The Particle-in-Cell (PIC) method has been a useful tool for understanding basic plasma processes for over 50 years. In this paper we revisit an energy conserving (EPIC) scheme [1], [2] and demonstrate how useful it can be (particularly in 2D and 3D) in a large class of problems such as ion sources and capacitively coupled plasmas. The key to PIC performance is computing particle-particle interactions via discretized fields. The most straightforward PIC scheme uses the same interpolation scheme both to interpolate the charges to the grid and the field back to the charged particle location. This is known as a “momentum-conserving scheme” (MPIC). The severe limitation to this scheme is that the cell size must be smaller than the electron Debye length in order to avoid the so-called grid heating instability. Recently we have implemented an explicit energy-conserving (in the limit of infinitesimal timestep) particle deposition scheme (EPIC) [1], [2] in VSim [3], [4] in which the Debye length restriction can be relaxed. We follow previous work in 1D [1], [2] and extend the results to 2D and 3D. We find that EPIC is stable in the regime that the electron drift velocity is less than the thermal velocity and unstable for some cold beams. In this paper we first discuss the basic theory behind the implementation of EPIC. We then discuss the limitations of its application. Finally, we show simulations which benchmark results between MPIC and EPIC. We find that for a large class of problems EPIC can decrease the computational cost by allowing for grid sizes larger than the electron Debye length.

Given many parameters to be varied, the optimization of an objective function can be hastened by computing the gradient (the change in the parameters that maximally improves the objective function). Unfortunately, finding the gradient can be prohibitively expensive when each evaluation of the objective function involves running a separate particle-in-cell simulation. We derive a general (so called “adjoint”) method to find both the value and gradient of an objective function using only two simulations, a substantial savings. To do this, we consider the general case where particle motion is described by a Hamiltonian with arbitrary dependence on external parameters. The structure of the perturbed Hamilton's equations yields a simple recipe for the evaluation of the adjoint equation. Our work offers a new perspective on the method of Antonsen et al. (2019) for optimization of trajectories in an electron gun [1]. We generalize their method to accommodate field-dependent particle emission, and use this new formulation to compute geometric optimizations of nanoscale vacuum-channel transistors.

Relativistic magnetic reconnection is a powerful agent through which magnetic energy can be tapped in astrophysics, energizing particles that then produce observed radiation. In some systems, the highest energy photons come from particles Comptonizing an ambient radiation bath supplied by an external source. If the emitting particle energies are high enough, this inverse Compton (IC) scattering enters the Klein-Nishina regime, which differs from the low-energy Thomson IC limit in two significant ways. First, radiative losses become inherently discrete, with particles delivering an order-unity fraction of their energies to single photons. Second, Comptonized photons may pair-produce with the ambient radiation, opening up another channel for radiative feedback on magnetic reconnection. We analytically study externally illuminated highly magnetized reconnecting systems for which both of these effects are important. We identify a universal (initial magnetization-independent) quasi-steady state in which gamma-rays emitted from the reconnection layer are absorbed in the upstream region, and the resulting hot pairs dominate the energy density of the inflow plasma. However, a true pair cascade is unlikely, and the number density of created pairs remains subdominant to that of the original plasma for a wide parameter range. Future particle-in-cell simulation studies may test various aspects. Pair-regulated Klein-Nishina reconnection may explain steep spectra (quiescent and flaring) from flat-spectrum radio quasars and black hole accretion disc coronae.

