Electromagnetic Turbulence Research Articles

Fundamental emission via wave advection from a collapsing wave packet in electromagnetic strong plasma turbulence

Zakharov simulations of nonlinear wave collapse in continuously driven two-dimensional, electromagnetic strong plasma turbulence with electron thermal speeds v⩾0.01c show that for v≲0.1c, dipole radiation occurs near the plasma frequency, mainly near arrest, but for v≳0.1c, a new mechanism applies in which energy oscillates between trapped Langmuir and transverse modes until collapse is arrested, after which trapped transverse waves are advected into incoherent interpacket turbulence by an expanding annular density well, where they detrap. The multipole structure, Poynting flux, source current, and radiation angular momentum are computed.

Structure of Langmuir and electromagnetic collapsing wave packets in two-dimensional strong plasma turbulence

Nucleating and collapsing wave packets relevant to electromagnetic strong plasma turbulence are studied theoretically in two dimensions. Model collapsing Langmuir and transverse potentials are constructed as superpositions of approximate eigenstates of a spherically symmetric density well. Electrostatic and electromagnetic potentials containing only components with azimuthal quantum numbers m=0, 1, 2 are found to give a good representation of the electric fields of nucleating collapsing wave packets in turbulence simulations. The length scales of these trapped states are related to the electron thermal speed ve and the length scale of the density well. It is shown analytically that the electromagnetic trapped states change with ve and that for ve≲0.17c they are delocalized, in accord with recent simulations. In this case, the Langmuir mode collapses independently, as in electrostatic plasma turbulence. For ve≳0.17c, the Langmuir and transverse modes remain coupled during collapse, with autocorrelation lengths in a constant ratio. An investigation of energy transfer to packets localized in density wells shows that the strongest power transfer to the nucleating state occurs for Langmuir waves. Energy transitions between different trapped and free states for collapsing wave packets are studied, and the transition rate from trapped Langmuir to free plane electromagnetic waves is calculated and related to the emission of electromagnetic waves at the plasma frequency.

Electromagnetic strong plasma turbulence

The first large-scale simulations of continuously driven, two-dimensional electromagnetic strong plasma turbulence are performed, for electron thermal speeds 0.01c⩽v⩽0.57c, by integrating the Zakharov equations for coupled Langmuir and transverse (T) waves near the plasma frequency. Turbulence scalings and wave number spectra are calculated, a transition is found from a mix of trapped and free T eigenstates for v⩾0.1c to just free eigenstates for v⩽0.1c, and wave energy densities are observed to undergo slow quasiperiodic oscillations.

Initial results of H-mode edge pedestal turbulence evolution with quadrature reflectometer measurements on DIII-D

High-resolution quadrature reflectometer measurements of density fluctuation levels have been obtained on DIII-D for H-mode edge pedestal studies. Initial results are presented from the L–H transition to the first ELM for two cases: (i) a low pedestal beta discharge, in which density turbulence in the pedestal has little change during the ELM-free phase, and (ii) a high pedestal beta discharge in which both density and magnetic turbulence are observed to increase before the first ELM. These high beta data are consistent with the existence of electromagnetic turbulence suggested by some transport models. During Type-I ELM cycles, when little magnetic turbulence can be observed, pedestal turbulence increases just after an ELM crash and then decreases before next ELM strikes, in contrast to a drop after ELM crash and then it re-grows when strong magnetic turbulence shows similar behavior. Clear ELM precursors are observed on ⩽20% of Type-I ELMs observed to date.

The operational phase-space of the edge plasma and its sensitivity to magnetic topology in Alcator C-Mod

The range of ‘edge plasma states’ (i.e., the combination of densities, temperatures and gradients in the scrape-off layer near the separatrix) accessible to a tokamak are highly restricted. Experiments in Alcator C-Mod suggest that this restriction is a consequence of electromagnetic fluid drift turbulence (EMFDT), which sets the cross-field transport levels; plasma states are constrained to lie in a narrow region of EMFDT ‘phase-space’ defined by poloidal beta gradient (αMHD) and normalized plasma collisionality. Recent experiments have investigated this behavior over an increased parameter range in lower- and upper-null (LSN/USN) discharges. L-mode edge pressure gradients are found to exhibit clear sensitivity to magnetic topology, favoring higher αMHD for LSN compared to USN. These variations may be caused, in part, by the different edge plasma flow patterns in LSN versus USN. Such flows arise from a ballooning-like transport drive and can produce a topology-dependent modulation in the toroidal plasma rotation.

