The velocity-space moments of the often troublesome nonlinear Landau collision operator are
expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions.
The collisional moments are shown to be generated by derivatives of two well-known functions,
namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The
resulting formula has a nonlinear dependency on the relative mean flow of the colliding species
normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency
on densities and higher-order velocity moments of the distribution functions, with no restriction
on temperature, flow, or mass ratio of the species. The result can be applied to both the classic
transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional
fluid equations that follow Grad’s moment approach. As an illustrative example, we provide
the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer
rates.
Parametric decay of plasma waves near the upper-hybrid resonance
An intense X wave propagating perpendicularly to dc magnetic field is unstable with respect to a parametric decay into an electron Bernstein wave and a lower-hybrid wave. A modified theory of this effect is proposed that extends to the high-intensity regime, where the instability rate $\gamma$ ceases to be a linear function of the incident-wave amplitude. An explicit formula for $\gamma$ is derived and expressed in terms of cold-plasma parameters. Theory predictions are in reasonable agreement
with the results of the particle-in-cell simulations presented in a separate publication.
Extending geometrical optics: A Lagrangian theory for vector waves
Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are
not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely
described by their coordinates and momenta, but vector-wave rays have another degree of freedom,
namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical)
“wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A
well-known manifestation of polarization dynamics is mode conversion, which is the linear
exchange of quanta between different wave modes and can be interpreted as a rotation of the wave
spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories.
This work presents an extension and reformulation of GO as a first-principle Lagrangian theory,
whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously.
As an example, the theory is applied to describe the polarization-driven divergence of right-hand
and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.
Ponderomotive dynamics of waves in quasiperiodically modulated media
Similarly to how charged particles experience time-averaged ponderomotive forces in high-frequency fields,
linear waves also experience time-averaged refraction in modulated media. Here we propose a covariant
variational theory of this ponderomotive effect on waves for a general nondissipative linear medium. Using
the Weyl calculus, our formulation accommodates waves with temporal and spatial period comparable to that of
the modulation (provided that parametric resonances are avoided). Our theory also shows that any wave is, in
fact, a polarizable object that contributes to the linear dielectric tensor of the ambient medium. The dynamics
of quantum particles is subsumed as a special case. As an illustration, ponderomotive Hamiltonians of quantum
particles and photons are calculated within a number of models. We also explain a fundamental connection
between these results and the well-known electrostatic dielectric tensor of quantum plasmas.
Total fluid pressure imbalance in the scrape-off layer of tokamak plasmas
Simulations using the fully kinetic neoclassical code XGCa ( X-point included guiding- center
axisymmetric) were undertaken to explore the impact of kinetic effects on scrape-off layer
(SOL) physics in DIII-D H-mode plasmas. XGCa is a total-f, gyrokinetic code which selfconsistently
calculates the axisymmetric electrostatic potential and plasma dynamics, and
includes modules for Monte Carlo neutral transport.
Previously presented XGCa results showed several noteworthy features, including large
variations of ion density and pressure along field lines in the SOL, experimentally relevant
levels of SOL parallel ion flow (Mach number ∼ 0.5), skewed ion distributions near the sheath
entrance leading to subsonic flow there, and elevated sheath potentials (Churchill 2016 Nucl.
Mater. Energy 1–6).
In this paper, we explore in detail the question of pressure balance in the SOL, as it was
observed in the simulation that there was a large deviation from a simple total pressure balance
(the sum of ion and electron static pressure plus ion inertia). It will be shown that both the
contributions from the ion viscosity (driven by ion temperature anisotropy) and neutral source
terms can be substantial, and should be retained in the parallel momentum equation in the
SOL, but still falls short of accounting for the observed fluid pressure imbalance in the XGCa
simulation results.
Photon polarizability and its effect on the dispersion of plasma waves
High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.
Kinetic simulations of scrape-off layer physics in the DIII-D tokamak
Simulations using the fully kinetic code XGCa were undertaken to explore the impact of kinetic effects on scrape-off layer (SOL) physics in DIII-D H-mode plasmas. XGCa is a total-f, gyrokinetic code which self-consistently calculates the axisymmetric electrostatic potential and plasma dynamics, and includes modules for Monte Carlo neutral transport. Fluid simulations are normally used to simulate the SOL, due to its high collisionality. However, depending on plasma conditions, a number of discrepancies have been observed between experiment and leading SOL fluid codes (e.g. SOLPS), including underestimating outer target temperatures, radial electric field in the SOL, parallel ion SOL flows at the low field side, and impurity radiation. Many of these discrepancies may be linked to the fluid treatment, and might be resolved by including kinetic effects in SOL simulations.
The XGCa simulation of the DIII-D tokamak in a nominally sheath-limited regime show many noteworthy features in the SOL. The density and ion temperature are higher at the low-field side, indicative of ion orbit loss. The SOL ion Mach flows are at experimentally relevant levels (Mi ∼ 0.5), with similar shapes and poloidal variation as observed in various tokamaks. Surprisingly, the ion Mach flows close to the sheath edge remain subsonic, in contrast to the typical fluid Bohm criterion requiring ion flows to be above sonic at the sheath edge. Related to this are the presence of elevated sheath potentials, eΔΦ/Te∼3−4, over most of the SOL, with regions in the near-SOL close to the separatrix having eΔΦ/Te > 4. These two results at the sheath edge are a consequence of non-Maxwellian features in the ions and electrons there.
Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables. Here, a different approach is proposed. We show that, for a broad class of dissipative systems of practical interest, variational principles can be formulated using constant Lagrange multipliers and Lagrangians nonlocal in time, which allow treating reversible and irreversible dynamics on the same footing. A general variational theory of linear dispersion is formulated as an example. In particular, we present a variational formulation for linear geometrical optics in a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously.
