Showing papers in "Physics of fluids. B, Plasma physics in 1992"
TL;DR: The W7•AS experiment as discussed by the authors has successfully demonstrated two aspects of advanced stellarators, the improved equilibrium and the modular coil concept, which can best be realized with a modular coil system.
Abstract: The theoretical and experimental development of stellarators has removed some of the specific deficiencies of this configuration, viz., the limitations in β, the high neoclassical transport, and the low collisionless confinement of α particles. These optimized stellarators can best be realized with a modular coil system. The W7‐AS experiment [Plasma Phys. Controlled Fusion 31, 1579 (1989)] has successfully demonstrated two aspects of advanced stellarators, the improved equilibrium and the modular coil concept. Stellarator optimization will much more viably be demonstrated by W7‐X [Plasma Physics and Controlled Fusion Research, Proceedings of the 12th International Conference, Nice, 1988 (IAEA, Vienna, 1989), Vol. 2, p. 369], the successor experiment presently under design. Optimized stellarators seem to offer an independent reactor option. In addition, they supplement, in a unique form, the toroidal confinement fusion program, e.g., energy transport is anomalous in stellarators too, but possibly more easily understandable in the frame of existing theoretical concepts than in tokamaks.
296 citations
TL;DR: In this paper, the role of the backward stimulated Raman scattering in the process of the leading front steepening is traced, and the evidence that the final stage of the pulse depletion can be accompanied by the formation of relativistically strong solitonlike electromagnetic modes is presented.
Abstract: The depletion of a relativistically strong laser pulse in the course of interaction with underdense plasmas is considered. The driving mechanisms of distortion and fast depletion of the pulse due to the nonlinear plasma wake excitation are discussed. The role of the backward stimulated Raman scattering in the process of the leading front steepening is traced. Electron acceleration and heating due to plasma wave breaking are demonstrated. The evidence that the final stage of the pulse depletion can be accompanied by the formation of relativistically strong solitonlike electromagnetic modes is presented.
221 citations
TL;DR: In this article, an analytic kinetic description of the toroidicity-induced Alfven eigenmode (TAE) is presented, which includes electron parallel dynamics nonperturbatively, an effect that is found to strongly influence the character and damping of the TAE−contrary to previous theoretical predictions.
Abstract: An analytic kinetic description of the toroidicity‐induced Alfven eigenmode (TAE) is presented. The theory includes electron parallel dynamics nonperturbatively, an effect that is found to strongly influence the character, and damping of the TAE−contrary to previous theoretical predictions. A parallel conductivity model that includes collisionless (Landau) damping on the passing electrons and collisional damping on both trapped and passing electrons is used. Together, these mechanisms damp the TAE more strongly than previously expected. This is because the TAE couples (or merges) with the kinetic Alfven wave (KAW) within the gap region under conditions that depend on the gap size, the shear, the magnitude of the conductivity, and the mode numbers. The high damping could be relevant to recent experimental measurements of the TAE damping coefficient. In addition, the theory predicts a ‘‘kinetic’’ TAE, whose eigenfreqeuency lies just above the gap, whose existence depends on finite conductivity, and that is formed by the coupling of two KAW’s
197 citations
TL;DR: In this paper, a collisionless phase mixing model is proposed to explain anomalous transport in plasmas, which is based on a nonlocal damping term with a damping rate ∼ vt'k∥'√'k' in the closure approximation for the nth velocity space moment of the distribution function f.
Abstract: Fluidlike models have long been used to develop qualitative understanding of the drift‐wave class of instabilities (such as the ion temperature gradient mode and various trapped‐particle modes) which are prime candidates for explaining anomalous transport in plasmas. Here, the fluid approach is improved by developing fairly realistic models of kinetic effects, such as Landau damping and gyroradius orbit averaging, which strongly affect both the linear mode properties and the resulting nonlinear turbulence. Central to this work is a simple but effective fluid model [Phys. Rev. Lett. 64, 3019 (1990)] of the collisionless phase mixing responsible for Landau damping (and inverse Landau damping). This model is based on a nonlocal damping term with a damping rate ∼ vt‖k∥‖ in the closure approximation for the nth velocity space moment of the distribution function f, resulting in an n‐pole approximation of the plasma dispersion function Z. Alternatively, this closure approximation is linearly exact (and therefore physically realizable) for a particular f0 which is close to Maxwellian. ‘‘Gyrofluid’’ equations (conservation laws for the guiding‐center density n, momentum mnu∥, and parallel and perpendicular pressures p∥ and p⊥) are derived by taking moments of the gyrokinetic equation in guiding‐center coordinates rather than particle coordinates. This naturally yields nonlinear gyroradius terms and an important gyroaveraging of the shear. The gyroradius effects in the Bessel functions are modeled with robust Pade‐like approximations. These new fluid models of phase mixing and Landau damping are being applied by others to a broad range of applications outside of drift‐wave turbulence, including strong Langmuir turbulence, laser–plasma interactions, and the α‐driven toroidicity‐induced Alfven eigenmode (TAE) instability.
