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

Application of CIP-Soroban method to implosion process of heavy-ion-beam
driven inertial confinement fusion
Z. Lin1, K. Takahashi1, T. Sasaki1, T. Kikuchi1, A. Sunahara2
1
Nagaoka University of Technology,
2
Purdue University
e-mail (speaker): s195084@stn.nagaokaut.ac.jp

An implosion process of heavy-ion-beam (HIB) driven
inertial confinement fusion (HIF) is key issue to achieve
fusion energy release. The uniformity of HIB irradiation
should be improved due to spherically symmetric
implosion in a direct-drive fuel pellet. Modification of thefuel pellet structure was proved to be effective to reducethe irradiation nonuniformity in our previous study [1].
Figure 1(a) shows a typical fuel pellet for HIF, which
consists of a tamper layer of lead (Pb), an ablator layer ofAl (aluminum) and a fuel layer of Deuterium-Tritium(DT). The tamper layer is used to keep the hydrodynamic
energy inside the fuel pellet to raise the implosion
efficiency [2]. For this reason, the tamper layer is made ofheavy element with high mass number, which has higher
stopping power for more electrons that it possessedcompared to the ablator material.
The derivatives of physical values grow dramaticallyespecially after the void closure phase of the fuel pellet.
As the results, the truncation errors grow fast and decrease
the accuracy of the numerical simulation for the implosion
process. Coarse arrangement of the calculation grid points(mesh) works bad in capturing the shape of tamper layer,and small errors of the shape of tamper layer can cause bigshifts of the stopping range of the HIBs in ablator layer
for the stronger stopping power of tamper layer thanablator layer.
CIP-Soroban method is a good adaptive mesh refinement

method, which was developed for numerical simulations
for hydrodynamics of incompressible fluids [3]. The meshsize of CIP-Soroban method varies inversely to thederivatives of physical values meantime capable solves
the equations with CIP method, which has 3rd orderaccuracy. On the other hand, CIP-Soroban method works
well in capturing object surface [4] which is good for
capturing the shape of tamper layer of fuel pellet.
We have built a developed code with CIP-Soroban
method for compressible fluid to simulate the implosion
process of HIF [5]. Figure 1(b) shows one snapshot ofvelocity distribution during implosion simulated by thecode. The dots in Fig. 1(b) were the grid points of CIPSoroban, which distributed suitably dense in the areas
with high derivatives of physical values and the shape offuel pellet were well captured. We will report the detailduring our presentation.
References[1] Z. Lin, et al., Plasma Fusion Res. 17, 2404064 (2022)[2] S. Kawata, Advances Phys. X. 6, 1873860 (2021)[3] T. Yabe, et al., Int. J. Numer. Methods Fluids 4, 655,(2005)[4] K. Takizawa, et al., Comput. Mech. 40, 167, (2007)[5] Z. Lin, et al., 39th Annual Meeting of the Japan
Society of Plasma Science and Nuclear Fusion
Research, 24P30 (2022)

Figure 1. (a) The structure in r-z cylindrical coordinate of a typical fuel pellet for heavy-ion-beam driven
inertial confinement fusion; (b) a snapshot of grid points and velocity distribution during implosion calculatedwith CIP-Soroban method.