Comment on: Diffusion through a slab

Mahan [J. Math. Phys. 36, 6758 (1995)] has calculated the transmission coefficient and angular distribution of particles which enter a thick slab at normal incidence and which diffuse in the slab with linear anisotropic, non-absorbing, scattering. Using orthogonality relations derived by McCormick & Kuscer [J. Math. Phys. 6, 1939 (1965); 7, 2036 (1966)] for the eigenfunctions of the problem, this calculation is generalised to a boundary condition with particle input at arbitrary angles. It is also shown how to use the orthogonality relations to relax in a simple way the restriction to a thick slab.Comment: 3 pages, LaTeX, uses RevTe

Kinetic approaches to particle acceleration at cosmic ray modified shocks

Kinetic approaches provide an effective description of the process of particle acceleration at shock fronts and allow to take into account the dynamical reaction of the accelerated particles as well as the amplification of the turbulent magnetic field as due to streaming instability. The latter does in turn affect the maximum achievable momentum and thereby the acceleration process itself, in a chain of causality which is typical of non-linear systems. Here we provide a technical description of two of these kinetic approaches and show that they basically lead to the same conclusions. In particular we discuss the effects of shock modification on the spectral shape of the accelerated particles, on the maximum momentum, on the thermodynamic properties of the background fluid and on the escaping and advected fluxes of accelerated particles.Comment: 22 pages, 7 figures, accepted for publication in MNRA

Single-spacecraft techniques for shock parameters estimation : A systematic approach

Spacecraft missions provide the unique opportunity to study the properties of collisionless shocks utilising in situ measurements. In the past years, several diagnostics have been developed to address key shock parameters using time series of magnetic field (and plasma) data collected by a single spacecraft crossing a shock front. A critical aspect of such diagnostics is the averaging process involved in the evaluation of upstream/downstream quantities. In this work, we discuss several of these techniques, with a particular focus on the shock obliquity (defined as the angle between the upstream magnetic field and the shock normal vector) estimation. We introduce a systematic variation of the upstream/downstream averaging windows, yielding to an ensemble of shock parameters, which is a useful tool to address the robustness of their estimation. This approach is first tested with a synthetic shock dataset compliant with the Rankine-Hugoniot jump conditions for a shock, including the presence of noise and disturbances. We then employ self-consistent, hybrid kinetic shock simulations to apply the diagnostics to virtual spacecraft crossing the shock front at various stages of its evolution, highlighting the role of shock-induced fluctuations in the parameters' estimation. This approach has the strong advantage of retaining some important properties of collisionless shock (such as, for example, the shock front microstructure) while being able to set a known, nominal set of shock parameters. Finally, two recent observations of interplanetary shocks from the Solar Orbiter spacecraft are presented, to demonstrate the use of this systematic approach to real events of shock crossings. The approach is also tested on an interplanetary shock measured by the four spacecraft of the Magnetospheric Multiscale (MMS) mission. All the Python software developed and used for the diagnostics (SerPyShock) is made available for the public, including an example of parameter estimation for a shock wave recently observed in-situ by the Solar Orbiter spacecraft.Peer reviewe

Programmable Quantum Processors based on Spin Qubits with Mechanically-Mediated Interactions and Transport

Solid state spin qubits are promising candidates for quantum information processing, but controlled interactions and entanglement in large, multi-qubit systems are currently difficult to achieve. We describe a method for programmable control of multi-qubit spin systems, in which individual nitrogen-vacancy (NV) centers in diamond nanopillars are coupled to magnetically functionalized silicon nitride mechanical resonators in a scanning probe configuration. Qubits can be entangled via interactions with nanomechanical resonators while programmable connectivity is realized via mechanical transport of qubits in nanopillars. To demonstrate the feasibility of this approach, we characterize both the mechanical properties and the magnetic field gradients around the micromagnet placed on the nanobeam resonator. Furthermore, we show coherent manipulation and mechanical transport of a proximal spin qubit by utilizing nuclear spin memory, and use the NV center to detect the time-varying magnetic field from the oscillating micromagnet, extracting a spin-mechanical coupling of 7.7(9) Hz. With realistic improvements the high-cooperativity regime can be reached, offering a new avenue towards scalable quantum information processing with spin qubits.Comment: 7 pages, 4 figure

Connecting remote and in situ observations of shock-accelerated electrons associated with a coronal mass ejection

One of the most prominent sources for energetic particles in our solar system are huge eruptions of magnetised plasma from the Sun called coronal mass ejections (CMEs), which usually drive shocks that accelerate charged particles up to relativistic energies. In particular, energetic electron beams can generate radio bursts through the plasma emission mechanism, for example, type II and accompanying herringbone bursts. Here, we investigate the acceleration location, escape, and propagation directions of various electron beams in the solar corona and compare them to the arrival of electrons at spacecraft. To track energetic electron beams, we use a synthesis of remote and direct observations combined with coronal modelling. Remote observations include ground-based radio observations from the Nancay Radioheliograph (NRH) combined with space-based extreme-ultraviolet and white-light observations from the Solar Dynamics Observatory (SDO), the Solar Terrestrial Relations Observatory (STEREO) and Solar Orbiter (SolO). We also use direct observations of energetic electrons from the STEREO and Wind spacecraft. These observations are then combined with a three-dimensional (3D) representation of the electron acceleration locations that combined with results from magneto-hydrodynamic models of the solar corona is used to investigate the origin and link of electrons observed remotely at the Sun to in situ electrons. We observed a type II radio burst followed by herringbone bursts that show single-frequency movement through time in NRH images. The movement of the type II burst and herringbone radio sources seems to be influenced by the regions in the corona where the CME is more capable of driving a shock. We also found similar inferred injection times of near-relativistic electrons at spacecraft to the emission time of the type II and herringbone bursts.Comment: 16 pages, 15 figure

Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere

Einstein realised that the fluctuations of a Brownian particle can be used to ascertain properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics, and leading to applications from energy harvesting to medical imaging. Here we use optically levitated nanospheres that are heated to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers new opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and a new means for testing non-equilibrium thermodynamicsComment: 5 pages, 4 figures, supplementary material available upon reques

A Multi-Frequency Radio Study of Supernova Remnant G292.0+1.8 and its Pulsar Wind Nebula

(Abridged) We present a detailed radio study of the young supernova remnant (SNR) G292.0+1.8 and its associated pulsar PSR J1124-5916, using the Australia Telescope Compact Array at observing wavelengths of 20, 13 and 6 cm. We find that the radio morphology of the source consists of three main components: a polarized flat-spectrum central core coincident with the pulsar J1124-5916, a surrounding circular steep-spectrum plateau with sharp outer edges and, superimposed on the plateau, a series of radial filaments with spectra significantly flatter than their surroundings. HI absorption argues for a lower limit on the distance to the system of 6 kpc. The core clearly corresponds to radio emission from a pulsar wind nebula powered by PSR J1124-5916, while the plateau represents the surrounding SNR shell. The plateau's sharp outer rim delineates the SNR's forward shock, while the thickness of the plateau region demonstrates that the forward and reverse shocks are well-separated. Assuming a distance of 6 kpc and an age for the source of 2500 yr, we infer an expansion velocity for the SNR of ~1200 km/s and an ambient density ~0.9 cm^-3. We interpret the flat-spectrum radial filaments superimposed on the steeper-spectrum plateau as Rayleigh-Taylor unstable regions between the forward and reverse shocks of the SNR. The flat radio spectrum seen for these features results from efficient second-order Fermi acceleration in strongly amplified magnetic fields.Comment: 11 pages of text, plus 7 embedded EPS figures. Accepted to ApJ. Added missing units on x-axis of Fig

Canonical Particle Acceleration in FRI Radio Galaxies

Matched resolution multi-frequency VLA observations of four radio galaxies are used to derive the asymptotic low energy slope of the relativistic electron distribution. Where available, low energy slopes are also determined for other sources in the literature. They provide information on the acceleration physics independent of radiative and other losses, which confuse measurements of the synchrotron spectra in most radio, optical and X-ray studies. We find a narrow range of inferred low energy electron energy slopes, n(E)=const*E^-2.1 for the currently small sample of lower luminosity sources classified as FRI (not classical doubles). This distribution is close to, but apparently inconsistent with, the test particle limit of n(E)=const*E^-2.0 expected from strong diffusive shock acceleration in the non-relativistic limit. Relativistic shocks or those modified by the back-pressure of efficiently accelerated cosmic rays are two alternatives to produce somewhat steeper spectra. We note for further study the possiblity of acceleration through shocks, turbulence or shear in the flaring/brightening regions in FRI jets as they move away from the nucleus. Jets on pc scales and the collimated jets and hot spots of FRII (classical double) sources would be governed by different acceleration sites and mechanisms; they appear to show a much wider range of spectra than for FRI sources.Comment: 16 figures, including 5 color. Accepted to Astrophysical Journa

Multi-spacecraft observations of the structure of the sheath of an interplanetary coronal mass ejection and related energetic ion enhancement

Context. Sheath regions ahead of coronal mass ejections (CMEs) are large-scale heliospheric structures that form gradually with CME expansion and propagation from the Sun. Turbulent and compressed sheaths could contribute to the acceleration of charged particles in the corona and in interplanetary space, but the relation of their internal structure to the particle energization process is still a relatively little studied subject. In particular, the role of sheaths in accelerating particles when the shock Mach number is low is a significant open research problem. Aims. This work seeks to provide new insights on the internal structure of CME-driven sheaths with regard to energetic particle enhancements. A good opportunity to achieve this aim was provided by multi-point, in-situ observations of a sheath region made by radially aligned spacecraft at 0.8 and similar to 1 AU (Solar Orbiter, the L1 spacecraft Wind and ACE, and BepiColombo) on April 19-21, 2020. The sheath was preceded by a weak and slowly propagating fast-mode shock. Methods. We apply a range of analysis techniques to in situ magnetic field, plasma and particle observations. The study focuses on smaller scale sheath structures and magnetic field fluctuations that coincide with energetic ion enhancements. Results. Energetic ion enhancements were identified in the sheath, but at different locations within the sheath structure at Solar Orbiter and L1. Magnetic fluctuation amplitudes at inertial-range scales increased in the sheath relative to the solar wind upstream of the shock, as is typically observed. However, when normalised to the local mean field, fluctuation amplitudes did not increase significantly; magnetic compressibility of fluctuation also did not increase within the sheath. Various substructures were found to be embedded within the sheath at the different spacecraft, including multiple heliospheric current sheet (HCS) crossings and a small-scale flux rope. At L1, the ion flux enhancement was associated with the HCS crossings, while at Solar Orbiter, the ion enhancement occurred within a compressed, small-scale flux rope. Conclusions. Several internal smaller-scale substructures and clear difference in their occurrence and properties between the used spacecraft was identified within the analyzed CME-driven sheath. These substructures are favourable locations for the energization of charged particles in interplanetary space. In particular, substructures that are swept from the upstream solar wind and compressed into the sheath can act as effective acceleration sites. A possible acceleration mechanism is betatron acceleration associated with a small-scale flux rope and warped HCS compressed in the sheath, while the contribution of shock acceleration to the latter cannot be excluded.Peer reviewe