Tomoya TATSUNO
| Department of Computer and Network Engineering | Professor |
| Cluster I (Informatics and Computer Engineering) | Professor |
Researcher Information
Research Keyword
Career
- Apr. 2022 - Present
The University of Electro-Communications, Professor - Jul. 2011 - Mar. 2022
University of Electro-Communications, Associate Professor - Aug. 2005 - Jun. 2011
University of Maryland, Assistant Research Scientist - Aug. 2003 - Aug. 2005
University of Maryland, Research Associate - Apr. 1999 - Aug. 2003
University of Tokyo, Assistant
Research Activity Information
Paper
- Freely decaying turbulence in two-dimensional electrostatic gyrokinetics
T. Tatsuno; G. G. Plunk; M. Barnes; W. Dorland; G. G. Howes; R. Numata
PHYSICS OF PLASMAS, AMER INST PHYSICS, 19, 12, 122305, Dec. 2012, Peer-reviwed, In magnetized plasmas, a turbulent cascade occurs in phase space at scales smaller than the thermal Larmor radius ("sub-Larmor scales") [Tatsuno et al., Phys. Rev. Lett. 103, 015003 (2009)]. When the turbulence is restricted to two spatial dimensions perpendicular to the background magnetic field, two independent cascades may take place simultaneously because of the presence of two collisionless invariants. In the present work, freely decaying turbulence of two-dimensional electrostatic gyrokinetics is investigated by means of phenomenological theory and direct numerical simulations. A dual cascade (forward and inverse cascades) is observed in velocity space as well as in position space, which we diagnose by means of nonlinear transfer functions for the collisionless invariants. We find that the turbulence tends to a time-asymptotic state, dominated by a single scale that grows in time. A theory of this asymptotic state is derived in the form of decay laws. Each case that we study falls into one of three regimes (weakly collisional, marginal, and strongly collisional), determined by a dimensionless number D*, a quantity analogous to the Reynolds number. The marginal state is marked by a critical number D* = D-0 that is preserved in time. Turbulence initialized above this value become increasingly inertial in time, evolving toward larger and larger D*; turbulence initialized below D0 become more and more collisional, decaying to progressively smaller D*. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4769029]
Scientific journal, English - Considering fluctuation energy as a measure of gyrokinetic turbulence
G. G. Plunk; T. Tatsuno; W. Dorland
NEW JOURNAL OF PHYSICS, IOP PUBLISHING LTD, 14, 10, 103030, Oct. 2012, Peer-reviwed, In gyrokinetic theory, there are two quadratic measures of fluctuation energy, left invariant under nonlinear interactions, that constrain turbulence. In a recent work (Plunk and Tatsuno 2011 Phys. Rev. Lett. 106 165003) we reported on the novel consequences that this constraint has for the direction and locality of spectral energy transfer. This paper builds on that previous work. We provide a detailed analysis in support of the results of Plunk and Tatsuno (2011 Phys. Rev. Lett. 106 165003), but significantly broaden the scope and use additional methods to address the problem of energy transfer. The perspective taken here is that the fluctuation energies are not merely formal invariants of an idealized model (two-dimensional gyrokinetics (Plunk et al 2010 J. Fluid Mech. 664 407-35)) but also general measures of gyrokinetic turbulence, i.e. quantities that can be used to predict the behavior of turbulence. Although many questions remain open, this paper collects evidence in favor of this perspective by demonstrating in several contexts that constrained spectral energy transfer governs the dynamics.
