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Preserving the quality of a positron beam in a plasma-based accelerator, where a wakefield suitable for positron transport and acceleration is generated by means of an electron filament, is challenging. This is due to the nature of the wakefields, characterized by focusing fields that vary nonlinearly in the transverse direction, and by accelerating fields that are non-uniform. These fields also change slice-by-slice along the beam. Maintaining a high beam quality is pivotal for application of positron beams in a plasma-based collider. In this paper, we show that an initial background plasma temperature can help mitigate the positron beam quality degradation in plasma-based accelerators that rely on electron filaments. We show that temperature effects broaden the electron filament and smooth radially both the non-linear transverse and the non-uniform longitudinal wakefields. Using warm plasmas opens up new possibilities to improve beam quality in several plasma-based positron acceleration concepts.

The paper presents computer simulation studies of burst injection of carbon and tungsten dust particles in DIII-D-like edge plasmas. The injection causes a large transient influx of the low- and high-Z impurities associated with the dust ablation in the plasmas. The dust transport and the effects of the ablated impurities on the edge plasma dynamics in a modern mid-size tokamak geometry are investigated for low- and high-power plasma discharge conditions. The core plasma contamination with dust-ablated impurities and the factors affecting it are evaluated.

Coulomb collisions with background plasma can cause emittance growth in plasma accelerators. This paper extends the theory to consider collisions with not only motionless plasma ions but also plasma electrons with relativistic motion, based on the Frankel cross section. The theory is verified by particle-in-cell simulations with a Monte Carlo collision module. It is shown that the electron contribution has the same amount as that of ions in linear acceleration regime and may not be negligible in nonlinear regime depending on the plasma electron density and its relativistic bulk velocity.

This paper presents a theory for the collapse of the edge zonal shear layer, as observed at the density limit at low β. This paper investigates the scaling of the transport and mean profiles with the adiabaticity parameter α, with special emphasizes on fluxes relevant to zonal flow (ZF) generation. We show that the adiabaticity parameter characterizes the strength of production of zonal flows and so determines the state of turbulence. A 1D reduced model that self-consistently describes the spatiotemporal evolution of the mean density n¯, the azimuthal flow v¯y, and the turbulent potential enstrophy ε=⟨(ñ−∇2ϕ̃)2/2⟩—related to fluctuation intensity—is presented. Quasi-linear analysis determines how the particle flux Γn and vorticity flux Π=−χy∇2vy+Πres scale with α, in both hydrodynamic and adiabatic regimes. As the plasma response passes from adiabatic (α > 1) to hydrodynamic (α 1) to hydrodynamic (α

Reliable modeling of laser-plasma accelerators, where a short and intense laser pulse propagates in an underdense plasma over long distances, is a computationally challenging task. This is due to the great disparity among the scales involved in the modeling, ranging from the micrometer scale of the laser wavelength to, for instance, the meter scale of the laser-plasma interaction length for a multi-GeV-class laser-plasma accelerator. To reduce such imbalance, the time-averaged ponderomotive approximation may be used, where the plasma particle dynamics is analytically averaged over the laser frequency, and only spatiotemporal scales associated with the laser envelope are retained in the calculations, resulting in significant computational savings. In this paper, we characterize the accuracy and robustness of the time-averaged ponderomotive approximation for a range of laser parameters of interest for present and future laser-plasma accelerators, and we show that the error introduced by the averaging process is small in all relevant cases.

Reliable modeling of laser-plasma accelerators, where a short and intense laser pulse propagates in an underdense plasma over long distances, is a computationally challenging task. This is due to the great disparity among the scales involved in the modeling, ranging from the micrometer scale of the laser wavelength to, for instance, the meter scale of the laser-plasma interaction length for a multi-GeV-class laser-plasma accelerator. To reduce such imbalance, the time-averaged ponderomotive approximation may be used, where the plasma particle dynamics is analytically averaged over the laser frequency, and only spatiotemporal scales associated with the laser envelope are retained in the calculations, resulting in significant computational savings. In this paper, we characterize the accuracy and robustness of the time-averaged ponderomotive approximation for a range of laser parameters of interest for present and future laser-plasma accelerators, and we show that the error introduced by the averaging process is small in all relevant cases.

