The concept of available energy of a collisionless plasma is discussed in the context of magnetic confinement. The available energy quantifies how much of the plasma energy can be converted into fluctuations (including nonlinear ones) and is thus a measure of plasma stability, which can be used to derive linear and nonlinear stability criteria without solving an eigenvalue problem. In a magnetically confined plasma, the available energy is determined by the density and temperature profiles as well as the magnetic geometry. It also depends on what constraints limit the possible forms of plasma motion, such as the conservation of adiabatic invariants and the requirement that the transport be ambipolar. A general method based on Lagrange multipliers is devised to incorporate such constraints in the calculation of the available energy, and several particular cases are discussed. In particular, it is shown that it is impossible to confine a plasma in a Maxwellian ground state relative to perturbations with frequencies exceeding the ion bounce frequency.
A fast Alfvén wave with finite amplitude is shown to grow by a stimulated emission process that we propose for exploitation in toroidal magnetically confined fusion plasmas. Stimulated emission occurs while the wave propagates inward through the outer mid-plane plasma, where a population inversion of the energy distribution of fusion-born ions is observed to arise naturally. Fully nonlinear first principles simulations, which self-consistently evolve particles and fields under the Maxwell-Lorentz system, demonstrate this novel "alpha-particle channelling" scenario for the first time.
The idea of new diagnostics method for the small-scale irregular structures of magnetically confined plasma is suggested in the present paper. The method can be based on measurements of intensity attenuation of the normal sounding waves. Anomalous attenuation arises due to multiple scattering effects investigated earlier for ionospheric radio propagation. It has been shown that multiple scattering regime can realize in a tokamak plasma. Calculations of normal sounding wave anomalous attenuation in a tokamak plasma have been carried out. This quantity is large enough to be registered experiment…
Strong electrostatic turbulence in magnetically confined plasmas is characterized by trapping or eddying of particle trajectories produced by the $E\times B$ stochastic drift. Trapping is shown to produce strong effects on test particles and on test modes. It determines non-standard statistics of trajectories: non-Gaussian distribution, memory effects and coherence. Trapped trajectories form quasi-coherent structure. Trajectory trapping has strong nonlinear effects on the test modes on turbulent plasmas. We determine the growth rate of drift modes as function of the statistical characteristics…
Ion cyclotron emission (ICE) offers unique promise as a diagnostic of the fusion born alpha-particle population in magnetically confined plasmas. Pioneering observations from JET and TFTR found that ICE intensity $P_{ICE}$ scales approximately linearly with the measured neutron flux from fusion reactions, and with the inferred concentration, $n_α/n_i$, of fusion-born alpha-particles confined within the plasma. We present fully nonlinear self-consistent kinetic simulations that reproduce this scaling for the first time. This resolves a longstanding question in the physics of fusion alpha-partic…
The transport of energetic electrons is sensitive to magnetic perturbations. By using 3D numerical simulation of test particle drift orbits we show that the transport of untrapped electrons through an open region with magnetic perturbations cannot be described by a diffusive process. Based on our test particle simulations, we propose a model that leads to an exponential loss of particles.
Impact of geodesic curvature on zonal flow generation in magnetically confined plasmas
National Institute for Fusion Science（国立核聚变科学研究所）；The Graduate University for Advanced Studies（高级研究大学院大学）；PRESTO, Japan Science and Technology Agency（日本科学技术振兴机构 PRESTO 项目）；Faculty of Arts and Sciences, Komazawa University（驹泽大学文理学部）
It is shown that the thermodynamic maximum entropy principle predicts negative specific heat for a stationary magnetically self-confined current-carrying plasma torus. Implications for the magnetic self-confinement of fusion plasma are considered.
