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Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1. Solutions near an axisymmetric surface

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer, Phys. Fluids B, vol. 3, 1991, pp. 2805–2821; 2822–2834; Plunk & Helander, J. Plasma Phys. , vol. 84, 2018, 905840205), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic partial differential equation for a function $\eta$ such the field strength satisfies $B = B(\eta )$ . Closed-form solutions are obtained in cylindrical, slab and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasihelical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side. The local solutions thus obtained can be continued globally only for special initial surfaces.

Physics↗

A new model for the ion beams in the plasma sheet boundary layer

A new model is proposed for the ion beams frequently observed in the plasma sheet boundary layer. The model assumes injection of magnetosheath plasma onto closed tail field lines. The plasma then expands along the field lines and is convected towards the earth. Particle simulations of the expansion process are used to calculate properties of these beams. The expansion produces beams of ions at energies of up to a few tens of k(B)T(e), which are consistent with the observed energies of the beams.

Whelan, T.↗

Magnetic flux rope versus the spheromak as models for interplanetary magnetic clouds

Magnetic clouds form a subset of interplanetary ejecta with well-defined magnetic and thermodynamic properties. Observationally, it is well established that magnetic clouds expand as they propagate antisunward. The aim of this paper is to compare and contrast two models which have been proposed for the global magnetic field line topology of magnetic clouds: a magnetic flux tube geometry, on the one hand, and a spheromak geometry (including possible higher multiples), on the other. Traditionally, the magnetic structure of magnetic clouds has been modeled by force-free configurations. In a first step, we therefore analyze the ability of static force-free models to account for the asymmetries observed in the magnetic field profiles of magnetic clouds. For a cylindrical flux tube the magnetic field remains symmetric about closest approach to the magnetic axis on all spacecraft orbits intersecting it, whereas in a spheromak geometry one can have asymmetries in the magnetic field signatures along some spacecraft trajectories. The duration of typical magnetic cloud encounters at 1 AU (1 to 2 days) is comparable to their travel time from the Sun to 1 AU and thus magnetic clouds should be treated as strongly nonstationary objects. In a second step, therefore, we abandon the static approach and model magnetic clouds as self-similarly evolving MHD configurations. In our theory, the interaction of the expanding magnetic cloud with the ambient plasma is taken into account by a drag force proportional to the density and the velocity of expansion. Solving rigorously the full set of MHD equations, we demonstrate that the asymmetry in the magnetic signature may arise solely as a result of expansion. Using asymptotic solutions of the MHD equations, we least squares fit both theoretical models to interplanetary data. We find that while the central part of the magnetic cloud is adequately described by both models, the 'edges' of the cloud data are modeled better by the magnetic flux tube. Further comparisons of the two models necessarily involve thermodynamic properties, since real magnetic configurations are never exactly force-free and gas pressure plays an essential role. We consider a polytropic gas. Our theoretical analysis shows that the self-similar expansion of a magnetic flux tube requires the polytropic index gamma to be less than unity. For the spheromak, however, self-similar, radially expanding solutions are known only for gamma equal to 4/3. This difference, therefore, yields a good way of distinguishing between the two geometries. It has been shown recently that the polytropic relationship is applicable to magnetic clouds and that the corresponding polytropic index is approximately 0.5. This observational result is consistent with the self-similar model of the magnetic flux rope but is in conflict with the self-similar spheromak model.

Farrugia, C. J.↗

Cluster Observations of Multiple Dipolarization Fronts

We present Cluster observations of a series of dipolarization fronts (DF 1 to 6) at the central current sheet in Earth's magnetotail. The velocities of fast earthward flow following behind each DF 1.3 are comparable to the Alfven velocity, indicating that the flow bursts might have been generated by bursty reconnection that occurred tailward of the spacecraft. Based on multispacecraft timing analysis, DF normals are found to propagate mainly earthward at 160.335 km/s with a thickness of 900-1500 km, which corresponds to the ion inertial length or gyroradius scale. Each DF is followed by significant fluctuations in the x and y components of the magnetic field whose peaks are found 1.2 min after the DF passage. These (B(sub x), B(sub y)) fluctuations propagate dawnward (mainly) and earthward. Strongly enhanced field-aligned beams are observed coincidently with (B(sub x), B(sub y)) fluctuations, while an enhancement of cross-tail currents is associated with the DFs. From the observed pressure imbalance and flux tube entropy changes between the two regions separated by the DF, we speculate that interchange instability destabilizes the DFs and causes the deformation of the midtail magnetic topology. This process generates significant field-aligned currents and might power the auroral brightening in the ionosphere. However, this event is associated with neither the main substorm auroral breakup nor the poleward expansion, which might indicate that the observed multiple DFs have been dissipated before they reach the inner plasma sheet boundary.

