Laser-driven multi-MeV high-purity proton acceleration via anisotropic ambipolar expansion of micron-scale hydrogen clusters
Satoshi Jinno, Masato Kanasaki, Takafumi Asai, Ryutaro Matsui, Alexander S. Pirozhkov, Koichi Ogura, Akito Sagisaka, Yasuhiro Miyasaka, Nobuhiko Nakanii, Masaki Kando, Nobuko Kitagawa, Kunihiro Morishima, Satoshi Kodaira, Yasuaki Kishimoto, Tomoya Yamauchi, Mitsuru Uesaka, Hiromitsu Kiriyama & Yuji Fukuda

Multi-MeV high-purity proton acceleration by using a hydrogen cluster target irradiated with repetitive, relativistic intensity laser pulses has been demonstrated. Statistical analysis of hundreds of data sets highlights the existence of markedly high energy protons produced from the laser-irradiated clusters with micron-scale diameters. The spatial distribution of the accelerated protons is found to be anisotropic, where the higher energy protons are preferentially accelerated along the laser propagation direction due to the relativistic effect. These features are supported by three-dimensional (3D) particle-in-cell (PIC) simulations, which show that directional, higher energy protons are generated via the anisotropic ambipolar expansion of the micron-scale clusters. The number of protons accelerating along the laser propagation direction is found to be as high as 1.6 ±0.3 ×10^9/MeV/sr/shot with an energy of 2.8 ±1.9 MeV, indicating that laser-driven proton acceleration using the micron-scale hydrogen clusters is promising as a compact, repetitive, multi-MeV high-purity proton source for various applications.
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Gyrokinetic entropy balances and dynamics in toroidal flux-driven ITG turbulence
Mikiya Muto, Kenji Imadera and Yasuaki Kishimoto

Overall entropy balances and radial dynamics for thermodynamic entropy and conventional fluctuation entropy are investigated by means of newly derived coupled equations and the full-f gyrokinetic simulations for toroidal flux-driven ion-temperature-gradient turbulence. When the equations are integrated over the radial direction, in the quasi-steady state, fluctuation entropy production due to collisional dissipation in velocity space and thermodynamic entropy reduction due to energy input/output in real space are found to be balanced through the generation of a heat flux and associated phase mixing. The cross-correlation analysis indicates that collisional dissipation occurs after the formation of fine-scale structures by phase mixing, while there exists an in-phase relationship between thermodynamic entropy production due to profile relaxation and heat flux. However, when the radial dynamics are retained in the equations, this relationship is found to be violated in regions exhibiting heat avalanches. This is because the thermodynamic entropy is dominated by advection, leading to a time lag between heat flux and temperature variation.
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Study of Plasma Shaping Effects on ITG Instability Using Global Gyrokinetic Code GKNET with Analytical Magnetic Equilibrium
K. Imadera, Jhih-Yi Lin, D. Nakajima, and Y. Kishimoto

We extended the global gyrokinetic code GKNET (GyroKinetic Numerical Experiment of Tokamak) to non-circular shaped plasmas with analytical magnetic equilibria, which satisfy the Grad-Shafranov equation up to the second order with respect to aspect ratio. The extended version allows us to set the equilibria with non-unity elongation and non-zero triangularity, where the finite Shafranov shift is consistently determined. The allocated mesh follows the magnetic field line with periodic boundary conditions along the poloidal and toroidal directions so that the calculation cost for solving the gyrokinetic quasi-neutrality condition can be reduced by utilizing 1D FFT and MPI_ALLtoALL transpose technique. Based on the developed code, we studied the effect of elongation and triangularity on linear Ion Temperature Gradient (ITG) instability with adiabatic electrons in a non-circular shaped Tokamak by paying attention to the symmetry breaking of mode structure due to global profile effects. It is found that elongation reduces ITG instability owing to the effective reduction of flux-surface averaged ion temperature gradient and increases the asymmetry characterized by the Bloch angle. On the other hand, when elongation is approximately unity, triangularity weakly affects the growth rate, while negative triangularity stabilizes ITG modes and increases the asymmetry in a large elongation regime.
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Statistical study for ITG turbulent transport in flux-driven tokamak plasmas based on global gyro-kinetic simulation
W. Wang, Y. Kishimoto, K. Imadera, H.R. Liu, J.Q. Li, M. Yagi and Z.X. Wang

Flux-driven ion temperature gradient (ITG) turbulence and associated transport regulated by non-local and non-diffusive processes are investigated based on GKNET simulations in a global toroidal geometry. Among these processes, the instantaneous formation of radially extended quasi-coherent structure, which leads to the transport burst, is found to play an important role in causing global profile formation and relaxation. To elucidate the characteristics of such a transport process, we introduce the size probability distribution function (size-PDF) $P\left( S \right)$ to analyze heat flux eddies in the real space, with $S$ the eddy size, incorporated with Fourier-based approaches in spectral space. In the size-PDF to the quiescent phase, $P\left( S \right)$ is found to be fitted by three piecewise power laws which transitions at two typical sizes, ${S_a}$ and ${S_b}$, as $P \propto {S^{ - 2/3}}\,\left( {S \leqslant {S_a}} \right)$, $P \propto {S^{ - 2\,}}$ $\left( {{S_a} \leqslant S \leqslant {S_b}} \right)$, and $P \propto {S^{ - 4}}\,\left( {S \geqslant {S_b}} \right)$, where ${S_a}\sim50$ and ${S_b}\sim200$ in squared gyro-radius unit $\rho _{\text{i}}^2$ for the system with $a/{\rho _i}\sim225$ (a: the minor radius). On the other hand, the size-PDF in the bursting phase exhibits non-power-law irregular humps which corresponds to the quasi-coherent structures for $S \geqslant {S_b}$ reaching to ${S_{max}}\sim1500$. Such a coherent structure is ascribed to the spontaneous alignment of smaller scale eddies through phase matching in radial direction, which is classified as a quasi-deterministic process. Resultantly, a large amount of free energy is extracted from the system due to subsequent growth of the event, by which a self-organized profile is established. The coherent structure is then readily disintegrated by self-generated zonal flows, followed by the energy transferred to smaller eddies. Finally, turbulent transport in the steady state of a flux-driven system is found to be regulated by the mixture of such quasi-deterministic process and probabilistic processes, which leads to stiffness and resilience in the profile formation and self-similarity in the relaxation.
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Ionization and acceleration of multiply charged gold ions in solid film irradiated by high intensity laser
D. Kawahito and Y. Kishimoto

In this paper, we present the mechanisms of ionization of a thin gold film irradiated by a high-intensity, short-pulse laser in the range of I=1020?22?W/cm2 and the associated acceleration of multiply charged gold ions. A numerical one-dimensional simulation using an extended particle-in-cell code, which includes atomic and collisional relaxation processes, indicates that two types of acceleration, hole-boring radiation pressure acceleration (RPA) and target normal sheath acceleration (TNSA), contribute to the generation of highly charged ions with kinetic energies on the order of 10?MeV/u. In each acceleration, a longitudinal electrostatic field excited by different mechanisms dominantly ionizes atoms to higher charge states and accelerates them to the vacuum region from the rear surface, which is opposite the front surface irradiated by the laser field. The field ionization process dominantly ionizes high energy ions to the high charge state, while a large number of ions with energy <1?MeV/u are ionized by an electron impact ionization process. In TNSA, a multiply charged ion generated at the rear surface is accelerated to the maximum energy although the ion with the highest charge state is generated at the front surface in RPA. However, the existence of contamination, such as water vapor, suppresses the ion energy of TNSA to less than that of RPA since the sheath field readily accelerates the protons and oxygen prior to the acceleration of the gold ions. Our derived theoretical scaling describes the maximum ion energy for each charge state in the cases with and without contamination using the relationship between the longitudinal electrostatic field profile near the rear surface and the classical tunnel field ionization model.
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Dynamics of the boundary layer created by the explosion of a dense object in an ambient dilute gas triggered by a high power laser
R. Matsui, Y. Fukuda and Y. Kishimoto

The dynamics of the boundary layer in between two distinct collisionless plasmas created by the interaction between a dense object modeling a cluster and a short laser pulse in the presence of an ambient gas is studied with two dimensional relativistic particle-in-cell simulations, which are found to be described by three successive processes. In the first phase, a collisionless electrostatic shock wave, launched near the cluster expansion front, reflects the ambient gas ions at a contact surface as a moving wall, which allows a particle acceleration with a narrower energy spread. In the second phase, the contact surface disappears and the compressed surface of the ambient gas ions passes over the shock potential, forming an overlapping region between the cluster expansion front and the compressed surface of the ambient gas. Here, another type of nonlinear wave is found to be evolved, leading to a relaxation of the shock structure, while continuing to reflect the ambient gas ions. The nonlinear wave exhibits a bipolar electric field structure that is sustained for a long timescale coupled with slowly evolving ion dynamics, suggesting that a quasistationary kinetic equilibrium dominated by electron vortices in the phase space is established. In the third phase, a rarefaction wave is triggered and evolves at the compressed surface of ambient gas. This is because some of the ambient gas ions tend to pass over the potential of the bipolar electric field. Simultaneously, a staircase structure, i.e., a kind of internal shock, is formed in the cluster due to the deceleration of cluster ions. Such structure formations and successive dynamics accompanied by the transitions from the shock wave phase through the overlapping phase to the rarefaction wave phase are considered to be a unique nature at the boundary layer created by an explosion of a dense plasma object in an ambient dilute plasma.
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Quasimonoenergetic Proton Bunch Acceleration Driven by Hemispherically Converging Collisionless Shock in a Hydrogen Cluster Coupled with Relativistically Induced Transparency
R. Matsui, Y. Fukuda and Y. Kishimoto

