Perpendicular Momentum Research Articles

Electron tail suppression and effective collisionality due to synchrotron emission and absorption in mildly relativistic plasmas

Synchrotron radiation losses are a significant cause of concern for high-temperature aneutronic fusion reactions such as proton–Boron 11. The fact that radiation losses occur primarily in the high-energy tail, where the radiation itself has a substantial impact on the electron distribution, necessitates a self-consistent approach to modeling the diffusion and drag induced by synchrotron absorption and emission. Furthermore, an accurate model must account for the fact that the radiation emission spectrum is momentum-dependent, and the plasma opacity is frequency-dependent. Here, we present a simple Fokker–Planck operator, built on a newly solved-for blackbody synchrotron diffusion operator, which captures all relevant features of the synchrotron radiation. Focusing on magnetic mirror fusion plasmas, we show that significant suppression of the electron distribution occurs for relativistic values of the perpendicular electron momentum, which therefore emit much less radiation than predicted under the assumption of a Maxwell–Jüttner distribution.

Tripling of the scattering vector range of X-ray reflectivity on liquid surfaces using a double-crystal deflector.

The maximum range of perpendicular momentum transfer (q z) has been tripled for X-ray scattering from liquid surfaces when using a double-crystal deflector setup to tilt the incident X-ray beam. This is achieved by employing a higher-energy X-ray beam to access Miller indices of reflecting crystal atomic planes that are three times higher than usual. The deviation from the exact Bragg angle condition induced by misalignment between the X-ray beam axis and the main rotation axis of the double-crystal deflector is calculated, and a fast and straightforward procedure to align them is deduced. An experimental method of measuring scattering intensity along the q z direction on liquid surfaces up to q z = 7 Å-1 is presented, with liquid copper serving as a reference system for benchmarking purposes.

Angular Momentum Variation of the Milky Way Thick Disk: The Dependence of Chemical Abundance and Evidence of the Inside-out Formation Scenario

We investigate the angular momentum of mono-abundance populations (MAPs) of the Milky Way thick disk by using a sample of 26,076 giant stars taken from APOGEE Data Release (DR) 17 and Gaia early DR3. The vertical and perpendicular angular momentum components, L Z and L P , of the MAPs in narrow bins have significant variations across the [α/M]–[M/H] plane. L Z and L P systematically change with [M/H] and [α/M] and can be alternatively quantified by the chemical gradients: d[M/H]/dL Z = 1.2 × 10−3 dex kpc−1 km−1 s, d[M/H]/dL P = −5.0 × 10−3 dec kpc−1 km−1 s, and d[α/M]/dL Z = −3.0 × 10−4 dex kpc−1 km−1 s, d[α/M]/dL P = 1.2 × 10−3 dec kpc−1 km−1 s. These correlations can also be explained as the chemical dependence of the spatial distribution shape of the MAPs. We also exhibit the corresponding age dependence of the angular momentum components. Under the assumption that the guiding radius (R g ) is proportional to L Z , this provides direct observational evidence of the inside-out structure formation scenario of the thick disk, with dR g /dAge = −1.9 kpc Gyr−1. The progressive changes in the disk thickness can be explained by the upside-down formation or/and the consequent kinematical heating.

Quantum Level Instability of Transverse Excitation in Electron Flow

In current research, we use the effective Schrödinger-Poisson model to study a new kind of quantum-level instability in an infinite-wall slab electron flow. We use the Madelung fluid representation along with the conventional eigenvalue problem techniques in order to solve the linearized coupled differential equations representing the linear transverse collective excitations in the electron gas of arbitrary degree of degeneracy having a constant perpendicular drift. It is shown that the energy levels of collective electrostatic excitations are doubly quantized due to mutual interactions between single electron oscillations, analogous to the problem of a particle in a box, and collective Langmuir oscillations, which are modulated over single electron quantum state. We also report the transverse excitation instability of plasmon energy level in electron slab flow due to the interplay between the wave-like dispersion and the destabilizing perpendicular electron drift momentum. We further study in detail the parametric dependence of such instability in terms of different aspects of the many-electron system. Such a quantum-level instability may have important applications in characteristic behavior of plasmonic devices and their frequency response. Parametric quantization of drifting electron fluid may also have broad applications in nanoscale quantum device calibration and quantum measurements.

