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The observation of parallel ion velocity in the near-lunar wake approximately equal to external solar wind velocity can be explained within uncertainties by an analytic electrostatic expansion model. The one-dimensional model frequently used is inadequate because it does not account for the moon's spherical shape. However, application of a more recent generalization to three dimensions of the solution along characteristics predicts higher velocities and is probably sufficient to account for the SARA observations on the Chandrayaan-1 spacecraft.

The wake behind a large object (such as the moon) moving rapidly through a plasma (such as the solar wind) contains a region of depleted density, into which the plasma expands along the magnetic field, transverse to the flow. It is shown here that (in addition to any ion instability) a bump-on-tail which is unstable appears on the electrons' parallel velocity distribution function because of the convective non-conservation of parallel energy (drift-energization). It arises regardless of any non-thermal features on the external electron velocity distribution. The detailed electron distribution function throughout the wake is calculated by integration along orbits; and the substantial energy level of resulting electron plasma (Langmuir) turbulence is evaluated quasi-linearly. It peaks near the wake axis. If the mass of the electrons is artificially enhanced, for example in order to make numerical simulation feasible, then much more unstable electron distributions arise; but these are caused by the unphysical mass ratio., National Science Foundation (U.S.), United States. Dept. of Energy (Grant DE-FG02-06ER54982)

Operating experimental devices have provided key inputs to the design process for ITER axisymmetric control. In particular, experiments have quantified controllability and robustness requirements in the presence of realistic noise and disturbance environments, which are difficult or impossible to characterize with modelling and simulation alone. This kind of information is particularly critical for ITER vertical control, which poses the highest demands on poloidal field system performance, since the consequences of loss of vertical control can be severe. This work describes results of multi-machine studies performed under a joint ITPA experiment (MDC-13) on fundamental vertical control performance and controllability limits. We present experimental results from Alcator C-Mod, DIII-D, NSTX, TCV and JET, along with analysis of these data to provide vertical control performance guidance to ITER. Useful metrics to quantify this control performance include the stability margin and maximum controllable vertical displacement. Theoretical analysis of the maximum controllable vertical displacement suggests effective approaches to improving performance in terms of this metric, with implications for ITER design modifications. Typical levels of noise in the vertical position measurement and several common disturbances which can challenge the vertical control loop are assessed and analysed., United States Department of Energy (DE-FC02-04ER54698, DEAC52- 07NA27344, and DE-FG02-04ER54235)

A numerical scheme is described for accurately accommodating oblique, non-aligned, boundaries, on a three-dimensional cartesian grid. The scheme gives second-order accuracy in the solution for potential of Poisson's equation using compact difference stencils involving only nearest neighbors. Implementation for general "Robin" boundary conditions and for boundaries between media of different dielectric constant for arbitrary-shaped regions is described in detail. The scheme also provides for the interpolation of field (potential gradient) which, despite first-order peak errors immediately adjacent to the boundaries, has overall second order accuracy, and thus provides with good accuracy what is required in particle-in-cell codes: the force. Numerical tests on the implementation confirm the scalings and the accuracy., Comment: 15 pages, 7 figures

We present inboard (HFS) and outboard (LFS) radial electric field (E[subscript r]) and impurity temperature (T[subscript z]) measurements in the I-mode and H-mode pedestal of Alcator C-Mod. These measurements reveal strong Er wells at the HFS and the LFS midplane in both regimes and clear pedestals in T[subscript z], which are of similar shape and height for the HFS and LFS. While the H-mode E[subscript r] well has a radially symmetric structure, the E[subscript r] well in I-mode is asymmetric, with a stronger ExB shear layer at the outer edge of the E[subscript r] well, near the separatrix. Comparison of HFS and LFS profiles indicates that impurity temperature and plasma potential are not simultaneously flux functions. Uncertainties in radial alignment after mapping HFS measurements along flux surfaces to the LFS do not, however, allow direct determination as to which quantity varies poloidally and to what extent. Radially aligning HFS and LFS measurements based on the T[subscript z] profiles would result in substantial inboard-outboard variations of plasma potential and electron density. Aligning HFS and LFS E[subscript r] wells instead also approximately aligns the impurity poloidal flow profiles, while resulting in a LFS impurity temperature exceeding the HFS values in the region of steepest gradients by up to 70%. Considerations based on a simplified form of total parallel momentum balance and estimates of parallel and perpendicular heat transport time scales seem to favor an approximate alignment of the E[subscript r] wells and a substantial poloidal asymmetry in impurity temperature., United States. Dept. of Energy (Cooperative Agreement DE-FC02-99ER54512), Swiss National Science Foundation