Rapid gamma-ray flares pose an astrophysical puzzle, requiring mechanisms both to accelerate energetic particles and to produce fast observed variability. These dual requirements may be satisfied by collisionless relativistic magnetic reconnection. On the one hand, relativistic reconnection can energize gamma-ray emitting electrons. On the other, as previous kinetic simulations have shown, the reconnection acceleration mechanism preferentially focuses high-energy particles -- and their emitted photons -- into beams, which may create rapid blips in flux as they cross a telescope's line of sight. Using a series of 2D pair-plasma particle-in-cell simulations, we explicitly demonstrate the critical role played by radiative cooling in mediating the observable signatures of this `kinetic beaming' effect. Only in our efficiently cooled simulations do we measure kinetic beaming beyond one light crossing time of the reconnection layer. We find a correlation between the cooling strength and the photon energy range across which persistent kinetic beaming occurs: stronger cooling coincides with a wider range of beamed photon energies. We also apply our results to rapid gamma-ray flares in flat-spectrum radio quasars, suggesting that a paradigm of radiatively efficient kinetic beaming constrains relevant emission models. In particular, beaming-produced variability may be more easily realized in two-zone (e.g. spine-sheath) set-ups, with Compton seed photons originating in the jet itself, rather than in one-zone external Compton scenarios.

Speed-limited particle-in-cell (SLPIC) modeling is a new simulation technique [G. R. Werner et al., Phys. Plasmas 25,123512 (2018)], potentially much faster than conventional PIC, for modeling plasmas characterized by low-velocity kinetic processes. Numerical constraints (e.g. timestep limitations associated with particle cell-crossing times or stability limits) often place challenging restrictions on PIC models of these plasmas; even though the kinetic physics of interest predominantly involves slow particles, the fastest particles dictate the maximum allowable timestep. For high-Z plasmas, large ion/electron mass ratios separate the species timescales to the point that kinetic simulation may be prohibitive, and computational costs can be high even in hydrogenic plasmas. SLPIC provides a possible solution. SLPIC (like PIC) retains a fully kinetic description of the plasma, but imposes an artificial speed limit on fast particles whose kinetics do not play a meaningful role in the system dynamics. Larger simulation timesteps, which enable faster simulations of such discharges, are thus permitted. The speed-limiting is done in a mathematically rigorous sense to maintain accuracy over longer timescales; we may, for instance, speed-limit the bulk of the electron distribution to evolve only on characteristic ion timescales (and use larger simulation timesteps, which need only resolve these scales, to simulate the discharge). In this paper we'll demonstrate the use of SLPIC methods using the VSim code [C. Nieter and J. R. Cary, J. Comp. Phys. 196, 448 (2004)], moving from simple models of collisionless sheath formation (for which SLPIC has achieved >260x overall speedup relative to PIC with comparable accuracy) to discuss SLPIC applications in more general low-temperature plasma discharges (e.g. collisional plasmas). We'll also discuss prospects for using SLPIC in the rapid modeling of plasma discharge evolution through transient or fluid-like phases, and its capability to transition mid-simulation to a smaller-timestep conventional PIC model as kinetic processes in the discharge become important.

Magnetic reconnection in relativistic collisionless plasmas can accelerate particles and power high-energy emission in various astrophysical systems. Whereas most previous studies focused on relativistic reconnection in pair plasmas, less attention has been paid to electron-ion plasma reconnection, expected in black hole accretion flows and relativistic jets. We report a comprehensive particle-in-cell numerical investigation of reconnection in an electron-ion plasma, spanning a wide range of ambient ion magnetizations $\sigma_i$, from the semirelativistic regime (ultrarelativistic electrons but nonrelativistic ions, 0.001<<$\sigma_i$<<1) to the fully relativistic regime (both species are ultrarelativistic, $\sigma_i$>>1). We investigate how the reconnection rate, electron and ion plasma flows, electric and magnetic field structures, electron/ion energy partitioning, and nonthermal particle acceleration depend on $\sigma_i$. Our key findings are: (1) the reconnection rate is about 0.1 of the Alfvenic rate across all regimes; (2) electrons can form concentrated moderately relativistic outflows even in the semirelativistic, small-$\sigma_i$ regime; (3) while the released magnetic energy is partitioned equally between electrons and ions in the ultrarelativistic limit, the electron energy fraction declines gradually with decreased $\sigma_i$ and asymptotes to about 0.25 in the semirelativistic regime; (4) reconnection leads to efficient nonthermal electron acceleration with a $\sigma_i$-dependent power-law index, $p(\sigma_i) \simeq $const$+0.7 {\sigma_i}^{-1/2}$. These findings are important for understanding black hole systems and lend support to semirelativistic reconnection models for powering nonthermal emission in blazar jets, offering a natural explanation for the spectral indices observed in these systems.

Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron-positron plasmas, for a wide range of upstream magnetizations sigma and system sizes. L. The particle spectra are well-represented by a power law gamma(-alpha), with a combination of exponential and super-exponential high-energy cutoffs, proportional to sigma and L, respectively. For large L and sigma, the power-law index alpha approaches about 1.2.

The discovery of rapid synchrotron gamma-ray flares above 100 MeV from the Crab Nebula has attracted new interest in alternative particle acceleration mechanisms in pulsar wind nebulae. Diffuse shock-acceleration fails to explain the flares because particle acceleration and emission occur during a single or even sub-Larmor timescale. In this regime, the synchrotron energy losses induce a drag force on the particle motion that balances the electric acceleration and prevents the emission of synchrotron radiation above 160 MeV. Previous analytical studies and two-dimensional (2D) particle-in-cell (PIC) simulations indicate that relativistic reconnection is a viable mechanism to circumvent the above difficulties. The reconnection electric field localized at X-points linearly accelerates particles with little radiative energy losses. In this paper, we check whether this mechanism survives in three dimension (3D), using a set of large PIC simulations with radiation reaction force and with a guide field. In agreement with earlier works, we find that the relativistic drift kink instability deforms and then disrupts the layer, resulting in significant plasma heating but few non-thermal particles. A moderate guide field stabilizes the layer and enables particle acceleration. We report that 3D magnetic reconnection can accelerate particles above the standard radiation reaction limit, although the effect is less pronounced than in 2D with no guide field. We confirm that the highest-energy particles form compact bunches within magnetic flux ropes, and a beam tightly confined within the reconnection layer, which could result in the observed Crab flares when, by chance, the beam crosses our line of sight.

The Crab Nebula was formed after the collapse of a massive star about a thousand years ago, leaving behind a pulsar that inflates a bubble of ultra-relativistic electron-positron pairs permeated with magnetic field. The observation of brief but bright flares of energetic gamma rays suggests that pairs are accelerated to PeV energies within a few days; such rapid acceleration cannot be driven by shocks. Here, it is argued that the flares may be the smoking gun of magnetic dissipation in the Nebula. Using 2D and 3D particle-in-cell simulations, it is shown that the observations are consistent with relativistic magnetic reconnection, where pairs are subject to strong radiative cooling. The Crab flares may highlight the importance of relativistic magnetic reconnection in astrophysical sources.

It is generally accepted that astrophysical sources cannot emit synchrotron radiation above 160 MeV in their rest frame. This limit is given by the balance between the accelerating electric force and the radiation reaction force acting on the electrons. The discovery of synchrotron gamma-ray flares in the Crab Nebula, well above this limit, challenges this classical picture of particle acceleration. To overcome this limit, particles must accelerate in a region of high electric field and low magnetic field. This is possible only with a non-ideal magnetohydrodynamic process, like magnetic reconnection. We present the first numerical evidence of particle acceleration beyond the synchrotron burnoff limit, using a set of two-dimensional particle-in-cell simulations of ultra-relativistic pair plasma reconnection. We use a new code, Zeltron, that includes self-consistently the radiation reaction force in the equation of motion of the particles. We demonstrate that the most energetic particles move back and forth across the reconnection layer, following relativistic Speiser orbits. These particles then radiate > 160 MeV synchrotron radiation rapidly, within a fraction of a full gyration, after they exit the layer. Our analysis shows that the high-energy synchrotron flux is highly variable in time because of the strong anisotropy and inhomogeneity of the energetic particles. We discover a robust positive correlation between the flux and the cut-off energy of the emitted radiation, mimicking the effect of relativistic Doppler amplification. A strong guide field quenches the emission of > 160 MeV synchrotron radiation. Our results are consistent with the observed properties of the Crab flares, supporting the reconnection scenario.

