研究者詳細 - 河野晴彦

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Validity condition for the local sheath impedance boundary condition and a nonlocal generalization 査読有り国際誌

J. R. Myra, H. Kohno

AIP Conference Proceedings ( AIP Publishing ) 2984 ( 1 ) 060002-1 - 060002-6 2023年08月

担当区分：最終著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

ICRF sheaths can cause unwanted interactions of high-power RF waves with material surfaces in magnetic fusion devices. In previous work, a local RF sheath impedance boundary condition (BC) was derived for use in ICRF codes together with a microscale (i.e., Debye or sheath width scale) model for obtaining the sheath impedance used in that BC. This local RF sheath BC matches the normal component of current and electrostatic potential across the sheath-plasma interface. Collapsing the matching conditions at the sheath-plasma interface to a BC depends on the assumption of scale separation, which can be violated when conditions along the local radius of curvature of the surface vary sufficiently rapidly. The validity condition is explored in this contribution, with special attention to the case where the magnetic field approaches being tangent to the surface. When the local sheath BC no longer applies, a nonlocal sheath BC is developed under the assumption of a more relaxed scale separation assumption. It is shown that the nonlocal sheath BC reduces to the previous local sheath BC under appropriate conditions. A surface-integrated sheath admittance parameter [H. Kohno and J. R. Myra, this conference] describes the 2D physics in the new BC.

DOI： 10.1063/5.0163291

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Magnetic potential based formulation for linear and non-linear 3D RF sheath simulation 査読有り国際誌

S. Shiraiwa, N. Bertelli, W. Tierens, R. Bilato, J. Hillairet, J. Myra, H. Kohno, M. Poulos, M. Ono

Nuclear Fusion ( IOP Publishing ) 63 ( 2 ) 026024-1 - 026024-12 2023年01月

記述言語：英語掲載種別：研究論文（学術雑誌）

This paper reports a new numerical scheme to simulate the radio-frequency (RF) induced RF sheath, which is suitable for a large 3D simulation. In the RF sheath boundary model, the tangential component of the electric field ( E t ) is given by the gradient of a scalar electric field potential. We introduce two additional scalar potentials for the tangential components of the magnetic field, which effectively impose the normal electric displacement (D n ) on the plasma sheath boundary condition via in-homogeneous Neumann boundary condition and constrain the tangential electric field on the surface as curl-free ( ∇ × E t = 0 ). In our approach, the non-linear sheath impedance is formulated as a natural extension of the large thickness (or asymptotic) sheath limit ( D n = 0 ), allowing for handling both asymptotic and non-linear regimes seamlessly. The new scheme is implemented using the Petra-M finite element method analysis framework and is verified with simulations in the literature. The significance of non-linearity is discussed in various plasma conditions. An application of this scheme to asymptotic RF sheath simulation on the WEST ICRF antenna side limiters is also discussed.

DOI： 10.1088/1741-4326/aca6f9

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交流磁場下の3次元電磁流体流れにおける連成解析手法の検討査読有り

久米川知也，牟禮良晃，河野晴彦

日本計算工学会論文集 ( 日本計算工学会 ) 2022 20220016-1 - 20220016-9 2022年10月

担当区分：最終著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

複数の場の相互作用を伴う3次元連成解析では，一般に弱連成手法または強連成手法が用いられ，解の正確度を低下させることなく，妥当な計算時間で数値解が得られる手法を選択することが重要である．本研究では，電磁流体流れを計算するための弱連成スキームに分離反復型解法を導入した新たなスキーム（IPCスキーム）を構築し，両スキームを用いて得られた数値解の比較を通して，弱連成スキームの信頼性を評価する．流体・固体・気体を含む領域に一様な交流磁場が印加されるモデルを用いて，ハルトマン数が小さく，時間刻み幅が比較的大きい場合，IPCスキームにより得られる解は弱連成スキームにより得られる解よりも信頼性が高いことが示された．一方で，低ハルトマン数の条件においても，時間刻み幅を十分に小さくすると，両スキームにより得られる解はよく一致することも確かめられた．

DOI： 10.11421/jsces.2022.20220016

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ALE有限要素法による直流磁場下における導電性液滴の振動の数値解析

