Anomalous Radial Diffusion Research Articles

Turbulent drifts of impurity ions as an explanation for anomalous radial transport in the far-SOL of DIII-D

Successful fusion reactor operation relies on minimal core contamination by impurities, otherwise too much power may be radiated and harm performance. This requires reliable predictions of impurity transport from the scrape-off layer (SOL) into the core, beyond the traditional ‘anomalous’ diffusion approach. We report a set of far-SOL tungsten transport simulations that demonstrate the role of turbulent drifts on radial impurity transport. A turbulent plasma background is simulated using the gyrokinetic SOL code Gkeyll. Tungsten ions are followed within the plasma background using only their drifts. We find that tungsten tends to travel radially outwards with velocities between v r = 300–1200 m s−1 primarily due to polarization drift. We also extract an anomalous radial diffusion coefficient that varies from Dranom = 5–20 m2 s−1. These results are compared to and agree with previous interpretive modeling results. We also show how the turbulent polarization drift can transport some tungsten ions from the wall inwards with effective pinch velocities up to 10 000 m s−1. We conclude that turbulent drifts are a likely explanation for historically anomalous radial impurity transport.

The activity and radial dependence of anomalous diffusion by pitch angle scattering on split magnetic drift shells

AbstractAsymmetries in the magnetospheric magnetic field produce drift shell splitting, which causes the radial (drift shell) invariant to sometimes depend on pitch angle. Where drift shell splitting is significant, pitch angle scattering leads to diffusion in all three invariants of the particle's motion, including cross diffusion. We examine the magnitude of drift shell splitting‐related anomalous diffusion for outer zone electrons compared to conventional diffusion in the absence of drift shell splitting. We assume that the primary local scattering process is wave‐particle interactions with chorus. We find that anomalous radial diffusion can exceed that of conventional drift‐resonant radial diffusion for particles with energies near 0.1 MeV at all radial distances outside the plasmasphere during quiet to moderate geomagnetic activity, and it is significant at 0.5 MeV. Cross diffusion involving the radial invariant can exceed the geometric mean of the corresponding pure diffusion coefficients at 0.1 MeV, and that such cross diffusion is significant even at 0.5–1 MeV. At 1 MeV, cross diffusion is often significant. The highest radial distances and magnetic activity levels in our study do not always exhibit as much significant anomalous diffusion as moderate radial distances and activity levels. This can be explained by (a) stronger dependence of conventional diffusion on magnetic activity and radius, and (b) strongest drift shell splitting at moderate magnetic activity. Simulation codes that neglect the possibility for cross terms will likely systematically underperform, especially for 0.1–0.5 MeV electrons, for much of the outer zone for quiet to moderate levels of magnetic activity.

Breaking all the invariants: Anomalous electron radiation belt diffusion by pitch angle scattering in the presence of split magnetic drift shells

AbstractRelativistic electron observations near geostationary orbit routinely show pitch angle distributions peaked away from 90 degrees. These “butterfly” distributions are consistent with magnetic drift shell splitting combined with a radial flux gradient. During magnetic storms, nature adds pitch angle scattering to split drift shells, breaking all three adiabatic invariants of the particle's motion. Therefore, some degree of anomalous radial diffusion is likely, and cross terms between the gyration and drift invariants and between the bounce and drift invariants arise. Using typical assumptions about the pitch angle scattering and the magnetic field topology, we calculate these anomalous diffusion coefficients near geostationary orbit. We show that the anomalous radial diffusion can exceed that due to more traditional drift‐resonant wave‐particle interactions. We also show that the neglected cross terms, particularly the bounce‐drift cross term, can be significant. These results suggest necessary additions to some global electron radiation belt simulations.

Self-Sustained Tokamak Reactor due to Bootstrap Current with Finite Banana-Width Effect