Multiple harmonic plasma emission

A generalized weak turbulence theory for electromagnetic emission at multiple harmonics of the plasma frequency is developed. In the literature, the electromagnetic emission at the plasma frequency and/or its second harmonic has been intensively studied. However, the emission at harmonics higher than the second harmonic is scarcely discussed. In the present paper, the higher harmonic plasma emission is explained by taking the interactions between the transverse mode and electrostatic nonlinear eigenmodes into consideration. The present analysis incorporates electrostatic nonlinear harmonic Langmuir waves into the fully electromagnetic weak turbulence formalism recently reformulated on the basis of the statistical mechanical Klimontovich approach. The wave kinetic equations for the transverse electromagnetic and Langmuir waves interacting with the harmonic Langmuir waves are derived, on the basis of which the emission of electromagnetic waves near multiple harmonics of the plasma frequency is qualitatively discussed.

Study of nonlinear interaction of waves through plasma-maser in magnetosphere plasma

A theoretical study is made on the generation mechanism of electrostatic Bernstein mode wave in the presence of electromagnetic Kinetic Alfven wave turbulence in magnetized inhomogeneous plasma on the basis of plasma-maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Kinetic Alfven wave turbulence. Because of the universal existence of the Kinetic Alfven waves in large-scale plasmas, the result has potential importance in space and astrophysical radiation process. The growth rate of the test high-frequency Bernstein mode wave is obtained with the involvement of spatial density gradient parameter. A comparative study on the role of density gradient in the generation of Bernstein mode on the basis of plasma-maser effect is presented.

Computation of turbulence in magnetically confined plasmas

Plasmas are magnetically confined if the orbits of the charged particles around the magnetic field lines are small compared to the system size. Nevertheless, particles and energy are lost via transport resulting from the fluid-like drifts of these orbits across the magnetic field. Computation of this type of low frequency electromagnetic turbulence is introduced with emphasis on nonlinear character and energetics. The physical situation is low frequency dynamics with perpendicular forces in quasistatic balance and fast gyrofrequency leading to treating the orbit gyrocentres rather than the particles themselves. The broadband turbulence necessarily involves the ion gyroradius scale in any tokamak application. Hence the use of ‘gyrofluid’ and ‘gyrokinetic’ computational models. Computations must also treat the interplay between electromagnetic wave dynamics along the magnetic field and fluid-like turbulence across it, with a method independently checked against both of these sub-processes. Tokamak core and edge turbulence differ according to the ratios of the parallel (electron) and perpendicular (E-cross-B) transit frequencies. The turbulence is also in energetic contact with flows and currents associated with the equilibrium, so computations must be well behaved over very long run times and at least the perturbed equilibrium carried self-consistently. These considerations are illustrated by treating the case of ion temperature gradient instabilities giving rise to turbulence which is then suppressed by self generated E-cross-B flows. The methods of diagnosis of the physical processes are detailed. The situation of edge turbulence and interaction with the equilibrium is briefly addressed.

Arbitrary plasma shape and trapped electron modes in the GEM gyrokinetic electromagnetic turbulence simulation code

Here the recent developments in GEM, a quite comprehensive Gyrokinetic Electromagnetic (GEM) turbulence code are described. GEM is a δf particle turbulence simulation code that has kinetic electrons and electromagnetic perturbations. The key elements of the GEM algorithm are: (1) the parallel canonical formulation of the gyrokinetic system of equations; (2) an adjustable split-weight scheme for kinetic electrons; and (3) a high-β algorithm for the Ampere's equation. Additionally, GEM use a two-dimensional (2D) domain decomposition and runs efficiently on a variety of high performance architectures. GEM is now extended to include arbitrary toroidal equilibrium profiles and flux-surface shapes. The domain is an arbitrarily sized toroidal slice with periodicity assumed in the toroidal direction. It is global radially and poloidally along the magnetic field. Results are presented that demonstrate the effect of plasma shaping on the Ion-Temperature-Gradient (ITG) driven instabilities. An example of nonlinear simulation of the finite-β modified ITG turbulence in general geometry is also given. Finally, collisionless Trapped Electron Modes (TEM) are investigated and shown here is the transition from the TEM dominated core region to the Drift-Wave dominated edge region as the density gradient increases.