An approach for accelerating a quasimonoenergetic proton bunch via a hemispherically converging collisionless shock created in laser-cluster interactions at the relativistically induced transparency (RIT) regime is studied using three-dimensional particle-in-cell simulations. By the action of focusing a petawatt class laser pulse onto a micron-size spherical hydrogen cluster, a crescent-shaped collisionless shock is launched at the laser-irradiated hemisphere and propagates inward. The shock converges at the sphere center in concurrence with the onset of the RIT, thereby allowing the proton bunch to be pushed out from the shock surface in the laser propagation direction. The proton bunch experiences further acceleration both inside and outside of the cluster to finally exhibit a quasimonoenergetic spectral peak around 300 MeV while maintaining a narrow energy spread (~10%) and a small half-divergence angle (~5°) via the effect of the RIT. This mechanism works for finite ranges of parameters with threshold values concerning the laser peak intensity and the cluster radius, resulting from the synchronization of the multiple processes in a self-consistent manner. The present scheme utilizing the internal and external degrees of freedom ascribed to the spherical cluster leads to the proton bunch alternative to the plain target, which allows the operation with a high repetition rate and impurity free.
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Global Gyrokinetic Simulation of Linear Micro-Instability Using Parameters Referring to HL-2A Plasma with Ion Transport Barrier
Z. Qin, K. Imadera, J. Q. Li and Y. Kishimoto

We study linear micro-instabilities using parameters referring to HL-2A plasma with ion Internal Transport Barrier (ITB) by means of the global toroidal gyrokinetic code GKNET including kinetic electron dynamics. It is found that a type of drift mode, which real frequency is low and changes the sign from electron diamagnetic direction to that of ion continuously as the poloidal wavenumber increases, dominates plasmas with peaked density profile while with relatively flat ion/electron temperature profiles. The instability is found to be sensitive to the perpendicular electron temperature, similar to the standard trapped electron mode, which is consistent with the observation of ion-ITB collapse after ECRH in the HL-2A experiment.
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Micron-size hydrogen cluster target for laser-driven proton acceleration
S. Jinno, M. Kanasaki, M. Uno, R. Matsui, M. Uesaka, Y. Kishimoto and Y. Fukuda

As a new laser-driven ion acceleration technique, we proposed a way to produce impurity-free, highly reproducible, and robust proton beams exceeding 100 MeV using a Coulomb explosion of micron-size hydrogen clusters. In this study, micron-size hydrogen clusters were generated by expanding the cooled high-pressure hydrogen gas into a vacuum via a conical nozzle connected to a solenoid valve cooled by a mechanical cryostat. The size distributions of the hydrogen clusters were evaluated by measuring the angular distribution of laser light scattered from the clusters. The data were analyzed mathematically based on the Mie scattering theory combined with the Tikhonov regularization method. The maximum size of the hydrogen cluster at 25 K and 6?MPa in the stagnation state was recognized to be 2.15±0.10 μm. The mean cluster size decreased with increasing temperature, and was found to be much larger than that given by Hagena’s formula. This discrepancy suggests that the micron-size hydrogen clusters were formed by the atomization (spallation) of the liquid or supercritical fluid phase of hydrogen. In addition, the density profiles of the gas phase were evaluated for 25 to 80 K at 6 MPa using a Nomarski interferometer. Based on the measurement results and the equation of state for hydrogen, the cluster mass fraction was obtained. 3D particles-in-cell (PIC) simulations concerning the interaction processes of micron-size hydrogen clusters with high power laser pulses predicted the generation of protons exceeding 100 MeV and accelerating in a laser propagation direction via an anisotropic Coulomb explosion mechanism, thus demonstrating a future candidate in laser-driven proton sources for upcoming multi-petawatt lasers.
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A mechanism for the formation and sustainment of the self-organized global profile and E×B staircase in tokamak plasmas
W. Wang, Y. Kishimoto, K. Imadera, J. Q. Li and Z. X. Wang

The mechanism for the formation and sustainment of a self-organized global profile and the ‘E×B staircase’ are investigated through simulations of a flux-driven ion temperature gradient (ITG) turbulence based on GKNET, a 5D global gyrokinetic code. The staircase is found to be initiated from the radially extended ITG mode structures with nearly up?down symmetry during the saturation phase, and is established as it evolves into a quasi-steady turbulence, leading to a self-organized global temperature profile and to meso-scale isomorphic profiles of the radial electric field and the temperature gradient. It is found that the quasi-regular E×B shear flow pattern is primarily originated from an even-symmetrical zonal flow produced by the extended ITG mode, which flow pattern exhibits an in-phase relation with the mean flow variation induced by the temperature relaxation. Consequently, the staircase is initiated through the profiles of total electric field and temperature gradient with a self-organized manner. Since the sign of E×B shear flow at the central part are opposite to that at both edges, it disintegrates the ITG mode into smaller scale eddies. Meanwhile, smaller scale eddies tend to be aligned radially by spontaneous phase matching, which can provide the growth of mode amplitude and the formation of radially extended mode structures, leading to the bursty heat transport. This process is repeated quasi-periodically, sustaining self-organized structures and the E×B staircase. Moreover, the equilibrium mean field is found to be of specific importance in causing the structures and dynamics from meso- to macro scales in toroidal plasmas.
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Multi-phase ionization dynamics of carbon thin film irradiated by high power short pulse laser
Daiki Kawahito and Yasuaki Kishimoto

The ionization dynamics of a carbon thin film irradiated by a high power short pulse laser in the range of 10^19-20 W/cm^2 are studied using the extended particle-based integrated code (EPIC), which includes atomic and collisional processes. Two types of ionization dynamics exhibiting different spatio-temporal structures are found to predominantly regulate the process, and arise depending on the laser amplitude. The first is a fast convective propagation for charge states up to C^4+, which keeps a steep ionization front. The velocity of the front is of the order of the speed of light. The front formation results from the localized longitudinal electrostatic field and associated field ionization, which in turn propagates inside the film. This convective propagation is triggered when the laser field becomes high enough that electron bunches accelerated by the laser ponderomotive force reach relativistic energies and penetrate inside the film across the surface. The second dynamics is a fast non-diffusive propagation of ionization showing a long plasma density scale length for C^5+ and C^6+. This process results predominantly from electron impact ionization by high energy electron bunches successively produced by the laser. These electron bunches also excite wake fields that propagate inside the film and contribute to ionizing the film to higher charge states, i.e., C^5+ and C^6+, especially near the front surface. The effect of field ionization loss, which sensitively influences the ionization dynamics in the relatively low laser power regime, is also discussed.
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Characterization of micron-size hydrogen clusters using Mie scattering
S. Jinno, H. Tanaka, R. Matsui, M. Kanasaki, H. Sakaki, M. Kando, K. Kondo, A. Sugiyama, M. Uesaka, Y. Kishimoto and Y. Fukuda

Hydrogen clusters with diameters of a few micrometer range, composed of 108-10 hydrogen molecules, have been produced for the first time in an expansion of supercooled, high-pressure hydrogen gas into a vacuum through a conical nozzle connected to a cryogenic pulsed solenoid valve. The size distribution of the clusters has been evaluated by measuring the angular distribution of laser light scattered from the clusters. The data were analyzed based on the Mie scattering theory combined with the Tikhonov regularization method including the instrumental functions, the validity of which was assessed by performing a calibration study using a reference target consisting of standard micro-particles with two diferent sizes. The size distribution of the clusters was found discrete peaked at 0.33±0.03, 0.65±0.05, 0.81±0.06, 1.40±0.06 and 2.00±0.13 μm in diameter. The highly reproducible and impurity-free nature of the micron-size hydrogen clusters can be a promising target for laser-driven multi-MeV proton sources with the currently available high power lasers.
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Development of a new zonal flow equation solver by diagonalization and its application in non-circular cross-section tokamak plasmas
Kevin Obrejan, Kenji Imadera, Jiquan Li and Yasuaki Kishimoto

A toroidal gyrokinetic full-f code GKNET (GyroKinetic Numerical Experimental Tokamak) with field solver in real space has been developed recently to simulate micro-turbulence dynamics in the circular cross-section tokamak plasmas (Obrejan et al., 2015). In this work, we introduce a new high accuracy Zonal Flow (ZF) equation solver which makes use of a parametrisation of the D-shaped magnetic flux surfaces to diagonalise the ZF equation. In addition to being more rigorous near the magnetic axis of the poloidal plane compared to methods based on local approximations, the ZF solver here allows to properly take into account the shape of magnetic flux surfaces independently of the coordinate system used in the rest of the code. The upgraded GKNET code is applied to study the collisionless damping of the Geodesic Acoustic Modes (GAMs) in elliptic and both positive and negative D-shaped magnetic configurations. We found that in addition to the influence of elongation, triangularity is effective in increasing the damping rate of GAMs, independently of the sign of the triangularity.
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Theory on Bright and Dark Soliton formation in Strongly Magnetized Plasmas
Wu Feng, Jiquan Li and Yasuaki Kishimoto