Witness beam stability and preservation of its ultra-low emittance have been identified as critical challenges toward realizing a TeV-class, plasma-based linear collider. In fact, the witness bunch parameters required by a future TeV-class collider have been expected to trigger hosing instability and background ion motion, leading to emittance degradation and, potentially, to bunch loss. Recently, it has been shown that ion motion suppresses the hosing instability, and proper longitudinal bunch shaping can eliminate the ion-motion-induced emittance growth. In this paper, we propose and analyze a plasma-based method to generate the shaped bunches that enable emittance preservation in the presence of ion motion. The method is based on an adiabatic matching procedure, where a bunch with an initially untapered profile is injected in the plasma accelerator stage with an energy low enough that ion motion effects are initially small. As the bunch accelerates, it is adiabatically compressed, ion motion is gradually triggered, and the bunch slowly but continuously readjusts itself in the ion motion-perturbed wakefield acquiring the desired taper. The production of tapered witness bunch profiles that minimize energy spread and preserve emittance for collider-relevant parameters could enable the use of plasma-based accelerators for high-energy physics applications.

Witness beam stability and preservation of its ultra-low emittance have been identified as critical challenges toward realizing a TeV-class, plasma-based linear collider. In fact, the witness bunch parameters required by a future TeV-class collider have been expected to trigger hosing instability and background ion motion, leading to emittance degradation and, potentially, to bunch loss. Recently, it has been shown that ion motion suppresses the hosing instability, and proper longitudinal bunch shaping can eliminate the ion-motion-induced emittance growth. In this paper, we propose and analyze a plasma-based method to generate the shaped bunches that enable emittance preservation in the presence of ion motion. The method is based on an adiabatic matching procedure, where a bunch with an initially untapered profile is injected in the plasma accelerator stage with an energy low enough that ion motion effects are initially small. As the bunch accelerates, it is adiabatically compressed, ion motion is gradually triggered, and the bunch slowly but continuously readjusts itself in the ion motion-perturbed wakefield acquiring the desired taper. The production of tapered witness bunch profiles that minimize energy spread and preserve emittance for collider-relevant parameters could enable the use of plasma-based accelerators for high-energy physics applications.

Coulomb collisions with background plasma are one source of emittance degradation in plasma accelerators. This paper shows that the emittance growth due to Coulomb collisions can be correctly captured in particle-in-cell simulations, with a proper Monte Carlo binary collision module. The theory of the emittance growth due to Coulomb collisions is extended from a monoenergetic matched beam to a mismatched beam with energy spread and is compared with simulation results.

Coulomb collisions with background plasma are one source of emittance degradation in plasma accelerators. This paper shows that the emittance growth due to Coulomb collisions can be correctly captured in particle-in-cell simulations, with a proper Monte Carlo binary collision module. The theory of the emittance growth due to Coulomb collisions is extended from a monoenergetic matched beam to a mismatched beam with energy spread and is compared with simulation results.

Laser-heated capillary discharge waveguides are novel, low plasma density guiding structures able to guide intense laser pulses over many diffraction lengths and have recently enabled the acceleration of electrons to 7.8 GeV by using a laser-plasma accelerator (LPA). These devices represent an improvement over conventional capillary discharge waveguides, as the channel matched spot size and plasma density can be tuned independently of the capillary radius. This has allowed the guiding of petawatt-scale pulses focused to small spot sizes within large diameter capillaries, preventing laser damage of the capillary structure. High performance channel-guided LPAs require control of matched spot size and density, which experiments and simulations reported here show can be tuned over a wide range via initial discharge and laser parameters. In this paper, measurements of the matched spot size and plasma density in laser-heated capillary discharges are presented, which are found to be in excellent agreement with simulations performed using the MHD code MARPLE. Strategies for optimizing accelerator performance are identified based on these results.

Laser-heated capillary discharge waveguides are novel, low plasma density guiding structures able to guide intense laser pulses over many diffraction lengths and have recently enabled the acceleration of electrons to 7.8 GeV by using a laser-plasma accelerator (LPA). These devices represent an improvement over conventional capillary discharge waveguides, as the channel matched spot size and plasma density can be tuned independently of the capillary radius. This has allowed the guiding of petawatt-scale pulses focused to small spot sizes within large diameter capillaries, preventing laser damage of the capillary structure. High performance channel-guided LPAs require control of matched spot size and density, which experiments and simulations reported here show can be tuned over a wide range via initial discharge and laser parameters. In this paper, measurements of the matched spot size and plasma density in laser-heated capillary discharges are presented, which are found to be in excellent agreement with simulations performed using the MHD code MARPLE. Strategies for optimizing accelerator performance are identified based on these results.