Advances in measurement and modeling of the high-confinement-mode pedestal on the Alcator C-Mod tokamak

Edge transport barrier (ETB) studies on the Alcator C-Mod tokamak [Phys. Plasmas 1, 1511 (1994)] investigate pedestal scalings and the radial transport of plasma and neutrals. Pedestal profiles show trends with plasma operational parameters such as total current IP. A ballooning-like IP2 dependence is seen in the pressure gradient, despite calculated stability to ideal ballooning modes. A similar scaling is seen in the near scrape-off layer for both low-confinement (L-mode) and H-mode discharges, possibly due to electromagnetic fluid drift turbulence setting transport near the separatrix. Neutral density diagnosis allows an examination of D0 fueling in H-modes, yielding profiles of effective particle diffusivity in the ETB, which vary as IP is changed. Edge neutral transport is studied using a one-dimensional kinetic treatment. In both experiment and modeling, the C-Mod density pedestal exhibits a weakly increasing pedestal density and a nearly invariant density pedestal width as the D0 source rate increases. Identical modeling performed on pedestal profiles typical of DIII-D [Nucl. Fusion 42, 614 (2002)] reveal differences in pedestal scalings qualitatively similar to experimental results.

Gyrokinetic study of the edge shear layer

The delta-f gyrokinetic model originally formulated for core turbulence is extended to treat medium-amplitude electromagnetic turbulence expected in the transcollisional edge regions of modern tokamaks. Both electrons and ions, and the field polarization equations, are followed. The effect on the turbulence of an externally applied E × B velocity shear and alternatively an initial E × B vorticity profile to which the turbulence can back-react are studied. Imposed shear reduces the short wavelength component but increases the long wavelengths. The localized vorticity layer has a more general suppressive effect.

Monte Carlo modeling of toroidal ion distributions and ion temperatures at high altitudes equatorward of the cusp: Effect of finite gyroradius

We report that the effect of finite gyroradius is responsible for production of the H+ and O+ toroids at high altitudes equatorward of the cusp that are observed by TIDE and TIMAS ion instruments on board the polar spacecraft. The energization of charged particles, owing to interaction with electromagnetic turbulence, has an important influence on the plasma outflow in space. The effect of wave‐particle interactions (WPI) on H+ and O+ outflow at high altitudes equatorward of the cusp was investigated by using Monte Carlo method. The Monte Carlo model includes the effect of WPI, gravity, polarization electrostatic field, and the divergence of the geomagnetic field within the simulation tube (1.2–10 Earth radii, RE). As the ions drift upward along the geomagnetic field lines, they interact with the electromagnetic turbulence and consequently get heated in the direction perpendicular to the geomagnetic field. The mirror force converts some of the gained ion energy in the perpendicular direction into parallel kinetic energy. These effects combine to form an ion‐conic velocity distribution. However, as the ions are heated and move to higher altitudes, the ion gyroradius ρi may become comparable to the perpendicular wavelength of the electromagnetic turbulence λ⊥. As the ratio ρi/λ⊥ becomes >1, then the heating rate turns to be self‐limited and the ion velocity distribution displays toroidal features. A comparison has been made between the Monte Carlo calculations obtained in this study and observations of H+ and O+ ion velocity distributions and temperatures. The comparison showed a remarkably close agreement in the corresponding results for the ion velocity distribution and its temperature. As a result of the comparison, we were able to predict the characteristic value of the perpendicular wavelength of the electromagnetic turbulence λ⊥ at high altitudes equatorward of the cusp. To our knowledge, this represents the first successful comparison of observed toroids with a theoretical model.

Statistical theory of electromagnetic weak turbulence

The weak turbulence theory as commonly found in the literature employs electrostatic approximation and is applicable to unmagnetized plasmas only. To this date, fully electromagnetic generalization of the existing weak turbulence theory based upon statistical mechanical approach remains largely incomplete. Instead, electromagnetic effects are incorporated into the weak turbulence formalism by means of the semiclassical approach. The present paper reformulates the fully electromagnetic weak turbulence theory from classical statistical mechanical (i.e., the Klimontovich) approach.