Quantum edge plasmon excitations and electron spill-out effect

In this paper, by using the effective Schrödinger–Poisson model, we investigate quantum edge plasmon excitations and electron spill-out effect in an arbitrary degenerate electron gas in the presence of perpendicular electron drift momentum. It is found that the single-electron Schrödinger equation solution produces a nonoscillatory electron number density distribution on the interface showing characteristic surface-dipole and electron spill-out effects. However, the Schrödinger–Poisson model produces large amplitude dual-tone density distribution due to both wave-like and particle-like plasmon dispersion other than surface-dipole and electron spill-out effects. The variations in the density structure are investigated in terms of different parameters such as the chemical potential, temperature, quantum electron tunneling parameter, and perpendicular electron de Broglie's wavenumber. Furthermore, we extend our study to the case of collective electron tunneling and reveal that the interface potential energy significantly differs from the case of single-electron quantum tunneling and strongly depends on the electron gas parameters. The current study reveals interesting features of the transverse plasmon excitations and electron spill-out in a current carrying narrow metal slab or metal–dielectric quantum sandwich interfaces incorporating both single-electron and collective quantum tunneling.

The non-ideal finite Larmor radius effect in the solar atmosphere

ABSTRACT The dynamics of the partially ionized solar atmosphere is controlled by the frequent collisions and charge exchange between the predominant neutral hydrogen atoms and charged ions. At signal frequencies below or of the order of either of the collision or charge exchange frequencies, the magnetic stress is felt by both the charged and neutral particles simultaneously. The resulting neutral-mass loading of the ions leads to the rescaling of the effective ion-cyclotron frequency (it becomes the Hall frequency), and the resultant effective Larmor radius becomes of the order of few kms. Thus, the finite Larmor radius effect that manifests as the ion and neutral pressure stress tensors operates over macroscopic scales. Whereas parallel and perpendicular (with respect to the magnetic field) viscous momentum transport competes with the Ohm and Hall diffusion of the magnetic field in the photosphere–chromosphere, the gyroviscous effect becomes important only in the transition region between the chromosphere and corona, where it competes with the ambipolar diffusion. The wave propagation in the gyroviscous effect-dominated medium depends on the plasma β (a ratio of the thermal and magnetic energies). The abundance of free energy makes gyro waves unstable with the onset condition exactly opposite of the Hall instability. However, the maximum growth rate is identical to the Hall instability. For a flow gradient of ${\sim} 0.1 \, \mbox{s}^{-1}$, the instability growth time is 1 min. Thus, the transition region may become subject to this fast-growing gyroviscous instability.

Plasma dynamics and vacuum pair creation using the Dirac-Heisenberg-Wigner formalism.

We derive a system of coupled partial differential equations for the equal-time Wigner function in an arbitrary strong electromagnetic field using the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a system of four coupled partial differential equations, which are completed by Ampères law. This electrostatic system is further studied for two different cases. In the first case, we consider linearized wave propagation in a plasma accounting for the nonzero vacuum expectation values. We then derive the dispersion relation and compare it with well-known limiting cases. In the second case, we consider Schwinger pair production using the local density approximation to allow for analytical treatment. The dependence of the pair production rate on the perpendicular momentum is investigated and it turns out that the spread of the produced pairs along with perpendicular momentum depends on the strength of the applied electric field.

