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Study of Low-Frequency Core-Edge Coupling in a Tokamak: II. Spatial Channeling & Focusing In Antenna-Driven MHD
Authors:
Andreas Bierwage,
Wonjun Lee,
Young-chul Ghim,
Panith Adulsiriswad,
Nobuyuki Aiba,
Seungmin Bong,
Gyungjin Choi,
Matteo Falessi,
Philipp W. Lauber,
Masatoshi Yagi
Abstract:
Motivated by evidence for core-edge coupling in the form of double-peaked fishbone-like low-frequency modes ($\lesssim 20\,{\rm kHz}$) in KSTAR, which exhibit synchronized Alfvénic activity both in the central core and near the plasma edge [1], we study the nonlocal response of a tokamak plasma in a visco-resistive full MHD simulation model using the code MEGA. The waves are driven by an internal…
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Motivated by evidence for core-edge coupling in the form of double-peaked fishbone-like low-frequency modes ($\lesssim 20\,{\rm kHz}$) in KSTAR, which exhibit synchronized Alfvénic activity both in the central core and near the plasma edge [1], we study the nonlocal response of a tokamak plasma in a visco-resistive full MHD simulation model using the code MEGA. The waves are driven by an internal "antenna" that is localized both radially and azimuthally in the poloidal $(R,z)$ plane and has a sinusoidal form $\exp(inζ- iωt)$ with Fourier mode number $n=\pm 1$ in the toroidal angle $ζ$ and fixed angular frequency $ω$ in time $t$. By flattening the safety factor profile $q(r)$ at suitable locations in the minor radius $r$, we created plateaus in the low-frequency Alfvén continua that act as wave "receivers". First, we confirm that such continuum plateaus respond with a coherent quasi-mode even when the driving antenna is located at a distant radius. Second, by varying the antenna location, we confirm the expectation of inward drive being more efficient than outward drive, which we attribute to volumetric focusing. Third, we find that the central core also responds well at frequencies below the central Alfvénic continuum plateau, which could facilitate chirping. Our results show that a core-localized low-frequency response does not necessarily require core-localized drive nor an exactly matching continuum, but may be driven from the edge and sub-resonantly. It remains to be seen to what extent the examined effects play a role in double-peaked fishbone-like activity. Other possible contributing mechanisms are discussed to motivate further study. Our analyses also elucidate the mode structure formation process, from transients to quasi- or eigenmodes, here in the realm of MHD, and to be followed by a verification study against kinetic models.
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Submitted 16 April, 2026; v1 submitted 25 March, 2026;
originally announced March 2026.
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Helical Core Formation and MHD Stability in ITER-Scale Plasmas with Fusion-born Alpha Particles
Authors:
P. Adulsiriswad,
A. Bierwage,
M. Yagi
Abstract:
The effect of fusion-born alpha particles on the helical core (HC), a long-lived ideal saturation state of the $m/n=1/1$ kink/quasi-interchange mode, is studied in the ITER-scale hybrid scenario where a core plasma has a low magnetic shear $q\gtrsim1$. The HC state is determined by 3-D MHD force balance and all factors that contribute to it, such as plasma shaping, the safety factor profile, and t…
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The effect of fusion-born alpha particles on the helical core (HC), a long-lived ideal saturation state of the $m/n=1/1$ kink/quasi-interchange mode, is studied in the ITER-scale hybrid scenario where a core plasma has a low magnetic shear $q\gtrsim1$. The HC state is determined by 3-D MHD force balance and all factors that contribute to it, such as plasma shaping, the safety factor profile, and the pressure profiles of all particle species. An incomplete but useful measure of the HC is the displacement of the magnetic axis, $δ_\mathrm{HC}$. Using MHD-PIC simulations, we find that $δ_\mathrm{HC}$ is enhanced by increasing alpha particle pressure $β_\mathrmα$. Within the ITER operating alpha pressure $β_\mathrmα(0) \lesssim 1\%$, $β_\mathrmα$ can be approximately treated as part of the total MHD pressure. In this regime, there is no notable flattening of the pressure profile, indicating that the HC preserves the omnigenity of the plasma. If one increases $β_\mathrmα(0)$ beyond $1\%$, $δ_\mathrm{HC}$ continues to increase with $β_\mathrmα$ until it reaches an upper limit at $β_\mathrmα(0)=3\%$ for our reference case. At this limit, both the bulk and alpha pressure profiles are partially flattened, indicating a reduction in omnigenity. After HC formation, a resistive pressure-driven MHD mode can become unstable, which is localized along the compressed magnetic flux region of the HC. This secondary mode consists of a broad spectrum of short-wavelength Fourier components that grow at same rates and are thus part of a single coherent entity. Our present simulation model is insufficient to adequately represent such a secondary mode; however, preliminary results suggest that it can facilitate magnetic chaos, which affects plasma confinement.
