The analytical treatment of nonlinear evolution of the shear-flow-modified current driven ion cyclotron instability and shear-flow-driven ion cyclotron kinetic instabilities of magnetic field--aligned plasma shear flow is presented. Analysis is performed on the base of the nonlinear dispersion equation, which accounts for a new combined effect of plasma turbulence and shear flow. It consists in turbulent scattering of ions across the shear flow with their convection by shear flow and results in enhanced nonlinear broadening of ion cyclotron resonances. This effect is found to lead to the saturation of ion cyclotron instabilities as well as to the development of nonlinear shear flow driven ion cyclotron instability. 52.35.Ra
The external and independent control of plasma flow velocity shears parallel and perpendicular to magnetic field lines is realized using segmented collisionless-plasma sources. Electrostatic ion-cyclotron instabilities are observed to be suppressed by the perpendicular flow velocity shears, the suppression physics of which is found to be distinguished into two aspects. On the other hand, the parallel flow velocity shears are demonstrated to destabilize the ion-cyclotron instabilities depending on the sign of the parallel shear in the absence of field-aligned electron drift flow.
The electrostatic shear-flow-driven ion cyclotron instability of magnetic field aligned sheared plasma flow is investigated analytically. It is shown that the shear-flow-driven electrostatic ion cyclotron instability can be considered as a combination of three different instabilities determined by theirs own mechanism of excitation: ion-kinetic, ion-hydrodynamic and electron-kinetic. Each of these instabilities are dominant in different ranges of the wavelength along the magnetic field. The linearized dispersion equation is solved within the limits of long and short waves along the magnetic fi…
The linear and renormalized nonlinear kinetic theory of drift instability of plasma shear flow across the magnetic field, which has the Kelvin's method of shearing modes or so-called non-modal approach as its foundation, is developed. The developed theory proves that the time-dependent effect of the finite ion Larmor radius is the key effect, which is responsible for the suppression of drift turbulence in an inhomogeneous electric field. This effect leads to the non-modal decrease of the frequency and growth rate of the unstable drift perturbations with time. We find that turbulent scattering …
We show that the space charge dynamics of high intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics gives a unified and intuitive framework to explain the beam spiraling and beam break up behavior observed in experiments and in simulations. In particular, we demonstrate that beam break up is the result of a classical instability occurring in fluids subject to a sheared flow. We give scaling laws for the instability and predict the nonlinear evolution of be…
In this paper, we develop the kinetic and hydrodynamic theories of the convective mesoscale flows driven by the spatially inhomogeneous electrostatic ion cyclotron parametric microturbulence in the pedestal plasma with a sheared poloidal flow. The developed kinetic theory predicts the generation of the sheared poloidal convective flow, and of the radial compressed flow with radial flow velocity gradient. The developed hydrodynamic theory of the convective flows reveals the radial compressed convective flow as the dominant factor in the formation of the steep pedestal density profile with densi…
It is found that in magnetized electrostatic plasma flows the velocity shear couples ion-acoustic waves with ion-cyclotron waves and leads, under favorable conditions, to their efficient reciprocal transformations. It is shown that in a two-dimensional setup this coupling has a remarkable feature: it is governed by equations that are exactly similar to the ones describing coupling of sound waves with internal gravity waves [Rogava & Mahajan: Phys. Rev. E vol.55, 1185 (1997)] in neutral fluid flows. Using another noteworthy quantum mechanical analogy we calculate transformation coefficients and…
Impurity particle transport in an ion cyclotron resonance heated Alcator C-Mod discharge is studied with local gyrokinetic simulations and a theoretical model including the effect of poloidal asymmetries and elongation. In spite of the strong minority temperature anisotropy in the deep core region, the poloidal asymmetries are found to have a negligible effect on the turbulent impurity transport due to low magnetic shear in this region, in agreement with the experimental observations. According to the theoretical model, in outer core regions poloidal asymmetries may contribute to the reduction…
The linear and renormalized nonlinear analysis of the temporal evolution of drift-type modes in plasma flows with strong time-varying velocity shear is developed. Analysis is performed in the time domain without spectral decomposition in time and admits time variation of the flow velocity with time scales which may be comparable with turbulent time scales. 52.35.Ra