Scientific journal, English - Gyrokinetic simulations of the tearing instability
Ryusuke Numata; William Dorland; Gregory G. Howes; Nuno F. Loureiro; Barrett N. Rogers; Tomoya Tatsuno
PHYSICS OF PLASMAS, AMER INST PHYSICS, 18, 11, 112106, Nov. 2011, Peer-reviwed, Linear gyrokinetic simulations covering the collisional-collisionless transitional regime of the tearing instability are performed. It is shown that the growth rate scaling with collisionality agrees well with that predicted by a two-fluid theory for a low plasma beta case in which ion kinetic dynamics are negligible. Electron wave-particle interactions (Landau damping), finite Larmor radius, and other kinetic effects invalidate the fluid theory in the collisionless regime, in which a general non-polytropic equation of state for pressure (temperature) perturbations should be considered. We also vary the ratio of the background ion to electron temperatures and show that the scalings expected from existing calculations can be recovered, but only in the limit of very low beta. (C) 2011 American Institute of Physics. [doi:10.1063/1.3659035]
Scientific journal, English - Gyrokinetic Simulations of Solar Wind Turbulence from Ion to Electron Scales
G. G. Howes; J. M. TenBarge; W. Dorland; E. Quataert; A. A. Schekochihin; R. Numata; T. Tatsuno
PHYSICAL REVIEW LETTERS, AMER PHYSICAL SOC, 107, 3, 035004, Jul. 2011, Peer-reviwed, A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfven wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.
Scientific journal, English - Energy Transfer and Dual Cascade in Kinetic Magnetized Plasma Turbulence
G. G. Plunk; T. Tatsuno
PHYSICAL REVIEW LETTERS, AMER PHYSICAL SOC, 106, 16, 165003, Apr. 2011, Peer-reviwed, The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this Letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this theory are the first observations of these phenomena, obtained via direct numerical simulations using the gyrokinetic code ASTROGK. The basic mechanisms that are found provide a framework for understanding the turbulent energy transfer that couples scales both locally and nonlocally.
Scientific journal, English - AstroGK: Astrophysical gyrokinetics code
Ryusuke Numata; Gregory G. Howes; Tomoya Tatsuno; Michael Barnes; William Dorland
JOURNAL OF COMPUTATIONAL PHYSICS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 229, 24, 9347-9372, Dec. 2010, Peer-reviwed, The gyrokinetic simulation code AstroGK is developed to study fundamental aspects of kinetic plasmas and for applications mainly to astrophysical problems. AstroGK is an Eulerian slab code that solves the electromagnetic gyrokinetic-Maxwell equations in five-dimensional phase space, and is derived from the existing gyrokinetics code GS2 by removing magnetic geometry effects. Algorithms used in the code are described. The code is benchmarked using linear and nonlinear problems. Serial and parallel performance scalings are also presented. (C) 2010 Elsevier Inc. All rights reserved.
Scientific journal, English - Numerical modeling of Large Plasma Device Alfveacuten wave experiments using AstroGK
Kevin D. Nielson; Gregory G. Howes; Tomoya Tatsuno; Ryusuke Numata; William Dorland
PHYSICS OF PLASMAS, AMER INST PHYSICS, 17, 2, Feb. 2010, Peer-reviwed, Collisions between counterpropagating Alfveacuten waves represent the fundamental building block of plasma turbulence, a phenomenon of great importance to a wide variety of fields, from space physics and astrophysics to controlled magnetic fusion. Proposed experiments to study Alfveacuten wave collisions on the Large Plasma Device (LAPD) [W. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 (1991)] at the University of California, Los Angeles, will benefit significantly from numerical modeling capable of reproducing not only the linear dispersive effects of kinetic and inertial Alfveacuten waves, but also the nonlinear evolution of the Alfveacutenic turbulence. This paper presents a comparison of linear simulation results using the astrophysical gyrokinetics code, AstroGK, to the measured linear properties of kinetic and inertial Alfveacuten waves in the LAPD plasma. Results demonstrate that: (1) finite frequency effects due to the ion cyclotron resonance do not prevent satisfactory modeling of the LAPD plasma using gyrokinetic theory; and (2) an advanced collision operator, recently implemented in AstroGK, enables the code to successfully reproduce the collisionally enhanced damping rates of linear waves measured in recent LAPD experiments. These tests justify the use of AstroGK in the modeling of LAPD Alfveacuten wave experiments and suggest that AstroGK will be a valuable tool in modeling the nonlinear evolution of proposed Alfveacuten wave collision experiments.
Scientific journal, English - Nonlinear Phase Mixing and Phase-Space Cascade of Entropy in Gyrokinetic Plasma Turbulence
T. Tatsuno; W. Dorland; A. A. Schekochihin; G. G. Plunk; M. Barnes; S. C. Cowley; G. G. Howes
PHYSICAL REVIEW LETTERS, AMER PHYSICAL SOC, 103, 1, 015003, Jul. 2009, Peer-reviwed, Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.