Hwang, K.-J.↗

Cluster Observations of Multiple Dipolarization Fronts

We present Cluster observations of a series of dipolarization fronts (DF 1 to 6) at the central current sheet in Earth's magnetotail. The velocities of fast earthward flow following behind each DF 1-3, are comparable to the Alfven velocity, indicating that the flow bursts might have been generated by bursty reconnection that occurred tailward of the spacecraft. Based on multi-spacecraft timing analysis, DF normals are found to propagate mainly earthward at $160-335$ km/s with a thickness of 900-1500 km, which corresponds to the ion inertial length or gyroradius scale. Each DF is followed by significant fluctuations in the $x$ and $y$ components of the magnetic field whose peaks are found 1-2 minutes after the DF passage. These $(B_{x},B_{y} )$-fluctuations propagate dawnward (mainly) and earthward. Strongly enhanced field-aligned beams are observed coincidently with $(B_{x},B_{y})$ fluctuations, while an enhancement of cross-tail currents is associated with the DFs. From the observed pressure imbalance and flux-tube entropy changes between the two regions separated by the DF, we speculate that interchange instability destabilizes the DFs and causes the deformation of the mid-tail magnetic topology. This process generates significant field-aligned currents, and might power the auroral brightening in the ionosphere. However, this event is neither associated with the main substorm auroral breakup nor the poleward expansion, which might indicate that the observed multiple DFs have been dissipated before they reach the inner plasma sheet boundary.

Hwang, Kyoung-Joo↗

THERMAL PLASMA IN THE GIANT LOBES OF THE RADIO GALAXY CENTAURUS A

We present a Faraday rotation measure (RM) study of the diffuse, polarized, radio emission from the giant lobes of the nearest radio galaxy, Centaurus A. After removal of the smooth Galactic foreground RM component, using an ensemble of background source RMs located outside the giant lobes, we are left with a residual RM signal associated with the giant lobes. We find that the most likely origin of this residual RM is from thermal material mixed throughout the relativistic lobe plasma. The alternative possibility of a thin-skin/boundary layer of magnetoionic material swept up by the expansion of the lobes is highly unlikely since it requires, at least, an order of magnitude enhancement of the swept-up gas over the expected intragroup density on these scales. Strong depolarization observed from 2.3 to 0.96 GHz also supports the presence of a significant amount of thermal gas within the lobes; although depolarization solely due to RM fluctuations in a foreground Faraday screen on scales smaller than the beam cannot be ruled out. Considering the internal Faraday rotation scenario, we find a thermal gas number density of {approx}10{sup -4} cm{sup -3}, implying a total gas mass of {approx}10{sup 10} M {sub Sun} within the lobes. The thermal pressure associated with this gas (with temperature kT {approx} 0.5 keV, obtained from recent X-ray results) is approximately equal to the non-thermal pressure, indicating that over the volume of the lobes, there is approximate equipartition between the thermal gas, radio-emitting electrons, and magnetic field (and potentially any relativistic protons present).

79 ASTRONOMY AND ASTROPHYSICS↗

Observation of warm, higher energy electrons transiting a double layer in a helicon plasma

Measurements of an inductive RF helicon argon plasma double layer with two temperature electron distributions including a fast (>80 eV) tail are observed at 0.17 mTorr Ar pressure. The fast, untrapped electrons observed downstream of the double layer have a higher temperature (13 eV) than the trapped (T{sub e} = 4 eV) electrons. The reduction of plasma potential and density observed in the double layer region would require an upstream temperature ten times the measured 4 eV if occurring via Boltzmann ambipolar expansion. The experimental observation in Madison helicon experiment indicates that fast electrons with substantial density fractions can be created at low helicon operating pressures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Minimizing separatrix crossings through isoprominence

Abstract A simple property of magnetic fields that minimizes bouncing to passing type transitions of guiding center orbits is defined and discussed. This property, called isoprominence, is explored through the framework of a near-axis expansion. It is shown that isoprominent magnetic fields for a toroidal configuration exist to all orders in a formal expansion about a magnetic axis. Some key geometric features of these fields are described.