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Submitted 21 November, 2025; v1 submitted 15 September, 2025;
originally announced September 2025.
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Construction and analysis of guiding center distributions for tokamak plasmas with ambient radial electric field
Authors:
Andreas Bierwage,
Philipp Lauber,
Noriyoshi Nakajima,
Kouji Shinohara,
Guillaume Brochard,
Young-chul Ghim,
Wonjun Lee,
Akinobu Matsuyama,
Shuhei Sumida,
Hao Yang,
Masatoshi Yagi
Abstract:
The contribution of a time-independent toroidally-symmetric radial electric field $E_r$ is implemented in VisualStart [Comp. Phys. Comm. 275 (2022) 108305; arXiv:2111.08224], a code whose purposes include the construction of guiding center (GC) drift orbit databases for the study of plasma instabilities in tokamaks. $E_r$ is important for the thermal part of the velocity distribution and for fast…
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The contribution of a time-independent toroidally-symmetric radial electric field $E_r$ is implemented in VisualStart [Comp. Phys. Comm. 275 (2022) 108305; arXiv:2111.08224], a code whose purposes include the construction of guiding center (GC) drift orbit databases for the study of plasma instabilities in tokamaks. $E_r$ is important for the thermal part of the velocity distribution and for fast particle resonances in the kHz frequency range. KSTAR, JT-60U and ITER tokamak cases are used as working examples to test our methods and discuss practical issues connected with $E_r$. Two points are worth noting: First, the GC orbit space is sampled in the magnetic midplane as before, and we find that in the presence of $E_r$, midplane-based coordinates are not only equivalent but superior to conventional constants of motion, allowing to attain high numerical accuracy and efficiency with a relatively simple mesh. Second, the periodic parallel acceleration and deceleration of GCs via the mirror force is modulated by $E_r$. Although this parallel electric acceleration averages to zero during a poloidal transit (or bounce) period, it has important consequences, one being the known shift of the trapped-passing boundary. Another consequence is that electric frequency shifts depend on the chosen reference point, so that some care is required when evaluating the $E_r$-dependence of transit frequencies for resonance analyses.
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Submitted 30 April, 2025; v1 submitted 28 November, 2024;
originally announced November 2024.
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Two-stage Crash Process in Resistive Drift Ballooning Mode Driven ELM Crash
Authors:
Haruki Seto,
Xueqiao Xu,
Benjamin D. Dudson,
Masatoshi Yagi
Abstract:
We report a two-stage crash process in edge localized mode (ELM) driven by resistive drift-ballooning modes (RDBMs) numerically simulated in a full annular torus domain. In the early nonlinear phase, the first crash is triggered by linearly unstable RDBMs and m/n = 2/1 magnetic islands are nonlinearly excited via nonlinear couplings of RDBMs. Simultaneously, middle-n RDBM turbulence develops but i…
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We report a two-stage crash process in edge localized mode (ELM) driven by resistive drift-ballooning modes (RDBMs) numerically simulated in a full annular torus domain. In the early nonlinear phase, the first crash is triggered by linearly unstable RDBMs and m/n = 2/1 magnetic islands are nonlinearly excited via nonlinear couplings of RDBMs. Simultaneously, middle-n RDBM turbulence develops but is poloidally localized around X-points of the magnetic islands, leading to the small energy loss. Here m is the poloidal mode number, n is the toroidal mode number, the q = 2 rational surface exists at the pressure gradient peak, and q is the safety factor, respectively. The second crash occurs in the late nonlinear phase. Low-n magnetic islands are also excited around the q = 2 surface via nonlinear couplings among the middle-n turbulence. Since the turbulence develops from the X-points of higher harmonics of m/n = 2/1 magnetic islands, it expands out poloidally. The second crash is triggered when the turbulence covers the whole poloidal region. A scan of toroidal wedge number N, where full torus is divided into N segments in the toroidal direction, also reveals that the first crash process becomes more prominent with the higher toroidal wedge number where the RDBMs play a dominant role. These results indicate that nonlinear interactions of all channels in the full torus domain can significantly affect the trigger dynamics of ELMs driven by the RDBMs.