194 citations
TL;DR: In this article, a stability analysis of toroidicity, ellipticity, and noncircular triangularity induced Alfven eigenmodes (TAE, EAE, and NAE) was carried out for a typical burning plasma device.
Abstract: A stability analysis is carried out for energetic particle‐Alfven gap modes. Three modes have been identified: the toroidicity, ellipticity, and noncircular triangularity induced Alfven eigenmodes (TAE, EAE, and NAE). In highly elongated plasma cross sections with κ−1∼1, the EAE may be a more robust mode than the TAE and NAE. It is found that electron Landau damping in highly elongated plasmas has a strong stabilizing influence on the n=1 EAE, while ion Landau damping stabilizes the n=1 TAE in high‐density regimes. Furthermore, the NAE turns out to be stable for all currently proposed ignition experiments. The stability analysis of a typical burning plasma device, Burning Plasma Experiment (BPX) [Phys. Scr. T16, 89 (1987)] shows that n>1 gap modes can pose a serious threat to the achievement of ignition conditions.
192 citations
TL;DR: In this article, the toroidicity-induced gaps of the shear wave spectrum in tokamaks are shown to satisfy an envelope equation and the structure of these gaps, and the location of the high n gap modes, which are localized modes with frequency in the gap, are studied for general numerically generated equilibria.
Abstract: The toroidicity‐induced gaps of the shear Alfven wave spectrum in tokamaks are shown to satisfy an envelope equation. The structure of these gaps, and the location of the high‐n gap modes, which are localized modes with frequency in the gap, are studied for general numerically generated equilibria. The dependence of the frequencies of the gaps and the gap modes on the equilibrium properties, such as elongation, triangularity, and β of the plasma are explored.
179 citations
TL;DR: In this article, the magnetic field dynamics and reconnection processes in a highly conducting plasma are investigated in the regimes where Ohm's law is dominated by the Hall term, using a single (electron) fluid description (Electron magnetohydrodynamics).
Abstract: The magnetic field dynamics and reconnection processes in a highly conducting plasma are investigated in the regimes where Ohm’s law is dominated by the Hall term, using a single (electron) fluid description (electron magnetohydrodynamics). In these regimes, which correspond to the frequency range of the so‐called whistler (helicon) mode, the electromagnetic field is nearly force free: (j×B)/c+eneE=0. The evolution of the magnetic field in the vicinity of an X line is discussed in the linear and nonlinear regimes. The propagation of whistler waves results in the steepening of their wave front and in the increase of the electric current density in the neighborhood of the magnetic separatrix surfaces. Small‐scale magnetic reconnection occurs near surfaces where k⋅B=0, with k the mode wave number, and tearing‐type modes can be unstable due to the effect of electron inertia. A class of exact self‐similar solutions is obtained. These describe, within the scope of a local approximation, the nonlinear time devel...
163 citations
TL;DR: In this paper, the gyrocenter-fluid moments of the nonlinear gyrokinetic Vlasov equation were used to derive reduced fluid equations with finite-Larmor-radius (FLR) corrections.