Few, if any, of the many papers on turbulence spreading address the key question of how turbulence spreading actually affects the profile structure. Here, we are using a reduced model to answer that question. Turbulence spreading is most relevant near regions where the profiles support a strong intensity gradient ∇I. One such case is at the edge of an L mode discharge, near a source of turbulence [i.e., either a localized source of edge turbulence or an influx of turbulence from the scrape-off layer (SOL)]. Another is in “No Man's Land” (NML), which connects the pedestal to the stiff core in H mode. In the case of L mode, without an edge intensity source, the turbulence intensity profile is nearly flat and spreading has a weak effect. An edge localized source increases the edge ∇I, which then drives inward spreading. Invasion of turbulence from the SOL to the edge softens the edge pressure gradient. In H mode, the strong shear suppression of pedestal turbulence necessarily forces a sharp ∇I in NML. This sharp ∇I drives a significant flux of turbulence from the core to the pedestal, where it is ultimately dissipated by shearing. Counter-intuitively, the results indicate that spreading actually increases the pedestal height and width and hence the energy content in H mode. This suggests that models of the pedestal structure should include NML turbulence spreading effects. The relation of avalanches to spreading is studied. Spreading weakly affects the avalanche distribution, but the spatiotemporal correlation of intensity increases with spreading.

This paper describes the ecology of drift wave turbulence and mean flows in the coupled drift-ion acoustic wave plasma of a CSDX linear device. A 1D reduced model that studies the spatiotemporal evolution of plasma mean density n¯, and mean flows v¯y and v¯z, in addition to fluctuation intensity ε, is presented. Here, ε=〈ñ2+(∇⊥ϕ̃)2+ṽz2〉 is the conserved energy field. The model uses a mixing length lmix inversely proportional to both axial and azimuthal flow shear. This form of lmix closes the loop on total energy. The model self-consistently describes variations in plasma profiles, including mean flows and turbulent stresses. It investigates the energy exchange between the fluctuation intensity and mean profiles via particle flux 〈ñṽx〉 and Reynolds stresses 〈ṽxṽy〉 and 〈ṽxṽz〉. Acoustic coupling breaks parallel symmetry and generates a parallel residual stress Πxzres. The model uses a set of equations to explain the acceleration of v¯y and v¯z via Πxyres∝∇n¯ and Πxyres∝∇n¯. Flow dynamics in the parallel direction are related to those in the perpendicular direction through an empirical coupling constant σVT. This constant measures the degree of symmetry breaking in the 〈kmkz〉 correlator and determines the efficiency of ∇n¯ in driving v¯z. The model also establishes a relation between ∇v¯y and ∇v¯z, via the ratio of the stresses Πxyres and Πxzres. When parallel to perpendicular flow coupling is weak, axial Reynolds power PxzRe=−〈ṽxṽz〉∇v¯z is less than the azimuthal Reynolds power PxyRe=−〈ṽxṽy〉∇v¯y. The model is then reduced to a 2-field predator/prey model where v¯z is parasitic to the system and fluctuations evolve self-consistently. Finally, turbulent diffusion in CSDX follows the scaling: DCSDX=DBρ⋆0.6, where DB is the Bohm diffusion coefficient and ρ⋆ is the ion gyroradius normalized to the density gradient |∇n¯/n¯| −1.

This paper presents a theory for the formation and evolution of coupled density staircases and zonal shear profiles in a simple model of drift-wave turbulence. Density, vorticity, and fluctuation potential enstrophy are the fields evolved in this system. Formation of staircase structures is due to inhomogeneous mixing of generalized potential vorticity (PV), resulting in the sharpening of density and vorticity gradients in some regions, and weakening them in others. When the PV gradients steepen, the density staircase structure develops into a lattice of mesoscale “jumps,” and “steps,” which are, respectively, the regions of local gradient steepening and flattening. The jumps merge and migrate in radius, leading to the development of macroscale profile structures from mesoscale elements. The positive feedback process, which drives the staircase formation occurs via a Rhines scale dependent mixing length. We present extensive studies of bifurcation physics of the global state, including results on the global flux-gradient relations (flux landscapes) predicted by the model. Furthermore, we demonstrate that, depending on the sources and boundary conditions, either a region of enhanced confinement, or a region with strong turbulence can form at the edge. This suggests that the profile self-organization is a global process, though one which can be described by a local, but nonlinear model. This model is the first to demonstrate how the mesoscale condensation of staircases leads to global states of enhanced confinement.

An analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases to exist because of the upstream ion reflection. The reflection transforms the soliton into a shock with a trailing wave and a foot populated by the reflected ions. The solution relates parameters of the entire shock structure, such as the maximum and minimum of the potential in the trailing wave, the height of the foot, as well as the shock Mach number, to the number of reflected ions. This relation is resolvable for any given distribution of the upstream ions. In this paper, we have resolved it for a simple "box" distribution. Two separate models of electron interaction with the shock are considered. The first model corresponds to the standard Boltzmannian electron distribution in which case the critical shock Mach number only insignificantly increases from M1.6 (no ion reflection) to M1.8 (substantial reflection). The second model corresponds to adiabatically trapped electrons. They produce a stronger increase, from M3.1 to M4.5. The shock foot that is supported by the reflected ions also accelerates them somewhat further. A self-similar foot expansion into the upstream medium is described analytically.

An analytic solution describing an ion-acoustic collisionless shock, self-consistently with the evolution of shock-reflected ions, is obtained. The solution extends the classic soliton solution beyond a critical Mach number, where the soliton ceases to exist because of the upstream ion reflection. The reflection transforms the soliton into a shock with a trailing wave and a foot populated by the reflected ions. The solution relates parameters of the entire shock structure, such as the maximum and minimum of the potential in the trailing wave, the height of the foot, as well as the shock Mach number, to the number of reflected ions. This relation is resolvable for any given distribution of the upstream ions. In this paper, we have resolved it for a simple "box" distribution. Two separate models of electron interaction with the shock are considered. The first model corresponds to the standard Boltzmannian electron distribution in which case the critical shock Mach number only insignificantly increases from M1.6 (no ion reflection) to M1.8 (substantial reflection). The second model corresponds to adiabatically trapped electrons. They produce a stronger increase, from M3.1 to M4.5. The shock foot that is supported by the reflected ions also accelerates them somewhat further. A self-similar foot expansion into the upstream medium is described analytically.

This paper studies effects of q-profile structure on turbulence spreading. It reports results of numerical experiments using global gyrokinetic simulations. We examine propagation of turbulence, triggered by an identical linear instability in a source region, into an adjacent, linearly stable region with variable q-profile. The numerical experiments are designed so as to separate the physics of turbulence spreading from that of linear stability. The strength of turbulence spreading is measured by the penetration depth of turbulence. Dynamics of spreading are elucidated by fluctuation intensity balance analysis, using a model intensity evolution equation which retains nonlinear diffusion and damping, and linear growth. It is found that turbulence spreading is strongly affected by magnetic shear s, but is hardly altered by the safety factor q itself. There is an optimal range of modest magnetic shear which maximizes turbulence spreading. For high to modest shear values, the spreading is enhanced by the increase of the mode correlation length with decreasing magnetic shear. However, the efficiency of spreading drops for sufficiently low magnetic shear even though the mode correlation length is comparable to that for the case of optimal magnetic shear. The reduction of spreading is attributed to the increase in time required for the requisite nonlinear mode-mode interactions. The effect of increased interaction time dominates that of increased mode correlation length. Our findings of the reduction of spreading and the increase in interaction time at weak magnetic shear are consistent with the well-known benefit of weak or reversed magnetic shear for core confinement enhancement. Weak shear is shown to promote locality, as well as stability.

This paper studies effects of q-profile structure on turbulence spreading. It reports results of numerical experiments using global gyrokinetic simulations. We examine propagation of turbulence, triggered by an identical linear instability in a source region, into an adjacent, linearly stable region with variable q-profile. The numerical experiments are designed so as to separate the physics of turbulence spreading from that of linear stability. The strength of turbulence spreading is measured by the penetration depth of turbulence. Dynamics of spreading are elucidated by fluctuation intensity balance analysis, using a model intensity evolution equation which retains nonlinear diffusion and damping, and linear growth. It is found that turbulence spreading is strongly affected by magnetic shear s, but is hardly altered by the safety factor q itself. There is an optimal range of modest magnetic shear which maximizes turbulence spreading. For high to modest shear values, the spreading is enhanced by the increase of the mode correlation length with decreasing magnetic shear. However, the efficiency of spreading drops for sufficiently low magnetic shear even though the mode correlation length is comparable to that for the case of optimal magnetic shear. The reduction of spreading is attributed to the increase in time required for the requisite nonlinear mode-mode interactions. The effect of increased interaction time dominates that of increased mode correlation length. Our findings of the reduction of spreading and the increase in interaction time at weak magnetic shear are consistent with the well-known benefit of weak or reversed magnetic shear for core confinement enhancement. Weak shear is shown to promote locality, as well as stability.