澁田謙太，河野晴彦

日本機械学会2021年度年次大会 ( 日本機械学会 ) 2021 S055-39 2021年09月

担当区分：最終著者,　責任著者記述言語：日本語掲載種別：研究論文（学術雑誌）

A numerical scheme to analyze oscillations of a conductive droplet under DC magnetic fields in zero gravity was developed, and the effect of DC magnetic fields on the oscillation of a conductive droplet is investigated. In the present scheme, the Navier-Stokes equations for the liquid-gas two-phase fluid flow are solved by a Galerkin finite element method and the ALE method is used to allow a conductive droplet to oscillate. An elliptical conductive droplet is placed in the center of a two-dimensional rectangular domain and uniform DC magnetic fields are applied in the x direction. It is confirmed that the DC magnetic fields generate Lorentz force in the directions which prevent oscillations of the conductive droplet, resulting in a damping effect of the oscillations. Furthermore, as compared with the case without applying a DC magnetic field, phase delay and phase advance are observed as a result of applying DC magnetic fields.

DOI： 10.1299/jsmemecj.2021.s055-39

その他リンク： https://www.jstage.jst.go.jp/article/jsmemecj/2021/0/2021_S055-39/_pdf

直流磁場下における導電性流体の2次元スロッシング解析

澁田謙太，河野晴彦

日本機械学会九州支部講演論文集 ( 日本機械学会 ) 2021.74 E44 2021年03月

Convergence improvement of the simultaneous relaxation method used in the finite element analysis of incompressible fluid flows 査読有り国際誌

Haruhiko Kohno

Engineering Computations ( Emerald Publishing ) 37 ( 2 ) 481 - 500 2020年03月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

Purpose: This paper aims to present an improved finite element method used for achieving faster convergence in simulations of incompressible fluid flows. For stable computations of incompressible fluid flows, it is important to ensure that the flow field satisfies the equation of continuity in each element of a generally distorted mesh. The study aims to develop a numerical approach that satisfies this requirement based on the highly simplified marker-and-cell (HSMAC) method and increases computational speed by introducing a new algorithm into the simultaneous relaxation of velocity and pressure. Design/methodology/approach: First, the paper shows that the classical HSMAC method is equivalent to a Jacobi-type method in terms of the simultaneous relaxation of velocity and pressure. Then, a Gauss–Seidel or successive over-relaxation (SOR)-type method is introduced in the Newton–Raphson iterations to take into account all the derivative terms in the first-order Taylor series expansion of a nodal-averaged error explicitly. Here, the nine-node quadrilateral (Q2–Q1) elements are used. Findings: The new finite element approach based on the improved HSMAC algorithm is tested on fluid flow problems including the lid-driven square cavity flow and the flow past a circular cylinder. The results show significant improvement of the convergence property with the accuracy of the numerical solutions kept unchanged even on a highly distorted mesh. Originality/value: To the best of the author’s knowledge, the idea of using the Gauss–Seidel or SOR method in the simultaneous relaxation procedure of the HSMAC method has not been proposed elsewhere.

DOI： 10.1108/EC-02-2019-0069

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環状流路内における進行磁場により駆動される電磁流体流れの3次元数値解析

牟禮良晃，河野晴彦

計算力学講演会講演論文集 ( 日本機械学会 ) 2019.32 28 2019年09月

担当区分：最終著者,　責任著者記述言語：日本語掲載種別：研究論文（学術雑誌）

Three-dimensional numerical simulation of incompressible, magnetohydrodynamic flows under traveling magnetic fields are carried out, which takes into account the coupling with the electromagnetic field in the solid and gas regions. A numerical scheme is constructed by combining the Galerkin finite element method and the edge-element based finite element method, which are applied to the discretizations of Navier-Stokes equations and the electromagnetic field equations, respectively. The solution algorithm for fluid flow is based on an explicit fractional step approach and the simultaneous relaxation of velocity and pressure to satisfy the continuity equation. The electromagnetic field equations are formulated with the use of the magnetic vector potential which is defined on the edge elements. Numerical simulations of the MHD flows in an annular channel are carried out under traveling magnetic fields. It is confirmed that the magnitude and oscillation amplitude of the z-component of the velocity becomes larger with the increase in the Hartmann number. It is also shown that the frequency of the velocity pulsation is doubled than the frequency of the externally applied traveling magnetic field.

