Plasma edge theorists in the Plasma Science and Fusion Center (PSFC) at the Massachusetts Institute of Technology in Cambridge; the Institute for Fusion Studies (IFS) at the University of Texas at Austin; the EURATOM/UKAEA Fusion Association at the Culham Science Centre in England; the Department of Electromagnetics at Chalmers University of Technology in Göteborg, Sweden; and Lodestar Research Corporation, headquartered in Boulder, Colorado, participate in the Joint Program to stimulate and perform innovative collaborative research on edge physics.

• Nonlinear Neoclassical Transport Theory for the Tokamak Edge, by Tünde Fülöp (Chalmers) and Per Helander (Culham), submitted to Phys. Plasmas.
• Effect of Neutrals on Edge Instabilities in a Partially Ionized Plasma, by A. Ödblom (Chalmers/Culham), P. J. Catto (MIT/Lodestar) and S. I. Krasheninnikov (MIT/Kurchatov), to appear in Phys. Plasmas.
• Investigation of Scrape-Off Layer Up-Down Asymmetries in Diverted Plasmas in TEXT-Upgrade, by X. Bonnin (UT/MIT) and W. L. Rowan (UT/MIT), submitted to Nucl. Fusion.

Jim Hastie (Culham), Jack Connor (Culham) and Peter Catto (MIT/Lodestar) attended a symposium in honor of Bryan Taylor's 70th birthday held at the University of Texas at Austin on January 11 - 12th and meticulously arranged and chaired by Jim Van Dam (IFS). Evidently, this very enjoyable celebration of Bryan's remarkable accomplishments was the first time Connor, Hastie and Taylor have been in the U. S. at the same place at the same time!

Tünde Fülöp (Chalmers) completed her visit to Culham on November 6th. While there she worked with Per Helander to extend the theory of neoclassical ion transport in an impure plasma to allow for steeper gradients than are usually considered (see research report section). Per Helander (Culham) visited Chalmers from 8 - 12 February to complete the work with Tünde on nonlinear neoclassical transport, and to discuss kinetic problems of runaway electrons with her advisors, Dan Anderson and Mietek Lisak, and their student Fredrik Andersson.

Drs. V.S. Vorob'ev (Institute for High Temperatures, Moscow) and V.G. Novikov (Keldysh Institute of Applied Mathematics, Moscow) visited the PSFC in December, as part of an ongoing collaboration with Sasha Pigarov (William & Mary/MIT) and Xavier Bonnin (MIT) aimed at constructing a detailed self-consistent radiation transfer and opacity model. Anders Ödblom (Culham) returned to the PSFC for a two week visit from November 23rd to December 4th to complete work with Peter Catto and Sergei Krasheninnikov on the effects of neutrals on edge instabilities.

Fabio Subba of the Politecnico di Torino, Italy is making his second visit to the PSFC from March 17th to June 6th. He came to particpate in Sherwood/APS Centennial meeting in Atlanta and to continue his collaboration with Oleg Batishchev (Lodestar/MIT) on developing adaptivity methods for plasma fluid modeling and comparing various adaptive methods. He will also continue previous work started with Sergei Krasheninnikov on the properties of nonlinear reaction-diffusion equations containing a time delay.

Other visitors to the PSFC included Dan McCarthy of Southeastern Louisiana University from Feb. 17 - 19 to continue his collaboration with Sergei Krasheninnikov and Peter Catto on modeling edge turbulence; Ben Carreras of Oak Ridge National Laboratory for discussions with Antonio Bruno (MIT) and Sergei on analysis of long-time correlations in the Da fluctuations near the density limit; and Dr. Noriyasu Ohno of Nagoya University to continue a collaboration with Sergei to improve the recombination diagnostics.

Jack Connor (Culham) attended a Toki Conference (ITC9) from December 7 - 11th and gave an invited talk on "The influence of the plasma edge region on the performance of tokamaks" which will be published in a special issue of Journal of Plasma and Fusion Research and presaented an Open Lecture to the citizens of Toki on "50 Years of Progress in Fusion".