This paper reports on the theoretical and simulation results of a gyro-Landau-fluid extension of the BOUT++ code, which contributes to increasing the physics understanding of edge-localized-modes (ELMs). Large ELMs with low-to-intermediate-n peeling-ballooning (P-B) modes are significantly suppressed due to finite Larmor radius (FLR) effects when the ion temperature increases. For type-I ELMs, it is found from linear simulations that retaining complete first order FLR corrections as resulting from the incomplete "gyroviscous cancellation" in Braginskii's two-fluid model is necessary to obtain good agreement with gyro-fluid results for high ion temperature cases (Ti3 keV) when the ion density has a strong radial variation, which goes beyond the simple local model of ion diamagnetic stabilization of ideal ballooning modes. The maximum growth rate is inversely proportional to Ti because the FLR effect is proportional to Ti. The FLR effect is also proportional to toroidal mode number n, so for high n cases, the P-B mode is stabilized by FLR effects. Nonlinear gyro-fluid simulations show results that are similar to those from the two-fluid model, namely that the P-B modes trigger magnetic reconnection, which drives the collapse of the pedestal pressure. Due to the additional FLR-corrected nonlinear E × B convection of the ion gyro-center density, for a ballooning-dominated equilibrium the gyro-fluid model further limits the radial spreading of ELMs. In six-field two fluid simulations, the parallel thermal diffusivity is found to prevent the ELM encroachment further into core plasmas and therefore leads to steady state L-mode profiles. The simulation results show that most energy is lost via ion channel during an ELM event, followed by particle loss and electron energy loss. Because edge plasmas have significant spatial inhomogeneities and complicated boundary conditions, we have developed a fast non-Fourier method for the computation of Landau-fluid closure terms based on an accurate and tunable approximation. The accuracy and the fast computational scaling of the method have been demonstrated. © 2013 AIP Publishing LLC.

This paper reports on the theoretical and simulation results of a gyro-Landau-fluid extension of the BOUT++ code, which contributes to increasing the physics understanding of edge-localized-modes (ELMs). Large ELMs with low-to-intermediate-n peeling-ballooning (P-B) modes are significantly suppressed due to finite Larmor radius (FLR) effects when the ion temperature increases. For type-I ELMs, it is found from linear simulations that retaining complete first order FLR corrections as resulting from the incomplete "gyroviscous cancellation" in Braginskii's two-fluid model is necessary to obtain good agreement with gyro-fluid results for high ion temperature cases (Ti3 keV) when the ion density has a strong radial variation, which goes beyond the simple local model of ion diamagnetic stabilization of ideal ballooning modes. The maximum growth rate is inversely proportional to Ti because the FLR effect is proportional to Ti. The FLR effect is also proportional to toroidal mode number n, so for high n cases, the P-B mode is stabilized by FLR effects. Nonlinear gyro-fluid simulations show results that are similar to those from the two-fluid model, namely that the P-B modes trigger magnetic reconnection, which drives the collapse of the pedestal pressure. Due to the additional FLR-corrected nonlinear E × B convection of the ion gyro-center density, for a ballooning-dominated equilibrium the gyro-fluid model further limits the radial spreading of ELMs. In six-field two fluid simulations, the parallel thermal diffusivity is found to prevent the ELM encroachment further into core plasmas and therefore leads to steady state L-mode profiles. The simulation results show that most energy is lost via ion channel during an ELM event, followed by particle loss and electron energy loss. Because edge plasmas have significant spatial inhomogeneities and complicated boundary conditions, we have developed a fast non-Fourier method for the computation of Landau-fluid closure terms based on an accurate and tunable approximation. The accuracy and the fast computational scaling of the method have been demonstrated. © 2013 AIP Publishing LLC.

This paper reports the results of gyrokinetic simulation studies of ion temperature gradient driven turbulence which investigate the role of non-resonant modes in turbulence spreading, turbulence regulation, and self-generated plasma rotation. Non-resonant modes, which are those without a rational surface within the simulation domain, are identified as nonlinearly driven, radially extended convective cells. Even though the amplitudes of such convective cells are much smaller than that of the resonant, localized turbulence eddies, we find from bicoherence analysis that the mode-mode interactions in the presence of such convective cells increase the efficiency of turbulence spreading associated with nonlocality phenomena. Artificial suppression of the convective cells shows that turbulence spreading is reduced, and that the turbulence intensity profile is more localized. The more localized turbulence intensity profile produces stronger Reynolds stress and E × B shear flows, which in turn results in more effective turbulence self-regulation. This suggests that models without non-resonant modes may significantly underestimate turbulent fluctuation levels and transport. © 2012 American Institute of Physics.