DOI： 10.1299/jsmecmd.2019.32.028

その他リンク： https://ci.nii.ac.jp/naid/130007817209

ALE法を用いた2次元スロッシング解析における安定性向上の検討

小島拓人，河野晴彦

計算力学講演会講演論文集 ( 日本機械学会 ) 2019.32 73 2019年09月

担当区分：最終著者,　責任著者記述言語：日本語掲載種別：研究論文（学術雑誌）

In this study, we investigate the stability required for a two-dimensional sloshing analysis with the use of an arbitrary Lagrangian–Eulerian (ALE) method. Here, two well-known upwind methods are employed for the discretization of the kinematic condition on the free surface: SUPG and CIP methods. On the other hand, the Navier-Stokes equations are discretized by a finite element scheme without any upwind method to see whether the stability is retained solely by introducing an appropriate upwind method into the calculation on the free surface. It is shown in both primary and tertiary modes that stable results are obtained when the CIP method is employed, while unstable grid-scale oscillations are observed at some point when the SUPG method is used. This suggests that a semi-Lagrangian scheme is essential for stable computation based on the ALE formulation.

DOI： 10.1299/jsmecmd.2019.32.073

その他リンク： https://ci.nii.ac.jp/naid/130007817141

正方形ダクト内における交流磁場下の3次元電磁流体流れ解析

坂井駿介，牟禮良晃，河野晴彦

計算力学講演会講演論文集 ( 日本機械学会 ) 2019.32 103 2019年09月

担当区分：最終著者,　責任著者記述言語：日本語掲載種別：研究論文（学術雑誌）

In our previous work, a three-dimensional numerical scheme for analyzing magnetohydrodynamic (MHD) flows under alternating-current magnetic fields was constructed, which takes into account the coupling with the electromagnetic fields in the solid and gas regions. In this study, a periodic boundary condition and an external traveling-wave magnetic field are introduced into the numerical scheme to investigate the dependences of the MHD flow in a square duct on the Hartmann number and the phase velocity of the external magnetic field. It is shown that the flow in the axial direction is encouraged with the increase in the Hartmann number or the angular frequency, while an opposite behavior is observed in terms of the oscillation amplitude of the fluid flow.

DOI： 10.1299/jsmecmd.2019.32.103

その他リンク： https://ci.nii.ac.jp/naid/130007817254

Calculation of RF sheath properties from surface wave-fields: a post-processing method 査読有り国際誌

J. R. Myra, H. Kohno

Plasma Physics and Controlled Fusion ( IOP Publishing ) 61 ( 9 ) 095003-1 - 095003-10 2019年07月

担当区分：最終著者記述言語：英語掲載種別：研究論文（学術雑誌）

In ion cyclotron range of frequency (ICRF) experiments in fusion research devices, radio frequency (RF) sheaths form where plasma, strong RF wave fields and material surfaces coexist. These RF sheaths affect plasma material interactions such as sputtering and localized power deposition, as well as the global RF wave fields themselves. RF sheaths may be modeled by employing a sheath boundary condition (BC) in place of the more customary conducting wall (CW) BC; however, there are still many ICRF computer codes that do not implement the sheath BC. In this paper we present a method for post-processing results obtained with the CW-BC. The post-processing method produces results that are equivalent to those that would have been obtained with the RF sheath BC, under certain assumptions. The post-processing method is also useful for verification of sheath BC implementations and as a guide to interpretation and understanding of the role of RF sheaths and their interactions with the waves that drive them.