Scientific journal, English - Magneto-flow instability in symmetric field profiles
T. Tatsuno; W. Dorland
PHYSICS OF PLASMAS, AMER INST PHYSICS, 13, 9, 092107, Sep. 2006, Peer-reviwed, Since Rayleigh's early work on shear-flow driven instabilities in fluids, it has been known that sheared flows are usually unstable only in the presence of an inflection point in the velocity profile. However, in magnetohydrodynamics, there are important instabilities for which no inflection point is required. In tokamak experiments, strongly sheared flows are associated with transport barriers. Instabilities that may limit the height and extent of transport barriers are of central importance. Here, we present linear and nonlinear simulations of an ideal magnetohydrodynamic instability that is driven by sheared flows without inflection points-instead, the instability mechanism requires reversed magnetic shear. Several symmetric field profiles are studied. In general, the instability leads to current profile modifications that push the local minimum value of the safety factor (q(min)) upward. The possibility of causing disruption in a relatively slow time scale is pointed out when q(min) crosses a rational (especially integral) value. The time scale of the instability is governed by the transit time of the shear flow, which is typically smaller than that of the Alfven velocity. Characteristics of this instability are compared with recent experimental observations. (c) 2006 American Institute of Physics.
Scientific journal, English - Resonance between continuous spectra: Secular behavior of Alfvén waves in a flowing plasma
M. Hirota; T. Tatsuno; Z. Yoshida
Physics of Plasmas, AIP Publishing, 12, 1, 1-11, 2005, Peer-reviwed, Conventional normal mode analysis often falls short in predicting a variety of transient phenomena in a non-self-adjoint (non-Hermitian) system. Laplace transform is capable of capturing all possible behavior in general systems. However, degenerate essential spectra require careful analysis. The Alfvén wave in a flowing plasma is an example in which the coalescence of the Alfvén singularities yields nonexponential growth of fluctuations. Invoking hyperfunction theory, rigorous expression of the Laplace transform leads to an accurate estimate of the asymptotic behavior of resonant singular modes. © 2005 American Institute of Physics.
Scientific journal, English - Statistical characterization of the interchange-instability spectrum of a separable ideal-magnetohydrodynamic model system
RL Dewar; T Tatsuno; Z Yoshida; C Nuhrenberg; BF McMillan
PHYSICAL REVIEW E, AMER PHYSICAL SOC, 70, 6, 066409-066409, Dec. 2004, Peer-reviwed, A Suydam-unstable circular cylinder of plasma with periodic boundary conditions in the axial direction is studied within the approximation of linearized ideal magnetohydrodynamics (MHD). The normal mode equations are completely separable, so both the toroidal Fourier harmonic index n and the poloidal index m are good quantum numbers. The full spectrum of eigenvalues in the range 1less than or equal tomless than or equal tom(max) is analyzed quantitatively, using asymptotics for large m, numerics for all m, and graphics for qualitative understanding. The density of eigenvalues scales like m(max)(2) as m(max)-->infinity. Because finite-m corrections scale as 1/m(max)(2), their inclusion is essential in order to obtain the correct statistics for the distribution of eigenvalues. Near the largest growth rate, only a single radial eigenmode contributes to the spectrum, so the eigenvalues there depend only on m and n as in a two-dimensional system. However, unlike the generic separable two-dimensional system, the statistics of the ideal-MHD spectrum departs somewhat from the Poisson distribution, even for arbitrarily large m(max). This departure from Poissonian statistics may be understood qualitatively from the nature of the distribution of rational numbers in the rotational transform profile.
Scientific journal, English - Degenerate continuous spectra producing localized secular instability - an example in a non-neutral plasma
M Hirota; T Tatsuno; Z Yoshida
JOURNAL OF PLASMA PHYSICS, CAMBRIDGE UNIV PRESS, 69, 397-412, Oct. 2003, Peer-reviwed, Fluctuations in ambient shear flow exhibit interesting transient phenomena. Shear flow produces not only Kelvin-Helmholtz modes (global exponential instabilities represented by point spectra) but also local algebraic instabilities associated with multiple continuous spectra. Since the generating operator is nonHermitian, the orthogonality of eigenmodes is broken, and unresolvable mode couplings (resonances) bring about secular behavior (algebraic instability). We analyze electrostatic fluctuations in a magnetized non-neutral (single species) plasma where the electrostatic potential parallels the stream function. This secular behavior is reproduced by solving the initial value problem with a renormalizatiou method.