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Submitted 7 October, 2023;
originally announced October 2023.
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Energy-selective confinement of fusion-born alpha particles during internal relaxations in a tokamak plasma
Authors:
Andreas Bierwage,
Kouji Shinohara,
Yevgen Kazakov,
Vasili Kiptily,
Philipp Lauber,
Massimo Nocente,
Žiga Štancar,
Shuhei Sumida,
Masatoshi Yagi,
Jeronimo Garcia,
Shunsuke Ide,
JET Contributors
Abstract:
Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined to heat the plasma. On the other hand, decelerated helium ash must be expelled before diluting the fusion fuel. Our kinetic-magnetohydrodynamic hybrid simulati…
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Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined to heat the plasma. On the other hand, decelerated helium ash must be expelled before diluting the fusion fuel. Our kinetic-magnetohydrodynamic hybrid simulations of a large tokamak plasma confirm the existence of a parameter window where such energy-selective confinement can be accomplished by exploiting internal relaxation events known as `sawtooth crashes'. The physical picture -- consisting of a synergy between magnetic geometry, optimal crash duration and rapid particle motion -- is completed by clarifying the role played by magnetic drifts. Besides causing asymmetry between co- and counter-going particle populations, magnetic drifts determine the size of the confinement window by dictating where and how much `reconnection' occurs in particle orbit topology.
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Submitted 12 January, 2022; v1 submitted 8 September, 2021;
originally announced September 2021.
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Drift reduced Landau fluid model for magnetized plasma turbulence simulations in BOUT++ framework
Authors:
Ben Zhu,
Haruki Seto,
Xue-qiao Xu,
Masatoshi Yagi
Abstract:
Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These i…
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Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transient (e.g., ELM, disruption) and transport time-scale simulations.
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Submitted 17 June, 2021; v1 submitted 9 February, 2021;
originally announced February 2021.
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A mass-energy-conserving discontinuous Galerkin scheme for the isotropic multispecies Rosenbluth--Fokker--Planck equation
Authors:
Takashi Shiroto,
Akinobu Matsuyama,
Nobuyuki Aiba,
Masatoshi Yagi
Abstract:
Structure-preserving discretization of the Rosenbluth-Fokker-Planck equation is still an open question especially for unlike-particle collision. In this paper, a mass-energy-conserving isotropic Rosenbluth-Fokker-Planck scheme is introduced. The structure related to the energy conservation is skew-symmetry in mathematical sense, and the action-reaction law in physical sense. A thermal relaxation t…
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Structure-preserving discretization of the Rosenbluth-Fokker-Planck equation is still an open question especially for unlike-particle collision. In this paper, a mass-energy-conserving isotropic Rosenbluth-Fokker-Planck scheme is introduced. The structure related to the energy conservation is skew-symmetry in mathematical sense, and the action-reaction law in physical sense. A thermal relaxation term is obtained by using integration-by-parts on a volume integral of the energy moment equation, so the discontinuous Galerkin method is selected to preserve the skew-symmetry. The discontinuous Galerkin method enables ones to introduce the nonlinear upwind flux without violating the conservation laws. Some experiments show that the conservative scheme maintains the mass-energy-conservation only with round-off errors, and analytic equilibria are reproduced only with truncation errors of its formal accuracy.
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Submitted 25 November, 2020;
originally announced November 2020.
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Nonlinear variational method for predicting fast collisionless magnetic reconnection
Authors:
M. Hirota,
P. J. Morrison,
Y. Ishii,
M. Yagi,
N. Aiba
Abstract:
A mechanism for fast magnetic reconnection in collisionless plasma is studied for understanding sawtooth collapse in tokamak discharges by using a two-fluid model for cold ions and electrons. Explosive growth of the tearing mode enabled by electron inertia is analytically estimated by using an energy principle with a nonlinear displacement map. Decrease of the potential energy in the nonlinear reg…
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A mechanism for fast magnetic reconnection in collisionless plasma is studied for understanding sawtooth collapse in tokamak discharges by using a two-fluid model for cold ions and electrons. Explosive growth of the tearing mode enabled by electron inertia is analytically estimated by using an energy principle with a nonlinear displacement map. Decrease of the potential energy in the nonlinear regime (where the island width exceeds the electron skin depth) is found to be steeper than in the linear regime, resulting in accelerated reconnection. Release of potential energy by such a fluid displacement leads to unsteady and strong convective flow, which is not damped by the small dissipation effects in high-temperature tokamak plasmas. Direct numerical simulation in slab geometry substantiates the theoretical prediction of the nonlinear growth.