The efficient production of electricity from nuclear fusion in magnetically confined plasmas relies on a good confinement of the thermal energy. For more than thirty years, the observation that such confinement depends on the mass of the plasma isotope and its interaction with apparently unrelated plasma conditions has remained largely unexplained and it has become one of the main unsolved issues. By means of numerical studies based on the gyrokinetic theory, we quantitatively show how the plasma microturbulence depends on the isotope mass through nonlinear multiscale microturbulence effects i…
Compared to present experiments, tokamak and stellarator reactors will be subject to higher heat loads, sputtering, erosion and subsequent coating, tritium retention, higher neutron fluxes, and a number of radiation effects. Additionally, neutral beam penetration in tokamak reactors will only be limited to the plasma edge. As a result, several optical, beam-based and magnetic diagnostics of today's plasmas might not be applicable to tomorrow's reactors, but the present discussion suggests that reactors could largely rely on microwave diagnostics, including techniques based on mode conversions …
We construct a model for the turbulence near the X-point of a Tokamak device and, under suitable assumptions, we arrive to a closed equation for the electric field potential fluctuations. The analytical and numerical analysis is focused on a reduced two-dimensional formulation of the dynamics, which allows a direct mapping to the incompressible Navier-Stokes equation. The main merit of this study is to outline how the turbulence near the X-point, in correspondence to typical operation conditions of medium and large size Tokamaks, is dominated by the enstrophy cascade from large to smaller spat…
We derive exact solutions of a linear form of the Grad-Shafranov (GS) equation, including incompressible equilibrium flow, using ansatz-based similarity reduction methods. The linearity of the equilibrium equation allows linear combinations of solutions in order to obtain axisymmetric MHD equilibria with closed and nested magnetic surfaces which are favorable for the effective confinement of laboratory plasmas. In addition, employing the same reduction methods we obtain analytical solutions for several non-linear forms of the GS equation. In this context analytic force-free solutions in both l…
The electromagnetic theory of the strongly driven ion-temperature-gradient (ITG) instability in magnetically confined toroidal plasmas is developed. Stabilizing and destabilizing effects are identified, and a critical $β_{e}$ (the ratio of the electron to magnetic pressure) for stabilization of the toroidal branch of the mode is calculated for magnetic equilibria independent of the coordinate along the magnetic field. Its scaling is $β_{e}\sim L_{Te}/R,$ where $L_{Te}$ is the characteristic electron temperature gradient length, and $R$ the major radius of the torus. We conjecture that a fast p…
We introduce the first approach to volumetrically generate relativistically thermal plasma at gas-jet--accessible density. Using fully kinetic simulations and theory, we demonstrate that two stages of direct laser acceleration driven by two laser pulses in an applied magnetic field can heat a significant plasma volume to multi-MeV average energy. The highest-momentum feature is 2D-isotropic, persists after the interaction, and includes the majority of electrons, enabling experimental access to bulk-relativistic, high-energy-density plasma in an optically diagnosable regime for the first time.
Ideally, binary-collision algorithms conserve kinetic momentum and energy. In practice, the finite size of collision cells and the finite difference in the particle locations affect the conservation properties. In the present work, we investigate numerically how the accuracy of these algorithms is affected when the size of collision cells is large compared with gradient scale length of the background plasma, a parameter essential in full-f fusion plasma simulations. Additionally, we discuss implications for the conserved quantities in drift-kinetic formulations when fluctuating magnetic and el…
We propose a new mechanism for the generation of zonal flows in magnetically confined plasmas, complementing previous theories based on a modulational instability. We derive a new conservation law that operates in the regime of weakly nonlinear dynamics, and show that it serves to focus the inverse cascade of turbulent drift wave energy into zonal flows. This mechanism continues to operate in the absence of the separation of dynamical scales typically assumed in instability calculations.
It is shown, using results of measurements of ion saturation current in the plasma edges of different magnetic fusion confinement devices (tokamaks and stellarators), that the plasma dynamics in the edges is dominated by distributed chaos with spontaneously broken translational symmetry at low magnetic field, and with spontaneously broken reflexional symmetry (by helical solitons) at high magnetic field.
Conceptual design of Thomson scattering system with high wavelength resolution in magnetically confined plasmas for electron phase-space measurements
National Institute for Fusion Science（国立研究开发法人核融合科学研究所）；Division of Quantum Science and Engineering, Graduate School of Engineering, Hokkaido University（北海道大学工学研究科量子科学与工程专攻）；The Graduate University for Advanced Studies (SOKENDAI)（综合研究大学院大学）；Graduate School of Science, Nagoya University（名古屋大学理学研究科）
A two-fluid flowing plasma model is applied to describe the plasma rotation and resulted instability evolution in magnetically enhanced vacuum arc thruster (MEVAT). Typical experimental parameters are employed, including plasma density, equilibrium magnetic field, ion and electron temperatures, cathode materials, axial streaming velocity, and azimuthal rotation frequency. It is found that the growth rate of plasma instability increases with growing rotation frequency and field strength, and with descending electron temperature and atomic weight, for which the underlying physics are explained. …
Measurement of radial density profile in both the source and expansion chambers of a helicon plasma device have revealed that it is always centrally peaked in the source chamber, whereas in the expansion chamber near the diverging magnetic field it becomes hollow above a critical value of the magnetic field. This value corresponds to that above which both electrons and ions become magnetized. The temperature profile is always peaked off- axis and tail electrons are found at the peak location in both the source and expansion chambers. Rotation of the tail electrons in the azimuthal direction in…
The ground state of an externally confined one-component Yukawa plasma is derived analytically. In particular, the radial density profile is computed. The results agree very well with computer simulations on three-dimensional spherical Coulomb crystals. We conclude in presenting an exact equation for the density distribution for a confinement potential of arbitrary geometry.