Scientific journal, English - Destabilizing effect of plane Couette flow
T. Tatsuno; Z. Yoshida; S. M. Mahajan
Physics of Plasmas, AIP Publishing, 10, 6, 2278-2286, Jun. 2003, Peer-reviwed, The destabilizing effect of plane Couette flow was discussed. It was found that in the presence of the flow shear, the growth rate of perturbation increased due to the coupling of the Alfve′n wave with a Rayleigh-Taylor instability drive. The analysis showed that at larger shear flow velocities, the stabilizing 'stretching' effect became dominant and the instability was quenched.
Scientific journal, English - Destabilizing effect of shear flow - beyond Kelvin-Helmholtz instability
T Tatsuno; M Hirota; A Ito; S Kondoh; Z Yoshida; SM Mahajan
PLASMA PHYSICS, AMER INST PHYSICS, 669, 666-669, 2003, Peer-reviwed, A few examples of shear flow destabilization are presented. The destabilization is driven by a different mechanism from Kelvin-Helmholtz instability. One is from the non-Hermiticity of the operator, which shows the secular growth of the field. The other is from the Alfven wave. The Alfven wave may act on the mode to escape from the shear flow stretching, and standing mode is allowed.
International conference proceedings, English - Kelvin-Helmholtz instability in Beltrami fields
A Ito; Z Yoshida; T Tatsuno; S Ohsaki; SM Mahajan
PHYSICS OF PLASMAS, AMER INST PHYSICS, 9, 12, 4856-4862, Dec. 2002, Peer-reviwed, The stability of Beltrami flows has been analyzed. The model equation represents the coupling of the Kelvin-Helmholtz (KH) instability with Alfven waves. In a single Beltrami flow that parallels a force-free magnetic field, the magnetic field reduces the growth rate of the KH instability, while the marginally stable wave number is unchanged. Calculating the marginally stable eigenfunction of a magnetohydrodynamic flow, the necessary and sufficient condition for the exponential stability has been derived. The stability of double Beltrami flows has also been analyzed, which is represented by linear combinations of two Beltrami flows. Coupling of two vortices yields both stabilizing and destabilizing effects depending on the amplitudes and the eigenvalues of two Beltrami functions. (C) 2002 American Institute of Physics.
Scientific journal, English - Secular behavior of electrostatic Kelvin-Helmholtz (diocotron) modes coupled with plasma oscillations
M Hirota; T Tatsuno; S Kondoh; Z Yoshida
PHYSICS OF PLASMAS, AMER INST PHYSICS, 9, 4, 1177-1184, Apr. 2002, Peer-reviwed, Electrostatic instabilities in electron plasmas have been studied by analyzing initial value problems. The self-electric field of a non-neutral plasma produces a flow that brings about non-Hermitian property into the generating operator. Because of the nonorthogonality of eigenmodes, the evolution of the system is rather complex. Secular behavior is a typical appearance of unresolvable mode couplings that may be cast in a representation of Jordan block. The coupling of the perpendicular (with respect to the magnetic field) electrostatic modes (Kelvin-Helmholtz or diocotron modes) and parallel plasma oscillations causes a more complex phenomena. (C) 2002 American Institute of Physics.
Scientific journal, English - Magnetic shear stabilization of diocotron instability
S Kondoh; T Tatsuno; Z Yoshida
NON-NEUTRAL PLASMA PHYSICS IV, AMER INST PHYSICS, 606, 311-316, 2002, Peer-reviwed, The diocotron instability in a magnetized non-neutral plasma is a close cousin of the Kelvin-Helmholtz instability. A sheared magnetic field brings about coupling between the diocotron modes and the Langmuir waves that propagate along the magnetic field. Motion of electrons parallel to the magnetic field cancels the electric charge produced by the diocotron modes, resulting in stabilization of the diocotron instability.