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Submitted 29 April, 2013; v1 submitted 14 January, 2013;
originally announced January 2013.
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Nonlinear Acceleration Mechanism of Collisionless Magnetic Reconnection
Authors:
M. Hirota,
P. J. Morrison,
Y. Ishii,
M. Yagi,
N. Aiba
Abstract:
A mechanism for fast magnetic reconnection in collisionless plasma is studied for understanding sawtooth collapse in tokamak discharges. Nonlinear growth of the tearing mode driven by electron inertia is analytically estimated by invoking the energy principle for the first time. Decrease of potential energy in the nonlinear regime (where the island width exceeds the electron skin depth) is found t…
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A mechanism for fast magnetic reconnection in collisionless plasma is studied for understanding sawtooth collapse in tokamak discharges. Nonlinear growth of the tearing mode driven by electron inertia is analytically estimated by invoking the energy principle for the first time. Decrease of potential energy in the nonlinear regime (where the island width exceeds the electron skin depth) is found to be steeper than in the linear regime, resulting in acceleration of the reconnection. Release of free energy by such ideal fluid motion leads to unsteady and strong convective flow, which theoretically corroborates the inertia-driven collapse model of the sawtooth crash [D. Biskamp and J. F. Drake, Phys. Rev. Lett. 73, 971 (1994)].
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Submitted 1 October, 2012;
originally announced October 2012.
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Entry Dispersion Analysis for the Hayabusa Spacecraft using Ground Based Optical Observation
Authors:
T. Yamaguchi,
M. Yoshikawa,
M. Yagi,
D. J. Tholen
Abstract:
Hayabusa asteroid explorer successfully released the sample capsule to Australia on June 13, 2010. Since the Earth reentry phase of sample return was critical, many backup plans for predicting the landing location were prepared. This paper investigates the reentry dispersion using ground based optical observation as a backup observation for radiometric observation. Several scenarios are calculated…
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Hayabusa asteroid explorer successfully released the sample capsule to Australia on June 13, 2010. Since the Earth reentry phase of sample return was critical, many backup plans for predicting the landing location were prepared. This paper investigates the reentry dispersion using ground based optical observation as a backup observation for radiometric observation. Several scenarios are calculated and compared for the reentry phase of the Hayabusa to evaluate the navigation accuracy of the ground-based observation. The optical observation doesn't require any active reaction from a spacecraft, thus these results show that optical observations could be a steady backup strategy even if a spacecraft had some trouble. We also evaluate the landing dispersion of the Hayabusa only with the optical observation.
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Submitted 28 June, 2011;
originally announced June 2011.
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Effect of the curvature and the β parameter on the nonlinear dynamics of a drift tearing magnetic island
Authors:
Magali Muraglia,
Olivier Agullo,
Masatoshi Yagi,
Sadruddin Benkadda,
Beyer Peter,
Xavier Garbet,
Sanae -I. Itoh,
Kimitaka Itoh,
Abhijit Sen
Abstract:
We present numerical simulation studies of 2D reduced MHD equations investigating the impact of the electronic βparameter and of curvature effects on the nonlinear evolution of drift tearing islands. We observe a bifurcation phenomenon that leads to an amplification of the pressure energy, the generation of E \times B poloidal flow and a nonlinear diamagnetic drift that affects the rotation of the…
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We present numerical simulation studies of 2D reduced MHD equations investigating the impact of the electronic βparameter and of curvature effects on the nonlinear evolution of drift tearing islands. We observe a bifurcation phenomenon that leads to an amplification of the pressure energy, the generation of E \times B poloidal flow and a nonlinear diamagnetic drift that affects the rotation of the magnetic island. These dynamical modifications arise due to quasilinear effects that generate a zonal flow at the onset point of the bifurcation. Our simulations show that the transition point is influenced by the βparameter such that the pressure gradient through a curvature effect strongly stabilizes the transition. Regarding the modified rotation of the island, a model for the frequency is derived in order to study its origin and the effect of the βparameter. It appears that after the transition, an E \times B poloidal flow as well as a nonlinear diamagnetic drift are generated due to an amplification of the stresses by pressure effects.