DOI： 10.1088/1361-6587/ab2f41

Kyutacar

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Radio frequency wave interactions with a plasma sheath: The role of wave and plasma sheath impedances 査読有り国際誌

J. R. Myra, H. Kohno

Physics of Plasmas ( AIP Publishing ) 26 ( 5 ) 052503-1 - 052503-14 2019年05月

担当区分：最終著者記述言語：英語掲載種別：研究論文（学術雑誌）

Radio frequency (RF) sheaths form near surfaces where plasma and strong RF fields coexist. The effect of these RF sheaths on wave propagation near the boundary can be characterized by an effective sheath impedance that includes both resistive and capacitive contributions describing RF sheath rectification and RF power absorption in the sheath [J. R. Myra and D. A. D'Ippolito, Phys. Plasmas 22, 062507 (2015)]. Here, we define a dimensionless parameter, the ratio of incoming wave impedance to the sheath impedance, which determines the characteristics of the interaction, ranging from quasi-conducting to quasi-insulating, or in the case of matched impedances, to either perfect absorption or a sheath-plasma resonance. A semi-analytical analysis is carried out for electrostatic slow waves in the ion cyclotron range of frequencies. For the propagating slow wave case, where the incident wave is partially reflected, the fraction of power dissipated in the sheath is calculated. For the evanescent slow wave case, which admits a sheath-plasma resonance, an amplification factor is calculated. Using the impedance ratio approach, RF sheath interactions are characterized for a range of RF wave and plasma parameters including plasma density, magnetic field angle with respect to the surface, wave frequency, and wave-vector components tangent to the surface. For a particularly interesting example case, results are compared with the rfSOL code [H. Kohno and J. R. Myra, Comput. Phys. Commun. 220, 129 (2017)]. Finally, electromagnetic effects, absent from the semi-analytical analysis, are assessed.

DOI： 10.1063/1.5088343

Kyutacar

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Radio-frequency wave interactions with a plasma sheath in oblique-angle magnetic fields using a sheath impedance model 査読有り国際誌

H. Kohno, J. R. Myra

Physics of Plasmas ( AIP Publishing ) 26 ( 2 ) 022507-1 - 022507-15 2019年02月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

The physics of interactions between waves in plasmas and sheaths for background magnetic fields which make oblique angles with sheath surfaces is studied with the use of the self-consistent finite element code rfSOL incorporating the recently developed sheath impedance model [J. R. Myra, Phys. Plasmas 24, 072507 (2017)]. The calculation based on this model employs the generalized sheath boundary condition (sheath BC), which surpasses the previously used capacitive sheath BC in reliability by taking into account the contributions of the ion and electron currents in the sheath and the displacement current. A series of numerical simulations is carried out in two-dimensional slab geometry with a flat or curved sheath surface as part of the boundary. It is shown that the sheath-plasma wave appears when the equilibrium magnetic field line angle with respect to the sheath surface is small, the absolute value of the radio-frequency (RF) sheath voltage is large, and the plasma density is slightly higher than the lower hybrid resonance density (LHR density), all of which bring the sheath property closer to being capacitive. It is also shown that the sharp variation of the magnetic field line angle along the sheath surface can sensitively affect the maximum absolute value of the RF sheath voltage at a plasma density slightly lower than the LHR density.

DOI： 10.1063/1.5054920

Kyutacar

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交流磁場下における導体壁に囲まれた電磁流体流れの3次元数値解析査読有り

牟禮良晃，河野晴彦

日本機械学会論文集 ( 日本機械学会 ) 84 ( 863 ) 17-00589-1 - 17-00589-16 2018年07月

担当区分：最終著者,　責任著者記述言語：日本語掲載種別：研究論文（学術雑誌）

Three-dimensional (3D) numerical simulation of incompressible, magnetohydrodynamic (MHD) flows under alternating-current (AC) magnetic fields are carried out, which takes into account the coupling with the electromagnetic fields in the solid and gas regions. A numerical scheme is constructed by combining the Galerkin finite element method and the edge-element based finite element method, which are applied to the discretizations of the Navier–Stokes equations and the electromagnetic field equations, respectively. The solution algorithm for fluid flow is based on an explicit fractional step approach and the simultaneous relaxation of velocity and pressure to satisfy the continuity equation. The electromagnetic field equations are formulated with the use of the magnetic vector potential which is defined on the edge elements. In the proposed numerical scheme, the advection term in the induction equation is not neglected, because the scheme needs to deal with the condition where the advection term is the same order with the diffusion term in that equation. The validity of the numerical scheme is verified through the analysis of the electromagnetic field under a direct-current magnetic field, and numerical simulations of the MHD flows under spatially uniform AC magnetic fields are carried out. It is confirmed that the spatio-temporal mean Lorentz force in the conducting fluid becomes weaker with the increase in the dimensionless frequency due to the skin effect. It is also shown that the flow pattern in a hexahedral closed domain is largely changed when the frequency is getting higher, which is associated with the change in the Lorentz force profile.