The ion drag force arising from plasma flow past an embedded spherical grain is calculated self-consistently and non-linearly using particle in cell codes, accounting for ion-neutral collisions. Using ion velocity distribution appropriate for ion drift driven by a force field gives wake potential and force greatly different from a shifted Maxwellian distribution, regardless of collisionality. The low-collisionality forces are shown to be consistent with estimates based upon cross-sections for scattering in a Yukawa (shielded) grain field, but only if non-linear shielding length is used. Finite collisionality initially enhances the drag force, but only by up to a factor of 2. Larger collisionality eventually reduces the drag force. In the collisional regime, the drift distribution gives larger drag than the shift distribution even at velocities where their collisionless drags are equal. Comprehensive practical analytic formulas for force that fit the calculations are provided., United States. Dept. of Energy (National Science Foundation (U.S.). Grant DE-FG02-06ER54982), United States. Dept. of Energy. Office of Science (Graduate Research Fellowship Program)

Boundary layer flows in the Alcator C-Mod tokamak are systematically examined as magnetic topology (upper versus lower-null) and plasma density are changed. Utilizing a unique set of scanning Langmuir–Mach probes, including one on the high-field side (HFS) midplane, the poloidal variation of plasma flow components in the parallel, diamagnetic and radial directions are resolved in detail. It is found that the plasma flow pattern can be decomposed into two principal parts: (1) a drift-driven component, which lies within a magnetic flux surface and is divergence-free and (2) a transport-driven component, which gives rise to near-sonic parallel flows on the HFS scrape-off layer (SOL). Toroidal rotation, Pfirsch–Schlüter and transport-driven contributions are unambiguously identified. Transport-driven parallel flows are found to dominate the HFS particle fluxes; the total poloidal-directed flow accounts for ~1/3 to all of the ion flux arriving on the inner divertor. As a result, heat convection is found to be an important player in this region, consistent with the observation of divertor asymmetries that depend on the direction of B × ∇B relative to the active x-point. In contrast, the poloidal projection of parallel flow in the low-field SOL largely cancels with E[subscript r] × B flow; toroidal rotation is the dominant plasma motion there. The magnitude of the transport-driven poloidal flow is found to be quantitatively consistent with fluctuation-induced radial particle fluxes on the low-field side (LFS), identifying this as the primary drive mechanism. Fluctuation-induced fluxes on the HFS are found to be essentially zero, excluding turbulent inward transport as the mechanism that closes the circulation loop in this region., United States. Dept. of Energy (Cooperative Agreement DE-FC02-99ER54512)

Elementary but general statistical analyses determine the uncertainty arising from photon statistics in measuring a line shift and width. Account is taken of a background as well as the required signal.

Ion cyclotron resonance heating is the primary auxiliary heating on the Alcator C-Mod tokamak and is commonly used on other devices, and is planned for use on ITER. The RF-power density on C-Mod is above 5 MW m−3 providing for a unique opportunity to study wave–particle effects in the high RF power per particle regime. Minority heating produces a highly energetic tail in the minority distribution function which is measured using a compact neutral particle analyser. In this paper, we present the measurements of the fast-ion spectrum between 200 and 2 MeV, compiled over an entire experimental campaign. We also estimate the effective tail temperatures for the fast-ion distribution. We find that the fast-ion distribution is less energetic and less dense with increasing electron density; is more energetic with increasing plasma current; and is more dense but has no measurable change in energy with increasing RF power. Some possible explanations for these findings are discussed., United States. Dept. of Energy (Award DE-FC02-99ER54512)

In the Alcator C-Mod tokamak, strong, steady-state variations of molybdenum density within a flux surface are routinely observed in plasmas using hydrogen minority ion cyclotron resonant heating. In/out asymmetries, up to a factor of 2, occur with either inboard or outboard accumulation depending on the major radius of the minority resonance layer. These poloidal variations can be attributed to the impurity's high charge and large mass in the neoclassical parallel force balance. The large mass enhances the centrifugal force, causing outboard accumulation while the high charge enhances ion-impurity friction and makes impurities sensitive to small poloidal variations in the plasma potential. Quantitative comparisons between existing parallel high-Z impurity transport theories and experimental results for r/a < 0.7 show good agreement when the resonance layer is on the high-field side of the tokamak but disagree substantially for low-field side heating. Ion-impurity friction is insufficient to explain the experimental results, and the accumulation of impurity density on the inboard side of flux surface is shown to be driven by a poloidal potential variation due to magnetic trapping of non-thermal, cyclotron heated minority ions. Parallel impurity transport theory is extended to account for cyclotron effects and shown to agree with experimentally measured impurity density asymmetries., United States. Dept. of Energy (Agreement DE-FC02-99ER54512), United States. Dept. of Energy. Office of Fusion Energy Sciences (Postdoctoral Research Program)