Marion Turner, Colin Roach and Jack Connor of Culham attended the Combined Workshop of the Core Confinement & Internal Transport Barrier, Confinement Database and Modelling and Edge Pedestal ITER Expert Groups in Garching from April 12 - 16th where Jack presented an "Overview on Theories of the H-mode Transition".

Per Helander (Culham) visited CEA Cadarache 7-8 December to give a talk on nonlinear neoclassical theory, discuss the development of a Monte Carlo code for runaway avalanches with L-G Eriksson, and attend the European Fusion Physics Workshop from 9-11 December. Geoff Maddison and Glenn Counsell of Culham also attended the workshop, and Glenn gave a talk on "Divertor Issues in Spherical Tokamaks".

Several members of the Joint program attended the Sherwood/APS Centennial Meeting in Atlanta where Phil Morrison (IFS), Peter Catto (MIT/Lodestar), Richard Fitzpatrick (IFS), and K. G. McClements (Culham) presented invited talks.

Background and motivation: It is widely recognized that the conventional theory of neoclassical transport in tokamaks is not applicable to regions where the pressure and temperature profiles are very steep, such as the pedestal at the plasma edge. This work is a continuation of the program initiated in Refs. 1 and 2 to extend the theory of neoclassical ion transport in an impure plasma to allow for steeper gradients than are usually considered. Contrary to the conventional theory, these gradients are allowed to be so large that the friction force between the bulk ions and heavy impurities is comparable to the parallel impurity pressure gradient. As found earlier [1,2], when this is the case the impurity density is no longer constant on flux surfaces, and the transport becomes nonlinear. For plasma parameters typical of the tokamak edge, the ion particle flux is a non-monotonic function of the pressure and temperature gradients. If either of these gradients is sufficiently steep (such as in the edge pedestal) the neoclassical particle flux is suppressed, and energy confinement can be improved substantially over the conventional neoclassical prediction.

Results: In the present work, the effects of toroidal rotation are also investigated. The impurities are pushed to the outboard side of each flux surface when the impurity Mach number Mz = Vf (mz/T)1/2, where Vf is the toroidal velocity, mz the impurity mass, and T the temperature, is of order unity (which is frequently the case experimentally). In a plasma where the gradients are as weak as in the conventional neoclassical theory, it is found that the rotation then increases the transport well over the usual Pfirsch-Schlüter value. The enhancement factor is of the order of the aspect ratio R/r. On the other hand, if either the pressure or temperature gradient is large, the transport not only becomes nonlinear, but also acquires a number of unusual features. For instance, in the particularly simple limit of low impurity concentration, the particle flux becomes independent of the collision frequency (although it is caused by collisions), and is sensitive to the geometry of the magnetic equilibrium. The flux can have either sign and is inward if the ion magnetic drift is toward the X-point in a single-null magnetic configuration. The impurities, whose flux is in the opposite direction, are then screened from the plasma core. These fluxes change sign if the toroidal field is reversed.

References:

[1] C.T. Hsu and D.J. Sigmar, Plasma Phys. Control. Fusion 32, 499 (1990).

[2] P. Helander, Phys. Plasmas 5, 3999 (1998).

Effect of Neutrals on Edge Instabilities in a Partially Ionized Plasma, by A. Ödblom (Chalmers/Culham), P. J. Catto (MIT/Lodestar) and S. I. Krasheninnikov (MIT/Kurchatov), to appear in Phys. Plasmas.

