion Energy (Saint Petersburg, 2014)[5] A. Froese et al., Plasma Fusion Res. 5 (2010) 026[6] S. Togo et al., Nucl. Fusion 59 (2019) 076041.
[7] S. Togo et al., J. Adv. Simulat. Sci. Eng.9 (2022) 185.
[8] M. Ichimura et al., Nucl Fusion 39 (1999) 1995.