The existence and properties of bright and dark solitons in strongly magnetized warm plasmas are investigated analytically. These solitons are solutions to a four-dimensional Hamiltonian system with zero and non-zero boundary conditions. Based on the dynamical systems theory, the parametric domains of magnetic field and soliton frequency for the existence of bright and dark solitons in both cold and warm plasmas are identified. It is found that the temperature effects play an important role in determining the parametric domains and properties of the solitons. Specifically, the temperature effects make it possible for the existence of multi-hump dark solitons and remove the constraint on magnetic field and soliton frequency caused by the non-negative condition of the density profile. The numerical integration of the soliton equations shows that the bright soliton amplitude increases with magnetic field while the dark soliton amplitude decreases with it. For both bright and dark solitons, the temperature effects suppress the soliton amplitude.
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Laser propagation and soliton generation in strongly magnetized plasmas
Wu Feng, Jiquan Li and Yasuaki Kishimoto

The propagation characteristics of various laser modes with different polarization, as well as the soliton generation in strongly magnetized plasmas are studied numerically through one-dimensional (1D) particle-in-cell (PIC) simulations and analytically by solving the laser wave equation. PIC simulations show that the laser heating efficiency substantially depends on the magnetic field strength, the propagation modes of the laser pulse and their intensities. Generally, large amplitude laser can efficiently heat the plasma with strong magnetic field. Theoretical analyses on the linear propagation of the laser pulse in both under-dense and over-dense magnetized plasmas are well confirmed by the numerical observations. Most interestingly, it is found that a standing or moving soliton with frequency lower than the laser frequency is generated in certain magnetic field strength and laser intensity range, which can greatly enhance the laser heating efficiency. The range of magnetic field strength for the right-hand circularly polarized (RCP) soliton formation with high and low frequencies is identified by solving the solitonequations including the contribution of ion's motion and the finite temperature effects under the quasi-neutral approximation. In the limit of immobile ions, the RCP soliton tends to be peaked and stronger as the magnetic field increases, while the enhanced soliton becomes broader as the temperature increases. These findings in 1D model are well validated by 2D simulations.
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Development of a global toroidal gyrokinetic Vlasov code with new real space field solver
Kevin Obrejan, Kenji Imadera, Jiquan Li and Yasuaki Kishimoto

This work introduces a new full-f toroidal gyrokinetic (GK) Vlasov simulation code that uses a real space field solver. This solver enables us to compute the gyro-averaging operators in real space to allow proper treatment of finite Larmor radius (FLR) effects without requiring any particular hypothesis and in any magnetic field configuration (X-point, D-shaped etc). The code was well verified through benchmark tests such as toroidal Ion Temperature Gradient (ITG) instability and collisionless damping of zonal flow.
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Zonal flow dynamics in the double tearing mode with antisymmetric shear flows
Aohua Mao, Jiquan Li, Jinyuan Liu and Yasuaki Kishimoto

The generation dynamics and the structural characteristics of zonal flows are investigated in the double tearing mode (DTM) with antisymmetric shear flows. Two kinds of zonal flow oscillations are revealed based on reduced resistive magnetohydrodynamics simulations, which depend on the shear flow amplitudes corresponding to different DTM eigen mode states, elaborated by Mao et al. [Phys. Plasmas 20, 022114 (2013)]. For the weak shear flows below an amplitude threshold, v_c , at which two DTM eigen states with antisymmetric or symmetric magnetic island structure are degenerated, the zonal flows grow oscillatorily in the Rutherford regime during the nonlinear evolution of the DTMs. It is identified that the oscillation mechanism results from the nonlinear interaction between the distorted islands and the zonal flows through the modification of shear flows. However, for the medium shear flows above vc but below the critical threshold of the Kelvin-Helmholtz instability, an oscillatory growing zonal flow occurs in the linear phase of the DTM evolution. It is demonstrated that the zonal flow oscillation originates from the three-wave mode coupling or a modulation instability pumped by two DTM eigen modes with the same frequency but opposite propagating direction. With the shear flows increasing, the amplitude of zonal flow oscillation increases first and then decreases, whilst the oscillation frequency as twice of the Doppler frequency shift increases. Furthermore, impacts of the oscillatory zonal flows on the nonlinear evolution of DTM islands and the global reconnection are also discussed briefly.
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Nonlinear interaction dynamics between the double tearing mode and the Kelvin-Helmholtz instability
Aohua Mao, Jiquan Li, Jinyuan Liu and Yasuaki Kishimoto

The nonlinear evolution of the double tearing mode (DTM) in the presence of shear flows is numerically simulated based on a reduced magnetohydrodynamics (MHD) model in slab geometry. The focus is on the case with strong shear flow for it the Kelvin-Helmholtz (KH) mode, characterized by electromagnetic fluctuations, is robustly unstable besides the DTM. Simulations exhibit a complex interaction process between two instabilities. Particularly, in a turbulent background dominated by the KH instability,a secondary KH-tearing mode is identified which is excited due to the generation of the zonal flow.
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On the abrupt growth dynamics of nonlinear resistive tearing mode and the viscosity effects
Ahamad Ali, Jiquan Li and Yasuaki Kishimoto

The nonlinear evolution of the resistive tearing mode exhibits an abrupt growth after an X-point collapse once the magnetic island exceeds a certain critical width Δ'w_c for large instability parameter Δ' , leading to a current sheet formation [N. F. Loureiro et al., Phys. Rev. Lett. 95, 235003 (2005)]. In this work, we investigate the underlying mechanism of the X-point collapse as well as the current sheet formation including the viscosity effects, based on a secondary instability analysis. The secondary instability is excited due to the quasilinear current modification by the zonal current. In particular, it is identified that the current peaking effect is plausibly responsible for the onset of the X-point collapse and the current sheet formation, leading to the explosive growth of reconnected flux. In the presence of finite viscosity, the Δ'w_c scaling with the resistivity gets modified. A transition behavior is revealed at Pr〜1 for the viscosity dependence of Δ'w_c and the linear tearing instability. However, the explosive growth seems to be independent of the viscosity in the magnetic Prandtl number Pr<1 regime, while large viscosity plays a strong dissipation role.
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Viscosity Effects on Explosive Growth Dynamics of the Nonlinear Resistive Tearing Mode
Ahamad Ali, Jiquan Li and Yasuaki Kishimoto

A collapse of the X-point occurs above a critical island width, Δ'w_c, in the resistive tearing mode for large instability parameter, Δ', leading to current sheet formation [N.F. Loureiro et al. Phys. Rev. Lett. 95, 235003 (2005)]. In this study, we analyze this problem by including viscosity effects on the onset of the X-point collapse and the explosive nonlinear growth dynamics of the reconnected flux. While explosive growth seems to be independent of viscosity in the magnetic Prandtl number regime Pr < 1, a transition behavior is revealed at Pr〜1 for the viscosity dependence of Δ'w_c, for the X-point collapse as well as the linear tearing instability. A secondary instability analysis, which included quasi-linear modifications of the equilibrium current profile due to the zonal current, shows that current peaking is plausibly responsible for the onset of the X-point collapse and the explosive growth of reconnected flux, which leads to the current sheet formation.
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Spatial localization of resistive drift wave structure in tokamak edge plasmas with an embedded magnetic island
Shilin Hu, Jiquan Li, Hongpeng Qu and Yasuaki Kishimoto

Resistive drift wave instability is investigated numerically in tokamak edge plasma confined by sheared slab magnetic field geometry with an embedded magnetic island. The focus is on the structural characteristics of eigenmode inside the island, where the density profile tends to be flattened. A transition of the dominant eigenmode occurs around a critical island width w_c. For thin islands with a width below w_c, two global long wavelength eigenmodes with approximately the same growth rate but different eigenfrequency are excited, which are stabilized by the magnetic island through two-dimensional mode coupling in both x and y (corresponding to radial and poloidal in tokamak) directions. On the other hand, a short wavelength eigenmode, which is destabilized by thick islands with a width above w_c, dominates the edge fluctuation, showing a prominent structural localization in the region between the X-point and the O-point of the magnetic island. The main destabilization mechanism is identified as the mode coupling in the y direction, which is similar to the so-called toroidal coupling in tokamak plasmas. These three eigenmodes may coexist in the drift wave fluctuation for the island with a width around w c . It is demonstrated that the structural localization results mainly from the quasilinear flattening of density profile inside the magnetic island.
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Nonlinear mutual destabilization of the tearing mode and ion temperature gradient mode
Z. Q. Hu, Z. X. Wang, L. Wei, Jiquan Li and Yasuaki Kishimoto

Multiscale interactions between the tearing mode (TM) and ion temperature gradient (ITG) turbulence are studied numerically using a self-consistent gyrofluid model in slab geometry. It is found that the multiscale system goes through five distinct phases and is then saturated in a dynamic quasi-steady state. During the nonlinear evolution, the macroscale TM and the microscale ITG turbulence can mutually destabilize each other. On the one hand, the fluctuation level of the turbulence is greatly raised when the magnetic island grows beyond a threshold. The contributions of different scale fluctuations to heat conductivity are calculated. Although the macroscale long wavelength TM plays a dominant role in inducing heat transport in comparison with micro turbulence, the secondary harmonics of the TM have a considerable effect on causing heat pinch. On the other hand, the island growth is significantly enhanced through increasing the ITG as the island width increases above a critical value or the island propagating velocity is reduced below a critical value. The underlying mechanisms of the mutual destabilizations are identified. In addition, the generation of zonal flows and the associated turbulent transport in the multiscale interaction process are analysed in detail.
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Response of microscale turbulence and transport to the evolution of resistive magnetohydrodynamic magnetic island
Jiquan Li, Y. Kishimoto and Z. X. Wang