Abstract: Nonlinear gyrofluid equations are obtained from the gyrocenter‐fluid moments of the nonlinear gyrokinetic Vlasov equation, which describes an equilibrium magnetized nonuniform plasma perturbed by electromagnetic field fluctuations (δφ,δA∥,δB∥), whose space‐time scales satisfy the gyrokinetic ordering: ω≪Ωi, ‖k∥‖/k⊥≪1, and e⊥≡(k⊥ρi)2≂O(1). These low‐frequency (reduced) fluid equations contain terms of arbitrary order in e⊥ and take into account the nonuniformity in the equilibrium density and temperature of the ion and electron species, as well as the nonuniformity in the equilibrium magnetic field. From the gyrofluid equations, one can systematically derive nonlinear reduced fluid equations with finite‐Larmor‐radius (FLR) corrections, which contain linear and nonlinear terms of O(e⊥), by expressing the gyrocenter‐fluid moments appearing in the gyrofluid equations in terms of the particle‐fluid moments, and then keeping terms up to O(e⊥) in the e⊥ expansion of the gyrofluid equations. By using gyrocenter‐fluid moments, this new gyrofluid approach effectively bypasses the issue of the gyroviscous cancellations, while retaining all the important diamagnetic effects and the gyroviscous corrections. From the present FLR‐corrected reduced fluid equations, the reduced Braginskii equations are recoverd for the ion and electron species (without collisional dissipation) and the ideal reduced magnetohydrodynamic (MHD) equations (in the absence of FLR effects).
160 citations
TL;DR: In this paper, a toroidal Alfven eigenmodes (TAE) eigenfunction is used to study the effect of toroidal drift motion on the loss boundary of a toroid eigenmode.
Abstract: Fusion‐born α particles moving parallel to the magnetic field can resonate with toroidal Alfven eigenmodes (TAE) leading to anomalous α‐orbit diffusion across the α‐loss boundaries in a tokamak. This is analyzed using the Hamiltonian guiding center code orbit in conjunction with the kinetic magnetohydrodynamics (MHD) eigenmode solving code nova‐k. Resonant single α orbits are studied below and above the threshold for orbit stochasticity and Monte Carlo randomized ensembles of alphas subjected to a finite amplitude time‐dependent TAE are followed with respect to their radial losses using realistic MHD equilibria and numerically computed toroidal Alfven eigenfunctions for one toroidal eigenmode n=1 and the full Fourier spectrum of poloidal harmonics m involved in the ‘‘gap mode.’’ The α‐loss mechanisms are resonant drift motion across the loss boundaries of alphas born near these boundaries and stochastic diffusion to the boundaries in constants of the motion (phase) space. After a first transient of resonant drift losses scaling as Br/B0, the number of alphas lost via diffusion scales as (Br/B0)2. For TAE amplitudes Br/ B0≥10−3, α orbit stochasticity sets in and, depending on the radial width of the fast α density nα(r), a substantial fraction of alphas can be lost in one slowing down time. For Br/ B0<10−4, the losses become insignificant.
158 citations
TL;DR: Friedman et al. as discussed by the authors developed warp, a multidimensional particle simulation code, which combines features of an accelerator code and a particle-in-cell plasma simulation.
Abstract: The beams in a heavy‐ion‐beam‐driven inertial fusion (HIF) accelerator are collisionless, nonneutral plasmas, confined by applied magnetic and electric fields. These space‐charge‐dominated beams must be focused onto small (few mm) spots at the fusion target, and so preservation of a small emittance is crucial. The nonlinear beam self‐fields can lead to emittance growth, and so a self‐consistent field description is needed. To this end, a multidimensional particle simulation code, warp [Friedman et al., Part. Accel. 37‐38, 131 (1992)], has been developed and is being used to study the transport of HIF beams. The code’s three‐dimensional (3‐D) package combines features of an accelerator code and a particle‐in‐cell plasma simulation. Novel techniques allow it to follow beams through many accelerator elements over long distances and around bends. This paper first outlines the algorithms employed in warp. A number of applications and corresponding results are then presented. These applications include studies ...
157 citations
TL;DR: In this article, two-dimensional electromagnetic particle simulations evidence a self-reformation of the shock front for a collisionless supercritical magnetosonic shock propagating at angle θ 0 around 90°.