This paper reports the results of gyrokinetic simulation studies of ion temperature gradient driven turbulence which investigate the role of non-resonant modes in turbulence spreading, turbulence regulation, and self-generated plasma rotation. Non-resonant modes, which are those without a rational surface within the simulation domain, are identified as nonlinearly driven, radially extended convective cells. Even though the amplitudes of such convective cells are much smaller than that of the resonant, localized turbulence eddies, we find from bicoherence analysis that the mode-mode interactions in the presence of such convective cells increase the efficiency of turbulence spreading associated with nonlocality phenomena. Artificial suppression of the convective cells shows that turbulence spreading is reduced, and that the turbulence intensity profile is more localized. The more localized turbulence intensity profile produces stronger Reynolds stress and E × B shear flows, which in turn results in more effective turbulence self-regulation. This suggests that models without non-resonant modes may significantly underestimate turbulent fluctuation levels and transport. © 2012 American Institute of Physics.

This response demonstrates that the comment by Peeters contains an incorrect and misleading interpretation of our paper [T. S. Hahm, Phys. Plasmas 15, 055902 (2008)] regarding the density gradient dependence of momentum pinch and the turbulent equipartition theory. © 2009 American Institute of Physics.

This response demonstrates that the comment by Peeters contains an incorrect and misleading interpretation of our paper [T. S. Hahm, Phys. Plasmas 15, 055902 (2008)] regarding the density gradient dependence of momentum pinch and the turbulent equipartition theory. © 2009 American Institute of Physics.

The experimental studies on zonal flows and turbulence have been carried out in Compact Helical System [K. Matsuoka, S. Kubo, M. Hosokawa, in Plasma Physics and Controlled Nuclear Fusion Research, Proc. 12th Int. Conf., Nice, 1988 (International Atomic Energy Agency, Vienna, 1989, Vol. 2, p. 411] using twin heavy ion beam probes. The paper presents the experimental observations of stationary zonal flow, nonlinear couplings between zonal flow and turbulence, and the role of zonal flow in the improved confinement, together with the recent discovery of zonal magnetic field. The presented experimental results strongly support the new paradigm that the plasma transport should be considered as a system of drift wave and zonal flows, and provides the first direct evidence for turbulence dynamo that the structured magnetic field can be really generated by turbulence. © 2008 American Institute of Physics.

The experimental studies on zonal flows and turbulence have been carried out in Compact Helical System [K. Matsuoka, S. Kubo, M. Hosokawa, in Plasma Physics and Controlled Nuclear Fusion Research, Proc. 12th Int. Conf., Nice, 1988 (International Atomic Energy Agency, Vienna, 1989, Vol. 2, p. 411] using twin heavy ion beam probes. The paper presents the experimental observations of stationary zonal flow, nonlinear couplings between zonal flow and turbulence, and the role of zonal flow in the improved confinement, together with the recent discovery of zonal magnetic field. The presented experimental results strongly support the new paradigm that the plasma transport should be considered as a system of drift wave and zonal flows, and provides the first direct evidence for turbulence dynamo that the structured magnetic field can be really generated by turbulence. © 2008 American Institute of Physics.

This paper presents a novel, unified approach to the theory of turbulent transport of parallel momentum by collisionless drift waves. The physics of resonant and nonresonant off-diagonal contributions to the momentum flux is emphasized, and collisionless momentum exchange between waves and particles is accounted for. Two related momentum conservation theorems are derived. These relate the resonant particle momentum flux, the wave momentum flux, and the refractive force. A perturbative calculation, in the spirit of Chapman-Enskog theory, is used to obtain the wave momentum flux, which contributes significantly to the residual stress. A general equation for mean k (〈 k 〉) is derived and used to develop a generalized theory of symmetry breaking. The resonant particle momentum flux is calculated, and pinch and residual stress effects are identified. The implications of the theory for intrinsic rotation and momentum transport bifurcations are discussed. © 2008 American Institute of Physics.

