D. J. Sigmar

Plasma recombination and divertor detachment

Abstract We consider the influence on plasma recombination of the formation of negative and molecular ions in a divertor plasma. We take into account different atomic processes (vibrational excitation of molecular hydrogen, electron dissociative attachment, ion conversion, charge exchange and dissociative recombinations, dissociation and ionization, etc.) and find the expression for the effective plasma recombination rate constant from a suitably reduced set of coupled rate equations. We estimate the influence of the recombination process on divertor plasma behavior and find that for AlcatorC-MOD-like parameters plasma recombination due to negative and molecular ions becomes significant in the temperature range below a few eV. We conclude that plasma recombination is a strongly contributing mechanism for the explanation of divertor plasma detachment in low temperature plasmas.

Plasma recombination and molecular effects in tokamak divertors and divertor simulators

Analysis of the experimental data from tokamaks and linear divertor simulators leads to the conclusion that plasma recombination is a crucial element of plasma detachment. Different mechanisms of plasma recombination relevant to the experimental conditions of the tokamak scrape-off layer (SOL) and divertor simulators are considered. The physics of Molecular Activated Recombination (MAR) involving vibrationally excited molecular hydrogen are discussed. Although conventional Electron–Ion Recombination (EIR) alone can strongly alter the plasma parameters, MAR impact can be substantial for both tokamak SOL plasma and divertor simulators. Investigation of the effects of EIR on the plasma flow in divertor simulators shows that due to the balances of (a) energy transport and electron cooling, and (b) the plasma flow and recombination, that EIR extinguishes the simulator plasma at an electron temperature about 0.15 eV.

Kinetic effects in tokamak scrape-off layer plasmas

The short mean-free path expansion used in fluid modeling of scrape-off layer plasmas is often violated for typical discharge parameters, especially by the superthermal particles, which carry most of the heat flux. Thus, the tail of the distribution function can strongly depart from Maxwellian due to nonlocal mean-free path effects, which can modify plasma transport, impurity radiation, and plasma–neutral gas interactions. These nonlocal effects become particularly pronounced for detached plasma conditions that are characterized by sharp gradients in the plasma parameters along the magnetic field. These problems are being addressed by developing one spatial dimension and two velocity variables, fully kinetic, collisional, and time-dependent particle-in-cell code, W1 [Contrib. Plasma Phys. 34, 436 (1994)], and its parallel-computer version, PW1 [Contrib. Plasma Phys. 34, 424 (1996)]. Comparisons are made with the Fokker–Planck code ALLA [Phys. Plasmas 3, 1634 (1996)] and with experimental results. Kinetic ...

Simulation of dense recombining divertor plasmas with a Navier–Stokes neutral transport model

A two‐dimensional combined edge plasma Navier–Stokes neutral transport model is presented for the simulation of dense recombining divertor plasmas. This model includes ions, electrons, and neutral atoms which undergo Coulomb collisions, electron impact ionization, ion–neutral elastic collisions, three‐body and radiative recombination, and neutral–neutral collisions. The advanced fully implicit solution algorithm is briefly described and a variety of results on a model geometry are presented. It is shown that interesting neutral flow patterns can exist and that these flows can convect significant energy. A solution that ignores neutral–neutral collisions is shown to be quantitatively different from one that includes neutral–neutral collisions. Solutions are also shown to be sensitive to the plasma opacity for Lyman α radiation.

PLASMA HEATING BY ENERGETIC PARTICLES.

The interaction of a tenuous energetic test-particle species with a multispecies high temperature plasma is calculated. The Balescu-Lenard kinetic equation is used in order to include collective effects through the dielectric constant. Quantum corrections are made for close collisions. The theory is first applied to the slowing down of fusion born alpha particles in a mirror-confined plasma and theory and numerical results are compared to previous treatments and corrections are found. In Tokamak-like plasmas most of the alpha-particle energy goes into the electrons and the thermalization time is somewhat larger than the plasma lifetime but heating can nevertheless be substantial. Heating of a Tokamak-like plasma by injection of energetic neutrals is shown to be effective at injection energies ≤ 70 keV, possibly doubling the ion temperature when the injected particle density reaches 1% of the plasma density. For analytic estimates, a simple binary collision model for injection heating is given.