Background: Instabilities in the tokamak edge plasma influence core confinement through the boundary conditions they impose and affect plate heat and particle loads by determining the SOL width. Moreover, the stability of a partially ionized plasma can be quite different from that of a fully ionized one. Because the plasma and neutrals are coupled through charge exchange an inhomogeneity in the neutrals can provide the source of free energy that drives instability [1]. Recent work[1,2] has shown that this coupling can influence the magnetohydrodynamic stability of tokamak divertor and SOL plasmas. It was shown that neutral gas pressure and plasma gradients in the same directions could lead to instability, but in most of the SOL, where the gradients were in the opposite direction, the neutrals act in a stabilizing manner. In general, the neutrals are important since the diffusivities of the neutral particle, momentum and energy are orders of magnitude larger than the corresponding anomalous cross-field diffusivities of the plasma. The neutral physics can therefore be expected to significantly alter the stability properties of the plasma edge even in situations where the neutral density is much less than the plasma density. As a result, it is often necessary to keep the neutral physics in the analysis when investigating the stability of the tokamak edge or ionospheric plasmas.

Results: The physics of the neutral atoms has been incorporated into a generalized description of edge instabilities in tokamaks and plasmas with a small neutral fraction. The description includes ideal and resistive ballooning modes [2, 3]; modes driven by a radial electron temperature gradient when the plasma is in contact with conducting material surfaces such as limitors or divertor target plates [4 - 6], the destabilizing effect of the parallel variation in the E¥B drift frequency [7], and effects due to the flow of the neutral gas [1, 2]. The analysis considers the neutral dynamics in both the short[k^lNi >> 1] and long [k^lNi << 1] neutral mean free path limits (relative to the wavelength of the instability) since the perturbed ion-neutral coupling depends on collisionality. Moreover, parallel and cross field variations in the equilibrium temperatures, densities, and potential are retained as well as the corresponding diamagnetic effects. In the short neutral mean free path limit the ion and neutral viscosities and heat fluxes must be retained, while in the long neutral mean free path limit the neutrals are not perturbed, but the ion viscosity and heat flux must still be considered. The possible destabilizing impact of the new heat flux and viscous terms is considered.

The derivation and analysis of the general ballooning mode equations in the presence of collisional [k^lNi << 1] and collisionless [k^lNi >> 1] neutrals has revealed interesting new phenomena associated with ion-neutral collisional coupling, and neutral and ion heat fluxes and viscosities. The most unusual is the effect of the neutral density perturbation of the neutral viscosity which modifies the stability condition found by Daughton et al. [1] since they neglected ion and neutral temperature gradients. Depending on the magnitude and direction of the neutral temperature gradient, permits instability to occur even if the neutral pressure and ion density gradients are in the opposite direction. Although, it remains an open question whether the resulting instability would be further modified by a kinetic neutral description.

In addition, neutral and ion viscous effects are found to result in an order unity reduction in the sheath induced —^Te instability in the collisional neutral limit. Moreover, in the presence of a moderately large neutral population, neutral and ion heat flux modifications are found to result in a temperature gradient modification of the ballooning drive in addition to the expected ion-neutral coupling modifications. This situation can be encountered in the ionosphere where the perpendicular scale lengths w might be comparable with the radius of curvature R, while the neutral mean free path between collisions with the ions remained much smaller.

Motivation: In order to study the individual impact of physical drift mechanisms (E¥B, diamagnetic, B¥—T) [1] on observed divertor asymmetries in the particle and energy flow, a set of dedicated plasma discharges were obtained on the TEXT-Upgrade tokamak and then analyzed with the help of the B2-Eirene code [2, 3]. Because of its topological symmetry and low-density operating regime, TEXT-U was an ideal test-bed to disentangle the different drift influences.

Experiment: The two sequences of shots are studied: an X-point position scan and a density scan. The X-point is brought from 0.05 m away from the plates to full contact. The density scan covers the ne range of 1.2 to 4.0 ¥ 1019 m-3. All other plasma parameters are kept constant. As the X-point moves in closer to the wall, the Da emission region in the divertor narrows and becomes unbalanced, favoring the ion diamagnetic side. The density scan, done for plasmas with the X-point far from the wall, also shows the asymmetry evolving. As ne is increased from 1.2 to 4.0 ¥ 1019 m-3, the level difference between the two Da maxima shifts. At the lowest densities, the ion diamagnetic side of the divertor is brighter. At high density, the electron side dominates. The point of approximate symmetry is for ne between 1.8 and 2.4 ¥ 1019 m-3.