Abstract: Two‐dimensional electromagnetic particle simulations evidence a self‐reformation of the shock front for a collisionless supercritical magnetosonic shock propagating at angle θ0 around 90°, where θ0 is the angle between the normal to the shock front and the upstream magnetostatic field. This self‐reformation is due to reflected ions which accumulate in front of the shock and is observed (i) in both electric and magnetic components, (ii) for both resistive and nonresistive two‐dimensional shocks, and (iii) over a cyclic time period equal to the mean ion gyroperiod measured downstream in the overshoot; resistive effects may be self‐consistently included or excluded for θ0≂90° according to a judicious choice of the upstream magnetostatic field orientation. The self‐reformation leads to a nonstationary behavior of the shock; however, present results show evidence that the shock becomes stationary for θ less than a critical value θr, below which the self‐reformation disappears. Present results are compared to p...
TL;DR: In this article, the nonlinear evolution of the m=1 mode was examined in high-temperature plasmas where the mode is in the semicollisional or collisionless regime.
Abstract: Nonlinear evolution of the m=1 mode is examined in high‐temperature plasmas where the mode is in the semicollisional or collisionless regime. Unlike the finite −Δ’(m≥2) tearing modes, the nonlinear evolution of which is collisional, both the semicollisional and collisionless m=1 modes exhibit nonlinearly enhanced growth rates that far exceed their linear values, thus making their nonlinear evolution collisionless; this accelerated growth of a collisionless m=1 mode may explain the fast sawtooth crashes observed in large tokamaks.
TL;DR: In this paper, the development of compact high-intensity laser, made possible by the technique of chirped pulse amplification, is reviewed, including the complexities of high-power laser implementation, such as the generation of short pulses, pulse cleaning, widebandwidth amplification, temporal stretching and compression, and the requirements for high average powers.
Abstract: The development of compact high‐intensity lasers, made possible by the technique of chirped pulse amplification, is reviewed. This includes the complexities of high‐power laser implementation, such as the generation of short pulses, pulse cleaning, wide‐bandwidth amplification, temporal stretching and compression, and the requirements for high‐average powers. Details of specific solid‐state laser systems are given. Some applications of these lasers to short‐pulse coherent short‐wavelength [x‐ray ultraviolet (XUV)] sources are also reviewed. This includes several nonlinear effects observed by focusing a subpicosecond laser into a gas; namely, an anomalous scaling of harmonic generation in atomic media, an upper limit on the conversion efficiency of relativistic harmonics in a plasma, and the observation of short‐pulse self‐focusing and multifoci formation. Finally, the effects of large ponderomotive pressures (100 Mbars) in short‐pulse high‐intensity laser–plasma interactions are discussed, with relevance both to recombination x‐ray lasers and a novel method of igniting thermonuclear fusion.
TL;DR: In this paper, the effect of resonant continuum damping is investigated for the lowmode-number, toroidicity-induced, global shear Alfven eigenmodes, which can be self-excited by energetic circulating alpha particles in an ignited tokamak plasma.
Abstract: The effect of resonant continuum damping is investigated for the low‐mode‐number, toroidicity‐induced, global shear Alfven eigenmodes, which can be self‐excited by energetic circulating alpha particles in an ignited tokamak plasma. Resonant interaction with the shear Alfven continuum is possible for these eigenmodes, especially near the plasma periphery, leading to significant dissipation, which is typically larger than direct bulk plasma dissipation rates. Two perturbation methods are developed for obtaining the Alfven resonance damping rate from the ideal fluid zeroth‐order shear Alfven eigenvalue and eigenfunction. In both methods the real part of the frequency is estimated to zeroth order, and the imaginary part, which includes the damping rate, is then obtained by perturbation theory. One method, which is applicable when the eigenfunction is nearly real, can readily be incorporated into general magnetohydrodynamic (MHD) codes. In the second method, the zeroth‐order eigenfunctions may be complex; however, the application of this method to general MHD codes needs more detailed development. Also, an analytical estimate is found for the next‐order real frequency shift of the fluid global Alfven mode. Analytical and numerical studies of this continuum damping effect indicate that it can substantially reduce the alpha particle‐induced growth rate. Thus, either it is possible to prevent instability or, if unstable, to use the Alfven resonance damping to estimate the saturation amplitude level predicted from quasilinear theory.
TL;DR: In this paper, it was shown that a much larger relative error field (Br21/BT ≊ 1 × 10−3) is required to produce a locked mode in the small, rapidly rotating plasma of COMPASS•C (R0 = 0.56 m, f≊13 kHz) than in the medium-sized plasmas of DIII•D (R 0 = 1.67 m,f≊1.6 kHz), where the critical relative error fields is Br21/ BT ≊ 2 × 10 −4.