The concept of a tokamak sustained only by the neoclassical bootstrap current is quite attractive. According to the conventional neoclassical transport theory, this completely bootstrapped tokamak is considered to be impossible since the bootstrap current vanishes at the magnetic axis and thus a seed current near the axis must be generated by an external source. However, several authors have suggested that the seed current can be generated through the anomalous radial diffusion of the bootstrap current and the inclusion of this effect may lead to the completely bootstrapped tokamak. Another suggestion for the possibility of the completely bootstrapped tokamak comes from the break-down of the conventional neoclassical transport theory near the magnetic axis. A particle orbit near the magnetic axis is quite different from the conventional banana orbit, and a thin-banana approximation in the conventional theory is broken down. The modification of the conventional neoclassical transport theory around the magnetic axis by the finite banana-width effect has been studied, and several expressions for the bootstrap current are presented. In these studies, the bootstrap current is found to remain finite on the magnetic axis. Therefore, this finite banana-width effect leads to the possibility of the completely bootstrapped tokamak. In order to calculate the bootstrapped tokamak equilibrium, we need the expression for the bootstrap current which can be used in entire region of plasma. Several formulae interpolating the expression at the magnetic axis and that of the conventional neoclassical transport theory have been presented. In a previous paper, the author obtained the bootstrap current at the magnetic axis by applying the Wang’s method, and proposed a more sophisticated interpolation formula between this bootstrap current at the axis and the conventional one. Our obtained expression for the bootstrap current reduces to the conventional one when the ratio 1=3 a = ffiffi p is much less than unity, where is the inverse aspect ratio, and a 1⁄4 2q0 a=kR0 with the major radius R0, the elongation parameter k, the safety factor q0 at the magnetic axis, and the Larmor radius a for species a. The finite banana-width effect is shown to modify the conventional bootstrap current around the magnetic axis satisfying the condition ffiffi p < 1=3 a . This modification is significant for high energy particles. In ref. 12, the author also obtained the expression for the bootstrap current due to fusion-produced alpha particles by taking into account the finite banana-width effect. In this paper, using the modified bootstrap current by the finite banana-width effect, we study a simple equilibrium model of completely bootstrapped tokamak. The bootstrap current Jbulk due to bulk particles is expressed as Jbulk 1⁄4 ðB=hBiÞðneTe=BpÞĴbulk with Ĵbulk 1⁄4 L1 pe pe þ 1

Impurity transport in edge plasmas with application to liquid walls

The transport of impurity ions in a magnetically confined plasma is studied in the region between their origin at a material surface and the core plasma as defined by closed magnetic flux surfaces. The focus is physics understanding of the results of two-dimensional (2-D) transport modeling of the plasma and neutrals. A simple one-dimensional model is introduced to identify key processes and illustrate how such processes affect the core-edge impurity level. The 2-D simulation gives detailed results of scaling of the impurity level with parameters such as anomalous radial diffusion, hydrogen–plasma recycling, core power flux, and core-edge density. The results are obtained for a slab model of a tokamak, but by changing the magnetic connection length, scaling to other types of devices can be inferred. Lithium and fluorine impurities are considered explicitly as examples with low and moderate charge-state number, Z, for liquid wall materials; trends found for these cases provide guidance to the behavior of other impurities. The tolerable amount of impurity influx can be closely associated with the partial thermal collapse of the edge plasma. The results are used to provide a physics picture of previous results on the acceptable evaporative impurity flux from different types of liquid wall materials, and to show how these results can be expected to scale with parameters.

Two-dimensional electric fields and drifts near the magnetic separatrix in divertor tokamaks

A two-dimensional calculation is presented for the transport of plasma in the edge region of a divertor tokamak solving continuity, momentum, and energy balance fluid equations. The model uses classical processes of parallel transport along the magnetic field and cross-field drifts together with anomalous radial diffusion, including perpendicular ion viscosity. The self-consistent electrostatic potential is calculated on both sides of the magnetic separatrix via quasineutrality and current continuity. Outside the separatrix, the model extends to material divertor plates where the incident plasma is recycled as neutral gas and where the plate sheath and parallel currents dominate the potential structure. Inside the separatrix, various radial current terms—from anomalous viscosity, collisional damping, inertia, and ∇B drifts—contribute to determining the potential. The model rigorously enforces cancellation of gyroviscous and magnetization terms from the transport equations. The results emphasize the importance of E×B particle flow under the X-point which depends on the sign of the toroidal magnetic field. Radial electric field profiles at the outer midplane show strong variation with the magnitude of the anomalous diffusion coefficients and the core toroidal rotation velocity, indicating that shear stabilization of edge turbulence can likewise be sensitive to these parameters.

Notched velocity profiles and the radial electric field in high ion temperature plasmas in the Tokamak Fusion Test Reactor

A large “notch,” or non-monotonic feature, appears in measured toroidal velocity profiles of the carbon impurity in the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Fusion 26, 11 (1984)], centered near the radius of strongest ion temperature gradient. This is explained as a consequence of radial momentum transport dominated by anomalous diffusion together with parallel heat friction on the impurity ions arising from the hydrogenic neoclassical parallel heat flow. The toroidal velocity profile of the hydrogenic species is predicted to be monotonic, from measurements of the impurity toroidal velocity, consistent with the anomalous radial diffusion of toroidal momentum. This supports a neoclassical calculation of the radial electric field for near-balanced beam injection. In supershot plasmas [Phys. Rev. Lett. 58, 1004 (1987)], a well structure in the radial electric field profile is found in the enhanced confinement region. An associated shear layer separates the core, where the local confinement trends are favorable, from the degraded outer region. This provides a mechanism for the nonlinear coupling of the ion temperature gradient, ion thermal confinement, and the radial electric field, which may help explain the favorable core confinement trends of very high temperature supershot plasmas.