International conference proceedings, English - Stabilization effect of magnetic shear on the diocotron instability
S Kondoh; T Tatsuno; Z Yoshida
PHYSICS OF PLASMAS, AMER INST PHYSICS, 8, 6, 2635-2640, Jun. 2001, Peer-reviwed, The diocotron instability in a magnetized non-neutral plasma is a close cousin of the Kelvin-Helmholtz instability. A sheared magnetic field brings about coupling between the diocotron modes and the Langmuir waves that propagate along the magnetic field. The motion of electrons parallel to the magnetic field cancels the electric charge produced by the diocotron modes, resulting in stabilization of the diocotron instability. (C) 2001 American Institute of Physics.
Scientific journal, English - Transient phenomena and secularity of linear interchange instabilities with shear flows in homogeneous magnetic field plasmas
T Tatsuno; F Volponi; Z Yoshida
PHYSICS OF PLASMAS, AMER INST PHYSICS, 8, 2, 399-406, Feb. 2001, Peer-reviwed, Transient and secular behaviors of interchange fluctuations are analyzed in an ambient shear flow by invoking Kelvin's method of shearing modes. Because of its non-Hermitian property, complex transient phenomena can occur in a shear flow system. The combined effect of shear flow mixing and Alfven wave propagation overcomes the instability driving force at sufficiently large time, and damps all fluctuations of the magnetic flux. On the other hand, electrostatic perturbations can be destabilized for sufficiently strong interchange drive. The time asymptotic behavior in each case is algebraic (nonexponential). (C) 2001 American Institute of Physics.
Scientific journal, English - Shear-flow induced stabilization of kinklike modes
F Volponi; Z Yoshida; T Tatsuno
PHYSICS OF PLASMAS, AMER INST PHYSICS, 7, 6, 2314-2319, Jun. 2000, Peer-reviwed, The stabilizing effect of a shear flow on a current-driven instability has been studied by means of Kelvin's representation of spatially-inhomogeneous Galilean transform. Even though conspicuous transient growth may occur, the mixing effect of the shear flow overcomes the instability and damps kinklike modes. (C) 2000 American Institute of Physics. [S1070-664X(00)01506-8].
Scientific journal, English
MISC
- 位相空間における磁化プラズマの2次元乱流解析
龍野智哉
Sep. 2012, 日本物理学会誌, 67, 9, 614, 640-644, Japanese, Peer-reviwed, Introduction other - Parallel simulation of phase-space turbulence in magnetized plasmas
龍野 智哉
宇宙空間や実験室に見られる，磁化された完全電離プラズマのダイナミクスを位相空間でシミュレーションする数値コード AstroGK の並列化に関する概要と，近年行われた位相空間乱流に関するシミュレーション結果を概観した．This document summarizes the parallelization scheme of numerical code AstroGK which simulates the dynamics of fully-ionized, magnetized plasmas seen in space and laboratory; and recent simulation results made for phase-space turbulence., 25 May 2012, 研究報告ハイパフォーマンスコンピューティング（HPC）, 2012, 8, 1-4, Japanese, 110009453402, AN10463942
Courses
Affiliated academic society
Research Themes
- Experimental Studies on the High-beta Equilibrium and Stability of Rapidly Flowing Plasma Produced in Toroidal Non-neutral Plasma Trap
YOSHIDA Zensho; FURUKAWA Masaru; SAITOH Haruhiko; OGAWA Yuichi; MORIKAWA Junji
