On the Analytical Solution of the Kuwabara-Type Particle-in-Cell Model for the Non-Axisymmetric Spheroidal Stokes Flow via the Papkovich–Neuber Representation

Modern engineering technology often involves the physical application of heat and mass transfer. These processes are associated with the creeping motion of a relatively homogeneous swarm of small particles, where the spheroidal geometry represents the shape of the embedded particles within such aggregates. Here, the steady Stokes flow of an incompressible, viscous fluid through an assemblage of particles, at low Reynolds numbers, is studied by employing a particle-in-cell model. The mathematical formulation adopts the Kuwabara-type assumption, according to which each spheroidal particle is stationary and it is surrounded by a confocal spheroid that creates a fluid envelope, in which the Newtonian fluid moves with a constant velocity of arbitrary orientation. The boundary value problem in the fluid envelope is solved by imposing non-slip conditions on the surface of the spheroid, which is also considered as non-penetrable, while zero vorticity is assumed on the fictitious spheroidal boundary along with a uniform approaching velocity. The three-dimensional flow fields are calculated analytically for the first time, in the spheroidal geometry, by virtue of the Papkovich–Neuber representation. Through this, the velocity and the total pressure fields are provided in terms of a vector and the scalar spheroidal harmonic potentials, which enables the thorough study of the relevant physical characteristics of the flow fields. The newly obtained analytical expressions generalize to any direction with the existing results holding for the asymmetrical case, which were obtained with the aid of a stream function. These can be employed for the calculation of quantities of physical or engineering interest. Numerical implementation reveals the flow behavior within the fluid envelope for different geometrical cell characteristics and for the arbitrarily-assumed velocity field, thus reflecting the different flow/porous media situations. Sample calculations show the excellent agreement of the obtained results with those available for special geometrical cases. All of these findings demonstrate the usefulness of the proposed method and the powerfulness of the obtained analytical expansions.

Ion-Focused Propagation of Relativistic Electron Beam in the Self-Generated Plasma in the Atmosphere

It is known that ion-focused regime can effectively suppress the expansion of relativistic electron beam (REB). By using particle in cell-Monte Carlo collision (PIC-MCC) method, the propagation of REBs in neutral gas is numerically investigated. The numerical results demonstrate that the beam body is charge neutralization and a stable IFR can be established. As a result, the beam transverse dimensions and longitudinal velocities keep close to the initial parameters. We also calculated the charge and current neutralization factors of REBs. Combined with envelope equations, we obtained the variations of beam envelopes, which agree well with the PIC simulations. However, both the energy loss and instabilities of REBs may lead to a low transport efficiency during long-range propagation. It has been proved that decreasing the initial pulse length of REBs can avoid the influence of electron avalanche. Using parts of REB pulses to build a long-distance IFR in advance can improve the beam quality of subsequent pulses. Further, a long-distance IFR may contribute to the implementation of long-range propagation of REBs in the space environment.

Scissor-cross ionization injection in laser wakefield accelerators

We propose to use a frequency doubled pulse colliding with the driving pulse at an acute angle to trigger ionization injection in a laser wakefield accelerator. This scheme effectively reduces the duration that injection occurs, thus high injection quality is obtained. Three-dimensional particle-in-cell simulations show that electron beams with energy of ~500 MeV, charge of ~40 pC, energy spread of ~1% and normalized emittance of a few millimeter milliradian can be produced by ~100 TW laser pulses. By adjusting the angle between the two pulses, the intensity of the trigger pulse and the gas dope ratio, the charge and energy spread of the electron beam can be controlled.

Particle Acceleration in Mildly Relativistic Outflows of Fast Energetic Transient Sources

Recent discovery of fast blue optical transients (FBOTs)—a new class of energetic transient sources—can shed light on the long-standing problem of supernova—long gamma-ray burst connections. A distinctive feature of such objects is the presence of modestly relativistic outflows which place them in between the non-relativistic and relativistic supernovae-related events. Here we present the results of kinetic particle-in-cell and Monte Carlo simulations of particle acceleration and magnetic field amplification by shocks with the velocities in the interval between 0.1 and 0.7 c. These simulations are needed for the interpretation of the observed broad band radiation of FBOTs. Their fast, mildly to moderately relativistic outflows may efficiently accelerate relativistic particles. With particle-in-cell simulations we demonstrate that synchrotron radiation of accelerated relativistic electrons in the shock downstream may fit the observed radio fluxes. At longer timescales, well beyond those reachable within a particle-in-cell approach, our nonlinear Monte Carlo model predicts that protons and nuclei can be accelerated to petaelectronvolt (PeV) energies. Therefore, such fast and energetic transient sources can contribute to galactic populations of high energy cosmic rays.

PIC Simulations of Excited Waves in the Plasmoid Instability

Fragmentation of an elongated current sheet into many reconnection X-points, and therefore multiple plasmoids, occurs frequently in the solar corona. This speeds up the release of solar magnetic energy in the form of thermal and kinetic energy. Moreover, due to the presence of multiple reconnection X-points, the particle acceleration is more efficient in terms of the number of accelerated particles. This type of instability called “plasmoid instability” is accompanied with the excitation of some electrostatic/electromagnetic waves. We carried out 2D particle-in-cell simulations of this instability in the collisionless regime, with the presence of non-uniform magnetic guide field to investigate the nature of excited waves. It is shown that the nature and properties of waves excited inside and outside the current sheet are different. While the outside perturbations are transient, the inside ones are long-lived, and are directly affected by the plasmoid instability process.