Adiabatic Focusing Research Articles

Particle Scattering in the Presence of Moderate to Strong Adiabatic Focusing

AbstractStarting from the Vlasov‐Boltzmann equation, we derive corrections to the quasi linear Fokker‐Planck pitch angle scattering coefficient caused by a non‐uniformity of the background magnetic field. Integration of the perturbed particle distribution function is performed along a modified unperturbed trajectory that takes into account the effects of focusing and mirroring on pitch angle and gyrophase. We calculate the changes to the quasi‐linear scattering rate owing to a variations in the field strength and the gyrophase drift that affects the resonance between particles and magnetic fluctuations. It is shown that the scattering coefficient has an oscillating behavior in pitch angle when the focusing lengthscale is comparable to the correlation length of the turbulence and the particle's Larmor radius. The applicability of analytic results are demonstrated with a simple model of charged particles trapped in a magnetic field of a planet. It is suggested that the pitch angle diffusion coefficient could become negative for the case of very strong focusing.

Effects of adiabatic focusing and free-escape boundaries in coronal shock acceleration

Solar energetic particles (SEPs) are considered a serious radiation threat to space technologies and humans in space. SEPs are accelerated to high energies by solar explosive phenomena such as solar flares and in particular by shocks driven by coronal mass ejections (CMEs). We aim to better understand the effects of magnetic field gradient-induced adiabatic focusing on the coronal acceleration of SEPs and to test whether free-escape boundaries produce the same effects as focusing. We present results from a one-dimensional oblique shock model with a mean free path similar to Bell’s (1978) theory using Monte Carlo simulations. We show that the momentum spectrum at a shock and far upstream will attain a steady state in a model with adiabatic focusing, whereas it does not in a non-focusing model. However, the effects of focusing can be mimicked in a non-focused simulation by introducing a free-escape boundary ahead of the shock close to the position where the particles will escape from the shock by focusing in a focused transport simulation. This provides a promising avenue for constructing computationally efficient codes that can model the particle emission from shocks.

Large-amplitude Bidirectional Anisotropy of Cosmic-Ray Intensity Observed with Worldwide Networks of Ground-based Neutron Monitors and Muon Detectors in 2021 November

We analyze the cosmic-ray variations during a significant Forbush decrease observed with worldwide networks of ground-based neutron monitors and muon detectors during 2021 November 3–5. Utilizing the difference between primary cosmic-ray rigidities monitored by neutron monitors and muon detectors, we deduce the rigidity spectra of the cosmic-ray density (or omnidirectional intensity) and the first- and second-order anisotropies separately for each hour of data. A clear two-step decrease is seen in the cosmic-ray density with the first ∼2% decrease after the interplanetary shock arrival followed by the second ∼5% decrease inside the magnetic flux rope (MFR) at 15 GV. Most strikingly, a large bidirectional streaming along the magnetic field is observed in the MFR with a peak amplitude of ∼5% at 15 GV, which is comparable to the total density decrease inside the MFR. The bidirectional streaming could be explained by adiabatic deceleration and/or focusing in the expanding MFR, which have stronger effects for pitch angles near 90°, or by selective entry of GCRs along a leg of the MFR. The peak anisotropy and density depression in the flux rope both decrease with increasing rigidity. The spectra vary dynamically, indicating that the temporal variations of density and anisotropy appear different in neutron monitor and muon detector data.

Strahl electrons kinematics of slow and fast solar winds between [formula omitted] in the solar magneto-gravitational field

In situ spacecraft measurements of the solar wind parameters exhibit high-energy tails in the electron velocity distribution function (eVDF) at heliocentric distances 0.3−1au. The suprathermal strahl electrons predominantly spread with heliospheric distance, broadening the beam where it would otherwise narrow under an adiabatic focusing. We show here that the magneto-gravitational coupling of the background solar field induces velocity increase along the magnetic field lines. In the velocity space the expansion is shown to be consistent with the observational data for the radial evolution of the electron strahl component both for the slow and fast solar winds between 0.3−1au. In the lower heliospheric regions the electron dynamics in the local magnetic field configuration can exhibit a sunward strahl also. We use the strahl eVDF to estimate the temperature distribution in the solar corona and deduce the observed coronal heating due to the magnetic field lines dragging.

