Anomalous Ion Research Articles

Reduction of ion thermal diffusivity associated with the transition of the radial electric field in neutral-beam-heated plasmas in the large helical device.

Recent large helical device experiments revealed that the transition from ion root to electron root occurred for the first time in neutral-beam-heated discharges, where no nonthermal electrons exist. The measured values of the radial electric field were found to be in qualitative agreement with those estimated by neoclassical theory. A clear reduction of ion thermal diffusivity was observed after the mode transition from ion root to electron root as predicted by neoclassical theory when the neoclassical ion loss is more dominant than the anomalous ion loss.

High-power heating of spherical tori by use of magnetic reconnection

A novel high-power heating experiment of spherical tori (ST) has been developed in the TS-3 reconnection device using magnetic reconnection of merging STs. This method enables us to inject whole magnetic and thermal energies of a colliding ST into a target ST within short reconnection time. The maximum heating power of 15 MW was obtained in our low-field (0.03–0.08 T) and small-scale (R < 0.2 m) merging experiment. This heating energy is provided mostly by anomalous ion heating effect of magnetic reconnection. The ion heating energy and the merging speed increases with decreasing the q-value (B t component) of the ST. This heating effect causes the β-values of STs to increase by factor 2–3.

Anomalous ion heating from ambipolar-constrained magnetic fluctuation-induced transport

A kinetic theory for the anomalous heating of ions from energy stored in magnetic turbulence is presented. Imposing self-consistency through the constitutive relations between particle distributions and fields, a turbulent Kirchhoff’s Law is derived that expresses a direct connection between rates of ion heating and electron thermal transport. This connection arises from the kinematics of electron motion along turbulent fields, which results in granular structures in the electron distribution. The drag exerted on these structures through emission into collective modes mediates an effective ambipolar constraint on transport. Resonant damping of the collective modes by ions produces the heating. In collisionless plasmas the rate of ion damping controls the rate of emission, and hence the ambipolar-constrained electron heat flux. The heating rate is calculated for both a resonant and nonresonant magnetic fluctuation spectrum and compared with observations. The theoretical heating rate is sufficient to account for the observed twofold rise in ion temperature during sawtooth events in experimental discharges.

Confinement in START beam heated discharges

Plasma profile data, from a number of neutral beam heated discharges in the START spherical tokamak, have been exploited for transport analysis over a wide range of β (where β = 2 μ0 p/B2, μ0 is the permeability of free space, p is plasma pressure, and B is toroidal magnetic field strength). Magnetic equilibrium reconstructions, and Monte Carlo calculations of the neutral beam heat and particle sources, are incorporated in a particle and power balance code to extract the thermal diffusivities. Ion transport is found to be close to the level predicted by the Chang-Hinton formulation of neoclassical theory, with little margin for significant anomalous ion heat transport, except close to the plasma edge. Off-diagonalcorrections to the Chang-Hinton formula for the neoclassical ion thermal diffusivity do not significantly modify our conclusion. The electron thermal diffusivity exceeds the ion thermal diffusivity across the plasma cross-section, and is comparable with the levels predicted by the Rebut-Lallia-Watkins and Lackner-Gottardi-Connor models of anomaloustransport. The measured START ion temperature gradients lie below the criticalgradients predicted by the IFS-PPPL modelfor the onset of ion temperature gradient driven drift wave turbulence. Data from the larger, higher current and lower collisionality devices, MAST and NSTX, will supplement START data and further improve our understanding of plasma transport in low aspect ratio tokamaks.In particular, these machines will be able to test whether ion transport remains dominated by neoclassical theoryin larger spherical tokamaks, and data from them will supplement those from conventionaltokamaks to improve discrimination between theoretical models of anomalous transport.

Fast magnetic reconnection with anomalous ion heating and its application

Magnetic reconnection of two toroidal plasmas with the third field component Bx parallel to the X-lines revealed a clear dependence of sheet-current resistivity and ion heating energy on the sheet-width normalized by the ion gyroradius. Initially, the effective resistivity of sheet-current stayed constant, but it increased significantly when the sheet was compressed shorter than the ion-gyroradius. The anomalous current-sheet dissipation was followed by large increase in ion outflow velocity and ion temperature. This anomalous effect caused both the reconnection speed and the ion heating energy to increase with external compression force and inversely with the Bx component. These properties of reconnection lead us to a new controlled plasma heating for various fusion plasmas and other industrial plasmas.