Subdimensional topologies, indicators, and higher order boundary effects

The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features. Within this context we recently reported on a class of unexplored topological structures that thrive on the concept of {\it sub-dimensional topology}. Although such phases have trivial indicators and band representations when evaluated over the complete Brillouin zone, they have stable or fragile topologies within sub-dimensional spaces, such as planes or lines. This perspective does not just refine classification pursuits, but can result in observable features in the full dimensional sense. In three spatial dimensions (3D), for example, sub-dimensional topologies can be characterized by non-trivial planes, having general topological invariants, that are compensated by Weyl nodes away from these planes. As a result, such phases have 3D stable characteristics such as Weyl nodes, Fermi arcs and edge states that can be systematically predicted by sub-dimensional analysis. Within this work we further elaborate on these concepts. We present refined representation counting schemes and address distinctive bulk-boundary effects, that include momentum depended (higher order) edge states that have a signature dependence on the perpendicular momentum. As such, we hope that these insights might spur on new activities to further deepen the understanding of these unexplored phases.

Wave Excitation by Energetic Ring-distributed Electron Beams in the Solar Corona

Abstract We analyzed properties of waves excited by mildly relativistic electron beams propagating along the magnetic field with a ring-shape perpendicular momentum distribution in neutral and current-free solar coronal plasmas. These plasmas are subject to both the beam and the electron cyclotron maser instabilities driven by the positive momentum gradients of the ring-beam electron distribution in the directions parallel and perpendicular to the ambient magnetic field, respectively. To explore the related kinetic processes self-consistently, 2.5D fully kinetic particle-in-cell simulations were carried out. To quantify excited wave properties in different coronal conditions, we investigated the dependences of their energy and polarization on the ring-beam electron density and magnetic field. In general, electrostatic waves dominate the energetics of waves, and nonlinear waves are ubiquitous. In weakly magnetized plasmas, where the electron cyclotron frequency ω ce is lower than the electron plasma frequency ω pe, it is difficult to produce escaping electromagnetic waves with frequency ω > ω pe and small refractive index (k and c are the wavenumber and the light speed, respectively). Highly polarized and anisotropic escaping electromagnetic waves can, however, be effectively excited in strongly magnetized plasmas with ω ce/ω pe ≥ 1. The anisotropies of the energy, circular polarization degree (CPD), and spectrogram of these escaping electromagnetic waves strongly depend on the number density ratio of the ring-beam electrons to the background electrons. In particular, their CPDs can vary from left-handed to right-handed with the decrease of the ring-beam density, which may explain some observed properties of solar radio bursts (e.g., radio spikes) from the solar corona.

Structure Distribution of Gaseous Ions in Strong Electrostatic Fields.

In drift tube experiments, where ions move in gases under the action of an electrostatic field, collision excitation is implemented for the study of the energy partitioning in the molecular degrees of freedom and the corresponding relaxation rates when the excitation is turned off. In the case of flexible ions, the vibration modes related to metastable molecular structures have been activated in ion mobility spectrometry and their population has been probed with respect to the field strength and the gas temperature. Here, we study the angular vibrational excitation and relaxation of such systems by examining the motion of molecular ions with one bending mode at strong fields using a nonequilibrium molecular dynamics simulation method. The relatively stable structures are introduced through the use of an intramolecular angular potential with minima at the position of the most stable conformations. We calculate the first few moments of the velocity and angular velocity distribution functions as well as the distribution of the conformers, and find that they follow unified curves when plotted with respect to the relative ion-atom collision energy. At high field strengths, the angular vibration is excited and a portion of the ions interchanges conformations continuously in time with the populations of the molecular structures to attain limiting values. In addition, orientational alignment, with the perpendicular angular momentum being greater than the one parallel to the field, is observed. Our observations, although based on a specific system, must be rather general for the case of large flexible molecular ions.