Electron Groups in Solar Wind and Gas Discharge Plasmas

The formation of electron groups is a common phenomenon in gas discharges and space plasmas. We describe similarities between electron kinetics in solar wind, cathode region of glow discharges, and magnetic nozzles. Remarkable resemblances between adiabatic focusing of magnetized electrons and spherical geometry effects for neutral particles escaping planet’s atmosphere are pointed out. The previously developed kinetic solvers for electrons coupled to Poisson equation for self-consistent simulations of the electric field are used to analyse the formation of electron groups in the cathode region of glow discharges and solar wind plasma.

The Diffusion Coefficient with Displacement Variance of Energetic Particles Caused by Adiabatic Focusing

Abstract The equation κ zz = dσ 2/(2dt) describing the relation of the parallel diffusion coefficient κ zz with the displacement variance σ 2 (hereafter DCDV) is a well-known formula. In this study, we find that DCDV is only applicable to two kinds of transport equations of the isotropic distribution function, one without cross-terms and the other without a convection term. Here, by employing the more general transport equation, i.e., the variable coefficient differential equation derived from the Fokker–Planck equation, a new equation of κ zz as a function of σ 2 is obtained. We find that DCDV is the special case of the new equation. In addition, another equation of κ zz as a function of σ 2 corresponding to the telegraph equation is also investigated preliminarily.

Propagation of Solar Energetic Particles in the Outer Heliosphere: Interplay between Scattering and Adiabatic Focusing

Abstract The turbulence and spatial nonuniformity of the guide magnetic field cause two competitive effects, namely, the scattering effect and the adiabatic focusing effect, respectively. In this work, we numerically solve the five-dimensional Fokker–Planck transport equation to investigate the radial evolutions of these important effects undergone by the solar energetic particles (SEPs) propagating through interplanetary space. We analyze the interplay process between the scattering and adiabatic focusing effects in the context of three-dimensional propagation, with special attention to the scenario of the outer heliosphere, in which some peculiar SEP phenomena are found and explained. We also discuss the radial dependence of the SEP peak intensities from the inner through the outer heliosphere, and conclude that it cannot be simply described by a single functional form such as R −α (R is radial distance), which is often used.

Stochastic Propagation of Solar Energetic Particles in Coronal and Interplanetary Magnetic Fields

This paper describes a method of simulating solar energetic particle propagation through the magnetic fields of the solar corona and interplanetary medium. The simulation code is based on the focus transport equation of energetic particles in 3-d magnetic fields, which contains all the particle transport mechanisms, including streaming, convection, gradient/curvature drift, adiabatic focusing, pitch angle scattering by Alfvénic magnetic field fluctuations and perpendicular diffusion due to the random walk of field lines. In the simulation, particles are injected at their source in the corona, and their guiding center trajectories are calculated using stochastic differential equations. Because of the vastly different time scales of particle transport mechanisms included in the equation, we use the 4-th order Runge-Kutta method to integrate the particle streaming and adiabatic focusing terms, while the stochastic terms of pitch angle scattering and perpendicular diffusion are integrated with the Euler scheme. The model is applied to the 2017 September 10 solar energetic particle event. With perpendicular diffusion, we are able to explain SEP observations from Earth and STEREO-A. A pattern of SEP precipitation on the solar surface is also predicted.

Parallel and Perpendicular Diffusion Coefficients of Energetic Charged Particles with Adiabatic Focusing

Abstract It is very important to understand stochastic diffusion of energetic charged particles in the nonuniform background magnetic field in plasmas of astrophysics and fusion devices. Using different methods considering an along-field adiabatic focusing effect, various authors derived a parallel diffusion coefficient and its correction T to , where is the parallel diffusion coefficient without an adiabatic focusing effect. In this paper, using the improved perturbation method developed by He & Schlickeiser and iteration process, we obtain a new correction to . Furthermore, by employing the isotropic pitch-angle scattering model , we find that has a different sign from that of T. In this paper, the spatial perpendicular diffusion coefficient with the adiabatic focusing effect is also obtained.