This paper presents a novel, unified approach to the theory of turbulent transport of parallel momentum by collisionless drift waves. The physics of resonant and nonresonant off-diagonal contributions to the momentum flux is emphasized, and collisionless momentum exchange between waves and particles is accounted for. Two related momentum conservation theorems are derived. These relate the resonant particle momentum flux, the wave momentum flux, and the refractive force. A perturbative calculation, in the spirit of Chapman-Enskog theory, is used to obtain the wave momentum flux, which contributes significantly to the residual stress. A general equation for mean k (〈 k 〉) is derived and used to develop a generalized theory of symmetry breaking. The resonant particle momentum flux is calculated, and pinch and residual stress effects are identified. The implications of the theory for intrinsic rotation and momentum transport bifurcations are discussed. © 2008 American Institute of Physics.

This paper analyzes the properties of a two-field critical gradient model that couples a heat equation to an evolution equation for the turbulence intensity. It is shown that the dynamics of a perturbation is ballistic or diffusive depending on the shape of the pulse and also on the distance of the temperature gradient to the instability threshold. This dual character appears in the linear response of this model for a wave packet. It is recovered when investigating the nonlinear solutions of this system. Both self-similar diffusive fronts and ballistic fronts are shown to exist. When the propagation is ballistic, it is found that the front velocity is the geometric mean between the turbulent diffusion coefficient and a microinstability growth rate. © 2007 American Institute of Physics.

This paper analyzes the properties of a two-field critical gradient model that couples a heat equation to an evolution equation for the turbulence intensity. It is shown that the dynamics of a perturbation is ballistic or diffusive depending on the shape of the pulse and also on the distance of the temperature gradient to the instability threshold. This dual character appears in the linear response of this model for a wave packet. It is recovered when investigating the nonlinear solutions of this system. Both self-similar diffusive fronts and ballistic fronts are shown to exist. When the propagation is ballistic, it is found that the front velocity is the geometric mean between the turbulent diffusion coefficient and a microinstability growth rate. © 2007 American Institute of Physics.

The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied with a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart. Recent numerical studies have shown that in such configurations high-m modes are strongly unstable and may peak around m similar to 10. In this paper, it is first demonstrated that this result agrees with existing linear theory for DTMs. Based on this theory, a semiempirical formula for the dependence of m(peak) on the system parameters is proposed. Second, with the use of nonlinear simulations, it is shown that the presence of fast growing high-m modes leads to a rapid turbulent collapse in an annular region, where small magnetic island structures form. Furthermore, consideration is given to the evolution of low-m modes, in particular the global m=1 internal kink, which can undergo nonlinear driving through coupling to fast growing linear high-m DTMs. Factors influencing the details of the dynamics are discussed. These results may be relevant to the understanding of the magnetohydrodynamic activity near the minimum of q and may thus be of interest for studies on stability and confinement of advanced tokamaks.(c) 2007 American Institute of Physics.

The DIII-D Advanced Tokamak (AT) program in the DIII-D tokamak [J. L. Luxon, Plasma Physics and Controlled Fusion Research, 1986, Vol. I (International Atomic Energy Agency, Vienna, 1987), p. 159] is aimed at developing a scientific basis for steady-state, high-performance operation in future devices. This requires simultaneously achieving 100% noninductive operation with high self-driven bootstrap current fraction and toroidal beta. Recent progress in this area includes demonstration of 100% noninductive conditions with toroidal beta, ΒT =3.6%, normalized beta, ΒN =3.5, and confinement factor, H89 =2.4 with the plasma current driven completely by bootstrap, neutral beam current drive, and electron cyclotron current drive (ECCD). The equilibrium reconstructions indicate that the noninductive current profile is well aligned, with little inductively driven current remaining anywhere in the plasma. The current balance calculation improved with beam ion redistribution that was supported by recent fast ion diagnostic measurements. The duration of this state is limited by pressure profile evolution, leading to magnetohydrodynamic (MHD) instabilities after about 1 s or half of a current relaxation time (τCR). Stationary conditions are maintained in similar discharges (∼90% noninductive), limited only by the 2 s duration (1 τCR) of the present ECCD systems. By discussing parametric scans in a global parameter and profile databases, the need for low density and high beta are identified to achieve full noninductive operation and good current drive alignment. These experiments achieve the necessary fusion performance and bootstrap fraction to extrapolate to the fusion gain, Q=5 steady-state scenario in the International Thermonuclear Experimental Reactor (ITER) [R. Aymar, Fusion Energy Conference on Controlled Fusion and Plasma Physics, Sorrento, Italy (International Atomic Energy Agency, Vienna, 1987), paper IAEA-CN-77/OV-1]. The modeling tools that have been successfully employed to both plan and interpret the experiment are used to plan future DIII-D experiments with higher power and longer pulse ECCD and fast wave and co- and counterneutral beam injection in a pumped double-null configuration. The models predict our ability to control the current and pressure profiles to reach full noninductivity with increased beta, bootstrap fraction, and duration. The same modeling tools are applied to ITER, predicting favorable prospects for the success of the ITER steady-state scenario. © 2006 American Institute of Physics.