Effects of anomalous alpha particle diffusion on fusion power coupling into tokamak plasma

The alpha particle power coupling efficiency to the bulk plasma, ηalpha identical to Pα(coupled)/Pα(birth), is reduced when the energetic alpha particles are subject to anomalous radial diffusion, Dαan, caused by alpha particle instabilities. If ηα is appreciably smaller than 1, this has a strong effect on the ignition margin MI [≡ Palpha (coupled)/Ploss] of a tokamak plasma. First, a simple analytical form of ηα is found to be ηα = 1 - (τSD/τL), where τL ≃ α2/4Dα is the spatial loss time and τSD is the slowing down time. The power coupling efficiency ηα decreases with increasing Te and increases with ne. Second, a reduced time dependent alpha particle kinetic equation containing the term ∇.Dα ∇nα, where Dα can be a non-linear function of δnα/δτ, is derived and solved using a multiple energy group method. An Alfven wave turbulence theory by Gang (Phys. Fluids B 4 (1992) 3152) is used to parametrize Dα from first principles. When Dαan ≈ 3 m2/s, ηα is reduced to 0.95. The consequence for the accessible operating regimes of an ITER-like fusion device are also discussed

Alpha physics in tokamaks

After briefly reviewing recent experimental and theoretical alpha -particle physics simulation results self-consistent values of the anomalous radial diffusion coefficient Dalpha from two related theories and/or numerical simulations of energetic alpha -excited shear Alfven wave turbulence are derived and used in a reduced drift kinetic equation (DKE) for the alpha distribution function Falpha (r,E,t) which contains a diffusion term 1/r delta rDalpha delta . Since Dalpha depends on delta nalpha / delta r through w* alpha the ensuing nonlinear diffusion equation for nalpha (r,t) is solved iteratively with the DKE for Falpha and the effects of Dalpha on the alpha -power coupling efficiency eta alpha and the ignition margin are analyzed for an ITER-like device ('ignited operation' of the ITER conceptual design activity (CDA)). From a power balance point of view the resulting Dalpha >or approximately=1 m2/s appears tolerable, Dalpha >3 m2/s would yield eta alpha <0.95.

Alpha physics in tokamaks

After briefly reviewing recent experimental and theoretical alpha -particle physics simulation results self-consistent values of the anomalous radial diffusion coefficient Dalpha from two related theories and/or numerical simulations of energetic alpha -excited shear Alfven wave turbulence are derived and used in a reduced drift kinetic equation (DKE) for the alpha distribution function Falpha (r,E,t) which contains a diffusion term 1/r delta rDalpha delta . Since Dalpha depends on delta nalpha / delta r through w* alpha the ensuing nonlinear diffusion equation for nalpha (r,t) is solved iteratively with the DKE for Falpha and the effects of Dalpha on the alpha -power coupling efficiency eta alpha and the ignition margin are analyzed for an ITER-like device ('ignited operation' of the ITER conceptual design activity (CDA)). From a power balance point of view the resulting Dalpha >or approximately=1 m2/s appears tolerable, Dalpha >3 m2/s would yield eta alpha <0.95.

Drift shell splitting by internal geomagnetic multipoles

Computations on an 80-coefficient model of the earth's field illustrate the 'topography' of the magnetic equatorial surface and the geometry of the drift shells of geomagnetically trapped particles. Individual terms in the spherical harmonic expansion of the geomagnetic scalar potential V(r, theta, phi) are either even or odd in cos theta, where theta = 90 deg denotes the dipole equator. Terms that are even in cos theta tend to 'warp' the equatorial surface, but do not (in first order) distort particle drift shells radially nor split the drift shells of particles having different equatorial pitch angles. Azimuthally asymmetric terms that are odd in cos theta do cause shell splitting in first order. Shell splitting at large L values (neglecting deformation of the earth's field by the solar wind) is found to be dominated by the geomagnetic octupole. At L approximately equal to 1, shell splitting is strongly enhanced by the South American and South African anomalies. When combined with pitch angle diffusion caused by atmospheric scattering, these results may be able to account for anomalous radial diffusion of inner zone electrons.