Experimental Study on the Balance between Microscopic Water Production and Temperature Rise During Cold Startup in PEFC

In a polymer electrolyte fuel cell (PEFC) startup below freezing point, the produced water freezes, and then shutdown occurs. The authors’ research group has been conducting experimental studies on the freezing behaviors and mechanism. At -20℃, the generated water freezes at the moment when the water comes out into the catalyst layer (CL) pores, and at -10℃, the generated water moves inside the fuel cell in the supercooled state and freezes (1)-(2). It was also reported that the ice frozen at the micro porous layer (MPL) and CL interface absorbs generated water through the ionomer in the CL (3). Based on the fundamental findings of isothermal cold start characteristics and freezing behaviors, we conducted experimental investigations simulating a condition that the cell temperature is rising during cold startup due to the heat of reaction of power generation. A method to realize adiabatic condition focusing on the cell at central part in a stack mounted on automobile was developed, and the cold start characteristics and the freezing behavior during rising temperature were investigated. A single cell with an active area of 25 cm2 (5 cm × 5 cm) was used in this study. As shown in Fig. 1, a heat insulating plate and heater were inserted between the end plate and current collector plate to simulate the adiabatic condition by controlling the cell temperature. Heat release from the sides of in-plane direction was suppressed by winding a heat insulating material. After a preconditioning process to enhance the performance of a MEA, the initial conditions of water in the cell were carefully controlled by the procedure described in Ref. 1. Then the cell and the chamber were cooled to a target value in the range of -10℃ to -15℃, and cell operation was started and maintained at a constant current density 0.2 A/cm2. Dry hydrogen and dry air were supplied to anode and cathode. In order to observe the ice distribution with a cryo-SEM after stopping the current load, the MEA sample was quickly removed from the cell and immersed in liquid nitrogen and the sample was set to a sample holder. The sample was cut by a cold knife in a vacuumed chamber, and the cut section area was coated with gold-palladium alloy (Au-Pd), and observed at -150℃. As a result of the startups with the initial temperature range of -10℃ to -13℃, shutdown due to freezing was not observed, while startup failure occurred at -15℃. At the startup at -14℃, the different results (two startup successes and two failures) were confirmed. Figure 2 shows the time variation of the cell voltage, cell resistance, and cell temperature during cold startup with the initial temperature -14℃. Figure 2(a) is for the startup failure and Fig. 2(b) is for the success. In the both cases (Figs. 2 (a) and (b)), similar behaviors were observed until 70 seconds. However, after 70 seconds, the voltage decreases in Fig. 2 (a) and continues to rise in Fig. 2(b). These suggest that supercooling release of product water occurs at 70 seconds in Fig. 2(a), and does not occur in Fig. 2(b). Figure 3 shows the ice distribution on the cathode side after the shutdown in Fig. 2(a). Figure 3(a) is a cryo-SEM image around the MPL and the CL interface, and Fig. 3(b) an image of the CL at high magnification. As shown in Fig. 3(a), a layer of ice was observed at the interface between the MPL and CL, and there is, almost no ice in the CL (Fig. 3(b)). From this result, it is considered that in the operation of Fig. 2(a), the generated water moved to the MPL and CL interface, then the supercooled state was released, and the ice grew at the interface. The supply of oxygen was hindered by the formation of the ice layer, and the shutdown was induced. This indicates that adequately removing the generated water at the MPL and CL interface may be effective to improve the cold start characteristics. Reference (1) Y. Tabe, et al. , J. Power Sources 208 (2012), 366. (2) Y. Tabe, et al. , J. Electrochem. Soc. 163 (10) (2016), F1139. (3) N. Wakatake, et al. , ECS Trans. 75 (14) (2016), 623. Figure 1

Tapering of plasma density ramp profiles for adiabatic lens experiments

One of the key elements of the plasma wakefield blowout regime is the strong, linear focusing provided by the ion density. One advantage of this focusing is its extraordinary strength whose gradient is proportional to the local background plasma density, that is particularly important for adiabatic focusing schemes in future compact linear colliders. Local plasma density variations can be obtained in gas-filled capillaries by varying monotonically the diameter of the capillary. Here we present the ongoing study of the plasma density profile obtained for different tapering angles of the capillary shape and we discuss their use for the adiabatic plasma lens experiment proposed at SPARC_LAB.