A combined theoretical and experimental analysis of the normal modes of three-dimensional spherially confined Yukawa clusters is presented. Particular attention is paid to the breathing mode and the existence of multiple monopole oscillations in Yukawa systems. Finally, the influence of dissipation on the mode spectrum is investigated.
We consider the tilting instability of a magnetically confined spheromak using 3D MHD and relativistic PIC calculations with an application to astrophysical plasmas, specifically those occurring in magnetar magnetospheres. The instability is driven by the counter alignment of the spheromak's intrinsic magnetic dipole with the external magnetic field. Initially the spheromak rotates - tilts - trying to lower its magnetic potential energy. As a result a current sheet forms between the internal magnetic field of a spheromak and the confining field. Magnetic reconnection sets in; this leads to the…
Magnetic energy around astrophysical compact objects can strongly dominate over plasma rest mass. Emission observed from these systems may be fed by dissipation of Alfvén wave turbulence, which cascades to small damping scales, energizing the plasma. We use 3D kinetic simulations to investigate this process. When the cascade is excited naturally, by colliding large-scale Alfvén waves, we observe quasithermal heating with no nonthermal particle acceleration. We also find that the particles are energized along the magnetic field lines and so are poor producers of synchrotron radiation. At low pl…
A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized "spikes" in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that lo…
We investigate the intermittency of magnetic turbulence as measured in Reversed Field Pinch plasmas. We show that the Probability Distribution Functions of magnetic field differences are not scale invariant, that is the wings of these functions are more important at the smallest scales, a classical signature of intermittency. We show that scaling laws appear also in a region very close to the external wall of the confinement device, and we present evidences that the observed intermittency increases moving towards the wall.
Chirping frequency patterns have been observed in the electron cyclotron emission from strongly nonequilibrium plasma confined in a table-top mirror magnetic trap. Such patterns are typical for the formation of nonlinear phase space structures in a proximity of the wave-particle resonances of a kinetically unstable plasma, also known as the "holes and clumps" mechanism. Our data provides the first experimental evidence for acting of this mechanism in the electron cyclotron frequency domain.
A Multi-dipole line cusp configured Plasma Device (MPD) having six electromagnets with embedded Vacoflux-50 as a core material and a hot filament-based cathode for Argon plasma production has been characterized by changing the pole magnetic field values. For the next step ahead, a new tungsten ionizer plasma source for contact ionization cesium plasma has been designed, fabricated, and constructed and thus plasma produced will be confined in MPD. An electron bombardment heating scheme at high voltage is adopted for heating of 6.5cm diameter tungsten plate. This article describes the detailed a…
The generation of astrophysically relevant jets, from magnetically collimated, laser-produced plasmas, is investigated through three-dimensional, magneto-hydrodynamic simulations. We show that for laser intensities I ~ 10^12 - 10^14 W/cm^2, a magnetic field in excess of ~ 0.1 MG, can collimate the plasma plume into a prolate cavity bounded by a shock envelope with a standing conical shock at its tip, which re-collimates the flow into a super magneto-sonic jet beam. This mechanism is equivalent to astrophysical models of hydrodynamic inertial collimation, where an isotropic wind is focused into…
It is shown through analytical modeling and numerical simulations that external magnetic fields can relax the self-trapping thresholds in plasma based accelerators. In addition, the transverse location where self-trapping occurs can be selected by adequate choice of the spatial profile of the external magnetic field. We also find that magnetic-field assisted self-injection can lead to the emission of betatron radiation at well defined frequencies. This controlled injection technique could be explored using state-of-the-art magnetic fields in current/next generation plasma/laser wakefield accel…
We report on experiments in which magnetically driven radiatively cooled plasma jets were produced by a 1 MA, 250 ns current pulse on the MAGPIE pulsed power facility. The jets were driven by the pressure of a toroidal magnetic field in a ''magnetic tower'' jet configuration. This scenario is characterized by the formation of a magnetically collimated plasma jet on the axis of a magnetic ''bubble'', confined by the ambient medium. The use of a radial metallic foil instead of the radial wire arrays employed in our previous work allows for the generation of episodic magnetic tower outflows which…
In [Viktorov M. E. et al., Eur. Phys. Lett., V.116, P.55001, 2016] we reported on chirping frequency patterns that have been observed in the electron cyclotron emission from strongly nonequilibrium plasma confined in a table-top mirror magnetic trap. These patterns were interpreted qualitatively as the first experimental evidence for so-called "holes and clumps" mechanism acting at such high frequencies (1-10 GHz). In the present paper, we prove this statement on a more rigorous basis, considering the formation of nonlinear phase space structures in proximity of the wave-particle resonances wi…
Zebra-like patterns have been observed in the electron cyclotron emission spectra from strongly nonequilibrium plasma confined in a table-top mirror magnetic trap. The analysis of the experimental data suggests that the formation of zebra-like patterns could eventually be related to modulation of the whistler waves by the ion-acoustic waves excited during the abrupt ejection of electrons into a loss cone caused by the development of the whistler instability under the electron cyclotron resonance condition.