Analysis: One can estimate the influence of the E¥Bdrift in the TEXT-Upgrade SOL plasma following the treatment of Hinton and Staebler [6] and Stangeby and Chankin [4]. In the low-recycling isothermal conditions typical of TEXT-U diverted discharges, there is little pressure gradient poloidally until just in front of the target plates and the poloidal electric field is mainly governed by the presheath accelerating potential, which is of order/2e, where is measured at the stagnation point, near the outer midplane. Then, the total radial E¥B flow crossing the separatrix becomes:

. (1)

The poloidal E¥B flow can be found in the same way if one considers that the radial electric field is governed by the plasma potential sheath drop F ~ 3/e where  is now the temperature in front of the sheath at the divertor plate. Then, the total poloidal E¥Bflow integrated across the SOL is given by [5]:

. (2)

Hence, the poloidal flow dominates and only a small fraction of the particles advected close the flux loop. This poloidal flow must be compared to the total diffusive flow across the separatrix. Taking the ratio of these flows, we can compute the fraction of particles effectively carried by the E¥B flow. Assuming poloidally isothermal conditions in the SOL, we have ƒE¥B = 19%. Thus, we can expect an asymmetry in particle flows to the divertor in ESN plasmas of order 20% favoring the poloidal E¥Bflow direction, which would translate into favoring the ion side. This particle influx results in stronger Da emissions at the plate where the flowing particles must recombine. This analysis is only valid at low density where the assumptions of low recycling conditions and isothermicity hold. At higher densities, a poloidal density variation is established and , so the radial flow eventually dominates. Qualitatively, the particles are pushed downward (in the TEXT-U geometry) and there is not enough poloidal drift flow to carry them away from the bottom divertor region (the electron side). In a sense, because of the high density regimes at which today’s tokamaks operate, this latter behavior is now the norm. TEXT-Upgrade gave us a window into a low density regime not routinely observed.

The diamagnetic flow contribution to the asymmetry can be computed along the same lines, in the case where the flow loop cannot close upon itself, i.e. for belt-limited plasmas or when the X-point is on the plates. If we again compare these flows with the expected rapid parallel flows to the target plates, we obtain a flow fraction  of 2%. Consequently, we can infer that, in low-recycling conditions, the diamagnetic drift will have a smaller influence on the divertor asymmetries than the E¥Bdrift.

Lastly, we estimate the magnitude of the —T¥B heat flow, with the sign convention that flow towards the ion side is positive, and obtain a net heat flux of:

. (3)

This total heat flow amounts to about 10 kW in towards the electron diamagnetic side, which represents about 5% of the total Ohmic power delivered to the plasma. Thus, this effect is of comparable magnitude to the asymmetries one can expect from the E¥B and diamagnetic drifts.

Simulations, using B2-Eirene [2], of the Da emission have also been performed. To properly reproduce the experimental signal, the inclusion of both carbon impurities and —T¥Bdrift terms was necessary. The simplest one-fluid approach leads to a small but insufficient asymmetry. The addition to the —T¥B drift term to the D-only simulation does not significantly alter the results. However, the subsequent inclusion of the carbon impurity dynamics makes a large difference, and the asymmetry level is now approximately matched. The presence of carbon establishes large parallel temperature gradients which are otherwise practically absent in the simulated SOL. In turn, this poloidal —T drives an increased radial drift heat flux and promotes recycling asymmetries.

Conclusions: Scans of the density and X-point position were performed. By increasing the density, the plasma went from a regime where the poloidal E¥B flow dominated the divertor asymmetry to one where the radial E¥B took over and the asymmetry inverted. Also, by bringing the X-point in contact with the divertor plate structure, the diamagnetic flow loops [5] were forbidden from closing, and their impact was measured to be small. The effect of the B¥—T drift was determined to be very sensitive to the strength of the parallel temperature gradients in front of the plates. Such gradients are sustained by the sputtering carbon from the divertor and the consequent ionization and radiation losses.