Abstract: Otherwise stable discharges can become nonlinearly unstable to disruptive locked modes when subjected to a resonant m=2, n=1 error field from irregular poloidal field coils, as in DIII‐D [Nucl. Fusion 31, 875 (1991)], or from resonant magnetic perturbation coils as in COMPASS‐C [Proceedings of the 18th European Conference on Controlled Fusion and Plasma Physics, Berlin (EPS, Petit‐Lancy, Switzerland, 1991), Vol. 15C, Part II, p. 61]. Experiments in Ohmically heated deuterium discharges with q≊3.5, n ≊ 2 × 1019 m−3 and BT ≊ 1.2 T show that a much larger relative error field (Br21/BT ≊ 1 × 10−3) is required to produce a locked mode in the small, rapidly rotating plasma of COMPASS‐C (R0 = 0.56 m, f≊13 kHz) than in the medium‐sized plasmas of DIII‐D (R0 = 1.67 m, f≊1.6 kHz), where the critical relative error field is Br21/BT ≊ 2 × 10−4. This dependence of the threshold for instability is explained by a nonlinear tearing theory of the interaction of resonant magnetic perturbations with rotating plasmas that p...
TL;DR: In this article, a 3D hybrid gyrokinetic and magnetohydrodynamic simulation scheme is presented, which is used to study the nonlinear behavior of energetic particle effects in tokamaks, such as the energetic particle stabilization of sawteeth, fishbone oscillations, and alpha particle driven toroidal Alfven eigenmode (TAE) modes.
Abstract: A three‐dimensional (3‐D) hybrid gyrokinetic‐MHD (magnetohydrodynamic) simulation scheme is presented. To the 3‐D toroidal MHD code, MH3D‐K the energetic particle component is added as gyrokinetic particles. The resulting code, mh3d‐k, is used to study the nonlinear behavior of energetic particle effects in tokamaks, such as the energetic particle stabilization of sawteeth, fishbone oscillations, and alpha‐particle‐driven toroidal Alfven eigenmode (TAE) modes.
TL;DR: In this article, a set of nonlinear perturbed fluid equations for n, u∥ and T is developed using a drift ordering analysis and a new gyroviscous force (△⋅Πg).
Abstract: Unified fluid/kinetic equations for the plasma perturbed density (n), parallel flow velocity (u∥) and temperature (T) are developed in a sheared slab geometry by calculating the fluid moment closure relations kinetically. At first, a set of (unclosed) nonlinear perturbed fluid equations for n, u∥ and T is developed using a drift ordering analysis and a new gyroviscous force (△⋅Πg). Thereafter, to develop linear closure relations for b⋅∇⋅Π∥ and q∥, a drift‐kinetic version of a new Chapman–Enskog‐like (CEL) equation is developed and solved by using a moment approach and a physically realistic collision operator (Lorentz scattering operator plus the momentum restoring terms). The resultant closure relations for b⋅△⋅Π∥ and q∥ unify the fluid and kinetic approaches. In the collisional fluid limit the equations reduce to the well‐known Braginskii equations. In the adiabatic limit they reproduce the usual kinetic results, including Landau damping. It is shown that this new CEL approach is more compatib...
TL;DR: In this article, the stability of high-n toroidicity-induced shear Alfven eigenmodes (TAE) in the presence of fusion alpha particles or energetic ions in tokamaks is investigated.