Nonlinear evolution of microscale turbulence interacting with a naturally growing MHD magnetic island is simulated based on a Landau-fluid model. Here, we report on a new short wavelength magnetic-island-induced ion temperature gradient (ITG) instability triggered by a critical threshold of magnetic island width in multiscale turbulence, which is referred to as sw-MITG mode. The sw-MITG mode is characterized by a substantially low stability threshold and a global structure propagating along the ion diamagnetic drift direction. Its generation results from the response of microscale fluctuations to turbulent cross-field heat transport associated with increasing boundary layer width about the island separatrix. An intermittency of heat transport is caused by the sw-MITG mode interacting with dynamical magnetic island and microturbulence.
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Higher-Order Nonlocal Effects of a Relativistic Ponderomotive Force in High-Intensity Laser Fields
Natsumi Iwata and Yasuaki Kishimoto

We have developed a new formula for a relativistic ponderomotive force of transversely localized laser fields based on the noncanonical Lie perturbation method by finding proper coordinates and gauges in the variational principle. The formula involves new terms represented by second and third spatial derivatives of the field amplitude, so that the ponderomotive force depends not only on the local field gradient, but also on the curvature and its variation. The formula is then applicable to a regime in which the conventional formula is hardly applied such that nonlocal and/or global extent of the field profile becomes important. The result can provide a theoretical basis for describing nonlinear laser-plasma interaction including such nonlocal effects, which is examined via particle-in-cell simulation of laser propagation in a plasma with a super Gaussian transverse field profile.
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The effect of weak collisionality on damped modes and its contribution to linear mode coupling in gyrokinetic simulation
Paul P. Hilscher, Kenji Imadera, Jiquan Li and Yasuaki Kishimoto

We revisit the characteristics of stable, damped modes originating from the Landau damping by employing a discretized gyrokinetic Vlasov simulation and also eigenvalue analysis in an unsheared slab geometry. By comparing results between gyrokinetic simulation and an eigenvalue analysis, we found that there exists a critical collisionality at which the Case-van Kampen (CvK) modes are damped down to the analytically estimated Landau damping rate and an eigenmode consistent with Landau's theory emerges. Consequently, the recurrence phenomenon disappears so that the Landau damping can be properly reproduced. The critical collisionality depends on the resolution in velocity space; i.e., a higher (lower) resolution requires a lower (higher) collisionality, while tends to zero as Δv→0. It is found through a reduced model that even in the collisionless case with marginally stable CvK modes, the linear mode coupling between unstable and stable/damped components through a tertiary mode and the resultant energy transfer can be properly calculated such that the stable/damped mode persists as an eigenstate.
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Role of Stable Modes in the ITG-Driven Instability in a Mode-Coupled System
Paul P. Hilscher, Kenji Imadera, Jiquan Li and Yasuaki Kishimoto

Kinetic damping in linear gyrokinetic (GK) Vlasov simulations is found to exhibit a bifurcation at the collisionality βc = βc*, above which, i.e. βc > βc*, the damping is represented by a Landau eigenmode in velocity space, while below which, i.e. βc < βc*, by the phase mixing of a finite number of marginally stable, discretized Case-van Kampen eigenmodes. The latter causes a recurrence that restricts the damping and then the energy transfer from wave to particles within a finite recurrence time. In order to address whether the stabilization effect due to such stable damped modes on unstable modes via mode coupling can be evaluated in long timescale GK simulations, we introduced a triad model consisting of stable and unstable modes incorporated with a tertiary vortex flow. We identified βc* numerically and found that the stabilization effect works properly beyond the recurrence time even in the phase mixing regime across βc = βc*.
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Gyrokinetic Simulations of Short-Wavelength ITG Instability in the Presence of a Static Magnetic Island
Paul P. Hilscher, Kenji Imadera, Jiquan Li and Yasuaki Kishimoto

The ion-temperature-gradient (ITG) mode instability in sheared slab geometry in the presence of a mesoscale magnetic island is investigated with a focus on the short-wavelength regime. We found that a static magnetic island causes radial and poloidal modes to couple and therefore plays a stabilizing role by allowing energy transfer from unstable modes to stable modes. However, for large island widths, the short-wavelength ITG mode becomes strongly destabilized and tends to dominate over the standard ITG mode. A reduced model is proposed in this paper to understand this destabilization mechanism.
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On the nonlocal properties of relativistic ponderomotive force
Natsumi Iwata and Yasuaki Kishimoto

A theory of relativistic ponderomotive force of transversely localized laser fields is presented by taking into account the nonlocal effects that correspond to higher order terms of the expansion parameter e=l/L, i.e., the ratio between particle excursion length and scale length of the field amplitude gradient, while the existing local theory is the first order of e. As a method for preserving the Hamiltonian structure up to higher orders, we employ the variational principle in noncanonical phase space coordinates incorporated with the Lie transformation. By finding noncanonical coordinates and gauges, we obtain a new formula for the ponderomotive force that involves new terms in the third order represented by the second and third spatial derivatives. The force then depends not only on the local field gradient but also on the curvature and its variation which represent the effects of higher-order nonlocal particle motion. The higher-order terms are found to be subject to the symmetry of the field structure. The obtained formula is accessible to the regime in which the higher derivatives of the field amplitude regulate the interaction. We have applied the formula to laser fields exhibiting flat-top super Gaussian and concave hollow transverse structures which are effective in maintaining the long time scale interaction. The associated nonlocal effects are found to play a key role in determining the interactions. Comparison with the direct integration of the particle orbit demonstrates the validity of the derived formula.
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Relativistic Ponderomotive Force Including Higher Order Nonlocal Effects in High Intensity Laser Fields
Natsumi Iwata and Yasuaki Kishimoto

We have applied the theory of the nonlocal ponderomotive force which we derived recently using the noncanonical Lie perturbation approach to investigate a long time scale particle motion in a super Gaussian laser beam. In such a flat-top beam profile, the local field gradient is diminished near the axis, so that the conventional ponderomotive formula is hardly applied. Numerical analyses of the interaction time and its dependence on the initial position and momentum of particles show that the nonlocal effect of the ponderomotive force, which is associated with higher order spatial derivatives, regulates the dynamics predominantly and sensitively.
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Nonlocal Ponderomotive Force in a Super Gaussian Laser Beam and the Conditions for Long Time Scale Interaction
Natsumi Iwata and Yasuaki Kishimoto

Based on the noncanonical Lie perturbation theory, we derived a new formula for relativistic ponderomotive force in a transversely localized laser field, which is accessible to the regime where the conventional formula described in terms of the local field gradient can hardly be applied. The formula involves new terms represented by second and third spatial derivatives; therefore, the force depends not only on the local field gradient, but also on the curvature and its variation. A physical explanation for these terms is given.
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Stability of Double Tearing Mode in the Presence of Shear Flows
Aohua Mao, Jiquan Li, Yasuaki Kishimoto and Jinyuan Liu

The stability of two eigen states of double tearing mode (DTM) with symmetric or antisymmetric islands in the presence of shear flows is numerically simulated based on a reduced MHD model in slab geometry. For given antisymmetric flow profile, a degenerated state is observed at a critical flow amplitude vc. Below vc, the shear flow stabilizes the DTM with antisymmetric islands and destabilizes the other one through distorting the magnetic flux mainly governed by the global effect of flow profile. Above vc, the degenerated state bifurcates into two eigen states with the same growth rate but opposed propagating direction. These two eigen modes show single tearing mode structure due to one of two islands is prevented by the Alfven resonance (AR). However, the AR can destabilize the DTMs through enhancing the inflow to the X-point of the remaining island, then competing with the stabilization of local flow shear, leading to distinctive features of DTM eigen states.
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Eigenmode characteristics of the double tearing mode in the presence of shear flows
Aohua Mao, Jiquan Li, Yasuaki Kishimoto and Jinyuan Liu

The double tearing mode (DTM) is characterized by two eigen states with antisymmetric or symmetric magnetic island structure, referred to as the even or odd DTM. In this work, we systematically revisit the DTM instabilities in the presence of an antisymmetric shear flow with a focus on eigenmode characteristics as well as the stabilization or destabilization mechanism in a wide parameter region. Both initial value simulation and eigenvalue analysis are performed based on reduced resistive MHD model in slab geometry. A degenerated eigen state is found at a critical flow amplitude vc. The even (or odd) DTM is stabilized (or destabilized) by weak shear flow below vc through the distortion of magnetic islands mainly due to the global effect of shear flow rather than the local flow shear. The distortion can be quantified by the phase angles of the perturbed flux, showing a perfect correspondence to the growth rates. As the shear flow increases above vc, the degenerated eigen state bifurcates into two eigen modes with the same growth rate but opposite propagating direction, resulting in an oscillatory growth of fluctuation energy. It is identified that two eigen modes show the single tearing mode structure due to the Alfven resonance (AR) occurring on one current sheet. Most importantly, the AR can destabilize the DTMs through enhancing the plasma flow exerting on the remaining island. Meanwhile, the local flow shear plays a remarkable stabilizing role in this region. In addition, the eigenmode characteristic of the electromagnetic Kelvin-Helmholtz instability is also discussed.
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Small-scale dynamo action in multi-scale magnetohydrodynamic and micro-turbulence
Jiquan Li and Yasuaki Kishimoto