confinement↗

Nonextensive hydrodynamics of boost-invariant plasmas

We use quasiparticle anisotropic hydrodynamics to study the non-conformal and non-extensive dynamics of a system undergoing boost-invariant Bjorken expansion. To introduce nonextensivity, we use an underlying Tsallis distribution with a time-dependent nonextensivity parameter q. By taking moments of the quasiparticle Boltzmann equation in the relaxation-time approximation, we obtain dynamical equations which allow us to determine the time evolution of all microscopic parameters including q. We compare numerical solutions for bulk observables obtained using the nonextensive evolution with results obtained using quasiparticle anisotropic hydrodynamics with a Boltzmann distribution function (q → 1). We show that the evolution of the temperature, pressure ratio, and scaled energy density, are quite insensitive to which distribution function is assumed. However, we find significant differences in the early-time evolution of the bulk pressure which are observed for even small deviations from the Boltzmann distribution function. Finally, we discuss the existence of non-conformal hydrodynamic attractors for the longitudinal and transverse pressures, the bulk and shear viscous corrections, and the nonextensivity parameter q.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Towards a complete conceptual model of substorm onsets and expansions

Observational results from the CRRES satellite near times of substorm onsets support the theoretical premise that substorms initiate near the inner edge of the plasma sheet. The region is connected latitudinally to the equatorward-most pre-breakup arc. During the growth phase, the inner edge of the plasma sheet moves towards the earth. This motion is modulated by various cavity oscillations of the magnetosphere-ionosphere coupled magnetosphere. This modulation can locally reverse the background convection electric field. The reversed convection taps energy stored in the inner-edge region of the plasma sheet. The near earth plasma sheet moves out of equilibrium with the lobes, and a rarefaction is launched tailward. This allows current driven dissipation to grow and a near-earth X-line to form. A model is presented which explains the observations of the CRRES satellite, and can account for the behavior associated with auroral intensification and substorm onset.

Erickson, Gary M.↗

Inverse Compton Scattering in Mildly Relativistic Plasma

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and calculated the Sunyaev-Zel'dovich effect in the cosmic background radiation. Our semi-analytic method is based on a separation of photon diffusion in frequency and real space. We use Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zel'dovich effect (not possible with the extended Kompaneets equation) and discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high temperature clusters (k(sub B)T(sub e) greater than or approximately equal to 15 keV) relativistic corrections based on a fifth order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zel'dovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the cross-over frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections, and should be taken into account for high-precision work, but are smaller than the typical kinematic effect from cluster radial velocities.

Molnar, S. M.↗

Boundary, SOL, and Divertor Physics Studies on TCV (Final Report for Research Funded by DoE Award DE-SC0020327)

Research supported under this grant was organized around two diagnostic systems installed on the TCV tokamak located at EPFL in Lausanne, Switzerland: Multi-Spectral Imaging (MSI) and Gas-Puff Imaging (GPI). MSI monitors 2-d time-history images of up to 10 spectral lines, in the visible, using identical views for all wavelengths. The primary application of MSI is to infer 2-d time histories of electron temperature and density in the Scrape-Off-Layer (SOL) of diverted plasmas, utilizing ratios of emission from multiple neutral helium lines. The atomic models are validated against 1-d Thomson scattering measurements. SOL density and temperature maps are analyzed to infer divertor dynamics, including particle and power flows, for a variety of divertor configurations, and specifically as flux expansion along the long-legged outboard divertor is systematically varied. GPI is used to measure details of edge fluctuations in the SOL, particularly as a function of plasma triangularity (δ), including both positive and negative δ. A threshold is found, whereby for δ<-0.3, edge turbulence in the far SOL is completely suppressed. Dynamics of the filamentary turbulence was also analyzed using advance machine learning techniques. Research in support of four PhD theses was carried out within the scope of this Award, including 2 at MIT and 2 at EPFL.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Collisional transport coefficients of dense high-temperature plasmas within the quantum Landau-Fokker-Planck framework

In this paper, we extend the long-established formulas for the transport coefficients of classical plasmas inside the dense plasma regime for temperatures and densities where the classical Landau equation breaks down but its quantum extension that includes quantum degeneracy effects is valid. To this end, the quantum Landau kinetic equation is solved by the Chapman-Enskog method. The mathematical derivation is done in full generality, i.e., for multicomponent systems and to all orders of the polynomials expansion used to approximate the distribution functions. We apply the general results to two important examples, the electron gas model and an electron-ion plasma model consisting of one type of ions of any charge. We discuss the combined effects of the Pauli exclusion principle, of the electron-electron, and of the electron-ion collisions on the transport coefficients and on the convergence of the Chapman-Enskog method. For the electron gas model, the effect of the Pauli exclusion principle on the transport coefficients rapidly becomes non-negligible outside the domain of validity of the classical Landau equation. For the electron-ion plasmas, the effect of the Pauli exclusion principle depends sensitively on the ion charge Z and varies non-monotonically with Θ. For instance, for ion charge Z = 1, the electrical conductivity is increased by up to ~30% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~9%, and the shear viscosity coefficient is increased by up to ~13%. Finally, in the Lorentz gas ( Z → ∞ ) limit, the electrical conductivity is reduced by up to ~14% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ~39%, and the shear viscosity coefficient is not affected.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Anticipated Electrical Environment Within Permanently Shadowed Lunar Craters