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Tokyo, Grant-in-Aid for Scientific Research (S), We have studied the self-organization mechanism in flowing plasmas to explore the diversity of structures created in space and astronomical systems, and also examined the applicability of the high-beta equilibrium for advanced-fusion concept. 1.Results of Theoretical Studies We have developed some innovative methods for the analysis of equilibria and stability of flowing plasmas. Unlike the conventional theories of stationary (non-flowing) plasmas, the analysis of flowing plasmas may not invoke the well-known methods of spectral decomposition or energy principle. Analyzing the topological singularities of the non-canonical Hamiltonian formalisms, we have succeeded to characterize the basic vertical structures of flow-field coupling in terms of Casimir invariants (helicities). The corresponding variational principle yields a Lyapunov function, whose coercivity warrants the stability of the "Beltrami fields", the minimizer of the variational principle. The theory has been applied to explain the structural instabilities in solar corona, high-beta equilibria in Jupiter's magnetosphere, as well as new-type of flowing equilibria in Proto-RT and RT-1 devices. 2.Results of Experimental Studies We have demonstrated stable formation of super-sonic (Mach number > 5) rotating plasma in the Proto-RT Device. The Proto-RT device can confine a non-neutral (pure electron) plasma in a "magnetosphere-like" configuration. A non-neutral plasma produces a flowing (spinning) equilibrium by its self-electric field. By applying an internal electric field in a quasi-neutral plasma, we can achieve a similar flowing plasma. We have established a unified understanding of non-neutral and flowing plasmas : (1)We have demonstrated stable confinement of non-neutral plasma in a magnetic-surface configuration,; (2)By applying a radial electric field, we have demonstrated the self-organization of stable super-sonic flowing plasma ; (3)We have demonstrated the production of a new branch of equilibrium by the effect of fast flow ; (4)We have developed new technologies to construct magnetosphere-like plasma confinement device., 14102033
2002 - 2006 - プラズマにおける流れの安定化―不安定化効果の競合
龍野 智哉
日本学術振興会, 科学研究費助成事業, 東京大学, 若手研究(B), 流れのあるプラズマに関する安定性理論の研究を行った. プラズマ中の平行流のうち,流れによって平衡が不安定化される例としてKelvin-Helmholtz不安定性が良く知られているが,流れそのものが安定であっても,それを付加することによりプラズマ中の潜在的な不安定性が更に不安定化される場合があることを示し,その結果をPhysics of Plasmasに発表した[Destabilizing effect of plane Couette flow, Phys. Plasmas 10,2278(2003)]. Couette流は空間的に線形なプロファイルを持つ流れであり,その空間的な不均一性により,従来まではモードを引き伸ばすことで不安定性を抑制する働きがあると理解されてきた.ところが,我々が今回示した例では,プラズマ中の波(正確にはAlfvenと呼ばれる横波)には流れの引き伸ばし効果に逆らって渦度を運ぶ働きがあり,背景流はそのAlfven波に打ち勝つほど速くない限り引き神ばし効果は弱く,却って元々あった磁力線の曲げによる安定化効果をキャンセルするために不安定性を助長する. 中性流体におけるKelvin-Helmholtz不安定性について,Rayleighの表面波モデルに対するスペクトル構造の詳細な解析を行った.このモデルは区分的に線形なプロファイルの背景流を仮定した簡単なものであるが,我々の構築したスペクトル分解理論により,連続スペクトルと点スペクトルとの間に周波数縮退が存在することが示されている.このモデルに対して,今回の研究では流れのプロファイルが線形からずれた場合,点スペクトルが連続スペクトルに転移することを示した.この転移に伴う時間挙動は,漸近的には大きな変化をもたらすが,ある時間までは線形流の場合とそれほど変わらないと想像される.また非中性プラズマにおけるダイオコトロン不安定性を考えれば,上記の周波数縮退にプラズマ振動がカップリングすることにより代数的な不安定性が生じることを示し,その結果を国際会議International Congress on Industrial and Applied Mathematics(Sydney,2003)において口頭発表した. これらの知見をまとめてレビュー論文を執筆し,プラズマ・核融合学会誌に投稿した(Stabilizing and destabilizing effect of shear flow,プラズマ・核融合学会誌に採録が決定)., 15740323
2003 - 2004 - 流れのあるプラズマに関する安定性理論の数学的基礎
龍野 智哉
日本学術振興会, 科学研究費助成事業, 東京大学, 奨励研究(A), 流れのあるプラズマに関する安定性理論の研究を行った. 1887年にKelvinによって発表された解析手法が,線形プロファイルをもつ流れのあるプラズマについて一般解を与えることを数学的に示し,その手法に基づいて磁場閉じ込めプラズマ中の電流駆動不安定性,及び圧力駆動不安定性の解析を行った.流れによって作用素がエルミートでない場合にも,プラズマの線形運動が変形していくモードに分解できることを示した.これらのモードはエルミート作用素に対する指数関数から大きく外れ,過渡的な成長を示すと共に,漸近的には時間について代数的に減衰することを示した.すなわち,流れの効果がプラズマ中に内在する不安定性を安定化させるわけである. また表面波モデルを用いたKelvin-Helmholtz不安定性の解析において,従来見過ごされてきた連続スペクトルと点スペクトルとの非エルミートな相互作用による,共鳴現象が存在することを示し,数学的なスペクトル理論を構築した.非中性プラズマにおけるdiocotron不安定性についても解析を行った.固有値解析では流れによる不安定性が磁気シアーによって安定化されることを示した.初期値問題を数値的に解くと,作用素の非エルミート性から連続スペクトル同士の周波数縮退による共鳴現象が起こり,空間的に局在化する代数的な密度揺動の成長が起こることを示した. 次に,相対論的速度をもつプラズマについて,高周波の波動は1次元縞状のソリトン解をもつ.これは中性流体において有名なKelvin-Helmholtz不安定性に類似した不安定性によって2次元に崩壊するが,その際に角運動量を生成する.この2次元解は非常に安定であり,それらが何らかの理由である距離以上に離れると,その角運動量は保存される.不安定性の非線形発展に関しても数値計算を行い,実際に縞状ソリトンから2次元の渦ソリトンの形成まで,時間発展を追うことによって角運動量の生成が起こることを示した.この研究に関してさらに論文を執筆中である.これは応用上,初期宇宙の角運動量形成に関連がある解として興味深いものである., 12780353