Nonlinear interplay between resistive magnetohydrodynamic (MHD) magnetic island and drift wave micro-turbulence is investigated using direct Landau-fluid simulations. A twisting oscillation of magnetic island associated with the driving force of micro-turbulence is observed, which is referred to as magnetic island seesaw. In the initiating phase of the seesaw oscillation, small-scale current and magnetic field fluctuations increase dramatically while the magnetic induction grows exponentially at small-scales corresponding to the spatial scale of micro-turbulence, showing a small-scale dynamo action. A minimal model consisting of reduced MHD turbulence and a micro-instability is proposed to elucidate the underlying mechanism. It is identified that the island seesaw is driven by a net oscillatory electromagnetic torque, which results from small-scale dynamo-generated current and magnetic field. The dynamo mechanism may offer an important energy exchange channel between MHD and micro-turbulence in magnetic fusion plasmas.
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Nonlocal properties of the ponderomotive force in high intensity laser fields -An approach based on the noncanonical Lie perturbation theory-
Natsumi Iwata, Yasuaki Kishimoto and Kenji Imadera

In order to study the nonlocal particle dynamics in tightly focused laser fields in the order of wave length, we present a theoretical framework of relativistic ponderomotive force by using the noncanonical Lie perturbation theory based on the phase space Lagrangian formalism that keeps the Hamiltonian structure rigorously. Introducing a smallness parameter ε, the ratio of the particle excursion length to the scale length of the gradient of the laser field amplitude, we perform the perturbation analysis up to the second order ε2, which contain the effect of the field curvature, and obtain the oscillation center equation of motion averaged over the fast laser period. A betatron-like oscillation which corresponds to a confinement state of the particle in the laser field without suffering ejection due to the field curvature is analytically found.
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Role of Field and Electron Impact Ionization in Ionization Front Generated by an Intense Electron Beam
Susumu KATO, Yasuaki KISHIMOTO, Eiichi TAKAHASHI and Akira SASAKI

The interaction of an intense electron beam with a neutral background material is studied. The neutral material is ionized by the electrostatic field generated by the intense electron beam and electron impact ionization. The structure of the ionization front is analyzed using a one-dimensional model. The structure is determined primarily by electron impact ionization of the ionized background electrons. In addition, the field ionization contributes to the generation of the ionization front by increasing the density of the electron beam.
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Analysis of relativistic ponderomotive force and higher-order particle motion in a non-uniform laser field using the noncanonical Lie perturbation method
Natsumi Iwata, Yasuaki Kishimoto and Kenji Imadera

Relativistic particle motion in a non-uniform linearly polarized high intensity laser field is analyzed by using the noncanonical Lie perturbation method, which is based on the perturbation theory of the phase space Lagrangian. By introducing the smallness parameter ε as the ratio between the excursion length l and the scale length of the laser field amplitude L, the relativistic ponderomotive force and particle motion are derived up to the second order with respect to ε, which correspond to the nonlocal extension of the conventional ponderomotive force. Specifically, the particle is found to exhibit a betatron-like oscillation with long period characterized by the curvature of the laser field amplitude.
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Wave-number spectral characteristics of drift wave micro-turbulence with large-scale structures
Jiquan Li and Y. Kishimoto

Wave-number spectral characteristics of drift wave micro-turbulence with large-scale structures (LSSs) including zonal flows (ZFs) and Kelvin-Holmheltz (KH) mode are investigated based on three dimensional gyrofluid simulations in a slab geometry. The focus is on the property of the wave-number spectral scaling law of the ambient turbulence under the back reaction of the self-generated LSSs. A comparison of the spectral scaling laws between ion/electron temperature gradient (ITG/ETG) driven turbulences is presented. It is shown that the spectral scaling of the ITG turbulence with robust ZFs is fitted well by an exponential-law function in kx and a power-law one in ky. However, the ETG turbulence is characterized by a mixing Kolmogorov-like power-law and exponential-law scaling for both kx and ky spectra due to the ZFs and KH mode dynamics, with λ and β the slope index factors. The underlying physical mechanism is understood as the spectral scattering caused by the back-reaction of the LSSs on the ambient turbulence. These findings may provide helpful guideline to diagnose the plasma fluctuations and flow structures in experiments.
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Multi-scale Turbulence Simulation in Magnetic Fusion Plasma
Jiquan Li, K. Imadera, P. Hillscher, Y. Kishimoto and Z. X. Wang

Complex nonlinear interaction of multi-mode multi-scale electromagnetic (EM) turbulence in magnetic confinement fusion (MCF) plasmas is explored based on large-scale direct simulations. As a practical step towards a full-scale turbulence simulation, two numerical approaches suitable for different spectral regime are proposed with an emphasis on the interaction mechanism among different fluctuations and structures. A gyrofluid model is employed to simulate the nonlinear evolution of mixed resistive MHD and micro-turbulence at ion-scale, which may clarify the energy-exchange mechanism between electrostatic and EM fluctuations. As a result, a magnetic island seesaw oscillation and a short wavelength ion-scale drift wave are observed in multi-scale turbulence simulations with different equilibrium magnetic field. The underlying mechanism for the former one is identified as a cross-scale dynamo generation by the micro-turbulence through an elucidation of minimal modeling analysis. Meanwhile the latter one is induced by a wide magnetic island under the ion temperature island collapse. On the other hand, a strategic gyrokinetic simulation plan is presented to explore the micro-turbulence and transport property with both adiabatic kinetic ion and electron responses. A gyrokinetic Vlasov code is advanced to simulate the nonlinear interaction between ion and electron scale turbulence aiming at understanding the long time behaviors of turbulent transport in burning plasmas. The code parallelization is also introduced briefly.
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Critical parameters for the nonlinear destabilization of double tearing modes in reversed shear plasmas
M.Janvier, Y.Kishimoto and Jiquan Li

To investigate the nonlinear evolution of the double tearing mode (DTM) in reversed magnetic shear plasmas, characterized by a sudden and abrupt growth of the kinetic and magnetic energies, leading to full reconnection, we conduct a systematic study of the parameters based on the numerical resolution of the reduced magnetohydrodynamic equations in slab geometry. By introducing an instability parameter Δ′DTM , we reveal three regimes for the evolution of the DTM: (1) a linearly stable regime (0 < Δ′DTM < Δ′1 ), (2) a linearly unstable regime but leading to the saturation of magnetic islands (Δ′1 < Δ′DTM < Δ′2 ) and (3) a linearly unstable regime leading to full reconnection (Δ′2 < Δ′DTM ). The critical value Δ′2 delimiting regimes (2) and (3) corresponds to a critical island width w c above which the nonlinear destabilization is triggered. We successfully determine the critical threshold in (x s , k y ) space, which is fundamental for the prediction of explosive DTMs, as well as to understand the underlying mechanisms. Here, x s and k y , respectively the distance between the two rational surfaces and the unstable wavenumber, determine the free energy contained in the equilibrium system. Moreover, w c calculated at the trigger of regime (3) is found to be independent of resistivity, supporting the idea that the nonlinear destabilization results from a structure-driven instability.
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Theoretical Study of Particle Motion under High Intensity Laser-Plasma Interaction Aiming for High Energy Density Science
Natsumi Iwata, Yasuaki Kishimoto and Kenji Imadera

Being a high-quality and coherent energy source, ultra-short high power lasers have opened up attractive applications such as fast ignition-based laser fusion, which has been eagerly studied as one of the clean and abundant energy sources to replace fossil fuel. Furthermore, higher intensities of 1023-26 W/cm2 that will be achieved in the near future enable the exploration of an entirely new scientific regime called high energy density science. In these studies, it is strongly required to understand relativistic interaction between tightly-focused high intensity lasers and plasmas. Among the physics dominating such an interaction, the ponderomotive force (light pressure) plays an essential role. The force has been expressed in the form proportional to the laser field gradient, using the averaging method to the equation of motion. However, as the laser field is tightly focused, not only gradient but also higher-order structures such as field curvature become important. These higher-order effects are generally difficult to be precisely investigated applying the conventional averaging method. In order to investigate such a complicated particle motion in non-uniform laser fields, here, we apply the noncanonical Lie perturbation theory based on the phase space Lagrangian dynamics [1]. The method has been shown to be powerful in determining the relativistic particle dynamics in complex electromagnetic fields [2, 3]. As a result, we derived equations of motion describing the relativistic ponderomotive force including the effect of higher-order field structures. Moreover, we found an analytical solution corresponding to a betatron-like oscillation, by which the particle is confined to a finite radial region.
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Structure-driven nonlinear instability as the origin of the explosive reconnection dynamics resistive double tearing modes
M. Janvier, Y. Kishimoto and Jiquan Li

The onset of abrupt magnetic reconnection events, observed in the nonlinear evolution of double tearing modes (DTM), is investigated via reduced resistive magnetohydrodynamic simulations. We have identified the critical threshold for the parameters characterizing the linear DTM stability leading to the bifurcation to the explosive dynamics. A new type of secondary instability is discovered that is excited once the magnetic islands on each rational surface reach a critical structure characterized here by the width and the angle rating their triangularization. This new instability is an island structure-driven nonlinear instability, identified as the trigger of the subsequent nonlinear dynamics which couples flow and flux perturbations. This instability only weakly depends on resistivity.
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Role of the Pressure Force in the Explosive Dynamics of Magnetic Islands in Double Tearing Modes
M.Janvier, A.Ishizawa, Jiquan Li and Y.Kishimoto

