Abstract.A technique is developed and applied for analyzing pedestal and internal transport barrier (ITB) regions in a tokamak by formulating a special version of gyrokinetics. In contrast to typical gyrokinetic treatments, canonical angular momentum is taken as the gyrokinetic radial variable rather than the radial guiding center location. Such an approach allows strong radial plasma gradients to be treated, while retaining zonal flow and neoclassical (including orbit squeezing) behavior and the effects of turbulence. The new, nonlinear gyrokinetic variables are constructed to higher order than is typically the case. The nonlinear gyrokinetic equation obtained is capable of handling such problems as collisional zonal flow damping with radial wavelengths comparable to the ion poloidal gyroradius, as well as zonal flow and neoclassical transport in the pedestal or ITB. This choice of gyrokinetic variables allows the toroidally rotating Maxwellian solution of the isothermal tokamak limit to be recovered. More importantly, we prove that a physically acceptable solution for the lowest order ion distribution function in the banana regime anywhere in a tokamak and, in particular, in the pedestal must be nearly this same isothermal Maxwellian solution. That is, the ion temperature variation scale must be much greater than the poloidal ion gyroradius. Consequently, in the banana regime the background radial ion temperature profile cannot have a pedestal similar to that of plasma density.

In the core of a tokamak, turbulent transport normally dominates over neoclassical. The situation could be different in a high confinement (or H) mode pedestal, where the former may be suppressed by a strongly sheared equilibrium electric field. On the other hand, this very field makes conventional neoclassical results inapplicable in the pedestal by significantly modifying ion drift orbits. We present the first calculation of the banana regime neoclassical ion heat flux and poloidal flow in the pedestal accounting for the strong ExB drift inherent to this tokamak region.Interestingly, we find that due to the electric field the pedestal poloidal ion flow can change its direction as compared to its core counterpart. This result elucidates the discrepancy between the conventional banana regime predictions and recent experimental measurements of the impurity flow performed at Alcator C-Mod.

In a plasma of multiple ion species, thermodynamic forces such as pressure and temperature gradients can drive ion species separation via inter-species diffusion. Unlike its neutral mix counterpart, plasma thermo-diffusion is found comparable to, or even much larger than, baro-diffusion. It is shown that such a strong effect is due to the long-range nature of the Coulomb potential, as opposed to short-range interactions in neutral gases. A special composition of the tritium and 3 He fuel is identified to have vanishing net diffusion during adiabatic compression, and hence provides an experimental test in which yield degradation is minimized during ICF implosions.In inertial confinement fusion (ICF), the central "hotspot" plasma, assembled by laser-driven spherical implosion [1], contains multiple ion species. Common combinations include low-Z fuel mixtures such as deuterium (D)/tritium (T) and D 3 He with possible addition of high-Z pusher ions, such as carbon or silicon, due to plastic or glass shell mixing [2,3] into the gas fill. Sometimes high-Z gas dopants such as Ar [4] or Kr [5] are intentionally introduced for diagnostic purposes, as well as to specifically study the pre-mix effects [6,7]. The powerful thermodynamic forces (e.g. pressure [8][9][10] and temperature gradients [9,10]) in an imploding target can drive ion species separation via inter-species diffusion. Observation of the resulting fuel stratification in the DT implosion, which upsets the initially optimal arrangement of equal number densities of D and T, in experiments [11] and kinetic simulations [12][13][14][15] have recently been reported. The targets with high-Z dopants show a particularly strong yield anomaly [6,7,16], suggesting that even stronger fuel stratification may take place.Perhaps the most intriguing physics aspect of interion-species diffusion in a collisional plasma is the role of thermo-diffusion, which, as its name suggests, is driven by the gradients of ion and electron temperatures. The novelty comes through as a sharp contrast to the better-known case of a neutral mixture, where thermo-diffusion is substantially less important than baro-diffusion, though often counteracts it [9]. According to statistical physics, thermo-diffusion strongly depends on the details of the collisional exchange between and within the species [10]. Due to the long range nature of Coulomb collisions in plasmas, as opposed to short range collisions between neutral particles, one may expect thermo-diffusion in plasmas and neutral mixtures to be fundamentally different. This difference becomes particularly striking with the observation that plasma baro-diffusion ratio k p is identical to its neutral counterpart [17].