General structure of the neutral ρ meson self-energy and its spectral properties in a hot and dense magnetized medium

The one loop self energy of the neutral $\rho$ meson is obtained for the effective $\rho\pi\pi$ and $\rho NN$ interaction at finite temperature and density in the presence of a constant background magnetic field of arbitrary strength. In our approach, the eB-dependent vacuum part of the self energy is extracted by means of dimensional regularization where the ultraviolet divergences corresponding to the pure vacuum self energy manifest as the pole singularities of gamma as well as Hurwitz zeta functions. This improved regularization procedure consistently reproduces the expected results in the vanishing magnetic field limit and can be used quite generally in other self energy calculations dealing with arbitrary magnetic field strength. In presence of the external magnetic field, the general Lorentz structure for the in-medium vector boson self energy is derived which can also be implemented in case of the gauge bosons such as photons and gluons. It has been shown that with vanishing perpendicular momentum of the external particle, essentially two form factors are sufficient to describe the self energy completely. Consequently, two distinct modes are observed in the study of the effective mass, dispersion relations and the spectral function of $\rho^0$ where one of the modes possesses two fold degeneracy. For large baryonic chemical potential, it is observed that the critical magnetic field required to block the $\rho^0\rightarrow\pi^+\pi^-$ decay channel increases significantly with temperature. However, in case of smaller values reaching down to vanishing chemical potential, the critical field follows the opposite trend.

4D texture of circular dichroism in soft-x-ray photoemission from tungsten

Photoemission-intensity distributions IRCP/LCP (EB, k) measured for right- and left-circularly polarized soft x-rays revealed a large circular dichroism in angular distribution (CDAD) in the 4D parameter space (EB binding energy, k momentum vector). Full-field k-imaging combined with time-of-flight energy recording at a high-brilliance soft x-ray beamline allowed mapping the CDAD in the bulk Brillouin zone of tungsten and the entire d-band complex within a few hours. CDAD-asymmetries are very high (up to 90%), persist throughout the whole photon-energy range (300–1300 eV) and show a pronounced dependence on momentum k and binding energy EB, visualized as movies or sequences of cuts through the 4D object. One-step photoemission calculations for the same photon energies show fair agreement with the measured results. In addition to the requirement of a ‘handed’ experimental geometry, known from previous experiments on adsorbates and surface states, we find an anti-symmetric behavior of the CDAD with respect to two bulk mirror planes. A new symmetry condition along the perpendicular momentum kz makes CDAD a valuable tool for an unambiguous identification of high-symmetry planes in direct transitions in the periodic zone scheme. Technically, the method provides a circular polarimeter for soft, tender and hard x-rays.

Semiclassical description of chiral geometry in triaxial nuclei

A triaxial particle-rotor Hamiltonian for three mutually perpendicular angular momentum vectors corresponding to two high-$j$ quasiparticles and the rotation of a triaxial collective core, is treated within a time-dependent variational principle. The resulting classical energy function is used to investigate the rotational dynamics of the system. It is found that the classical energy function exhibits two minima starting from a critical angular momentum value which depends on the single-particle configuration and the asymmetry measure $\gamma$. The emergence of the two minima is attributed to the breaking of the chiral symmetry. Quantizing the energy function for a given angular momentum, one obtains a Schr\"{o}dinger equation with a coordinate dependent mass term for a symmetrical potential which changes from a single to a double well shape as the angular momentum pass the critical value. The energies of the chiral partner bands for a given angular momentum are then given by the lowest two eigenvalues. The procedure is exemplified for maximal triaxiality and two $h_{11/2}$ quasiparticles, with the results used for the description of the chiral doublet bands in $^{134}$Pr.

Three dimensional fluid-kinetic model of a magnetically guided plasma jet

A fluid-kinetic model of the collisionless plasma flow in a convergent-divergent magnetic nozzle is presented. The model combines the leading-order Vlasov equation and the fluid continuity and perpendicular momentum equation for magnetized electrons, and the fluid equations for cold ions, which must be solved iteratively to determine the self-consistent plasma response in a three-dimensional magnetic field. The kinetic electron solution identifies three electron populations and provides the plasma density and pressure tensor. The far downstream asymptotic behavior shows the anisotropic cooling of the electron populations. The fluid equations determine the electric potential and the fluid velocities. In the small ion-sound gyroradius case, the solution is constructed one magnetic line at a time. In the large ion-sound gyroradius case, ion detachment from magnetic lines makes the problem fully three-dimensional.