The evolution of magnetic islands at two resonant surfaces during the development of a global tearing mode is investigated via numerical simulations of a reduced set of magneto-hydrodynamic equations in slab plasmas. The explosive dynamics of the islands resulting in an interchange follows a Rutherford-like regime, also referred to as a weakly coupled double tearing mode. It is found that the latent mechanism of this dynamics is the reduction of the total pressure around the opposite X-point and the abrupt growth is associated with an imbalance of the pressure around the islands. Once this imbalance is well established, each plasmoid is pushed to the opposite X-point, increasing the drive for the field merging. A feedback loop then takes place as the reconnection itself decreases the strength of the magnetic field between the tearing layers, i.e., reinforces the pressure imbalance. This loop accelerates reconnection, thus leading to the observed explosive growth.
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Nonlocal properties of the ponderomotive force in tightly focused high intensity laser fields
Natsumi Iwata, Yasuaki Kishimoto and Kenji Imadera

In recent years, ultra-short high-power lasers in the range of 1022 W/cm2 have been developed and opened up various applications such as fast ignition-based laser fusion, compact accelerators and high-intensity X-ray/neutron sources. In order to realize such high intensities, the reduction of the pulse width and/or the spot size is necessary. In such spatially localized laser fields, the ponderomotive force (light pressure) exists inevitably and plays an important role in the particle dynamics.
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Stabilization of ion temperature gradient driven instability by a vortex flow
Z. X. Wang, J. Q. Li, J.Q. Dong and Y. Kishimoto

Stabilization of ion temperature gradient (ITG) driven mode by a large-scale vortex flow is investigated using a gyrofluid model in slab geometry. Extending a recent work [ Z. X. Wang et al., Phys. Rev. Lett. 103, 015004 (2009) ], the focus in this work is put on the effect of magnetic shear. It is shown that the vortex flow can effectively stabilize the ITG mode by inducing both radial and poloidal mode couplings. Furthermore, decreasing magnetic shear is identified to weaken the stabilizing role of the vortex flow. The effects of the magnetic shear on the ITG mode structure and on the growth rate in the presence of various shear flows are obtained and the relevant mechanisms are discussed in detail
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Gyrofluid Simulation of Slab ITG Turbulence in Plasmas Including Pressure Profile Corrugation
Sho MIYATA, Jiquan LI, Kenji IMADERA and Yasuaki KISHIMOTO

Ion temperature gradient driven drift wave instability and turbulence are investigated based on a gyrofluid slab model in the presence of a pressure gradient corrugation (PPC). It is shown that the PPC cannot only stabilize or destabilize the ITG mode through local flattening or steepening of the radial pressure gradient, but most importantly also play a stabilizing role due to the global effect of the wave-type corrugation. The latter effect dominates in the highly corrugated cases and is identified to result from a nonlocal mode coupling in radial wave-number space, which scatters the spectra from unstable modes to high dissipation region. While the local stabilization/destabilization is stronger than the global stabilization in the cases with less corrugation, the global stabilization effect dominates the highly corrugated cases. Interestingly, it is found that the global stabilization of the PPC causes ion heat intermittency, which closely connects to the zonal flow dynamics
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Numerical Method for Eulerian Vlasov Simulation Based on Multi-Moment Scheme
Takafumi KAWANO, Kenji IMADERA, Jiquan LI and Yasuaki KISHIMOTO

A new scheme referred to as the multi-moment (MM) scheme is explored to develop a more reliable Vlasov code from the viewpoint of numerical properties. The MM scheme is based on the Eulerian approach, where spatial derivatives are evaluated by interpolation functions locally constructed by not only grid values but also 0th-, 1st-, and 2nd-order moment values between grids, which largely increases numerical accuracy and resolution. Through the Fourier analyses and benchmark tests of one-dimensional (1D) and 2D transport simulations, it is found that the MM scheme exhibits significantly smaller numerical dissipation and dispersion even near the Nyquist wave-number, and as a result, the MM scheme decreases the numerical cost. The MM scheme is also applied to a 1D Vlasov-Poisson simulation and we find that the scheme captures finer scale structure in velocity space compared to the conservative form of interpolated differential operator (IDO-CF) scheme, while also maintaining good energy conservation
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Remote collaboration system based on large scale simulation II
Akihiro Sugahara, Yasuaki Kishimoto

近年，理工学分野における大規模シミュレーションの重要性はますます高まっている．このような状況を受 け，我々は，大規模シミュレーションを中心に据え，地域的・分野的に分散した研究者が共同で研究を推進する システム"SIMON (SImulation MONitoring) system［" １］を開発している．本システムは，・EEXーパーコンピュータ上 で起動してい・驛Vミュレーションコード（クライアント）が，その実行中に，データ解析や可視化，Web 配信等 の依頼情報を外部計算機（サーバ）に送り，これを受けたサーバが依頼情報に従って自動的に処理を行うクライ アント・サーバモデルに基づくものである． 本論文では，システムのネットワーク接続における信頼性を高めるために，SSH のlogin shell を動的に構築 する方法や，パスワードを複数の暗号化によって変換する方法を導入し，セキュリティレベルの向上を図った． また，Web 上での効率的な解析環境を構築するため，可視化アプリケーションの持つ機能を目的に応じて階層化 する手法を考案した．そして，これらの機能を有した本システムを大規模シミュレーション研究に導入し，その 有効性・有用性を検証した．
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Stability Analysis of Relativistic Electron Beams in a Wiggler with Harmonic Gyro-Resonance Using the Noncanonical Lie Perturbation Method
Kenji IMADERA and Yasuaki KISHIMOTO

The non-canonical Lie perturbation method for analyzing relativistic electron beams in free electron lasers [Y. Kishimoto et al., Phys. Plasmas 2, 1316 (1995)] is extended to the case with harmonic gyro-resonance due to the coexistence of a focusing wiggler and an axial guiding field, which allow the maximum beam current to be increased. By using non-canonical guiding-center variables, we have solved the particle motion not only far from the harmonic gyro-resonance but also near the resonance. Far from the resonance, the maximum beam current is found to increase in proportion to (B_g/B_w)^2 (B_w and B_g are the strength of the wiggler and guiding fields, respectively). On the other hand, near the resonance, the beam is found to be confined in a finite radial region and then transmitted because of higher order secular perturbations.
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Cross-scale Dynamo Action in Multiscale Plasma Turbulence
Jiquan LI and Yasuaki KISHIMOTO

The interplay mechanism between electromagnetic (EM) and electrostatic (ES) turbulence is explored using direct gyrofluid simulations of mixed resistive magnetohydrodynamic (MHD) and ion-scale microinstability. With an elucidation based on a minimal model, we propose a new concept of cross-scale dynamo action induced by microturbulence as the mechanism responsible for the interaction between multiscale ES and EM turbulence. The dynamo appears as a novel magnetic island seesaw oscillation pivoting around the singular surface. This island seesaw mechanism may be applicable to relaxation of mode locking in tokamaks to mitigate major disruptions, suggesting a promising nonlinear approach to plasma control.
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Mechanism of Structure-Driven Nonlinear Instability of Double Tearing Mode in Reversed Magnetic Shear Plasmas
Miho JANVIER, Yasuaki KISHIMOTO, Jiquan LI

The trigger for the nonlinear destabilization of the double tearing mode (DTM), referred to as a structure-driven instability leading to explosive growth and subsequent collapse, is investigated. We use the reduced MHD equations that solve the evolution of perturbations from an equilibrium deformed by two-dimensional magnetic islands during the slow evolution of the quasi-steady nonlinear regime. By examining conditions near marginal stability (under which the explosive growth is not triggered), we have identified a new secondary instability that starts growing when the magnetic energy of the primary fluctuations associated with the islands reaches a critical level. The energy source of this instability is different from that of the linear DTM; it originates in the spatial deformation due to the DTM-driven magnetic islands and is responsible for the subsequent nonlinear destabilization. The growth rate of this secondary instability is found to be proportional to the magnetic energy, suggesting that it exhibits modulational characteristics.
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Analysis of Relativistic Particle Orbit in a Transversely Focused High-Power Laser Field by Using the Noncanonical Lie Perturbation Method
Natsumi IWATA, Kenji IMADERA and Yasuaki KISHIMOTO

A methodology describing the particle motion in a spatially localized high-power laser field in the relativistic regime is presented based on the noncanonical Lie perturbation method, which is comprehensive compared with those based on the conventional averaging method to the equation of motion. We successfully derived the relativistic ponderomotive force in a laser field with a radial intensity gradient and the corresponding particle dynamics up to the first order with respect to the expansion parameter ε ? λ/L (= laser wavelength/scale length of the transverse laser amplitude). The longitudinal motion was found to be secular and characterized by a growing oscillation exhibiting a cubic dependence on the laser amplitude.
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Possible trigger mechanisms for the Double Tearing Mode nonlinear destabilization
Miho Janvier,Y. Kishimoto and Jiquan Li

