Grigory Kagan

Electro-diffusion in a plasma with two ion species

Electric field is a thermodynamic force that can drive collisional inter-ion-species transport in a multicomponent plasma. In an inertial confinement fusion 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.

Thermo-diffusion in inertially confined plasmas

Abstract 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.

Revised Knudsen-layer reduction of fusion reactivity

Recent work by Molvig et al. [Phys. Rev. Lett. 109, 095001 (2012)] examined how fusion reactivity may be reduced from losses of fast ions in finite assemblies of fuel. In this paper, this problem is revisited with the addition of an asymptotic boundary-layer treatment of ion kinetic losses. This boundary solution, reminiscent of the classical Milne problem from linear transport theory, obtains a free-streaming limit of fast ion losses near the boundary, where the diffusion approximation is invalid. Thermonuclear reaction rates have been obtained for the ion distribution functions predicted by this improved model. It is found that while Molvigs “Knudsen distribution function” bounds from above the magnitude of the reactivity reduction, this more accurate treatment leads to less dramatic losses of tail ions and associated reduction of thermonuclear reaction rates for finite fuel volumes.

Arbitrary poloidal gyroradius effects in tokamak pedestals and transport barriers

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.

Neoclassical ion heat flux and poloidal flow in a tokamak pedestal

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 E ? B 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 with 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.

Electrostatic turbulence in tokamaks on transport time scales

Simulating electrostatic turbulence in tokamaks on transport time scales requires retaining and evolving a complete turbulence modified neoclassical transport description, including all the axisymmetric neoclassical and zonal flow radial electric field effects, as well as the turbulent transport normally associated with drift instabilities. Neoclassical electric field effects are particularly difficult to retain since they require evaluating the ion distribution function to higher order in gyroradius over background scale length than standard gyrokinetic treatments. To avoid extending gyrokinetics an alternate hybrid gyrokinetic-fluid treatment is formulated that employs moments of the full Fokker–Planck kinetic equation to remove the need for a higher order gyrokinetic distribution function. The resulting hybrid description is able to model all electrostatic turbulence effects with wavelengths much longer than an electron Larmor radius such as the ion temperature gradient (ITG) and trapped electron modes (TEM).

Zonal flow in a tokamak pedestal

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 residua...

The effect of the radial electric field on neoclassical flows in a tokamak pedestal

Conventional formulae for neoclassical flows become inapplicable in subsonic tokamak pedestals with poloidal ion gyroradius scales since the associated strong radial electric field modifies the background ion orbits. The discrepancy has been measured to be substantial in the banana regime on Alcator C-Mod. We demonstrate that new expressions for the poloidal ion flow in the pedestal, that include the effect of the background electric field, are consistent with the boron impurity flow measurements in Alcator C-Mod.

Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging

The significance and nature of ion kinetic effects in D3He-filled, shock-driven inertial confinement fusion implosions are assessed through measurements of fusion burn profiles. Over this series of experiments, the ratio of ion-ion mean free path to minimum shell radius (the Knudsen number, NK) was varied from 0.3 to 9 in order to probe hydrodynamic-like to strongly kinetic plasma conditions; as the Knudsen number increased, hydrodynamic models increasingly failed to match measured yields, while an empirically-tuned, first-step model of ion kinetic effects better captured the observed yield trends [Rosenberg et al., Phys. Rev. Lett. 112, 185001 (2014)]. Here, spatially resolved measurements of the fusion burn are used to examine kinetic ion transport effects in greater detail, adding an additional dimension of understanding that goes beyond zero-dimensional integrated quantities to one-dimensional profiles. In agreement with the previous findings, a comparison of measured and simulated burn profiles shows...

Self-similar structure and experimental signatures of suprathermal ion distribution in inertial confinement fusion implosions

The distribution function of suprathermal ions is found to be self-similar under conditions relevant to inertial confinement fusion hot spots. By utilizing this feature, interference between the hydrodynamic instabilities and kinetic effects is for the first time assessed quantitatively to find that the instabilities substantially aggravate the fusion reactivity reduction. The ion tail depletion is also shown to lower the experimentally inferred ion temperature, a novel kinetic effect that may explain the discrepancy between the exploding pusher experiments and rad-hydro simulations and contribute to the observation that temperature inferred from DD reaction products is lower than from DT at the National Ignition Facility.