Abstract: The stability of high-n toroidicity-induced shear Alfven eigenmodes (TAE) in the presence of fusion alpha particles or energetic ions in tokamaks is investigated. The TAE modes are discrete in nature and thus can easily tap the free energy associated with energetic particle pressure gradient through wave particle resonant interaction. A quadratic form is derived for the high-n TAE modes using gyro-kinetic equation. The kinetic effects of energetic particles are calculated perturbatively using the ideal MHD solution as the lowest order eigenfunction. The finite Larmor radius (FLR) effects and the finite drift orbit width (FDW) effects are included for both circulating and trapped energetic particles. It is shown that, for circulating particles, FLR and FDW effects have two opposite influences on the stability of the high-n TAE modes. First, they have the usual stabilizing effects by reducing the wave particle interaction strength. Second, they also have destabilizing effects by allowing more particles to resonate with the TAE modes. It is found that the growth rate induced by the circulating alpha particles increase linearly with toroidal mode number n for small {kappa}{sub {theta}}{rho}{sub {alpha}}, and decreases as 1/n for {kappa}{sub {theta}}{rho}{sub {alpha}} {much gt} 1. The maximum growth rate is obtained atmore » {kappa}{sub {theta}}{rho}{sub {alpha}} on the order of unity and is nearly constant for the range of 0.7 < {upsilon}{sub {alpha}}/{upsilon}{sub A} < 2.5. On the other hand, the trapped particle response is dominated by the precessional drift resonance. The bounce resonant contribution is negligible. The growth rate peaks sharply at the value of {kappa}{sub {theta}}{rho}{sub {alpha}} such that the precessional drift resonance occurs for the most energetic trapped particles. The maximum growth rate due to the energetic trapped particles is comparable to that of circulating particles.« less
TL;DR: The nonlinear interaction of ultraintense laser pulses with electron beams and plasmas is rich in a wide variety of new phenomena as discussed by the authors, including laser excitation of large-amplitude plasma waves (wake fields), relativistic optical guiding of laser pulses in preformed plasma channels, laser frequency amplification by ionization fronts and plasma waves, and stimulated backscattering from plasma and electron beams, and cooling of electron beams by intense lasers.
Abstract: The nonlinear interaction of ultraintense laser pulses with electron beams and plasmas is rich in a wide variety of new phenomena. Advances in laser science have made possible compact terawatt lasers capable of generating subpicosecond pulses at ultrahigh powers (≥1 TW) and intensities (≥1018 W/cm2). These ultrahigh intensities result in highly relativistic nonlinear electron dynamics. This paper briefly addresses a number of phenomena including (i) laser excitation of large‐amplitude plasma waves (wake fields), (ii) relativistic optical guiding of laser pulses in plasmas, (iii) optical guiding by preformed plasma channels, (iv) laser frequency amplification by ionization fronts and plasma waves, (v) relativistic harmonic generation, (vi) stimulated backscattering from plasmas and electron beams, (vii) nonlinear Thomson scattering from plasmas and electron beams, and (viii) cooling of electron beams by intense lasers. Potential applications of these effects are also discussed.
TL;DR: A review of the recent work carried out at Lawrence Livermore National Laboratory can be found in this paper, where a large effort is underway to enhance the power output of the Ni-like Ta xray laser at 44.83 A as a source for x-ray imaging of live cells.
Abstract: Laboratory x‐ray lasers are currently being studied by researchers worldwide. This paper reviews some of the recent work carried out at Lawrence Livermore National Laboratory. Laser action has been demonstrated at wavelengths as short as 35.6 A while saturation of the small signal gain has been observed with longer wavelength schemes. Some of the most successful schemes to date have been collisionally pumped x‐ray lasers that use the thermal electron distribution within a laser‐produced plasma to excite electrons from closed shells in neon‐ and nickel‐like ions to metastable levels in the next shell. Attempts to quantify and improve the longitudinal and transverse coherence of collisionally pumped x‐ray lasers are motivated by the desire to produce sources for specific applications. Toward this goal there is a large effort underway to enhance the power output of the Ni‐like Ta x‐ray laser at 44.83 A as a source for x‐ray imaging of live cells. Improving the efficiency of x‐ray lasers in order to produce saturated output with smaller pump lasers is also a goal of this work.
TL;DR: In this article, the modulational instability of copropagating light waves was studied in rarefied plasma, where the RMI merges with stimulated Raman forward scattering.
Abstract: The modulational instability of copropagating light waves was studied recently by McKinstrie and Bingham [Phys Fluids B 1, 230 (1989)], who applied their general theory to the study of the relativistic modulational instability (RMI) of light waves in the beat‐wave accelerator However, in rarefied plasma, the RMI merges with stimulated Raman forward scattering The longitudinal RMI is suppressed over most of its expected range and the study of secondary instabilities in the beat‐wave accelerator must be amended accordingly A preliminary analysis indicates that stimulated Raman backward scattering is likely to be important in current beat‐wave experiments, while near‐resonant stimulated Raman forward scattering and near‐forward stimulated Raman scattering could be important in proposed beat‐wave experiments
TL;DR: In this article, the amplitude threshhold and the nonlinear mode structure reveal the shear-induced self-organization that is responsible for efficiently tapping the free energy in the temperature and density gradients.