Thermal bifurcation of scrape‐off layer plasma and divertor detachment

Models to investigate the main features of plasma–neutral interactions in the recycling region of a tokamak divertor are developed for the two opposite extremes of fluid and Knudsen neutrals. Both neutral models show that a reduction of the heat flux into the hydrogen recycling region below a critical value leads to bifurcation (or rapid change) of the plasma parameters near the target. This bifurcation causes behavior in the scrape‐off layer, which is in agreement with the following main features of detached divertor regimes in current tokamak experiments: (i) strong decrease of the plasma temperature near the target, (ii) plasma pressure drop in the recycling region, and (iii) strong decrease of the target heat load and plasma flux onto the target. It is also shown that in the Knudsen limit, the neutral density in the divertor region cannot exceed a maximum density, which is of the order of 1–2×1013 cm−3 for current experiments.

Neoclassical analysis of impurity transport following transition to improved particle confinement

Strongly peaked impurity density profiles have been observed in Alcator C after injection of frozen hydrogen pellets. Recent experiments in TEXT, ASDEX, PBX, JET and TFTR have exhibited similar impurity accumulation during regimes of improved confinement. The paper presents calculations of the neoclassically predicted equilibrium profiles of intrinsic light and heavy impurities in Alcator C and light impurities in TEXT. These calculations were performed for comparison with experimentally determined peaked profiles observed after pellet fuelling. In both machines, carbon exists in the plateau collisionality regime and its transport is dominated by collisions with the hydrogen background ions and by temperature gradient effects. In Alcator C, molybdenum is in the Pfirsch-Schliiter regime and is driven mostly by collisions with carbon inside r/a ? 0.25 and by temperature gradients outside this radius. The full neoclassical multi-ion, mixed regime calculation required for the transport of carbon and molybdenum is presented. The predicted carbon profile in TEXT is in good agreement with observation; in Alcator C, less outward diffusion or an additional inward drift is required for the predicted carbon profile to agree with observation. The profile predicted for molybdenum (which may not be as close to equilibrium as carbon) is in fair agreement with observation. While the results of these studies do not support a rigorous claim of agreement with neoclassical impurity transport, the observed profiles for different regimes and experiments are consistently close to neoclassical-like peaking predictions.

Kinetic effects on particle and heat fluxes in detached plasmas

A model of high recycling scrape‐off layer plasmas in tokamaks is presented where both ion and electron species are described by nonlinear kinetic equations. Coulomb and charged‐neutral particle collisions are included. The ambipolar electric field and electrostatic sheath potential are evaluated self‐consistently. Two models of fluid neutral transport are used to distinguish the neutral density variation for different tokamak divertor geometries. These models are incorporated into a comprehensive three‐dimensional (1‐D, 2 V) hybrid collisional particle‐in‐cell–Monte Carlo code W1 [Contrib. Plasma Phys. 34, 436 (1994)]. This code is used to investigate the effects of neutrals on divertor plasma detachment phenomena and on parallel heat and particle fluxes in the presence of strong gradients where fluid descriptions break down. Results are given for simulations of detached and attached divertor plasmas, and comparisons are made with solutions from a one‐dimensional fluid model and with experimental observa...

Effects of alpha particles on the scattering function in CO2 laser scattering

It is shown that the alpha-particle contribution to the scattered power can be dominant in the coherent scattering of a CO2 laser in a Maxwellian plasma. For Ti = Te = 10 keV, the optimal forward-scattering angle is around 1.0°, with detection of the electron density fluctuation wavenumbers k⊥ >> k|| (relative to the toroidal magnetic field). A strong resonance occurs at the lower hybrid frequency. Because of the strong dependence of the scattered signal on the alpha-particle temperature and the alpha distribution function, it seems feasible that CO2 laser scattering, using heterodyne techniques, could give detailed local information on fusion alphas.

Effect of E×B drift on divertor plasma flows

Due to the influence of a sheared E×B drift affecting the inertia term in the plasma momentum equation a strong variation of the plasma pressure along the magnetic field lines can appear similar to experimental observations of the ‘‘detached divertor’’ regimes. The typical radial scale length of plasma parameter variation, such that the E×B drift becomes important, is of the order of the poloidal ion gyroradius.