Simulation of edge-plasma profiles and turbulence related toL-H transitions in tokamaks

Results are presented for fluid-equation simulations of transport and turbulence in the edge region of a tokamak using the transport code UEDGE and the turbulence code BOUT. UEDGE calculates two-dimensional plasma and neutral gas profiles using empirical radial transport coefficients, whileBOUT simulates three-dimensional plasma turbulence and resulting transport using experimental or UEDGE plasma profiles. Using UEDGE, the radial electric field structure near the magnetic separatrix is studied for variations of core power, anomalous perpendicular ion viscosity, νa⊥, and prompt ion loss. A BOUT simulation measures the effective νa⊥ from the calculated turbulence-induced radial ion current, giving a value similar to the ion heat diffusivity.

Electromagnetic ion-temperature-gradient modes and anomalous transport in a nonuniform magnetized plasma with equilibrium flows

The linear and nonlinear properties of electrostatic and electromagnetic waves in the presence of ion-temperature gradient, magnetic-field gradient, density gradient, and velocity gradients are examined. In the linear limit, a dispersion relation is obtained that admits new instabilities of drift waves. It is found that parallel velocity shear couples the electrostatic and magnetostatic modes and can cause an instability. An estimate of the anomalous ion energy transport and particle flux on the basis of mixing length hypothesis is made and the results are discussed for some interesting limiting cases. Furthermore, stationary solutions of the nonlinear equations without dissipation are also presented. The findings of the present investigation should be useful in understanding fluctuations and transport phenomena in space and laboratory plasmas.

Formation of vortex streets due to nonlinearly interacting ion–temperature–gradient modes

Stationary solutions of the nonlinear equations, which govern the dynamics of ion–temperature–gradient (ITG) electrostatic modes, are re-examined without and with magnetic field inhomogeneities. It is shown that for both cases the nonlinear equations admit vortex street solutions in those parameter regimes where spatially bounded double vortex solutions are forbidden. The ITG-driven vortex streets can be associated with coherent nonlinear structures that are observed in laboratory and computer simulation experiments. Furthermore, vortex streets might play a detrimental role in the study of anomalous ion thermal transport in magnetically confined plasmas.

Three-dimensional particle simulation of plasma instabilities and collisionless reconnection in a current sheet

Generation of anomalous resistivity and dynamical development of collisionless reconnection in the vicinity of a magnetically neutral sheet are investigated by means of a three-dimensional particle simulation. For no external driving source, two different types of plasma instabilities are excited in the current layer. The lower hybrid drift instability (LHDI) is observed to grow in the periphery of current layer in an early period, while a drift kink instability (DKI) is triggered at the neutral sheet in a late period as a result of the nonlinear deformation of the current sheet by the LHDI. A reconnection electric field grows at the neutral sheet in accordance with the excitation of the DKI. When an external driving field exists, the convective electric field penetrates into the current layer through the particle kinetic effect and collisionless reconnection is triggered by the convective electric field earlier than the DKI is excited. It is also found that the anisotropic ion distribution is formed through the anomalous ion heating by the DKI.

Pinches-Induced Transport Reduction in Reversed Shear/Optimized Shear Tokamak Plasmas

The analytical formulas for anomalous particle and ion thermal diffusivities, Det and χit, are derived on the basis of the two-fluid equations of our previous paper [Chin. Phys. Lett. 15 (1998) 721]. The two formulas involve five factors: (reversed/optimized) magnetic shear LB(r), E × B sheared velocity VE(r), where E is from the gradient of the ion pressure Pi, and the three ways of coupling between them, LB-1(dVE/dr), LB-1VE, and κ · VE, where κ is the LB-dependent wavevector. It is found that the five factors can produce turbulent particle- and heat-pinch, i.e., Det < 0 and χit < 0, in the core region of tokamaks, and hence the effective particle and ion thermal diffusivities, Deeff and χieff, reduce significantly in that region. The numerical results for Deeff and χieff are in good agreement with experimental values.