Effect of 3D magnetic perturbations on divertor conditions and detachment in tokamak and stellarator

Enhanced perpendicular heat and momentum transport induces parallel pressure loss leading to divertor detachment, which can be produced by the increase of density in 2D tokamaks. However, in the 3D configurations such as tokamaks with 3D fields and stellarators, the fraction of perpendicular transport can be higher even in a lower density regime, which could lead to the early transition to detachment without passing through the high-recycling regime. 3D fields applied to the limiter tokamak plasmas produce edge stochastic layers close to the last closed flux surface (LCFS), which can allow for enhanced perpendicular transport and indeed the absence of high recycling regime and early detachment have been observed in TEXTOR and Tore Supra. However, in the X-point divertor tokamaks with the applied 3D fields, the parallel transport is still dominant and the detachment facilitation has not been observed yet. Rather, 3D fields affected detachment adversely under certain conditions, either by preventing detachment onset as seen in DIII-D or by re-attaching the existing detached plasma as shown in NSTX. The possible way for strong 3D effects to induce access to the early detachment in divertor tokamaks appears to be via significant perpendicular loss of parallel momentum by frictional force for the counter-streaming flows between neighboring flow channels in the divertor. In principle, the adjacent lobes in the 3D divertor tokamak may generate the counter-streaming flow channels. However, an EMC3-EIRENE simulation for ITER H-mode plasmas demonstrated that screened RMP leads to significantly reduced counter-flows near the divertor target, therefore the momentum loss effect leading to detachment facilitation is expected to be small. This is consistent with the observation in LHD, which showed screening (amplification) of RMP fields in the attachment (stable detachment) case. Work for optimal parameter window for best divertor operation scenario is needed particularly for the 3D divertor tokamak configuration.

Fokker-Planck simulation of runaway electron generation in disruptions with the hot-tail effect

To study runaway electron generation in disruptions, we have extended the three-dimensional (two-dimensional in momentum space; one-dimensional in the radial direction) Fokker-Planck code, which describes the evolution of the relativistic momentum distribution function of electrons and the induced toroidal electric field in a self-consistent manner. A particular focus is placed on the hot-tail effect in two-dimensional momentum space. The effect appears if the drop of the background plasma temperature is sufficiently rapid compared with the electron-electron slowing down time for a few times of the pre-quench thermal velocity. It contributes to not only the enhancement of the primary runaway electron generation but also the broadening of the runaway electron distribution in the pitch angle direction. If the thermal energy loss during the major disruption is assumed to be isotropic, there are hot-tail electrons that have sufficiently large perpendicular momentum, and the runaway electron distribution becomes broader in the pitch angle direction. In addition, the pitch angle scattering also yields the broadening. Since the electric field is reduced due to the burst of runaway electron generation, the time required for accelerating electrons to the runaway region becomes longer. The longer acceleration period makes the pitch-angle scattering more effective.

Numerical characterization of bump formation in the runaway electron tail

Runaway electrons are generated in a magnetized plasma when the parallel electric field exceeds a critical value. For such electrons with energies typically reaching tens of MeV, the Abraham–Lorentz–Dirac (ALD) radiation force, in reaction to the synchrotron emission, is significant and can be the dominant process limiting electron acceleration. The effect of the ALD force on runaway electron dynamics in a homogeneous plasma is investigated using the relativistic finite-difference Fokker–Planck codes LUKE (Decker and Peysson 2004 Report EUR-CEA-FC-1736, Euratom-CEA), and CODE (Landreman et al 2014 Comput. Phys. Commun. 185 847). The time evolution of the distribution function is analyzed as a function of the relevant parameters: parallel electric field, background magnetic field, and effective charge. Under the action of the ALD force, we find that runaway electrons are subject to an energy limit, and that the electron distribution evolves towards a steady-state. In addition, a bump is formed in the tail of the electron distribution function if the electric field is sufficiently strong. The mechanisms leading to the bump formation and energy limit involve both the parallel and perpendicular momentum dynamics; they are described in detail. An estimate for the bump location in momentum space is derived. We observe that the energy of runaway electrons in the bump increases with the electric field amplitude, while the population increases with the bulk electron temperature. The presence of the bump divides the electron distribution into a runaway beam and a bulk population. This mechanism may give rise to beam-plasma types of instabilities that could, in turn, pump energy from runaway electrons and alter their confinement.