Abstract: Although collisional drift waves in a sheared slab configuration are linearly damped, the corresponding turbulence is self‐sustaining if initialized at an electrostatic potential fluctuation amplitude of eφ/T≳03ρs/Ln, much less than that of observed fluctuations Within the context of two‐dimensional sheared slab magnetic geometry, computational investigations into the amplitude threshhold and the nonlinear mode structure reveal the shear‐induced self‐organization that is responsible for efficiently tapping the free energy in the temperature and density gradients They also show that the turbulence is nondiffusive in character, since the important assumptions behind turbulence‐as‐diffusion are all violated Many important features of experimentally observed tokamak edge fluctuations are reproduced by these single resonant surface nonlinear dynamics, suggesting that model components not treated may have an effect more additive than qualitative The ingredients giving rise to self‐organized turbulence, shear‐localized long‐wavelength modes of some width Δ0<λ, and isotropic intermediate wavelength modes with λ∼Δ0, in direct, coherent interaction, are at least potentially shared by most of the viable candidates for anomalous tokamak transport Consequently, such transport is unlikely to bear much resemblance to the simpler models currently in use
TL;DR: In this paper, a formula relating turbulence levels with arbitrary shear flow is derived, and the scaling laws governing turbulence suppression are considerably modified when the diffusion coefficient is made a functional of the corresponding turbulence level.
Abstract: A formula relating turbulence levels with arbitrary shear flow is derived. When the diffusion coefficient is made a functional of the corresponding turbulence level, it is found that the scaling laws governing turbulence suppression are considerably modified. The results are compared with known formulas in various limiting cases, indicating that turbulence suppression mainly pertains in the moderate shear flow regime. The results also show that a flattened (steep) radial equilibrium gradient tends to enhance (eliminate) turbulence suppression due to the shear flow.
TL;DR: The properties of single helicity and multiple helicity Ohmic states in reversed field pinches (RFPs) were investigated by a combination of analytic and numerical methods in this article.
Abstract: The properties of single helicity and multiple helicity Ohmic states in reversed‐field pinches (RFP’s) are investigated by a combination of analytic and numerical methods. The single helicity results show that toroidal field reversal can be provided in a helical Ohmic equilibrium driven by a toroidal loop voltage, and that reversal in helical symmetry is related to stellarator transform. Nevertheless, a constant λ≡j∥/B state cannot be sustained because λ must reverse at the toroidal field reversal surface. This helical equilibrium can be thought of as the saturated state of an unstable tearing mode. For a force‐free plasma, helical reversal can be maintained by a relatively small value of δB/B because it is accompanied by an inward paramagnetic pinch velocity. Conversely, in models with △⋅v=0, a large outward diffusive velocity must build up to balance the inward paramagnetic pinch velocity, requiring poloidal beta to be of order unity. It is shown that in three dimensions no multihelical Ohmic equilibriu...
TL;DR: In this paper, the authors revisited the neoclassical theory of plasma rotation in tokamaks in order to account for anomalous transport driven by a turbulence, and showed that this model yields both steep and gradual profiles for the poloidal rotation velocity at the edge corresponding to the H and L regimes of confinement.
Abstract: It is well known that usual assumptions of neoclassical theory become invalid if very large gradients occur at the plasma edge. Therefore neoclassical theory of plasma rotation in tokamaks is revisited in order to account for anomalous transport driven by a turbulence. It is shown that this model yields both steep and gradual profiles for the poloidal rotation velocity at the edge corresponding to the H and L regimes of confinement, respectively. Results and conclusions are focused on experiments employing the biased electrode technique. Regimes with fast poloidal rotation in excess of poloidal sound speed are considered with the emphasis on relaxation.
TL;DR: In this paper, the authors systematically study how the fast reconnection mechanism involving standing switch-off shocks can be established and sustained in a large-scale current sheet system and find that the reconnection process is strongly controlled by the resistivity model.