The ground state of an externally confined one-component Yukawa plasma is derived analytically using the local density approximation (LDA). In particular, the radial density profile is computed. The results are compared with the recently obtained mean-field (MF) density profile \cite{henning.pre06}. While the MF results are more accurate for weak screening, LDA with correlations included yields the proper description for large screening. By comparison with first-principle simulations for three-dimensional spherical Yukawa crystals we demonstrate that both approximations complement each other. …
A Unified theory of transport barriers (TBs) in magnetically confined systems
Institute for Fusion Studies, The University of Texas at Austin（德克萨斯大学奥斯汀分校聚变研究所）；Department of Mathematics, The University of Tokyo（东京大学数学系）；ExoFusion
In a plasma of multiple ion species, thermodynamic forces such as pressure and temperature gradients can drive ion species separation via inter-species diffusion. Unlike its neutral mix counterpart, plasma thermo-diffusion is found comparable to, or even much larger than, baro-diffusion. It is shown that such a strong effect is due to the long-range nature of the Coulomb potential, as opposed to short-range interactions in neutral gases. A special composition of the tritium and 3He fuel is identified to have vanishing net diffusion during adiabatic compression, and hence provides an experiment…
Degenerate plasmas with motionless ions show existence of three surface waves: the Langmuir wave, the electromagnetic wave, and the zeroth sound. Applying the separated spin evolution quantum hydrodynamics to half-space plasma we demonstrate the existence of the surface spin-electron acoustic wave (SSEAW). We study dispersion of the SSEAW. We show that there is hybridization between the surface Langmuir wave and the SSEAW at rather small spin polarization. In the hybridization area the dispersion branches are located close to each other. In this area there is a strong interaction between these…
The results of a recent fluid theory for the multipole modes of a Yukawa plasma in a spherical confinement [H. Kählert and M. Bonitz, Phys. Rev. E \textbf{82}, 036407 (2010)] are compared with molecular dynamics simulations and the exact $N$-particle eigenmodes in the crystalline phase. Simulations confirm the existence of high order modes found in cold fluid theory. We investigate the influence of screening, coupling and friction on the mode spectra in detail. Good agreement between theory and simulation is found for weak to moderate screening and low order modes. The relations between the br…
The normal modes of a three-dimensional Yukawa plasma in an isotropic, harmonic confinement are investigated by solving the linearized cold fluid equations. The eigenmodes are found analytically and expressed in terms of hypergeometric functions. It is found that the mode frequencies solely depend on the dimensionless plasma parameter $ξ=κR$, where $R$ is the plasma radius and $κ$ the inverse screening length. The eigenfrequencies increase monotonically with $ξ$ and saturate in the limit $ξ\to\infty$. Compared with the results in the Coulomb limit~[D. H. E. Dubin, Phys. Rev. Lett. \textbf{66},…
Kinetic instabilities in a dense plasma of a continuous ECR discharge in a mirror magnetic trap at the GISMO setup are studied. We experimentally define unstable regimes and corresponding plasma parameters, where the excitation of electromagnetic emission is observed, accompanied by the precipitation of energetic electrons from the magnetic trap. Comprehensive experimental study of the precipitating electron energy distribution and plasma electromagnetic emission spectra, together with theoretical estimates of the cyclotron instability increment proves that under the experimental conditions th…
Experiments to explore stability conditions and topology of a dense microparticle cloud supported against gravity by a gas flow were carried out. By using a nozzle shaped glass insert within the glass tube of a dc discharge plasma chamber a weakly ionized gas flow through a de Laval nozzle was produced. The experiments were performed using neon gas at a pressure of 100 Pa and melamine-formaldehyde particles with a diameter of 3.43 μm. The capturing and stable global confining of the particles behind the nozzle in the plasma were demonstrated. The particles inside the cloud behaved as a single …
we report the identification of a localised current structure inside the JET plasma. It is a field aligned closed helical ribbon, carrying current in the same direction as the background current profile (co-current), rotating toroidally with the ion velocity (co-rotating). It appears to be located at a flat spot in the plasma pressure profile, at the top of the pedestal. The structure appears spontaneously in low density, high rotation plasmas, and can last up to 1.4 s, a time comparable to a local resistive time. It considerably delays the appearance of the first ELM.