The transverse force on a spherical charged grain lying in the plasma wake of another grain is analyzed to assess the importance of ion-drag perturbation, in addition to the wake-potential-gradient. The ion-drag perturbation is intrinsically one order smaller than the wake-potential force in the ratio of grain size (rp) to Debye length (lambdaDe). So ion-drag perturbation is important only in nonlinear wakes. Rigorous particle-in-cell calculations of the force are performed in the nonlinear regime with two interacting grains. It is found that even for quite large grains, rp/lambdaDe=0.1, the force is dominated by the wake-potential gradient. The wake-potential structure can then help explain the preferred alignment of floating dust grains., National Science Foundation (U.S.) (NSF/DOE Grant DE-FG02-06ER54982)

The mitigation of divertor heat fluxes is an active topic of investigation on existing tokamaks. One approach uses radiation, both inside and outside the last closed flux surface (LCFS), to convert plasma thermal energy, usually directed towards dedicated plasma facing components, to soft X-ray and ultraviolet radiation, spread over a much larger surface area. Recent enhanced D-α H-mode experiments on Alcator C-Mod varied the ICRF input power and radiative power losses via impurity seeding to demonstrate that normalized energy confinement depends strongly on the difference between input power and the radiated power inside the LCFS. These investigations also show that when seeded with either Ne or N2, a factor of two and higher reduction in outer divertor heat flux is achieved while maintaining H[subscript 98,y2] ∼ 1.0. Conversely, when seeding with Ar, confinement is limited to H[subscript 98,y2] ∼ 0.8 for a similar level of exhaust power., United States. Dept. of Energy (DOE Contract Number DEFC0299ER54512)

The ion saturation current to a spherical probe in the entire range of ion magnetization is computed with SCEPTIC3D, a newthree-dimensional version of the kinetic code SCEPTIC designed to study transverse plasma flows. Results are compared with prior two-dimensional calculations valid in the magneticfree regime (Hutchinson 2002 Plasma Phys. Control. Fusion 44 1953), and with recent semi-analytic solutions to the strongly magnetized transverse Mach probe problem (Patacchini and Hutchinson 2009 Phys. Rev. E 80 036403). At intermediate magnetization (ion Larmor radius close to the probe radius) the plasma density profiles show a complex three-dimensional structure that SCEPTIC3D can fully resolve, and, contrary to intuition, the ion current peaks provided the ion temperature is low enough. Our results are conveniently condensed in a single factor M[subscript c], function of ion temperature and magnetic field only, providing the theoretical calibration for a transverse Mach probe with four electrodes placed at 45◦ to the magnetic field in a plane of flow and magnetic field.

The classical problem of the interaction of a nonemitting spherical body with a zero mean-free-path continuum plasma is solved numerically in the full range of physically allowed free parameters (electron Debye length to body radius ratio, ion to electron temperature ratio, and body bias), and analytically in rigorously defined asymptotic regimes (weak and strong bias, weak and strong shielding, thin and thick sheath). Results include current-voltage characteristics as well as floating potential and capacitance, for both continuum and collisionless electrons. Our numerical computations show that for most combinations of physical parameters, there exists a closest asymptotic regime whose analytic solutions are accurate to 15% or better.

