pw-- 3d13 Neoclassical Transport in Enhanced Confinement Toroidal Plasmas Z. Lin, W. M. Tang, and W. W. Lee Princeton Plasma Physics Labomtory, Princeton University, Princeton, NJ 08543 It has recently been reported that ion thermal transport levels in enhanced confinement tokamak plasmas have been observed to fall below the "irreducible minimum level" pre- dicted by standard neoclassical theory. This apparent con- tradiction is resolved in the present analysis by relaxing the basic neoclassical assumption that the ions orbital excursions are much smaller than the local toroidal minor radius and the equilibrium scale lengths of the system. PACS: 52.25.Fi, 52.55.43, 52.65.-y The striking improvement of plasma confinement to neoclassical levels was first theoretically predicted for a reversed magnetic shear configuration [I] and subsequently confirmed in recent tokamak experi- ments [24]. In the so-called enhanced reversed shear (Em) regime [2], the core ion thermal conductivity was actually observed to fall below the standard neo- classical level which was widely accepted as the irre- ducible minimum. The source of this apparent contra- diction lies in the fact that the experimental conditions in the ERS regime correspond to situations where the ion poloidal gyroradius pp can be comparable in magnitude or even greater than the equilibrium pressure gradient scale length L, and/or the local minor radius r. This violates a basic assumption in the standard neoclassical formalism and establishes the need for a revised theory where p, can be of the same order of magnitude as L, and/or T. This is accomplished in the present analy- sis, and the associated analytical and gyrokinetic particle simulation results are shown to be in agreement with key confinement trends observed in ERS plasmas. The standard neoclassical theory assumption that the ion poloidal gyroradius is much smaller than the local minor radius and the equilibrium scale lengths allows the expansion of the equilibrium distribution function around a local Maxwellian which is defined as a function of the flux surface. However, due to the combination of high central q (safety factor) and small local inverse aspect ratio (VIR0 with Ro being the tokamak major radius), the ion poloidal gyroradius can in fact be larger than the minor radius and comparable to the pressure gradient scale length in the ERS regime. Hence, both the trapped particle fraction and the banana width estimates can be significantly modified. In the present analysis, the newly derived form for the neoclassical ion heat conductivity is found to be strongly reduced by finite banana width dynamics in the ERS regime. Important properties which need to be taken i 7Y MSTRfSUPION OF TWlS DOCUMENT IS UNLIMITED 1 into account in an appropriate theoretical model include: (a) ion banana width is nearly constant close to the mag- netic axis and (b) counter-moving ions have a minimum trapped fraction and all co-moving ions are trapped. In the usual neoclassical picture, outward ion heat conduc- tivity results from energy flux imbalance between the in- ward moving slow (lower energy) particles and the out- ward moving fast (higher energy) particles. When the finite orbit width is taken into account, the outward ion heat conductivity is significantly reduced because this modification is much stronger on the fast particles (Le., net energy outflow reduced). Therefore, the ion heat conductivity xi decreases for smaller minor radius where orbit effects are strongest. In the following, it will be demonstrated that analytic results from a random-walk type argument and global gyrokinetic particle sirnula- tions using the GNC code [5] yield favorable agreement with key trends from the experimental measurements. ~ In an axisymmetric system, the guiding center trajec- tories are defined by the conservation of magnetic mo- ment, p, energy, E, and toroidal canonical angular mo- mentum, p, i.e., (17 where B is the magnetic field, rn is the particle mass, e is the charge, vc is the toroidal component of the parallel velocity VII, Q, is the electrostatic potential, R is the dis- tance from the geometric center, and c denotes toroidal angle in the plasma current direction. The toroidal mag- netic vector potential AC is related to the poloidal mag- netic field Be = V x Ac. In analyzing the dynamics of interest, it is convenient to consider a high aspect ratio torus with concentric flux surfaces and a constant q profile with constant @. The focus here is on the orbit topology of single energy (mv2/2) particles at a reference point of minor radius r and poloidal angle B = 0 (magnetic field minimum). The usual definition of a trapped particle is one for which vi1 = 0 somewhere along the orbit. The banana width Ab and trapped fraction ft are determined by the behavior of barely trapped particles with VII = 0 at the inside mid- plane (0 = .). In the limit of Ab << T, standard analysis of Eq.(l) yields, where E = r/Ro and p = v/n with E eB/rn.