Simulations of JET pellet fuelled ITB plasmas

Experiments were performed on JET where high-density plasmas with an internal transport barrier (ITB) were created by means of combined use of lower hybrid current drive (LHCD) and pellet injection before the barrier formation. Attempts were also made to use pellets to fuel the plasma and to sustain the density during the ITB phase. It was found that shallow pellets ablating in the region r/a ⩾ 0.8 and far from the foot of the barrier did not destroy the ITB, whereas deeper pellets penetrating up to 0.6 ⩽ r/a ⩽ 0.7 affected the barrier and led to its disappearance. Modelling of these experimental scenarios has been performed with transport and fluid turbulence codes. The codes used in the analysis were: JETTO, a 1.5 dimensional transport code, TRB, a global electrostatic fluid turbulence code and CUTIE, a global electromagnetic fluid turbulence code. The results show that for the shallow pellet case all codes reproduce the general features of the experiment, whereas for the deep pellet case, there are differences in the degree of agreement between the different codes and the experiment. Runs performed varying the pellet penetration depth indicate that not only the pellet penetration, but also the barrier strength plays a key role in the dynamics of the pellet-ITB interaction.

Electromagnetic fluid drift turbulence in static ergodic magnetic fields

Numerical simulations of three-dimensional nonlinear electromagnetic fluid drift turbulence in a tokamak plasma with externally applied stochastic magnetic-field perturbations are presented. The contributions to the radial particle transport due to nonlinearities arising from E×B advection and magnetic flutter are investigated for perturbation fields of varying strengths in the cases of low and high collisionalities. The perturbation strength is varied to study the physics for Chirikov parameters above 1. In all the cases considered a significant increase of E×B transport is found. A static contribution in the density and velocity perturbations contributes significantly to the total radial E×B transport. For low collisionality, the external perturbation leads to enhanced density and velocity fluctuations over a broad range in the toroidal wave-number spectrum, resulting in an enhanced turbulent flux. For high collisionality, the density fluctuations stay roughly the same and the velocity fluctuations are increased in an intermediate range of the toroidal wave number spectrum, separated from the maximum of the density fluctuations, thus leaving the turbulent flux almost unchanged.

Evidence for electromagnetic fluid drift turbulence controlling the edge plasma state in the Alcator C-Mod tokamak

Plasma profiles across the separatrix and scrape-off layer (SOL) in Alcator C-Mod are examined for a range of plasma densities, currents and magnetic fields in Ohmic L-mode discharges and for a subset of conditions in Ohmic H-mode discharges. In all plasmas, electron pressure gradient scale lengths () exhibit a minimum value just outside the separatrix (i.e. in the near SOL), forming the base of a weak (strong) pedestal in L-mode (H-mode) plasmas. Over a wide range of conditions in Ohmic L-mode discharges, at this location are found to track with a monotonic function of electron collision frequency, when this quantity is normalized according to the framework of electromagnetic fluid drift turbulence (EMFDT) theory. Moreover, at fixed values of normalized collisionality parameter (characterized as the ‘diamagnetic parameter’, αd), electron pressure gradients in the near SOL increase with plasma current squared, holding the MHD ballooning parameter, αMHD, unchanged. Thus, the state of the near SOL is restricted to a narrow region within this two-parameter phase-space. An implication is that cross-field heat and particle transport are strong functions of these parameters. Indeed, as αd is decreased below ∼0.3, cross-field heat convection increases sharply and competes with parallel heat conduction along open field lines, making high plasma density regions of αMHD–αd space energetically inaccessible. These observations are consistent with the idea that the operational space of the edge plasma, including boundaries associated with the tokamak density limit, is controlled by EMFDT.

Tokamak turbulence computations on closed and open magnetic flux surfaces

We study turbulence on closed and open flux surfaces in a comparative manner using the three-dimensional electromagnetic gyrofluid turbulence code GEM. A magnetic field on a tokamak is doubly periodic and sheared. This leads to the so-called field line connection, which ensures a finite parallel response for every degree of freedom. In contrast, in the scrape-off layer (SOL), the field lines end on plates, breaking this constraint and allowing the existence of convective cell modes. Since the parallel electron response provides a path to dissipation, whether or not it is allowed to vanish is important. For the SOL case, a standard Debye sheath model is used to provide the parallel boundary conditions. A zero loss model (no fluxes into the plates) is also used to assess the importance of the Debye currents. Turbulence on closed and open flux surfaces at the same parameters is found to be very different, a property which basic transport models should take into account.