Nonlinear dynamics and anomalous energy transport in an electrostatic ion-temperature-gradient driven drift-dissipative mode

By using Braginskii transport equations for ions and Boltzmann distribution for electrons, a new system of nonlinear equations governing the dynamics of low-frequency, short-wavelength electrostatic waves in the presence of equilibrium density, temperature, magnetic field, and electrostatic potential gradients has been derived. New ion-temperature-gradient (ITG) driven drift-dissipative modes are shown to exist. An expression for anomalous ion energy transport caused by nonthermal electrostatic fluctuations is also derived. Furthermore, possible stationary solutions of the nonlinear system are obtained in the form of double vortex. On the other hand, the temporal behavior of newly derived nonlinear dissipative systems can be described by the generalized Lorenz–Stenflo equations which admit chaotic solutions. The results of the present investigation should be helpful for understanding the wave phenomena in space and tokamak plasmas.

Particle simulation of collisionless reconnection in three dimensions

Generation of anomalous resistivity and dynamical development of collisionless reconnection in the vicinity of a magnetically neutral sheet are investigated by means of a three-dimensional particle simulation. For no external driving source, two different types of plasma instabilities are excited in the current layer in the same way as the two-dimensional case. The lower hybrid drift instability is observed to grow in the periphery of the current layer, but it cannot penetrate into a high-beta region near the neutral sheet. Instead, a low-frequency electromagnetic (EM) instability is excited at the neutral sheet after saturation of the lower hybrid drift wave. Thus, the interaction between this EM wave and charged particles can cause an anomalous resistivity in the neutral sheet. When an external driving flow exists, collisionless reconnection is triggered by the particle kinetic effect and the anisotropic ion distribution is formed through the anomalous ion heating inside the current layer.

Ionic reactions in two dimensions with disorder

We analyze the dynamics of the ion-dipole pairing reaction in the two-dimensional Coulomb gas in the presence of disorder. Sufficiently singular disorder forces the critical temperature of the Kosterlitz-Thouless-Berezinskii fixed point to be non-universal. This disorder leads to anomalous ion pairing kinetics with a continuously variable decay exponent. Sufficiently strong disorder eliminates the transition altogether. For ions that are chemically reactive, anomalous kinetics with a continuously variable decay exponent also occurs in the high-temperature regime. The Coulomb interaction inhibits reactant segregation, and so the ionic $A^+ +B^- \to \emptyset$ reaction behaves like the nonionic $A + A \to \emptyset$ reaction.

Description of contained mode solutions to the relevant magnetosonic-whistler wave equations

The generalization of magnetosonic-whistler modes having a dispersion relation of the form ω2=k⊥2(vA2+DH2k‖2), where vA is the Alfvén velocity and DH≡B/μ0ne, to the case of an inhomogeneous plasma leads to localized eigenmode solutions. These solutions, which are referred to as contained modes, are tightly confined in the direction of inhomogeneity. In this paper, the contained modes are analyzed for frequencies ω≳Ωi and for k‖≪k⊥. In a cylindrical or toroidal configuration, these modes propagate mostly in the poloidal direction and are localized within a narrow radial shell. Contained modes have been proposed as an underlying mechanism for anomalous ion cyclotron emission (ICE) in plasmas with an energetic ion population. Analytic expressions for the characteristics of these modes are obtained using an expansion in high poloidal mode number and are found to agree with numerical results. For typical plasma profiles, the contained modes are localized towards the edge of the plasma column. It is found that the key parameter which regulates the behavior of the mode is di0/a=DH/avA≪1. This quantity is related to the Hall term which is kept as the first significant correction to Ohm’s law for the frequencies being considered. The Hall term introduces to the eigenmode equation a dependence on the sign of the poloidal phase velocity, and when di0/a is sufficiently large contained solutions only exist for modes whose poloidal phase velocity has the same orientation as the ion cyclotron motion. The dependence of the mode characteristics on finite k‖ is examined in detail. In particular, the quantity R0q/di0 determines the poloidal mode number above which k‖ effects, such as a shift in the region of localization of the mode, become significant.

Dispersive transport of ions in column experiments: An explanation of long‐tailed profiles

We present a novel microscopic model of sorption and convection of ions in heterogeneous media. Our model is based on an analogy to electron transport in a semiconductor. A new feature of our model is a power law random distribution of the adsorption time of ions. Diverging standard deviation of the distribution function yields anomalous ion transport. We show that this anomalous transport explains a concentration profile with a long tail that has been observed in column experiments. We successfully fit recent experimental data. Finally, we propose new experiments by which we can check the validity of our model.