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Submitted 23 March, 2011;
originally announced March 2011.
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Shear flow effects on double tearing mode global magnetic reconnection
Authors:
Thibaut Voslion,
Olivier Agullo,
Peter Beyer,
Masatoshi Yagi,
Sadruddin Benkadda,
Xavier Garbet,
Kimitaka Itoh,
Sanae-I. Itoh
Abstract:
The dynamics of a global reconnection in the presence of a poloidal shear flow which is located in between magnetic islands is investigated. Different linear regimes are identified according to the value of the resistivity and the distance between the low-order resonant surfaces. It is found that the presence of a small shear flow affects and significantly delays the global reconnection processe…
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The dynamics of a global reconnection in the presence of a poloidal shear flow which is located in between magnetic islands is investigated. Different linear regimes are identified according to the value of the resistivity and the distance between the low-order resonant surfaces. It is found that the presence of a small shear flow affects and significantly delays the global reconnection processes. It is shown that this delay is linked to a breaking of symmetry imposed by the existence of the shear flow and the generation of a mean poloidal flow in the resistive layers.
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Submitted 3 December, 2009; v1 submitted 26 November, 2009;
originally announced November 2009.
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Transition Probability to Turbulent Transport Regime
Authors:
Mitsuhiro Kawasaki,
Atsushi Furuya,
Masatoshi Yagi,
Kimitaka Itoh,
Sanae-I. Itoh
Abstract:
Transition phenomena between thermal noise state and turbulent state observed in a submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains hysteresis characteristics. Transition rates between two states are analyzed. Transition from turbulent state to thermal noise state…
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Transition phenomena between thermal noise state and turbulent state observed in a submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains hysteresis characteristics. Transition rates between two states are analyzed. Transition from turbulent state to thermal noise state occurs in entire region between subcritical bifurcation point and linear stability boundary.
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Submitted 4 April, 2002;
originally announced April 2002.
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Stochastic Transition between Turbulent Branch and Thermodynamic Branch of an Inhomogeneous Plasma
Authors:
Mitsuhiro Kawasaki,
Sanae-I. Itoh,
Masatoshi Yagi,
Kimitaka Itoh
Abstract:
Transition phenomena between thermodynamic branch and turbulent branch in submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains submarginal characteristics. Probability density functions and transition rates between two states are analyzed. Transition from turbulent bra…
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Transition phenomena between thermodynamic branch and turbulent branch in submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation which contains submarginal characteristics. Probability density functions and transition rates between two states are analyzed. Transition from turbulent branch to thermodynamic branch occurs in almost entire region between subcritical bifurcation point and linear stability boundary.
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Submitted 4 April, 2002;
originally announced April 2002.
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Kinetic temperature gradient driven modes in inhomogeneous plasmas
Authors:
A. I. Smolyakov,
M. Yagi,
Y. Kishimoto
Abstract:
New unstable temperature gradient driven modes in an inhomogeneous plasma are identified. These modes represent transient $ω\simeq k_{\Vert }v_{th}^{(e,i)}$ sound oscillations in magnetized plasma that are kinetically destabilized via Landau interactions. Electron and ion sound branches are unstable for large values of the Larmor radius parameter $% k_{\bot}ρ_{e,i}\gg 1,$ respectively. The insta…
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New unstable temperature gradient driven modes in an inhomogeneous plasma are identified. These modes represent transient $ω\simeq k_{\Vert }v_{th}^{(e,i)}$ sound oscillations in magnetized plasma that are kinetically destabilized via Landau interactions. Electron and ion sound branches are unstable for large values of the Larmor radius parameter $% k_{\bot}ρ_{e,i}\gg 1,$ respectively. The instability occurs due to a specific plasma response that significantly deviates from Boltzmann distribution in the region $k_{\bot}ρ_{i,e}\gg 1$ . Pacs: 52.35 Kt, 52.35 Qz
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Submitted 20 November, 2001;
originally announced November 2001.