Magnetic Reconnection, Turbulence, and Collisionless Shock

A short summary of recent progress in measuring and understanding turbulence during magnetic reconnection in laboratory plasmas is given. Magnetic reconnection is considered as a primary process to dissipate magnetic energy in laboratory and astrophysical plasmas. A central question concerns why the observed reconnection rates are much faster than predictions made by classical theories, such as the Sweet-Parker model based on MHD with classical Spitzer resistivity. Often, the local resistivity is conjectured to be enhanced by turbulence to accelerate reconnection rates either in the context of the Sweet-Parker model or by facilitating setup of the Pestchek model. Measurements at a dedicated laboratory experiment, called MRX or Magnetic Reconnection Experiment, have indicated existence of strong electromagnetic turbulence in current sheets undergoing fast reconnection. The origin of the turbulence has been identified as right-hand polarized whistler waves, propagating obliquely to the reconnecting field, with a phase velocity comparable to the relative drift velocity. These waves are consistent with an obliquely propagating electromagnetic lower-hybrid drift instability driven by drift speeds large compared to the Alfven speed in high-beta plasmas. Interestingly, this instability may explain electromagnetic turbulence also observed in collisionless shocks, which are common in energetic astrophysical phenomena.

Shear flow generation and energetics in electromagnetic turbulence

Zonal flows are recognized to play a crucial role for magnetized plasma confinement. The genesis of these flows out of turbulent fluctuations is therefore of significant interest. Here the relative importance of zonal flow generation mechanisms via the Reynolds stress, Maxwell stress, and geodesic acoustic mode (GAM) transfer in drift-Alfvén turbulence is investigated. By means of numerical computations the energy transfer into zonal flows owing to each of these effects is quantified. The importance of the three driving ingredients in electrostatic and electromagnetic turbulence for conditions relevant to the edge of fusion devices is revealed for a broad range of parameters. The Reynolds stress is found to provide a flow drive, while the electromagnetic Maxwell stress is in the cases considered a sink for the flow energy. In the limit of high plasma β, where electromagnetic effects and Alfvén dynamics are important, the Maxwell stress is found to cancel the Reynolds stress to a high degree. The geodesic oscillations, related to equilibrium pressure profile modifications due to poloidally asymmetric transport, can act as both sinks as drive terms, depending on the parameter regime. For high-β cases the GAMs are the main drive of the flow. This is also reflected in the frequency dependence of the zonal flows, showing a distinct peak at the GAM frequency in that regime.

Density dependence of trace tritium transport in H-mode Joint European Torus plasma

Tritium transport in edge localized mode (ELM) high confinement (H-mode) plasmas is analyzed here as a function of density for discharges from the recent trace tritium experimental campaign performed on Joint European Torus. In this campaign small amounts of tritium have been puffed or injected (with neutral beam injectors) into deuterium plasmas [K.-D. Zastrow, J. M. Adams, Yu. Baranov et al., Plasma Phys. Controlled Fusion 46, B255 (2004)]. Information about the tritium has been obtained from the evolution of the profiles of neutron emission simulated via the TRANSP [R. J. Goldston, D. C. McCune, H. H. Towner, S. L. Davis, R. J. Hawryluk, and G. L. Schmidt, J. Comput. Phys. 43, 61 (1981)] and SANCO (L. Lauro-Taroni, B. Alper, R. Giannella, K. Lawson, F. Marcus, M. Mattioli, P. Smeulders, and M. Von Hellermann, Proceedings of the 21st European Conference on Controlled Fusion and Plasma Physics, Montpelier, France, 1994) codes. A strong inverse correlation of tritium transport with plasma density is found in this analysis. The low tritium transport at high density is close to neoclassical values while the transport becomes strongly anomalous in low density plasmas. The thermal transport does not exhibit such a strong density dependence, leading to a varying ratio of thermal to tritium transport in these discharges. An interpretation of the density effects on the trace tritium transport, partially based on the test particle simulations in plasmas with stochastic magnetic field, is proposed. A simple model for the tritium diffusion coefficient and convective velocity, which includes the modification of the neoclassical particle diffusion in presence of electromagnetic turbulence [A. I. Smolyakov and P. N. Yushmanov, Nucl. Fusion 35, 383 (1993)] completed with an empirical density dependence, is developed. This model has positive β dependence in agreement with the results of the similarity experiments performed for trace tritium transport.