Investigating the Effect of IMF Path Length on Pitch-angle Scattering of Strahl within 1 au

Abstract Strahl is the strongly field-aligned, beam-like population of electrons in the solar wind. Strahl width is observed to increase with distance from the Sun, and hence strahl electrons must be subject to in-transit scattering effects. Different energy relations have been both observed and modeled for both strahl width and the width increase with radial distance. Thus, there is much debate regarding what mechanism(s) scatter strahl. In this study, we use a novel method to investigate strahl evolution within 1 au by estimating the distance traveled by the strahl along the interplanetary magnetic field (IMF). We do this by implementing methods developed in previous studies, which make use of the onset of solar energetic particles at ∼1 au. Thus, we are able to obtain average strahl broadening in relation to electron energy and distance, while also taking into account the general effect of IMF topology and adiabatic focusing experienced by strahl. We find that average strahl width broadens with distance traveled along the IMF, which suggests that strahl width is related to the path length taken by the strahl from the Sun to 1 au. We also find that strahl pitch-angle width broadening per au along the IMF length increased with strahl energy, which suggests that the dominant strahl pitch-angle scattering mechanism likely has an inherent energy relation. Our pitch-angle broadening results provide a testable energy relation for the upcoming Parker Solar Probe and Solar Orbiter missions, which are both set to provide unprecedented new observations within 1 au.

Adiabatic plasma lens experiments at SPARC

Passive plasma lenses in the underdense regime have been shown to give extremely strong linear focusing, with strength proportional to the local plasma ion density. This technique has been proposed as the basis of a scheme for future linear colliders that mitigates the Oide effect through adiabatic focusing. In this scenario the plasma density in the lens is ramped slowly on the scale of betatron motion, to funnel the beam to its final focus while forgiving chromatic aberrations. We present to the physics design of an adiabatic plasma lens experiment to be performed at SPARC Lab. We illustrate the self-consistent plasma response and associated beam optics for symmetric beams in plasma, simulated by QuickPIC using exponentially rising density profiles. We discuss experimental plans including plasma source development and betatron-radiation-based beam diagnostics.

Increased rise time of electron temperature during adiabatic plasmon focusing

Decay of plasmons to hot carriers has recently attracted considerable interest for fundamental studies and applications in quantum plasmonics. Although plasmon-assisted hot carriers in metals have already enabled remarkable physical and chemical phenomena, much remains to be understood to engineer devices. Here, we present an analysis of the spatio-temporal dynamics of hot electrons in an emblematic plasmonic device, the adiabatic nanofocusing surface-plasmon taper. With femtosecond-resolution measurements, we confirm the extraordinary capability of plasmonic tapers to generate hot carriers by slowing down plasmons at the taper apex. The measurements also evidence a substantial increase of the “lifetime” of the electron gas temperature at the apex. This interesting effect is interpreted as resulting from an intricate heat flow at the apex. The ability to harness the “lifetime” of hot-carrier gases with nanoscale circuits may provide a multitude of applications, such as hot-spot management, nonequilibrium hot-carrier generation, sensing, and photovoltaics.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

Abstract The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

High quality semicontinuous deep reactive ion etching of silicon for the creation of x-ray lenses

In this work, the authors developed a deep reactive ion etching (DRIE) process to fabricate x-ray-nano-lenses and so-called adiabatic focusing lenses made of silicon. Based on the photolithographic fabrication of excellent etch masks, including a continued adjustment of the pattern layout and the application of a novel developed so-called semicontinuous DRIE process, the creation of several generations of silicon lenses was realized. This process enabled us to fulfill the extreme high demands on the pattern quality, which are an aspect ratio up to 10:1, a tilt angle of 90 ± 0.5°, a mask undercut ≤100 nm, parallelism of the sidewalls, and a surface roughness lower than 50 nm. Using this etching process, the authors successfully created patterns for x-ray-lenses in silicon with lateral dimensions from 20 μm down to 1 μm and etch depths of 19 μm for the 20-μm-lenses and 10 μm for the 1-μm-lenses.

The evolution of solar wind strahl with heliospheric distance

AbstractField‐aligned beams of suprathermal electrons, known as “strahl,” are a frequently observed constituent of solar wind plasma. However, the formation and interplanetary evolution of the strahl electron populations has yet to be fully understood. As strahl electrons travel away from the Sun, they move into regions of decreasing magnetic field strength and thus are subject to adiabatic focusing. However, the widths of strahl pitch angle distributions observed at 1 AU are significantly broader than expected. Previous investigations have found that the average observed strahl pitch angle width actually increases with heliocentric radial distance. This implies that strahl electrons must be subjected to some form of pitch angle scattering process or processes, details of which as of yet remain elusive. In this paper, we use Cassini electron measurements to examine strahl beams across a distance range of approximately 8 AU, from its Earth Flyby in 1999 until its insertion into orbit around Saturn in 2004. We find that, in general, there is a relatively constant rate of broadening of strahl pitch angle distributions with distance between ∼1 and 5.5 AU. Our results from beyond this distance indicate that the strahl population is likely to be completely scattered, presumably to form part of the halo. We find multiple energy dependences at different radial distances implying that there are multiple strahl scattering mechanisms in operation.