Recently, advanced scenarios seems to be a promising key to continuous operation with fusion plasmas. However, those are limited by MHD instabilities such as the double tearing mode (DTM), which leads to the formation/interaction of magnetic islands along 2 rational surfaces. Calculations with intermediate DTM [1-2] show explosive dynamics from a quasi-steady nonlinear behavior. In the later stage, the energies increase much and the islands deform each other up to total reconnection. To understand the mechanisms leading to such phenomenon, we have conducted an instability analysis of the quasi-steady equilibrium resulting from the first nonlinear stage of the DTM [3] by numerically solving the linearized 2-field reduced MHD equations. In slab geometry, the new equilibrium with steady magnetic islands is found to be unstable. Further investigations near marginal stability (=no nonlinear destabilization), show that the growth rate of the resulting secondary instability is strongly dependent on the amplitude of the flux function, suggesting similar features as a modulational instability. This secondary instability evolution is discussed as a possible mechanism for the generation of strong flows arising in the nonlinear evolution of the DTM, leading to the explosive dynamics. [1] Y.Ishii \textit{et al.}, PRL, \textbf{89}, 205002 (2002) [2] Z.X.Wang \textit{et al.}, Phys. Plasmas, \textbf{15} 082109 (2008) [3] M.Janvier \textit{et al.}, \textit{to be pub.} JPFR (2010)
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Wave-number spectral scaling law of drift wave-zonal flow turbulence in gyrofluid simulations
Jiquan Li and Y. Kishimoto

Wave-number spectral characteristics of ion temperature gradient (ITG) turbulence are investigated based on three-dimensional gyrofluid simulation. The focus is on the back reaction of the self-generated zonal flows (ZFs) on the ambient turbulence through nonlinear mode coupling. Detailed spectral analyses evidently show that the radial wave-number spectra of the ITG-ZF turbulence is characterized by an exponential-law scaling, which is deformed from the usual Kolmogorov-like power law by the back reaction of the ZFs. These results are qualitatively in agreement with a theoretical prediction [ Gurcan et al., Phys. Rev. Lett. 102, 255002 (2009) ] and fairly match with the experimental observation of the density fluctuation spectrum [ Hennequin et al., Plasma Phys. Controlled Fusion 46, B121 (2004) ]. The generality of such spectral characteristics in drift wave turbulence with large-scale coherent structures is discussed.
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Global Profile Relaxation and Entropy Dynamics in Turbulent Transport
Kenji Imadera, Y. Kishimoto and Jiquan Li

A hierarchical entropy balance equation retaining the dynamics in the radial direction is introduced to study non-local turbulent transport and the associated global profile relaxation. It consists of first- and second-order equations that describe the entropy dynamics related to thermodynamics/fluid quantity and the corresponding micro-scale phase space fluctuations, respectively. Specifically, the second-order equation describes not only a local entropy production related to heat and density flux (i.e., zonal flow), but also the spatial convection of perturbed entropy. We investigated the entropy dynamics in ion-temperature-gradient driven turbulence based on a global gyrokinetic Vlasov simulation in slab geometry. Entropy convection plays an important role in the relaxation dynamics dominated by the avalanche process. A self-organized relaxed state is established, in which short-wavelength temperature corrugation, i.e., zonal pressure, is regulated by zonal flow shear.
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A numerical method for solving the Vlasov−Poisson equation based on the conservative IDO scheme
Kenji Imadera, Yasuaki Kishimoto, Daisuke Saito, Jiquan Li, Takayuki Utsumi

We have applied the conservative form of the Interpolated Differential Operator (IDO-CF) scheme in order to solve the Vlasov-Poisson equation, which is one of the multi-moment schemes. Through numerical tests of the nonlinear Landau damping and two-stream instability, we compared the present scheme with other schemes such as the Spline and CIP ones. We mainly investigated the conservation property of the L1-norm, energy, entropy and phase space area for each scheme, and demonstrated that the IDO-CF scheme is capable of performing stable long time scale simulation while maintaining high accuracy. The scheme is based on an Eulerian approach, and it can thus be directly used for Fokker-Planck, high dimensional Vlasov-Poisson and also guiding-center drift simulations, aiming at particular problems of plasma physics. The benchmark tests for such simulations have shown that the IDO-CF scheme is superior in keeping the conservation properties without causing serious phase error.
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Collisional Effects on Absorption and Energy Transport in a Dense Solid-Carbon Thin Film Irradiated by Subpicosecond Lasers
Mo CHEN, Daisuke SAITOU and Yasuaki Kishimoto

The collisional effects on the kinetics of interactions between a high-power subpicosecond laser and a solid-carbon thin film in a fast-ignition scenario are investigated by one-dimensional particle-in-cell simulations. Collisions are found to play an essential role in energy absorption and transport, compared to collisionless cases. In the collisional cases, the absorption at the heating edge, heat transport inside the thin film, and hot electron production are reduced in the early transient process.
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Finite frequency zonal flows in multi-scale plasma turbulence including resistive MHD and drift wave instabilities
Jiquan Li, Y. Kishimoto, Y. Kouduki, Z. X. Wang, M. Janvier

The evolution of multi-scale plasma turbulence including resistive MHD and micro-instabilities is studied based on a 5-field slab gyrofluid simulation aiming to understand complex nonlinear interactions and turbulent transport. It is observed that the spatial structure of the mixed-scale electromagnetic turbulence is characterized by a power-law scaling spectrum typical of MHD perturbations, but the spectral amplitude is enhanced by the micro-instability at all scales. A robust oscillatory zonal flow (ZF) with finite frequency is created in slab geometry for the first time due to the multi-scale interaction so that the ion heat transport is not efficiently suppressed. It is identified that the finite frequency ZF results from a net oscillatory electromagnetic torque, which is sustained by micro-instability through multi-scale nonlinear interaction.
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Global characteristics of zonal flows due to the effect of finite bandwidth in drift wave turbulence
K. Uzawa, Jiquan Li, and Y. Kishimoto

The spectral effect of the zonal flow (ZF) on its generation is investigated based on the Charney?Hasegawa?Mima turbulence model. It is found that the effect of finite ZF bandwidth qualitatively changes the characteristics of ZF instability. A spatially localized (namely, global) nonlinear ZF state with an enhanced, unique growth rate for all spectral components is created under a given turbulent fluctuation. It is identified that such state originates from the successive cross couplings among Fourier components of the ZF and turbulence spectra through the sideband modulation. Furthermore, it is observed that the growth rate of the global ZF is determined not only by the spectral distribution and amplitudes of turbulent pumps as usual, but also statistically by the turbulence structure, namely, their probabilistic initial phase factors. A ten-wave coupling model of the ZF modulation instability involving the essential effect of the ZF spectrum is developed to clarify the basic features of the global nonlinear ZF state.
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Generic Mechanism of Microturbulence Suppression by Vortex Flows
Z. X. Wang , J. Q. Li, J. Q. Dong,Y. Kishimoto

The interaction between two-dimensional vortex flows and microturbulence is studied numerically using gyrofluid simulations. It is shown that, qualitatively different from usual mean flows, vortex flows can dramatically suppress microturbulence even with weak flow shear. A generic suppression mechanism is identified as the multiplied effect of both radial and poloidal mode couplings, which induce the formation of a new global mode. Furthermore, an oscillatory zonal flow is found to form through interaction between the vortex flows and microturbulence.
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Magnetic-island-induced ion temperature gradient mode
Z. X. Wang,J. Q. Li,Y. Kishimoto,and J. Q. Dong

Characteristics of ion temperature gradient (ITG) instability in the presence of a magnetic island are investigated numerically using a gyrofluid model. It is shown that when the magnetic island is wide enough to produce a broad distribution of rational surfaces near the O-point region, the ITG perturbations at these rational surfaces form a radially global-type eigenmode with a fast growth rate, which is referred to as the magnetic-island-induced ITG mode. Moreover, the magnetic island also causes both radial and poloidal mode couplings, which play a stabilizing role.
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Gyrofluid simulation of ion-scale turbulence in tokamak plasmas
Jiquan Li and Y.Kishimoto

An improved three-field gyrofluid model is proposed to numerically simulate ion-scale turbulence in tokamak plasmas, which includes the nonlinear evolution of perturbed electrostatic potential, parallel ion velocity and ion pressure with adiabatic electron response. It is benchmarked through advancing a gyrofluid toroidal　global (GFT G) code as well as the local version (GFT L), with the emphasis of the collisionless　damping of zonal flows. The nonlinear equations are solved by using Fourierdecom　position in poloidal and toroidal directions and semi-implicit finite difference　method along radial direction. The numerical implementation is briefly explained, especially　on the periodic boundary condition in GFT L version. As a numerical test and　also practical application, the nonlinear excitation of geodesic acoustic mode (GAM), as well as its radial structure, is investigated in tokamak plasma turbulence.
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Role of secondary long wavelength structures in the saturation of electron temperature gradient driven turbulence
Jiquan Li and Y. Kishimoto

The dynamics of secondary long wavelength structures (LWSs) in electron temperature gradient (ETG) driven turbulence are investigated by performing gyrofluid simulations and modeling analyses in a slab geometry with an emphasis of the underlying nonlinear interaction processes. It is shown that the back-reaction of the secondary LWS on the ambient fluctuations essentially contributes to saturating ETG instability and limiting the electron transport. The LWS is nonlinearly generated mainly through the beating of the most unstable ETG modes, even a weak modulation instability. The back-reaction is identified as the enhanced stabilization of the ETG modes due to the streamer-type feature of the LWS, which dominantly produces a local poloidal mode coupling among unstable and highly damped spectral components to form a global mode, besides the suppression effect of the LWS due to the radial shearing decorrelation and/or the radial mode coupling. Finally, the correspondence between the LWS in the slab model and the quasimode observed in toroidal ETG simulation [Z. Lin et al., Phys. Plasmas 12, 056125 (2005)] and the importance of the nonlinear mode coupling in the multiscale turbulence interaction are discussed.
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Shear flows induced by nonlinear evolution of double tearing modes
Zheng-Xiong Wang, Xiaogang Wang, J. Q. Dong, Y. Kishimoto, and J. Q. Li