Direct transition resonance in atomically uniform topological Sb(111) thin films

Atomically uniform Sb(111) films are fabricated by the method of molecular beam epitaxy on an optimized Si(111) surface. Two dimensional quantum well states and topological surface states in these films are well resolved as measured by angle-resolved photoemission spectroscopy. We observe an evolution of direct transition resonances by varying the excitation photon energy (and thus the perpendicular crystal momentum). The experimental results are reproduced in a comprehensive model calculation taking into account first-principles calculated initial states and time-reversed low-energy-electron-diffraction final states in the photoexcitation process. The resonant behavior illustrates that the topological surface states and the quantum well states are analytically connected in momentum space in all three dimensions.

ELECTRON ACCELERATION BY CASCADING RECONNECTION IN THE SOLAR CORONA. I. MAGNETIC GRADIENT AND CURVATURE DRIFT EFFECTS

We investigate the electron acceleration by magnetic gradient and curvature drift effects in cascading magnetic reconnection of a coronal current sheet via a test particle method in the framework of the guiding center approximation. After several Alfvén transit times, most of the electrons injected at the current sheet are still trapped in the magnetic islands. A small fraction of the injected electrons precipitate into the chromosphere. The acceleration of trapped electrons is dominated by the magnetic curvature drifts, which change the parallel momentum of the electron, and appears to be more efficient than the acceleration of precipitating electrons, which is dominated by the perpendicular momentum change caused by the magnetic gradient drifts. With the resulting trapped energetic electron distribution, the corresponding hard X-ray (HXR) radiation spectra are calculated using an optically thin Bremsstrahlung model. Trapped electrons may explain flare loop top HXR emission as well as the observed bright spots along current sheets trailing coronal mass ejections. The asymmetry of precipitating electrons with respect to the polarity inversion line may contribute to the observed asymmetry of footpoint emission.

Electron acceleration by parallel and perpendicular electric fields during magnetic reconnection without guide field

AbstractElectron acceleration due to the electric field parallel to the background magnetic field during magnetic reconnection with no guide field is investigated by theory and two‐dimensional electromagnetic particle‐in‐cell simulations and compared with acceleration due to the electric field perpendicular to the magnetic field. The magnitude of the parallel electric potential shows dependence on the ratio of the plasma frequency to the electron cyclotron frequency as (ωpe/Ωe)−2 and on the background plasma density as . In the Earth's magnetotail, the parameter ωpe/Ωe∼9 and the background (lobe) density can be of the order of 0.01 cm−3, and it is expected that the parallel electric potential is not large enough to accelerate electrons up to 100 keV. Therefore, we must consider the effect of the perpendicular electric field to account for electron energization in excess of 100 keV in the Earth's magnetotail. Trajectories for high‐energy electrons are traced in a simulation to demonstrate that acceleration due to the perpendicular electric field in the diffusion region is the dominant acceleration mechanism, rather than acceleration due to the parallel electric fields in the exhaust regions. For energetic electrons accelerated near the X line due to the perpendicular electric field, pitch angle scattering converts the perpendicular momentum to the parallel momentum. On the other hand, for passing electrons that are mainly accelerated by the parallel electric field, pitch angle scattering converting the parallel momentum to the perpendicular momentum occurs. In this way, particle acceleration and pitch angle scattering will generate heated electrons in the exhaust regions.