Trans-activator of transcription (Tat) is a cell penetrating peptide which can translocate and carry macromolecular cargoes through cell membranes. This study investigated the hypoglycemic activity of orally delivered insulin - Tat mixture in alloxan-induced diabetic mice. The mixtures of insulin and Tat at 1:1, 1:3 and 1:6 molar ratios were given orally at the insulin doses ranging from 1-200 IU/kg. The fasting blood glucose (FBG) levels were measured at initial, 1, 2, 4, 6, and 12 h after administration. At 1:3 molar ratio of the mixture and after 12 h of administration, insulin at 200 IU/kg showed the highest with prolonged hypoglycemic activity of 74.0±10.3% FBG reduction (2.18 folds of subcutaneously injected (SC) insulin). Free insulin administered orally did not show any hypoglycemic activity. The mixtures at the insulin doses of 100 and 50 IU/kg also showed potent FBG reduction of 73.8±8.2 and 71.3±16.9% at 12 h after administration (2.18 and 2.10 folds of SC insulin, respectively). After incubation with Mono-Mac-6 cells, only the -mixtures but not the free insulin showed intra-cellular insulin uptake, indicating the insulin penetration through the cell membranes via Tat. In simulated gastric fluid, the insulin content in the mixture was not found, demonstrating the degradation of insulin in the gastric environments. Insulin may be absorbed at upper gastrointestinal tract facilitated by Tat. The potent and prolonged hypoglycemic activity of insulin co-administered orally with Tat can be further developed as an effective oral insulin delivery system.

We report on the first study of the angular distribution of energetic particles and radiation generated in relativistic collisionless electron-positron pair plasma reconnection using two-dimensional particle-in-cell simulations. We discover a strong anisotropy of the particles accelerated by reconnection and the associated strong beaming of their radiation. The focusing of particles and radiation increases with their energy; in this sense, this "kinetic beaming" effect differs fundamentally from the relativistic Doppler beaming usually invoked in high-energy astrophysics, in which all photons are focused and boosted achromatically. We also present, for the first time, the modeling of the synchrotron emission as seen by an external observer during the reconnection process. The expected light curves comprise several bright symmetric sub-flares emitted by the energetic beam of particles sweeping across the line of sight intermittently, and exhibit super-fast time variability as short as about one-tenth of the system light-crossing time. The concentration of the energetic particles into compact regions inside magnetic islands and particle anisotropy explain the rapid variability. This radiative signature of reconnection can account for the brightness and variability of the gamma-ray flares in the Crab Nebula and in blazars.

The frequency extraction algorithm (Werner and Cary 2008 J. Comp. Phys. 227 5200) that enables a simple finite-difference time-domain algorithm to be transformed into an efficient eigenmode solver is applied to a realistic accelerator cavity modeled with embedded boundaries. Previously, the frequency extraction method was shown to be capable of distinguishing M degenerate modes by running M different simulations and to permit mode extraction with minimal post-processing effort that requires solving only a small eigenvalue problem. Realistic calculations for an accelerator cavity are presented in this paper to validate the method for realistic modeling scenarios and to illustrate the complexities of the computational validation process. The approach is able to extract frequencies that differ by corrected experimentally measured frequencies by about 1 part in 104, which is accounted for (in largest part) by machining errors. The extraction of frequencies and modes from accelerator cavities provides engineers and physicists with an understanding of potential cavity performance as it depends on the shape without incurring manufacture and measurement costs.