Attosecond-controlled photoemission from metal nanowire tips in the few-electron regime

Metal nanotip photoemitters have proven to be versatile in fundamental nanoplasmonics research and applications, including, e.g., the generation of ultrafast electron pulses, the adiabatic focusing of plasmons, and as light-triggered electron sources for microscopy. Here, we report the generation of high energy photoelectrons (up to 160 eV) in photoemission from single-crystalline nanowire tips in few-cycle, 750-nm laser fields at peak intensities of (2-7.3) × 1012 W/cm2. Recording the carrier-envelope phase (CEP)-dependent photoemission from the nanowire tips allows us to identify rescattering contributions and also permits us to determine the high-energy cutoff of the electron spectra as a function of laser intensity. So far these types of experiments from metal nanotips have been limited to an emission regime with less than one electron per pulse. We detect up to 13 e/shot and given the limited detection efficiency, we expect up to a few ten times more electrons being emitted from the nanowire. Within the investigated intensity range, we find linear scaling of cutoff energies. The nonlinear scaling of electron count rates is consistent with tunneling photoemission occurring in the absence of significant charge interaction. The high electron energy gain is attributed to field-induced rescattering in the enhanced nanolocalized fields at the wires apex, where a strong CEP-modulation is indicative of the attosecond control of photoemission.

Numerical analysis of the Fokker-Planck equation with adiabatic focusing: Realistic pitch-angle scattering

We solve the focused transport equation of cosmic rays numerically to investigate non-isotropic models of the pitch-angle scattering coefficient. In previous work, the Fokker-Planck equation was solved either analytically by using approximations, or by using a numerical approach together with simple models for the pitch-angle scattering coefficient. It is the purpose of the current article so compute particle distribution functions as well as the parallel diffusion coefficient by solving numerically the focused transport equation for a more realistic Fokker-Planck coefficient of pitch-angle scattering. Our analytical form for the scattering parameter is based on non-linear diffusion theory that takes into account realistic scattering at pitch-angles close to 90°. This general form contains the isotropic form as well as the quasi-linear limit as special cases. We show that the ratio of the diffusion coefficients with and without focusing sensitively depends on the ratio of the turbulent magnetic field and the mean field. The assumed form of the pitch-angle Fokker-Planck coefficient has an influence on the parallel diffusion coefficient. In all considered cases we found a reduction of the ratio of the diffusion coefficients if the ratio of magnetic fields is reduced.

TRANSPORT OF HELIUM PICKUP IONS WITHIN THE FOCUSING CONE: RECONCILING STEREO OBSERVATIONS WITH IBEX

ABSTRACT Recent observations of the pickup helium focusing cone by STEREO/Plasma and Suprathermal Ion Composition indicate an inflow longitude of the interstellar wind that differs from the observations of IBEX by . It has been under debate whether the transport of helium pickup ions with an anisotropic velocity distribution is the cause of this difference. If so, the roughly field-aligned pickup ion streaming relative to the solar wind should create a shift in the pickup ion density relative to the focusing cone. A large pickup ion streaming depends on the size of the mean free path. Therefore, the observed longitudinal shift in the pickup ion density relative to the neutral focusing cone may carry fundamental information about the mean free path experienced by pickup ions inside 1 au. We test this hypothesis using the Energetic Particle Radiation Environment Module (EPREM) model by simulating the transport of helium pickup ions within the focusing cone finding a mean free path of au. We calculate the average azimuthal velocity of pickup ions and find that the anisotropic distribution reaches ∼8% of the solar wind speed. Lastly, we isolate transport effects within EPREM, finding that pitch-angle scattering, adiabatic focusing, perpendicular diffusion, and particle drift contribute to shifting the focusing cone 20.00%, 69.43%, 10.56%, and , respectively. Thus we show with the EPREM model that the transport of pickup ions does indeed shift the peak of the focusing cone relative to the progenitor neutral atoms and this shift provides fundamental information on the scattering of pickup ions inside 1 au.