Shear flows induced by nonlinear evolution of double tearing modes are investigated in a resistive magnetohydrodynamic model with slab geometry. It is found that intensive and thin poloidal shear flow layers are generated in the magnetic island region driven by coupled reconnection process at both rational surfaces. The structure of the flow layers keeps evolving after the merging of magnetic separatrices and forms a few narrow vortices along the open field lines in the final stage of magnetic reconnection. The effects of the distance between both rational surfaces and the initial magnetic shear on the nonlinear evolution of the plasma flows are also taken into consideration and the relevant mechanism is discussed.
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Quasilinear analysis of the zonal flow back-reaction on ion-temperature-gradient mode turbulence
Johan Anderson, Jiquan Li, Yasuaki Kishimoto, Eun-jin Kim

There is strong evidence in favor of zonal flow suppression in the Ion-Temperature-Gradient (ITG) mode turbulence, specifically close to the linear stability threshold. The present Letter attempts to analytically calculate the effects of zonal flow suppression of the ITG turbulence by deriving a modified dispersion relation including the back-reaction of the zonal flows on the ITG turbulence based on the quasilinear theory. The results are manifested in a reduction of the linear growth rate and an increase in the effective linear ITG threshold.
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Global nature of zonal flow due to the finite band width
K. Uzawa, J.Q. Li, and Y. Kishimoto

The spectral effects of both micro-scale electron temperature gradient driven turbulence and zonal flow on the zonal flow generation are investigated theoretically and computationally based on the Hasegawa-Mima turbulence equation. As the minimum model describing the most primary spectral feature, we have developed an eight-wave interaction model which includes two sets of the conventional four-wave coupling systems with adjacent radial spectral difference of dkx. It is found that the zonal flow is characterized by a global nature with an enhancement of growth rate γq, namely, global zonal flow eigen-mode, which is attributed to the appearance of new cross mode couplings due to the finite band width of zonal flow. This is qualitatively different from the monochromatic character of zonal flow described in the conventional four-wave coupling model. Direct numerical simulations of the Hasegawa-Mima equation with a zonal flow spectral structure have clearly proven the analytical results by employing a rigorous spectral code. The calculations further show that the global zonal mode is not only governed by the spectral structure of pump waves, but also their phase relation.
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A. Model of GAM intermittency near critical gradient in toroidal plasmas
K. Miki, Y. Kishimoto, N. Miyato, and Jiquan Li

We have constructed a four-field minimal model that describes the growing intermittency of turbulence associated with the geodesic acoustic mode (GAM) observed in our toroidal Landau-fluid simulations [K Miki et al. 2007 Phys. Rev. Lett. 99, 145003]. The intermittent dynamics are well reproduced by the model for the reference parameters used in the simulation. The model can also reproduce characteristics of turbulent transport associated with the GAM, such as a single burst leading to a full quench of turbulence and also a steady state turbulence mixed with steady zonal flows and GAMs. Investigating the behaviour of the solution trajectories around the fixed points in four-dimensional phase space, we study the comprehensive properties of the model and identify the bifurcation property between Dimits shift and steady state turbulence regimes, which correspond to different eigen-states.
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Gyro-fluid simulation on the nonlinear excitation and radial structure of geodesic acoustic modes in ITG turbulence
J.Q. Li, Y. Kishimoto, N. Miyato, K. Miki, J. Anderson, and S. R. Shi

The nonlinear excitation and saturation mechanism of geodesic acoustic mode (GAM), as well as its radial structure, in tokamak plasmas are investigated by applying a newly well-benchmarked gyrofluid model. At first, an empirical closure relation for the conventional three-field gyrofluid modeling is presented for ion temperature gradient (ITG) fluctuations and the GAMs. The zonal flow damping is precisely examined by comparing with theoretical predictions and other kinetic calculations. Then, a local code and the global version are advanced to simulate the nonlinear excitation of the GAMs by ITG fluctuations through the Reynolds stress. It is found that the GAM instability can be nonlinearly excited under the competition between the nonlinear driving and the collisionless damping. The pump amplitude threshold of the GAM instability is higher than that of the zonal flow instability. Meanwhile, the unstable GAMs are mainly saturated by the intrinsic Landau damping, which is different from the stationary zonal flow counterpart. It is testified that the sound waves are damped fluctuations in ITG turbulence. Furthermore, the radial structure of the GAMs is shown as krρi ? 1.0, which is shorter than that of the pure zonal flows.
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Dynamics of turbulent transport dominated by the geodesic acoustic mode near the critical gradient regime
K. Miki, Y. Kishimoto, Jiquan Li, and N. Miyato

The effects of geodesic acoustic modes (GAMs) on the toroidal ion temperature gradient turbulence and associated transport near the critical gradient regime in tokamak plasma are investigated based on global Landau-fluid simulations and extended predator-prey modeling analyses. A new type of intermittent dynamics of transport accompanied with the emission and propagation of the GAMs, i.e., GAM intermittency [ K. Miki et al., Phys. Rev. Lett. 99, 145003 (2007)] , has been found. The intermittent bursts are triggered by the onset of spatially propagating GAMs when the turbulent energy exceeds a critical value. The GAMs suffer collisionless damping during the propagation and nonlocally transfer local turbulence energy to wide radial region. The stationary zonal flows gradually increase due to the accumulation of non-damped residual part over many periods of quasi-periodic intermittent bursts and eventually quench the turbulence, leading to a nonlinear upshift of the linear critical gradient; namely, the Dimits shift. This process is categorized as a new class of transient dynamics, referred to as growing intermittency. The Dimits shift is found to be established through this dynamical process. An extended minimal predator-prey model with collisionless damping of the GAMs is proposed, which qualitatively reproduce the main features of the growing intermittency and approximately predict its various time scales observed in the simulations.
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Remote collaboration system based on large scale simulation
Y. Kishimoto, A. Sugahara and J.Q. Li

Large scale simulation using super-computer, which generally requires long CPU time and produces large amount of data, has been extensively studied as a third pillar in various advanced science fields in parallel to theory and experiment. Such a simulation is expected to lead new scientific discoveries through elucidation of various complex phenomena, which are hardly identified only by conventional theoretical and experimental approaches. In order to assist such large simulation studies for which many collaborators working at geographically different places participate and contribute, we have developed a unique remote collaboration system, referred to as SIMON (simulation monitoring system), which is based on client?server system control introducing an idea of up-date processing, contrary to that of widely used post-processing. As a key ingredient, we have developed a trigger method, which transmits various requests for the up-date processing from the simulation (client) running on a super-computer to a workstation (server). Namely, the simulation running on a super-computer actively controls the timing of up-date processing. The server that has received the requests from the ongoing simulation such as data transfer, data analyses, and visualizations, etc. starts operations according to the requests during the simulation. The server makes the latest results available to web browsers, so that the collaborators can monitor the results at any place and time in the world. By applying the system to a specific simulation project of laser?matter interaction, we have confirmed that the system works well and plays an important role as a collaboration platform on which many collaborators work with one another.
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Effect of Wave-Type Mean Flow on the Modulational Process of Zonal Flow Instability
K. Uzawa, Y. Kishimoto and J. Q. Li

The effects of an external mean flow on the modulational instability process of zonal flow in drift wave turbulence are theoretically studied based on Hasegawa-Mima (HM) turbulence model. Based on the coherent mode coupling approach, a dispersion relation of the zonal flow instability involving the external mean flow with a wave-type characterized by the amplitude |Φ f |, radial wave number k f , and frequency ω f is derived. As an example, the zonal flow driven by ion temperature gradient (ITG) turbulence is sampled as the mean flow acting on the modulational process of zonal flow instability in electron temperature gradient (ETG) turbulence. It is shown that the growth rate of the zonal flow, Yq, is suppressed by the mean flow with a fitting relation γ q ? γ q0 -α|Φ f | 2 k 2 f , where γ q0 is the growth rate of the zonal flow in the absence of mean flow and a is a positive numerical constant. This formula is applicable to a strong shearing regime where the zonal flow instability is stabilized. The suppression mechanism is investigated and found to originate from frequency mismatch due to an increase of the real frequency of zonal flow |Ω q |
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Spectral effect of zonal flows and enhanced growth rate
K. Uzawa, J. Q. Li and Y. Kishimoto

The effect of the spectrum of the radial wave number of zonal flows on zonal flow generation is theoretically investigated using the Hasegawa-Mima turbulence model by representing the spectrum by means of two monochromatic waves. Based on this method, we explored a ten-wave coupling model of modulational instability. We found that the zonal flow generation is qualitatively different in cases with and without such a spectral effect, exhibiting the enhancement of the growth rate. This originates from the coupling property of the new zonal flow eigenmode equation system. We refer to this state as a coupled zonal flows eigenmode, which leads to a spatial modulation of zonal flows affected by the turbulence structure.
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大規模シミュレーションを中心に据えた遠隔研究システム
菅原章博、岸本泰明

多様化した最先端研究分野においてシミュレーションの果す役割は益々重要になって来てい る。そこでは、超並列計算機を中心としたハードウェアと共に、複雑化した大規模シミュレーシ ョン結果・ﾌ円滑な解析・評価や広範囲の学術分野・技術分野との迅速な討議・情報交換を行うシ ステムの存在が課題解決の鍵をにぎる。ここでは、大規模シミュレーションを中心に据え、イン ターネットを駆使することにより外国機関も含めた広範囲の研究者と迅速な情報交換や共同研究 を行うことを目的としたシステム（SIMON）の開発について紹介する。
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