The RF properties of photonic crystals (PhCs) can be exploited to avoid the parasitic higher order modes (HOMs) that degrade beam quality in accelerator cavities and reduce efficiency and power in RF generators. Computer simulations show that long-range wake fields are significantly reduced in accelerator structures based on dielectric PhC cavities, which can be designed to trap only those modes within a narrow frequency range. A 2D PhC structure can be used to create a 3D accelerator cavity by using metal end-plates to confine the fields in the third dimension; however, even when the 2D photonic structure allows only a single mode, the 3D structure may trap HOMs, such as guided modes in the dielectric rods, that increase wake fields. For a 3D cavity based on a triangular lattice of dielectric rods, the rod positions can be optimized (breaking the lattice symmetry) to reduce radiation leakage using a fixed number of rods; moreover, the optimized structure has reduced wake fields. Using computer simulation, wake fields in pillbox, PhC, and optimized photonic cavities are calculated; a design for a klystron using the optimized photonic cavity structure is presented. CONTRIBUTION NOT RECEIVED Proceedings of PAC09, Vancouver, BC, Canada WE6RFP057

Dielectric materials and photonic crystal structures have electromagnetic properties that could potentially offer great benefits for accelerators. Computer simulation plays a critical role in designing, understanding, and optimizing these structures, especially the non‐intuitive photonic crystal structures for which there is no relevant zeroth‐order analytic model.

Recent developments have shown that one can get around the difficulties of finding the eigenvalues and eigenmodes of the large systems studied with high performance computation by using broadly filtered diagonalization [G. R. Werner and J. R. Cary, J. Comp. Phys. 227, 5200 (2008)]. This method can be used in conjunction with any time-domain computation, in particular those that scale very well up to 10000s of processors and beyond. Here we present results that show that this method accurately obtains both modes and frequencies of electromagnetic cavities, even when frequencies are nearly degenerate. The application was to a well-characterized Kaon separator cavity, the A15. The computations are shown to have a precision to a few parts in 10(5). Because the computed frequency differed from the measured frequency by more than this amount, a careful validation study to determine all sources of difference was undertaken. Ultimately, more precise measurements of the cavity showed that the computations were correct, with remaining differences accounted for by uncertainties in cavity dimensions and atmospheric and thermal conditions. Thus, not only was the method validated, but it was shown to have the ability to predict differences in cavity dimensions from fabrication specifications.

Characteristics and physical stability of luciferase plasmid (pLuc) entrapped in cationic bilayer vesicles prepared from various molar ratios of amphiphiles (DPPC, Tween61 or Span60), cholesterol (Chol) and cationic charge lipid (DDAB) were investigated. The cationic liposomes were composed of DPPC/Chol/DDAB in the molar ratio of 7:2:1. The cationic (Tween61 or Span60) niosomes were composed of Tween61/Chol/DDAB or Span60/Chol/DDAB in the molar ratio of 1:1:0.05. The maximum loading of pLuc was 15.29, 22.70, and 18.92μg/mg of the total lipids or surfactants of liposomes, Tween61 and Span60 niosomes, respectively. The morphology of the vesicles showing multilamellar structure was characterized by transmission electron microscope (TEM). The particle sizes of the vesicles in nanosize range (160–850nm) were determined by Photon Correlation Spectroscopy (PCS). Gel electrophoresis and gel documentation were modified to determine the entrapment efficiency of pLuc in cationic bilayer vesicles. The cationic bilayer vesicles gave the pLuc entrapment efficiency of 100%. The pLuc entrapped in cationic liposomes exhibited higher stability than pLuc in solution and pLuc entrapped in cationic Tween61 or Span60 niosomes, when stored at 4, 30 and 50°C for 8 weeks. After 8 weeks at 4°C, pLuc contents remained in cationic liposomes was 2 and 3 times higher than cationic Span60 and Tween61 niosomes, respectively. After 3 weeks, 50 and 2% of pLuc was remained in cationic liposomes at 30 and 50°C respectively, whereas all pLuc in cationic Span 60 and Tween61 niosomes were degraded within 2 and 1 week, respectively. At 30 and 50°C, pLuc in an aqueous solution or in bilayer vesicular formulations were not in a stable supercoil form. This study has indicated that the stability of pLuc can be enhanced by entrapping in cationic liposomes more than in niosomes. Higher temperature with increase storage time can affect the stability of pLuc even entrapped in bilayer vesicles.