C. J. McDevitt

Reduced Fokker-Planck models for fast particle distribution across a transition layer of disparate plasma temperatures

Across a transition layer of disparate plasma temperatures, the high energy tail of the plasma distribution can have appreciable deviations from the local Maxwellian distribution due to the Knudson layer effect. The Fokker-Planck equation for the tail particle population can be simplified in a series of practically useful limiting cases. The first is the approximation of background Maxwellian distribution for linearizing the collision operator. The second is the supra-thermal particle speed ordering of vTi ≪ v ≪ vTe for the tail ions and vTi ≪ vTe ≪ v for the tail electrons. Keeping both the collisional drag and energy scattering is essential for the collision operator to produce a Maxwellian tail distribution. The Fokker-Planck model for following the tail ion distribution for a given background plasma profile is explicitly worked out for systems of one spatial dimension, in both slab and spherical geometry. A third simplification is an expansion of the tail particle distribution using the spherical harm...

A comparative study of the tail ion distribution with reduced Fokker–Planck models

A series of reduced models are used to study the fast ion tail in the vicinity of a transition layer between plasmas at disparate temperatures and densities, which is typical of the gas and pusher interface in inertial confinement fusion targets. Emphasis is placed on utilizing progressively more comprehensive models in order to identify the essential physics for computing the fast ion tail at energies comparable to the Gamow peak. The resulting fast ion tail distribution is subsequently used to compute the fusion reactivity as a function of collisionality and temperature. While a significant reduction of the fusion reactivity in the hot spot compared to the nominal Maxwellian case is present, this reduction is found to be partially recovered by an increase of the fusion reactivity in the neighboring cold region.

A hybrid model for coupling kinetic corrections of fusion reactivity to hydrodynamic implosion simulations

Inertial confinement fusion requires an imploded target in which a central hot spot is surrounded by a cold and dense pusher. The hot spot/pusher interface can take complicated shape in three dimensions due to hydrodynamic mix. It is also a transition region where the Knudsen and inverse Knudsen layer effect can significantly modify the fusion reactivity in comparison with the commonly used value evaluated with background Maxwellians. Here, we describe a hybrid model that couples the kinetic correction of fusion reactivity to global hydrodynamic implosion simulations. The key ingredient is a non-perturbative treatment of the tail ions in the interface region where the Gamow ion Knudsen number approaches or surpasses order unity. The accuracy of the coupling scheme is controlled by the precise criteria for matching the non-perturbative kinetic model to perturbative solutions in both configuration space and velocity space.

Fusion yield rate recovery by escaping hot-spot fast ions in the neighboring fuel layer

Free-streaming loss by fast ions can deplete the tail population in the hot spot of an inertial confinement fusion (ICF) target. Escaping fast ions in the neighboring fuel layer of a cryogenic target can produce a surplus of fast ions locally. In contrast to the Knudsen layer effect that reduces hot-spot fusion reactivity due to tail ion depletion, the inverse Knudsen layer effect increases fusion reactivity in the neighboring fuel layer. In the case of a burning ICF target in the presence of significant hydrodynamic mix which aggravates the Knudsen layer effect, the yield recovery largely compensates for the yield reduction. For mix-dominated sub-ignition targets, the yield reduction is the dominant process.

Models of primary runaway electron distribution in the runaway vortex regime

A number of recent numerical calculations have shown the formation of a bump in runaway electron (RE) energy distribution by taking into account the synchrontron radiational damping force due to REs gyromotions. Here, we present a detailed examination on how the bump location changes at different pitch-angles and the characteristics of the RE pitch-angle distribution. Although REs moving along the magnetic field are preferably accelerated and then populate the phase-space of larger pitch-angle mainly through diffusions, an off-axis (i.e., at finite pitch) peak can still form due to the presence of a runaway vortex that accumulates REs at a finite pitch-angle. A simplified Fokker–Planck model and its semi-analytical solutions based on local expansions around the O point are used to illustrate the characteristics of RE distribution around the O point of the runaway vortex in phase-space. The calculated energy location of the O point together with the local energy and pitch-angle distributions agree with th...

Calculation of the fast ion tail distribution for a spherically symmetric hot spot

The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.

Control of runaway electron energy using externally injected whistler waves

One way of mitigating runaway damage of the plasma-facing components in a tokamak fusion reactor is by limiting the runaway electron energy under a few MeV, while not necessarily reducing the runaway current appreciably. Here, we describe a physics mechanism by which such momentum space engineering of the runaway distribution can be facilitated by externally injected high-frequency electromagnetic waves such as whistler waves. The drastic impact that wave-induced scattering can have on the runaway energy distribution is fundamentally the result of its ability to control the runaway vortex in the momentum space. The runaway vortex, which is a local circulation of runaways in momentum space, is the outcome of the competition between Coulomb collisions, synchrotron radiation damping, and runaway acceleration by the parallel electric field. By introducing a wave that resonantly interacts with runaways in a particular range of energies which is mildly relativistic, the enhanced scattering would reshape the vor...

Turbulent current drive mechanisms

Mechanisms through which plasma microturbulence can drive a mean electron plasma current are derived. The efficiency through which these turbulent contributions can drive deviations from neoclassical predictions of the electron current profile is computed by employing a linearized Coulomb collision operator. It is found that a non-diffusive contribution to the electron momentum flux as well as an anomalous electron-ion momentum exchange term provide the most efficient means through which turbulence can modify the mean electron current for the cases considered. Such turbulent contributions appear as an effective EMF within Ohms law and hence provide an ideal means for driving deviations from neoclassical predictions.

Fast ion transport at a gas-metal interface

Fast ion transport and the resulting fusion yield reduction are computed at a gas-metal interface. The extent of fusion yield reduction is observed to depend sensitively on the charge state of the surrounding pusher material and the width of the atomically mixed region. These sensitivities suggest that idealized boundary conditions often implemented at the gas-pusher interface for the purpose of estimating fast ion loss will likely overestimate fusion reactivity reduction in several important limits. In addition, the impact of a spatially complex material interface is investigated by considering a collection of droplets of the pusher material immersed in a DT plasma. It is found that for small Knudsen numbers, the extent of fusion yield reduction scales with the surface area of the material interface. As the Knudsen number is increased, however, the simple surface area scaling is broken, suggesting that hydrodynamic mix has a nontrivial impact on the extent of fast ion losses.