The object of this review is to summarize the achievements of research on the Alcator C-Mod tokamak [Hutchinson et al., Phys. Plasmas 1, 1511 (1994) and Marmar, Fusion Sci. Technol. 51, 261 (2007)] and to place that research in the context of the quest for practical fusion energy. C-Mod is a compact, high-field tokamak, whose unique design and operating parameters have produced a wealth of new and important results since it began operation in 1993, contributing data that extends tests of critical physical models into new parameter ranges and into new regimes. Using only high-power radio frequency (RF) waves for heating and current drive with innovative launching structures, C-Mod operates routinely at reactor level power densities and achieves plasma pressures higher than any other toroidal confinement device. C-Mod spearheaded the development of the vertical-target divertor and has always operated with high-Z metal plasma facing components—approaches subsequently adopted for ITER. C-Mod has made ground-breaking discoveries in divertor physics and plasma-material interactions at reactor-like power and particle fluxes and elucidated the critical role of cross-field transport in divertor operation, edge flows and the tokamak density limit. C-Mod developed the I-mode and the Enhanced Dα H-mode regimes, which have high performance without large edge localized modes and with pedestal transport self-regulated by short-wavelength electromagnetic waves. C-Mod has carried out pioneering studies of intrinsic rotation and demonstrated that self-generated flow shear can be strong enough in some cases to significantly modify transport. C-Mod made the first quantitative link between the pedestal temperature and the H-mode's performance, showing that the observed self-similar temperature profiles were consistent with critical-gradient-length theories and followed up with quantitative tests of nonlinear gyrokinetic models. RF research highlights include direct experimental observation of ion cyclotron range of frequency (ICRF) mode-conversion, ICRF flow drive, demonstration of lower-hybrid current drive at ITER-like densities and fields and, using a set of novel diagnostics, extensive validation of advanced RF codes. Disruption studies on C-Mod provided the first observation of non-axisymmetric halo currents and non-axisymmetric radiation in mitigated disruptions. A summary of important achievements and discoveries are included., United States. Dept. of Energy (Cooperative Agreement DE-FC02-99ER54512), United States. Dept. of Energy (Cooperative Agreement DE-FG03-94ER-54241), United States. Dept. of Energy (Cooperative Agreement DE-AC02-78ET- 51013), United States. Dept. of Energy (Cooperative Agreement DE-AC02-09CH11466), United States. Dept. of Energy (Cooperative Agreement DE-FG02-95ER54309), United States. Dept. of Energy (Cooperative Agreement DE-AC02-05CH11231), United States. Dept. of Energy (Cooperative Agreement DE-AC52-07NA27344), United States. Dept. of Energy (Cooperative Agreement DE-FG02- 97ER54392), United States. Dept. of Energy (Cooperative Agreement DE-SC00-02060)

The plasma force on grains of specified charge and height in a collisional DC plasma sheath is calculated using the multidimensional particle in cell code COPTIC. The background ion velocity distribution functions for the unperturbed sheath vary substantially with collisionality. The grain force is found to agree quite well with a combination of background electric-field force plus ion drag force. However, the drag force must take account of the non-Maxwellian (and spatially varying) ion distribution function, and the collisional drag enhancement. It is shown how to translate the dimensionless results into practical equilibrium including other forces such as gravity., United States. Dept. of Energy (National Science Foundation (U.S.). Grant DE-FG02-06ER54982)

We demonstrate that existing theories are insufficient to explain up/down asymmetries of argon x-ray emission in Alcator C-Mod ohmic plasmas. Instead of the poloidal variation, ñ[subscript z]/〈n[subscript z]〉, being of order the inverse aspect ratio, ϵ, and scaling linearly with B[subscript t][superscript _ over n][subscript e]/I[2 over p], it is observed over 0.8 < r/a < 1.0 to be of order unity and exhibits a threshold behaviour between 3.5, United States. Dept. of Energy (Contract DE-FC02-99ER54512), United States. Dept. of Energy (Fusion Research Postdoctoral Research Program)

The forces acting on a spherical conducting particle in a transversely flowing magnetized plasma are calculated in the entire range of magnetization and Debye length, using the particle code SCEPTIC3D (Patacchini and Hutchinson 2010 Plasma Phys. Control. Fusion 52 035005, 2011 Plasma Phys. Control. Fusion 53 025005). In short Debye length (i.e. high density) plasmas, both the ion-drag and Lorentz force arising from currents circulating inside the dust show strong components antiparallel to the convective electric field, suggesting that a free dust particle should gyrate faster than what predicted by its Larmor frequency. In intermediate to large Debye length conditions, by a downstream depletion effect already reported in unmagnetized strongly collisional regimes, the ion-drag in the direction of transverse flow can become negative. The internal Lorentz force, however, remains in the flow direction, and large enough in magnitude so that no spontaneous dust motion should occur., National Science Foundation (U.S.), United States. Dept. of Energy (grant DE-FG02-06ER54891)

The wake behind a spherical particle smaller than the Debye length ( De) in owing plasma is calculated using a particle-in-cell code. The results with di erent magnitudes of charge reveal substantial non-linear e ects down to values that for a oating particle would correspond to a particle radius approximately 10􀀀2 De. The peak potential in the oscillatory wake structure is strongly suppressed by non-linearity, never exceeding approximately 0:4 times the unperturbed ion energy. By contrast, the density peak arising from ion focusing can be many times the ambient. Strong heating of the ions occurs in the non-linear regime. Direct ion absorption by the particle is not important for the far wake unless the radius exceeds 10􀀀1 De, and is therefore never signi cant (for the far wake) in the linear regime. Reasonable agreement with full-scale linear-response calculations are obtained in the linear regime. The wake wavelength is con rmed and an explanation, in terms of the conical potential structure, is proposed for experimentally- observed oblique alignment of di erent-sized grains.