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Electric field is a thermodynamic force that can drive collisional inter-ion-species transport in a multicomponent plasma. In an inertial confinement fusion (ICF) capsule, such transport causes fuel ion separation even with a target initially prepared to have equal number densities for the two fuel ion species. Unlike the baro-diffusion driven by ion pressure gradient and the thermo-diffusion driven by ion and electron temperature gradients, electro-diffusion has a critical dependence on the charge-to-mass ratio of the ion species. Specifically, it is shown here that electro-diffusion vanishes if the ion species have the same charge-to-mass ratio. An explicit expression for the electro-diffusion ratio is obtained and used to investigate the relative importance of electro- and baro-diffusion mechanisms. In particular, it is found that electro-diffusion reinforces baro-diffusion in the deuterium and tritium mix, but tends to cancel it in the deuterium and helium-3 mix.Comment: Submitted to Phys. Plasmas on 2012-03-06 (revised version 05/13/2012

Neoclassical shielding is the dominant mechanism reducing the collisionless zonal flow in a tokamak. Previously, this phenomenon was analyzed in the case of an essentially homogeneous equilibrium since the wavelength of the zonal flow perturbation was assumed to be much less than the scale length of background plasma parameters. This assumption is not appropriate in a tokamak pedestal. Therefore the pedestal neoclassical polarization and the zonal flow residual differ from the conventional results. This change is due to the strong electric field intrinsic to a subsonic pedestal that modifies neoclassical ion orbits so that their response to a zonal flow perturbation is qualitatively different from that in the core. In addition to orbit squeezing, we find a spatial phase shift between the initial and final zonal flow potentials -an effect absent in previous works.Moreover, we demonstrate that because of orbit modification neoclassical phenomena disappear in the large electric field limit making the residual close to one.

We consider the effects of a finite radial electric field on ion orbits in a subsonic pedestal. Using a procedure that makes a clear distinction between a transit average and a flux surface average we are able to solve the kinetic equation to retain the modifications due to finite E × B drift orbit departures from flux surfaces. Our approach properly determines the velocity space localized, as well as the nonlocal, portion of the ion distribution function in the banana and plateau regimes in the small aspect ratio limit. The rapid variation of the poloidal ion flow coefficient and the electrostatic potential in the total energy modify previous banana regime evaluations of the ion flow, the bootstrap current, and the radial ion heat flux in a subsonic pedestal. In the plateau regime, the rapid variation of the poloidal flow coefficient alters earlier results for the ion flow and bootstrap current, while leaving the ion heat flux unchanged since the rapid poloidal variation of the total energy was properly retained.

Anomalous reduction of the fusion yields by 50% and anomalous scaling of the burn-averaged ion temperatures with the ion-species fraction has been observed for the first time in D 3 He-filled shock-driven inertial confinement fusion implosions. Two ion kinetic mechanisms are used to explain the anomalous observations: thermal decoupling of the D and 3 He populations and diffusive species separation. The observed insensitivity of ion temperature to a varying deuterium fraction is shown to be a signature of ion thermal decoupling in shock-heated plasmas. The burn-averaged deuterium fraction calculated from the experimental data demonstrates a reduction in the average core deuterium density, as predicted by simulations that use a diffusion model. Accounting for each of these effects in simulations reproduces the observed yield trends. In inertial confinement fusion (ICF), targets are imploded to generate a high-density, high-temperature environment where fusion can occur [1,2]. In the current ignition design, four weak shocks compress the cryogenic deuterium-tritium (DT) fuel, then combine into a single strong shock with Mach number ∼10-50 in the central gas, a DT vapor with initial density 0.3 mg=cc [3]. Convergence of this shock at the implosion's center sets the initial entropy of the central plasma "hot spot" and generates a brief period of fusion production ("shock bang"). The rebounding shock strikes the imploding fuel, beginning the hot spot compression that generates the main period of nuclear production ("compression burn"). Understanding the evolution of the plasma during the shock transit phase is fundamentally important for achieving ICF ignition, as this sets the initial conditions for hot spot formation, compression, ignition, and burn [4].The simulations used to design ICF experiments generally assume a single average-ion hydrodynamic framework. The equations of motion for a single ion-species plasma are solved iteratively to model the implosion. Multiple ion species are not treated separately: the ion mass and charge are set as a weighted average of the individual species. Recent experimental and theoretical work has questioned the validity of the average-ion assumption [5][6][7][8][9][10][11][12][13][14][15]. Anomalous reduction of the compression-phase nuclear yield has been observed in implosions filled with multiple fuel species, such as deuteriumhelium-3 (D 3 He) [5], DT [6], and other combinations [7,8]. Anomalous reduction of the shock yield has been ambiguous in these studies. Diffusive ion species separation driven by gradients in pressure [9], electric potential [10,11], and temperature [12] is a potential cause of these observations [13]. Kinetic physics can impact the evolution and nuclear performance of multispecies plasmas in computational studies [14,15], although, to the best of our knowledge, no fully kinetic model is yet capable of simulating an entire ICF implosion.The experiments described in this Letter demonstrate, for the first time, signatures of two multiple-ion kinetic phys...