The DIII-D Advanced Tokamak (AT) program in the DIII-D tokamak [J. L. Luxon, Plasma Physics and Controlled Fusion Research, 1986, Vol. I (International Atomic Energy Agency, Vienna, 1987), p. 159] is aimed at developing a scientific basis for steady-state, high-performance operation in future devices. This requires simultaneously achieving 100% noninductive operation with high self-driven bootstrap current fraction and toroidal beta. Recent progress in this area includes demonstration of 100% noninductive conditions with toroidal beta, ΒT =3.6%, normalized beta, ΒN =3.5, and confinement factor, H89 =2.4 with the plasma current driven completely by bootstrap, neutral beam current drive, and electron cyclotron current drive (ECCD). The equilibrium reconstructions indicate that the noninductive current profile is well aligned, with little inductively driven current remaining anywhere in the plasma. The current balance calculation improved with beam ion redistribution that was supported by recent fast ion diagnostic measurements. The duration of this state is limited by pressure profile evolution, leading to magnetohydrodynamic (MHD) instabilities after about 1 s or half of a current relaxation time (τCR). Stationary conditions are maintained in similar discharges (∼90% noninductive), limited only by the 2 s duration (1 τCR) of the present ECCD systems. By discussing parametric scans in a global parameter and profile databases, the need for low density and high beta are identified to achieve full noninductive operation and good current drive alignment. These experiments achieve the necessary fusion performance and bootstrap fraction to extrapolate to the fusion gain, Q=5 steady-state scenario in the International Thermonuclear Experimental Reactor (ITER) [R. Aymar, Fusion Energy Conference on Controlled Fusion and Plasma Physics, Sorrento, Italy (International Atomic Energy Agency, Vienna, 1987), paper IAEA-CN-77/OV-1]. The modeling tools that have been successfully employed to both plan and interpret the experiment are used to plan future DIII-D experiments with higher power and longer pulse ECCD and fast wave and co- and counterneutral beam injection in a pumped double-null configuration. The models predict our ability to control the current and pressure profiles to reach full noninductivity with increased beta, bootstrap fraction, and duration. The same modeling tools are applied to ITER, predicting favorable prospects for the success of the ITER steady-state scenario. © 2006 American Institute of Physics.

Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of a plasma confined by an axisymmetric magnetic field. Nevertheless, they are limited to low beta or small plasma pressure. Combining a nonconservative variational principle with a contour dynamics approach, the approach presented in this paper converges for extreme high beta configurations. By reducing the dimension of the problem from two to one, a compact and efficient numerical algorithm can be developed, and a wide range of boundary shapes can be utilized. Furthermore, the iterative nature of this technique greatly facilitates convergence at high beta while minimizing computation times.

Theoretical studies of mean field electrodynamics for diffusive processes in the electron magnetohydrodynamic (EMHD) model is presented. In contrast to magnetohydrodynamics (MHD), the evolution of the magnetic field here is governed by a nonlinear equation in magnetic field variables. A detailed description of diffusive processes in two dimensions are presented in this paper. In particular, it has been shown analytically that the turbulent magnetic field diffusivity is suppressed from naive quasilinear estimates. It is shown that for complete whistlerization of the spectrum, turbulent diffusivity vanishes. The question of whistlerization of the turbulent spectrum is investigated numerically, and a reasonable tendency towards whistlerization is observed. Numerical studies also show suppression of magnetic field diffusivity in accordance with analytical estimates. © 2000 American Institute of Physics.

Theoretical studies of mean field electrodynamics for diffusive processes in the electron magnetohydrodynamic (EMHD) model is presented. In contrast to magnetohydrodynamics (MHD), the evolution of the magnetic field here is governed by a nonlinear equation in magnetic field variables. A detailed description of diffusive processes in two dimensions are presented in this paper. In particular, it has been shown analytically that the turbulent magnetic field diffusivity is suppressed from naive quasilinear estimates. It is shown that for complete whistlerization of the spectrum, turbulent diffusivity vanishes. The question of whistlerization of the turbulent spectrum is investigated numerically, and a reasonable tendency towards whistlerization is observed. Numerical studies also show suppression of magnetic field diffusivity in accordance with analytical estimates. © 2000 American Institute of Physics.