Shadowed locations ncar the lunar poles arc almost certainly electrically complex regions. At these locations near the terminator, the local solar wind flows nearly tangential to the surface and interacts with large-scale topographic features such as mountains and deep large craters, In this work, we study the solar wind orographic effects from topographic obstructions along a rough lunar surface, On the leeward side of large obstructions, plasma voids are formed in the solar wind because of the absorption of plasma on the upstream surface of these obstacles, Solar wind plasma expands into such voids) producing an ambipolar potential that diverts ion flow into the void region. A surface potential is established on these leeward surfaces in order to balance the currents from the expansion-limited electron and ion populations, Wc find that there arc regions ncar the leeward wall of the craters and leeward mountain faces where solar wind ions cannot access the surface, leaving an electron-rich plasma previously identified as an "electron cloud." In this case, some new current is required to complete the closure for current balance at the surface, and we propose herein that lofted negatively charged dust is one possible (nonunique) compensating current source. Given models for both ambipolar and surface plasma processes, we consider the electrical environment around the large topographic features of the south pole (including Shoemaker crater and the highly varied terrain near Nobile crater), as derived from Goldstone radar data, We also apply our model to moving and stationary objects of differing compositions located on the surface and consider the impact of the deflected ion flow on possible hydrogen resources within the craters

Farrell, W. M.↗

Thermophysical and mechanical property assessment of UB 2 and UB 4 sintered via spark plasma sintering

Uranium diboride (UB 2 ) and uranium tetraboride (UB 4 ) are candidate constituents for multi-phase accident tolerant fuel due to their anticipated high thermal conductivity. These fuels have high uranium density that contributes to fission, and by tailoring the ratio of 10 B/ 11 B, can also act as an integrated burnable poison. Understanding the thermophysical and mechanical properties of uranium borides, for which only limited data are available in the literature, is of importance to determine their accident tolerance. In this work UB 2 and UB 4 have been synthesized via arc melting and sintered to high densities via spark plasma sintering (SPS). High density samples, >90% theoretical density, were used to measure the thermal diffusivity and thermal expansion of UB 2 and UB 4 and, in conjunction with specific heat literature data, their thermal conductivities were calculated from 298 to 1773 K. Additionally, resonance ultrasound spectroscopy (RUS) and nanoindentation were performed to investigate the mechanical properties of the uranium borides. Our results are discussed in the context of available literature. Both UB 2 and UB 4 exhibit thermal conductivities higher than that of UO 2 , with UB 2 having the highest. The thermal conductivity of UB 2 increases with temperature above 874 K, while for UB 4 there is a linear increase over the entire measured range. X-ray diffraction (XRD) results indicate that impurity phases were present in the fabricated materials, which could explain why literature density functional theory (DFT) results predict higher values. As a result, this suggests that if impurity phases or any microstructural defects can be eliminated then the thermal conductivity can be further increased.

36 MATERIALS SCIENCE↗

Factorization for jet production in heavy-ion collisions

We develop an Effective Field Theory approach for jet observables in heavy-ion collisions, where the jet is treated as an open quantum system interacting with a hot and dense QCD medium. Within this framework, we derive a novel factorization formula for inclusive jet production, expressed as a series expansion with an increasing number of radiating subjet functions that encode forward scattering with the Quark-Gluon Plasma, convolved with perturbative matching coefficients. This work provides a systematic framework for computing jet observables at higher order and understanding their non-perturbative aspects, paving the way for future applications in heavy-ion phenomenology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Laser rocket system analysis

The laser rocket systems investigated in this study were for orbital transportation using space-based, ground-based and airborne laser transmitters. The propulsion unit of these systems utilizes a continuous wave (CW) laser beam focused into a thrust chamber which initiates a plasma in the hydrogen propellant, thus heating the propellant and providing thrust through a suitably designed nozzle and expansion skirt. The specific impulse is limited only by the ability to adequately cool the thruster and the amount of laser energy entering the engine. The results of the study showed that, with advanced technology, laser rocket systems with either a space- or ground-based laser transmitter could reduce the national budget allocated to space transportation by 10 to 345 billion dollars over a 10-year life cycle when compared to advanced chemical propulsion systems (LO2-LH2) of equal capability. The variation in savings depends upon the projected mission model.

Jones, W. S.↗

The telegraph equation in charged particle transport

We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

Gombosi, T. I.↗