Recently, it has been proposed that the turbulent fluctuations measured in a linear plasma device could be described as a superposition of uncorrelated Lorentzian pulses with a narrow distribution of durations, which would provide an explanation for the reported quasi-exponential power spectra. Here, we study the applicability of this proposal to edge fluctuations in toroidal magnetic confinement fusion plasmas. For the purpose of this analysis, we introduce a novel wavelet-based pulse detection technique that offers important advantages over existing techniques. It allows extracting the prope…
Over the last decades, significant advances in high-power laser systems have enabled rapid progress in the development of laser-driven plasma accelerators. Today, the results obtained in beam stability and reproducibility present laser plasma acceleration as a viable and promising alternative to conventional accelerators. As several electron beam and secondary sources applications require high average currents, a major focus is now on increasing the beam's repetition rate. In the following, we introduce a novel plasma source for kHz electron acceleration, providing a continuous and spatially c…
This paper presents the detailed study of the controlled experimental observation and characterization of Ion Acoustic soliton in the quiescent argon plasma produced by filamentary discharge and confined in a multi-pole line cusp magnetic field device named Multi-pole line Cusp Plasma Device (MPD). In this system, the electrostatic fluctuations are found to be less than 1%, a characteristic of quiescent plasma. Ion acoustic soliton has been excited in MPD, and its propagation velocity and width of them are measured experimentally and compared with the 1-D Korteweg-de Vries (KdV) equation. The …
In the presented field line map approach the simulation domain of a tokamak is covered with a cylindrical grid, which is Cartesian within poloidal planes. Standard finite-difference methods can be used for the discretisation of perpendicular (w.r.t.~magnetic field lines) operators. The characteristic flute mode property $\left(k_{\parallel}\ll k_{\perp}\right)$ of structures is exploited computationally by a grid sparsification in the toroidal direction. A field line following discretisation of parallel operators is then required, which is achieved via a finite difference along magnetic field …
We perform two-dimensional particle-in-cell simulations of reconnection in magnetically dominated electron-positron plasmas subject to strong Compton cooling. We vary the magnetization $σ\gg1$, defined as the ratio of magnetic tension to plasma inertia, and the strength of cooling losses. Magnetic reconnection under such conditions can operate in magnetically dominated coronae around accreting black holes, which produce hard X-rays through Comptonization of seed soft photons. We find that the particle energy spectrum is dominated by a peak at mildly relativistic energies, which results from bu…
This paper summarizes the studies of plasma kinetic instabilities in the electron cyclotron frequency range carried out over the last decade at the Institute of Applied Physics of Russian Academy of Sciences. We investigate the nonequilibrium plasma created and sustained by high-power microwave radiation of a gyrotron under the electron cyclotron resonance condition. Resonant plasma heating results in the formation of at least two electron components, one of which, more dense and cold, determines the dispersion properties of the high-frequency waves, and the second, a small group of energetic …
The constraint imposed by magnetic helicity conservation on the alpha effect is considered for both magnetically and flow dominated self-organizing plasmas. Direct numerical simulations are presented for a dominant contribution to the alpha effect, which can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven alpha ( H$α$) effect. Direct numerical simulations of the H$α$ effect are prese nted for two examples---the magnetically dominated toroidal plasma unstable to tearing modes, and the flow-dominated accretion disk.
Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann boundary conditions in one dimension are given. Applications for fluid and plasma turbulence in two and three space dimensions illustrate the applicability and the efficiency of the method in computing flows in complex geometries, for example in toroidal geometries with asymmetric poloidal cross-sections.
We derive the differential equation governing the asymptotic quasi-stationary states of the two dimensional plasma immersed in a strong confining magnetic field and of the planetary atmosphere. These two systems are related by the property that there is an intrinsic constant length: the Larmor radius and respectively the Rossby radius and a condensate of the vorticity field in the unperturbed state related to the cyclotronic gyration and respectively to the Coriolis frequency. Although the closest physical model is the Charney-Hasegawa-Mima (CHM) equation, our model is more general and is rela…