Triton burnup measurements and calculations on TFTR

Measurements of the burnup of fusion product tritons in TFTR are presented. Interpretation of triton burnup experiments requires three accurate components: the measurement of the 2.5 MeV neutron emission, the measurement of the 14 MeV neutron emission and a calculation of the expected burnup ratio from the measured plasma parameters. The absolute calibration for the 14 MeV neutron measurements is provided by an NE213 proton recoil spectrometer. Time dependent burnup measurements for three plasma conditions selected for optimum detector operation are shown. Measurements of the time integrated triton burnup from copper activation foils (cross-calibrated to the NE213 measurements) are presented. Descriptions are provided of the neutron detectors and the plasma diagnostics whose data are used as input to the calculation of the expected burnup. All these measurements find that the triton burnup on TFTR is 1/2 ± 1/4 the classical expectations for a wide variety of discharges. The burnup decreases for relatively longer triton slowing down times, implying possible fast ion diffusion coefficients of ∼0.1 m2/s. Alternatively, burnup appears to decrease with increasing major radius of the triton source and edge safety factor qcyl, implying that ripple losses may be playing a role. Triton burnup is a very sensitive measure of anomalous fast ion transport; similar levels of diffusive transport in an ignited reactor would have minimal impact on the alpha particles.

Fusion reactivity characterization of a spherically convergent ion focus

The deuterium-deuterium (D-D) fusion reaction rate in a spherically convergent ion focus is observed to significantly exceed the rate predicted by a collisionless flow model. However, a careful consideration of ion-neutral collisions and the trapped neutral density in the cathode account for the extra reactivity without invoking anomalous ion trapping in the converged core region. This conclusion is supported by proton collimation measurements, which indicate that the bulk of the observed reactivity originates outside the core region. In addition, a classical flow model, where charge exchange collisional effects on the ion and fast neutral distributions are included, provides fusion rate estimates that are quantitatively consistent with the observed D-D fusion neutron production rate.

Toward a realistic and tractable model for negative-ion extraction from volume sources

A negative-ion source extraction model has been formulated and implemented that explicitly considers the motion of positive ions and the volume generation of negative ions. It is found that (1) for high-beam currents, the beam current is limited by a transverse space-charge limit, meaning that an increase in negative-ion density at the extraction sheath will result in a lower-beam current (this result is universally observed at high-beam current); (2) there is a saddle point with a potential barrier preventing most volume-produced negative ions from being extracted [the combination of (1) and (2) indicates that most of the negative ions being created do not find their way into the beam]; (3) the introduction of cesium may cause an increase in the transverse space-charge limit; (4) cesium also results in an increase in the fraction of volume-produced negative ions that are extracted; (5) cesium may also result in reduction of extracted electrons by producing a less negative bias on the plasma electrode with respect to the plasma, thus allowing the transverse space-charge limit budget to be taken up virtually totally by the ions. [The combination of (3)–(5) represents the way an actual increase in the beam current can be achieved]; (6) a strong ion time scale sheath instability due to violation of the Bohm criteria produces an anomalous ion temperature, which increases with the beam current, as routinely seen in measurements; and (7) the introduction of cesium may result in a reduction in this instability. These insights may lead to improvements in volume negative-ion sources.

Investigation of forced turbulence and transport in toroidal magnetized plasmas

The effect of anomalous cross-field current on fluctuating equilibria in toroidal plasmas is studied experimentally and numerically. In cases where a cross-field discharge current is imposed, it is shown that this current determines the radial profiles of electron density and radial electric field. Moreover, it is well described by an heuristic anomalous Pedersen conductivity (or an anomalous ion collision frequency) which is approximately 4 times the ion-neutral collision frequency.

Stabilization of Ion-Temperature-Gradient–Driven Tokamak Modes by Magnetic-Field Gradient Reversal

Global gyrokinetic particle simulations have been used to search tokamak configurations which are stable against the ion-temperature-gradient--driven (ITG) modes commonly held responsible for the core anomalous ion heat transport. The stable configurations are characterized by strongly reduced or reversed $▽B$ drifts on the low-field side. Since excellent transport properties have been observed in high ${\ensuremath{\beta}}_{p}$ (poloidal beta) tokamak experiments, we conjecture, as a result of our simulations, that this may be due to the stabilization of ITG modes by the reduction of the $▽B$ drifts.