13MW of electron cyclotron current drive (ECCD) power deposited inside the q = 1 surface is likely to reduce the sawtooth period in ITER baseline scenario below the level empirically predicted to trigger neo-classical tearing modes (NTMs). However, since the ECCD control scheme is solely predicated upon changing the local magnetic shear, it is prudent to plan to use a complementary scheme which directly decreases the potential energy of the kink mode in order to reduce the sawtooth period. In the event that the natural sawtooth period is longer than expected, due to enhanced alpha particle sta…
We use particle-in-cell (PIC) simulations to study the nonlinear evolution of ion velocity space instabilities in an idealized problem in which a background velocity shear continuously amplifies the magnetic field. We simulate the astrophysically relevant regime where the shear timescale is long compared to the ion cyclotron period, and the plasma beta is ~ 1-100. The background field amplification in our calculation is meant to mimic processes such as turbulent fluctuations or MHD-scale instabilities. The field amplification continuously drives a pressure anisotropy with the perpendicular pre…
We study the stability of shear flows in a fully ionized plasma. Kelvin-Helmholtz is a well known, macroscopic and ideal shear-driven instability. In sufficiently low density plasmas, also the microscopic Hall magneto-shear instability can take place. We performed three-dimensional simulations of the Hall-MHD equations where these two instabilities are present, and carried out a comparative study. We find that when the shear flow is so intense that its vorticity surpasses the ion-cyclotron frequency of the plasma, the Hall magneto-shear instability is not only non-negligible, but it actually d…
A fluid theory has been developed by taking account of gyro-viscosity to study wave propagation characteristics in a homogeneous pair-ion magnetized plasma with a cylindrical symmetry. The exact dispersion relations derived by the Hankel-Fourier transformation are shown comparable with those observed in the experiment by Oohara and co-workers. The gyro-viscosity is responsible for the change in propagation characteristics of the ion cyclotron wave from forward to backward by suppressing the effect of the thermal pressure which normally causes the forward nature of dispersion. Although the expe…
Sawtooth control using steerable electron cyclotron current drive (ECCD) has been demonstrated in ASDEX Upgrade plasmas with a significant population of energetic ions in the plasma core and long uncontrolled sawtooth periods. The sawtooth period is found to be minimised when the ECCD resonance is swept to just inside the q = 1 surface. By utilising ECCD inside q = 1 for sawtooth control, it is possible to avoid the triggering of neoclassical tearing modes, even at significnatly higher pressure than anticipated in the ITER baseline scenario. Operation at 25% higher normalised pressure has been…
In this work, we modify the standard flux tube simulation domain to include arbitrary ion gyroradius-scale variation in the radial profile of the safety factor. To determine how to appropriately include such a modification, we add a strong ion gyroradius-scale source (inspired by electron cyclotron current drive) to the Fokker-Planck equation, then perform a multi-scale analysis that distinguishes the fast electrons driven by the source from the slow bulk thermal electrons. This allows us to systematically derive the needed changes to the gyrokinetic model. We find new terms that adjust the io…
Non-modal kinetic theory of the stability of the compressed-sheared plasma flows generated by the inhomogeneous microscale turbulence in the tokamak edge plasma
Using 1D and 2D particle-in-cell (PIC) simulations of a plasma with a growing magnetic field $\vec{B}$, we show that ions can be stochastically accelerated by the ion-cyclotron (IC) instability. As $\vec{B}$ grows, an ion pressure anisotropy $p_{\perp,i} > p_{||,i}$ arises, due to the adiabatic invariance of the ion magnetic moment ($p_{||,i}$ and $p_{\perp,i}$ are the ion pressures parallel and perpendicular to $\vec{B}$). When initially $β_i = 0.5$ ($β_i \equiv 8πp_i/|\vec{B}|^2$, where $p_i$ is the ion isotropic pressure), the pressure anisotropy is limited mainly by inelastic pitch-angle s…
Particle Acceleration in Stratified 2D MRI Turbulence: From Reconnection to First- and Second-Order Fermi and Shear Acceleration
Millennium Nucleus on Transversal Research and Technology to Explore Supermassive Black Holes (TITANS)（探索超大质量黑洞的横向研究与技术千年核）；Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez（阿道夫·伊巴涅斯大学自由艺术学院科学系）；Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile（智利大学物理与数学科学学院物理系）
We present a gyrokinetic theory for the electromagnetic waves and instabilities with frequencies much lower than the ion cyclotron frequency in finite-$β$ anisotropic uniform plasmas. Here, $β$ is the ratio between plasma and magnetic pressures. Kinetic effects due to both the finite Larmor radii and wave-particle resonances are fully kept in the analysis. Corresponding linear dispersion relation and wave polarizations, valid for general $β$ value and perpendicular wavelength, are then specifically derived for a bi-Maxwellian plasma. Analytic expressions for the criteria of kinetic firehose an…