Continuum kinetic and multi-fluid simulations of classical sheaths
The kinetic study of plasma sheaths is critical, among other things, to understand the deposition of
heat on walls, the effect of sputtering, and contamination of the plasma with detrimental impurities.
The plasma sheath also provides a boundary condition and can often have a significant global
impact on the bulk plasma. In this paper, kinetic studies of classical sheaths are performed with the
continuum kinetic code, Gkeyll, which directly solves the Vlasov-Maxwell equations. The code
uses a novel version of the finite-element discontinuous Galerkin scheme that conserves energy in
the continuous-time limit. The fields are computed using Maxwell equations. Ionization and scattering
collisions are included; however, surface effects are neglected. The aim of this work is to
introduce the continuum kinetic method and compare its results with those obtained from an
already established finite-volume multi-fluid model also implemented in Gkeyll. Novel boundary
conditions on the fluids allow the sheath to form without specifying wall fluxes, so the fluids and
fields adjust self-consistently at the wall. The work presented here demonstrates that the kinetic
and fluid results are in agreement for the momentum flux, showing that in certain regimes, a multi-
fluid model can be a useful approximation for simulating the plasma boundary. There are differences
in the electrostatic potential between the fluid and kinetic results. Further, the direct solutions
of the distribution function presented here highlight the non-Maxwellian distribution of electrons in
the sheath, emphasizing the need for a kinetic model. The densities, velocities, and the potential
show a good agreement between the kinetic and fluid results. However, kinetic physics is
highlighted through higher moments such as parallel and perpendicular temperatures which provide
significant differences from the fluid results in which the temperature is assumed to be isotropic.
Besides decompression cooling, the heat flux is shown to play a role in the temperature differences
that are observed, especially inside the collisionless sheath.
Zonal-flow dynamics from a phase-space perspective
The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the
studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the
exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometricaloptics
limit. We derive a modified theory that takes both of these effects into account, while still
treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by
an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation
of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms
missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system,
in addition to the total energy, which is the only conserved invariant in previous theories based on
the WKE. Numerical simulations are presented to illustrate the importance of these additional
terms. The proposed formulation can be considered as a phase-space representation of the second order
cumulant expansion, or CE2.
Dynamo-driven plasmoid formation from a current-sheet instability
Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations
during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry.
We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal
guide field. As helicity is injected, two types of current sheets are formed from (1) the oppositely
directed field lines in the injector region (primary reconnecting current sheet), and (2) the
poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetric
fluctuations arising from the current-sheet instability isolated near the plasma edge have
tearing parity but can nevertheless grow fast (on the poloidal Alfven time scale). These modes saturate
by breaking up the current sheet. Second, for the first time, a dynamo poloidal flux amplification
is observed at the reconnection site (in the region of the oppositely directed magnetic field).
This fluctuation-induced flux amplification increases the local Lundquist number, which then triggers
a plasmoid instability and breaks the primary current sheet at the reconnection site. The plasmoids
formation driven by large-scale flux amplification, i.e., a large-scale dynamo, observed here
has strong implications for astrophysical reconnection as well as fast reconnection events in laboratory
plasmas.
Magnetorotational Turbulence and Dynamo in a Collisionless Plasma
We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and
dynamo, using the local shearing-box model of a collisionless accretion disk. The kinetic magnetorotational
instability grows from a subthermal magnetic field having zero net flux over the computational
domain to generate self-sustained turbulence and outward angular-momentum transport. Significant
Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned
ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabilities through
particle trapping and pitch-angle scattering. The latter endow the plasma with an effective viscosity that is
biased with respect to the magnetic-field direction and spatiotemporally variable. Energy spectra suggest an
Alfvén-wave cascade at large scales and a kinetic-Alfvén-wave cascade at small scales, with strong smallscale
density fluctuations and weak nonaxisymmetric density waves. Ions undergo nonthermal particle
acceleration, their distribution accurately described by a κ distribution. These results have implications for
the properties of low-collisionality accretion flows, such as that near the black hole at the Galactic center.
Validation and benchmarking of two particle-in-cell codes for a glow discharge
The two particle-in-cell codes EDIPIC and LSP are benchmarked and validated for a
parallel-plate glow discharge in helium, in which the axial electric field had been carefully
measured, primarily to investigate and improve the fidelity of their collision models. The
scattering anisotropy of electron-impact ionization, as well as the value of the secondaryelectron
emission yield, are not well known in this case. The experimental uncertainty for the
emission yield corresponds to a factor of two variation in the cathode current. If the emission
yield is tuned to make the cathode current computed by each code match the experiment,
the computed electric fields are in excellent agreement with each other, and within about
10% of the experimental value. The non-monotonic variation of the width of the cathode fall
with the applied voltage seen in the experiment is reproduced by both codes. The electron
temperature in the negative glow is within experimental error bars for both codes, but the
density of slow trapped electrons is underestimated. A more detailed code comparison done
for several synthetic cases of electron-beam injection into helium gas shows that the codes are
in excellent agreement for ionization rate, as well as for elastic and excitation collisions with
isotropic scattering pattern. The remaining significant discrepancies between the two codes are
due to differences in their electron binary-collision models, and for anisotropic scattering due
to elastic and excitation collisions.
Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams
In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the
basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the
analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several
decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations
by intentionally introducing strong coupling. In this Letter, we report the full generalization of the KV
model by including all of the linear (both external and space-charge) coupling forces, beam energy
variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations.
The new generalized KV model yields spatially uniform density profiles and corresponding linear
self-field forces as desired. The corresponding matrix envelope equations and beam matrix for the
generalized KV model provide important new theoretical tools for the detailed design and analysis of
high-intensity beam manipulations, for which previous theoretical models are not easily applicable.