2000 - 2001 - Kinetic Effects on Self-Organization in Plasma
YOSHIDA Zensho; TATSUNO Tomoya; HIMURA Haruhiko; OGAWA Yuichi; MORIKAWA Junji
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Tokyo, Grant-in-Aid for Scientific Research (B)., To explore innovative concepts of fusion plasma confinement, especially in the high-beta regime that can host the D-3He advanced fusion, we have to develop a sound understanding on the physics of relaxation that self-organizes the most preferable structure in the plasma. The theory of the Taylor relaxed states succeeded to explain the self-organization of the reversed-field pinch (RFP) and ultra-low-q (ULQ) plasmas. In the present research, we have made a considerable generalization of the self-organization theory through the study of kinetic (particle dynamics) and flow effects. The results are summarized as follows ; (1) When a plasma has a macroscopic non-neutral charge, the self-electric field yields a strong rotating flow. The two-fluid model provides a self-consistent description of the relaxed states with a strong flow. A variety of interesting structures can be cast in the model of double Beltrami fields ; (2) The particle motion becomes chaotic in a strongly inhomogeneous electromagnetic field, resulting in a rapid production of the kinetic entropy. As a macroscopif effect of the chaos, the resistive dissipation is much enhanced, which accounts for the anomalous resistance in the magnetic reconnection process of the self-organization., 10044130
1998 - 2000 - Toroidal Magnetic Confinement of Non-neutral Plasmas
YOSHIDA Zensho; TATSUNO Tomoya; HIMURA Haruhiko; OGAWA Yuichi; MORIKAWA Junji
Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, The University of Tokyo, Grant-in-Aid for Scientific Research (A)., A new method of producing non-neutral plasmas has been developed with introducing an innovative scheme of injecting particles into a toroidal magnetic shear configuration. This method can be applied to various particle traps, as well as an ultra-high-beta fusion device that is suitable for advanced fusion. Unique features in this concept, in comparison with other conventional electric-field traps (such as the Penning trap), are summarized as follows ; (1) This pure magnetic confinement device can trap very high-energy particles directly ; (2) Continuous injection of particles enables to produce a high-density (up to the Brillouin limit) plasma ; (3) Multi-species particles with opposite charges can be confined simultaneously. The key issues of development were (A) the application of magnetic shear to stabilize the plasma and (B) the production of the chaos-induced collision-less diffusion to inject particles into the trapping region. Using this non-neutral plasma system, we have studied (I) the new-type of relaxed state in a plasma with an intense shear flow, (II) the anomalous diffusion and resistance induced by the chaos of particle motion in magnetic null region, (III) the non-Hermitian dynamics of vortices in a shear flow, and (IV) magnetic shear stabilization of electrostatic instabilities., 09308011
1997 - 2000