The nonlinear state of a high-beta collisionless plasma is investigated when an imposed linear shear amplifies or diminishes a uniform magnetic field, driving pressure anisotropies and hence firehose/mirror instabilities. The evolution of the resulting microscale turbulence is considered when the shear is switched off or reversed after one shear time (mimicking local behaviour of a macroscopic flow), so a new macroscale configuration is superimposed on the microscale state left behind by the previous one. There is a threshold value of plasma beta: when $β\llΩ/S$ (ion cyclotron frequency/shear …
The key result of the present work is the theoretical prediction and observation of the formation of a new type of transport barrier in fusion plasmas, called F-ATB (fast ion-induced anomalous transport barrier). As demonstrated through state-of-the-art global electrostatic and electromagnetic simulations, the F-ATB is characterized by a full suppression of the turbulent transport - caused by strongly sheared, axisymmetric $E \times B$ flows - and an increase of the neoclassical counterpart, albeit keeping the overall fluxes at significantly reduced levels. The trigger mechanism is shown to be…
In the Hall magnetohydrodynamics, the onset condition of the Kelvin Helmholtz instability is solely determined by the Hall effect and is independent of the nature of shear flows. In addition, the physical mechanism behind the super and sub Alfvenic flows becoming unstable is quite different: the high frequency right circularly polarized whistler becomes unstable in the super Alfvenic flows whereas low frequency, left circularly polarized ion-cyclotron wave becomes unstable in the presence of sub Alfvenic shear flows. The growth rate of the Kelvin Helmholtz instability in the super Alfvenic cas…
We study the linear stability of weakly magnetized differentially rotating plasmas in both collisionless kinetic theory and Braginskii's theory of collisional, magnetized plasmas. We focus on the very weakly magnetized limit that is important for understanding how astrophysical magnetic fields originate and are amplified at high redshift. We show that the single instability of fluid theory - the magnetorotational instability mediated by magnetic tension - is replaced by two distinct instabilities, one associated with ions and one with electrons. Each of these has a different way of tapping int…
We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model of a collisionless accretion disc. The kinetic magnetorotational instability grows from a subthermal magnetic field having zero net flux over the computational domain to generate self-sustained turbulence and outward angular-momentum transport. Significant Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabili…
We simulate decaying turbulence in a homogeneous pair plasma using three dimensional electromagnetic particle-in-cell (PIC) method. A uniform background magnetic field permeates the plasma such that the magnetic pressure is three times larger than the thermal pressure and the turbulence is generated by counter-propagating shear Alfvén waves. The energy predominately cascades transverse to the background magnetic field, rendering the turbulence anisotropic at smaller scales. We simultaneously move several ion species of varying charge to mass ratios in our simulation and show that the particles…
Magnetorotational Instability (MRI), the instability causing turbulent transport in accretion disks, is studied in the kinetic regime. Radiatively Inefficient Accretion Flows (RIAFs), like the one around the supermassive black hole in the center of our Galaxy, are believed to be collisionless. Kinetic MHD formalism, based on the moments of the Vlasov equation, is used for linear analysis and nonlinear simulations. ZEUS MHD code is modified to include key kinetic MHD terms: anisotropic pressure tensor and anisotropic thermal conduction. Simulations use the local shearing box approximation. Pres…
In low-collisionality plasmas, velocity-space instabilities are a key mechanism providing an effective collisionality for the plasma. We use particle-in-cell (PIC) simulations to study the interplay between electron and ion-scale velocity-space instabilities and their effect on electron pressure anisotropy, viscous heating, and thermal conduction. The adiabatic invariance of the magnetic moment in low-collisionality plasmas leads to pressure anisotropy, $p_{\perp,j} > p_{||,j}$, if the magnetic field $\vec{B}$ is amplified ($p_{\perp,j}$ and $p_{||,j}$ denote the pressure of species $j$ [elect…
Local (shearing box) simulations of the nonlinear evolution of the magnetorotational instability in a collisionless plasma show that angular momentum transport by pressure anisotropy ($p_\perp \ne p_\parallel$, where the directions are defined with respect to the local magnetic field) is comparable to that due to the Maxwell and Reynolds stresses. Pressure anisotropy, which is effectively a large-scale viscosity, arises because of adiabatic invariants related to $p_\perp$ and $p_\parallel$ in a fluctuating magnetic field. In a collisionless plasma, the magnitude of the pressure anisotropy, and…