DOI： 10.1299/transjsme.17-00589

その他リンク： https://ci.nii.ac.jp/naid/130007419065

A finite element procedure for radio-frequency sheath-plasma interactions based on a sheath impedance model 査読有り国際誌

H. Kohno, J. R. Myra

Computer Physics Communications ( Elsevier B.V. ) 220 129 - 142 2017年11月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

A finite element code that solves self-consistent radio-frequency (RF) sheath-plasma interaction problems is improved by incorporating a generalized sheath boundary condition in the macroscopic solution scheme. This sheath boundary condition makes use of a complex sheath impedance including both the sheath capacitance and resistance, which enables evaluation of not only the RF voltage across the sheath but also the power dissipation in the sheath. The newly developed finite element procedure is applied to cases where the background magnetic field is perpendicular to the sheath surface in one- and two-dimensional domains filled by uniform low- and high-density plasmas. The numerical results are compared with those obtained by employing the previous capacitive sheath model at a typical frequency for ion cyclotron heating used in fusion experiments. It is shown that for sheaths on the order of 100 V in a high-density plasma, localized RF power deposition can reach a level which causes material damage. It is also shown that the sheath-plasma wave resonances predicted by the capacitive sheath model do not occur when parameters are such that the generalized sheath impedance model substantially modifies the capacitive character of the sheath. Possible explanations for the difference in the maximum RF sheath voltage depending on the plasma density are also discussed.

DOI： 10.1016/j.cpc.2017.06.025

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A post-processing method to simulate the generalized RF sheath boundary condition 査読有り国際誌

James R. Myra, Haruhiko Kohno

EPJ Web of Conferences ( EDP Sciences ) 157 03037-1 - 03037-4 2017年10月

担当区分：最終著者記述言語：英語掲載種別：研究論文（国際会議プロシーディングス）

For applications of ICRF power in fusion devices, control of RF sheath interactions is of great importance. A sheath boundary condition (SBC) was previously developed to provide an effective surface impedance for the interaction of the RF sheath with the waves. The SBC enables the surface power flux and rectified potential energy available for sputtering to be calculated. For legacy codes which cannot easily implement the SBC, or to speed convergence in codes which do implement it, we consider here an approximate method to simulate SBCs by post-processing results obtained using other, e.g. conducting wall, boundary conditions. The basic approximation is that the modifications resulting from the generalized SBC are driven by a fixed incoming wave which could be either a fast wave or a slow wave. The method is illustrated in slab geometry and compared with exact numerical solutions; it is shown to work very well.

DOI： 10.1051/epjconf/201715703037

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A mixed-interpolation finite element method for incompressible thermal flows of electrically conducting fluids 査読有り国際誌

Haruhiko Kohno

International Journal for Numerical Methods in Fluids ( John Wiley & Sons ) 83 ( 11 ) 813 - 840 2017年04月

担当区分：筆頭著者,　責任著者記述言語：英語掲載種別：研究論文（学術雑誌）

A new mixed-interpolation finite element method is presented for the two-dimensional numerical simulation of incompressible magnetohydrodynamic (MHD) flows which involve convective heat transfer. The proposed method applies the nodal shape functions, which are locally defined in nine-node elements, for the discretization of the Navier–Stokes and energy equations, and the vector shape functions, which are locally defined in four-node elements, for the discretization of the electromagnetic field equations. The use of the vector shape functions allows the solenoidal condition on the magnetic field to be automatically satisfied in each four-node element. In addition, efficient approximation procedures for the calculation of the integrals in the discretized equations are adopted to achieve high-speed computation. With the use of the proposed numerical scheme, MHD channel flow and MHD natural convection under a constant applied magnetic field are simulated at different Hartmann numbers. The accuracy and robustness of the method are verified through these numerical tests in which both undistorted and distorted meshes are employed for comparison of numerical solutions. Furthermore, it is shown that the calculation speed for the proposed scheme is much higher compared with that for a conventional numerical integration scheme under the condition of almost the same memory consumption.

DOI： 10.1002/fld.4292