Abstract: Computer simulations systematically study how the fast reconnection mechanism involving standing switch‐off shocks can be established and sustained in a large‐scale current sheet system. Initiated by a small disturbance, all the phenomena spontaneously grow from near the origin and propagate outward. Under the same initial boundary conditions, different resistivity models are assumed, where the resistivity is self‐consistently determined by macroscopic quantities in the system. It is found that the reconnection process is strongly controlled by the resistivity model. Only when the resistivity is locally enhanced near an X‐type neutral point in accordance with the global reconnection flow, the fast reconnection mechanism can rapidly build up and be sustained steadily. The steady fast reconnection mechanism works as an engine that drastically drives the overall system into catastrophe. Since this mechanism depends on the resistivity parameter very weakly, it may be applicable to large dissipative events in space plasmas. It is argued that local conditions near an X neutral point should be fundamental for the fast reconnection mechanism to be realized.
TL;DR: In this article, a periodic array of convection cells is subject to a "shear flow" instability, and the generation of the sheared flow is a consequence of "peeling" of the convection cell.
Abstract: A periodic array of convection cells is subject to a ‘‘shear flow’’ instability. The generation of the sheared flow is a consequence of ‘‘peeling’’ of the convection cells. Fluid simulations demonstrate that the efficiency of shear flow generation is high. Implications for understanding poloidal rotation in tokamaks are discussed.
TL;DR: In this paper, the authors extended the work of Hammett and Perkins [Phys. Rev. 64, 3019 (1990)] for electrostatic motion parallel to the magnetic field and E×B motion to include the gyroaveraging linearly and the curvature drift motion.
Abstract: Gyro‐Landau fluid model equations provide first‐order time advancement for a limited number of moments of the gyrokinetic equation, while approximately preserving the effects of the gyroradius averaging and Landau damping. This paper extends the work of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for electrostatic motion parallel to the magnetic field and E×B motion to include the gyroaveraging linearly and the curvature drift motion. The equations are tested by comparing the ion‐temperature‐gradient mode linear growth rates for the model equations with those of the exact gyrokinetic theory over a full range of parameters.
TL;DR: In this paper, the linear resistive magnetohydrodynamical stability of the n = 1 internal kink mode in tokamaks is studied numerically, and it is suggested that weak resistive instabilities are stabilized during the ramp phase of the sawteeth.
Abstract: The linear resistive magnetohydrodynamical stability of the n=1 internal kink mode in tokamaks is studied numerically. The stabilizing influence of small aspect ratio [Holmes et al., Phys. Fluids B 1, 788 (1989)] is confirmed, but it is found that shaping of the cross section influences the internal kink mode significantly. For finite pressure and small resistivity, curvature effects at the q=1 surface make the stability sensitively dependent on shape, and ellipticity is destabilizing. Only a very restricted set of finite pressure equilibria is completely stable for q0 < 1. A typical result is that the resistive kink mode is slowed down by toroidal effects to a weak resistive tearing/interchange mode. It is suggested that weak resistive instabilities are stabilized during the ramp phase of the sawteeth by effects not included in linear resistive magnetohydrodynamics. Possible mechanisms for triggering a sawtooth crash are discussed.
TL;DR: In this article, numerical results of three-dimensional (3-D) resistive magnetohydrodynamic (MHD) plasma simulations are presented, where a system of coupled nonlinear differential equations is evolved in time over a significant fraction of the macroscopic resistive diffusion time scale.
Abstract: In this paper numerical results of three‐dimensional (3‐D) resistive magnetohydrodynamic (MHD) plasma simulations are presented. A system of coupled nonlinear differential equations is evolved in time over a significant fraction of the macroscopic resistive diffusion time scale. The dynamical evolution resembles the main features of the famous Lorenz system. In fact, sensitivity of MHD equations on initial distribution of spectral energy and stochastic oscillations in phase space have been found. At least two dynamic attractors of the motion have been identified. Moreover, in analogy with Lorenz’s system, the stochastic motion can be damped by an enhanced dissipation and the fixed point can be recovered. In this paper more specific topics are also considered, which are relevant to the reversed field pinch (RFP), such as the role of different modes in the ‘‘dynamo’’ mechanism for plasma sustainment and the associated transport due to stochastic diffusion.