Cosmological beam plasma instabilities

Blazars are the main source of extragalactic very high energy gamma-rays. These gamma rays annihilate on the extragalactic background light, producing electron-positron pair beams with TeV energies. The pair beams are very dilute, with beam-IGM density ratio of $\alpha \sim 10^{-15}$, ultra-relativistic, $\gamma \sim 10^6$, and energetically subdominant ($\gamma \alpha \sim 10^{-9}$). Such pair beams suffer from prevailing cosmological scale, linear beam-plasma instabilities. The associated instability growth rates suggest that at least initially these overwhelmingly dominate inverse Compton cooling, currently the only alternative mechanism by which the pair beams lose energy. Therefore, the full non-linear evolution of the instabilities is key to determining the mechanism by which these pair-beams lose their energy. Kinetic numerical simulations are the only method by which we can currently study the full non-linear evolution of the blazar-induced beam-plasma instabilities. However, the extreme parameters of the pair beams make direct simulations via existing particle-in-cell (PIC) codes infeasible. To address this, we developed a new Spatially Higher-order Accurate, Relativistic PIC algorithm (SHARP). A one dimensional implementation of the SHARP algorithm (SHARP-1D) is given in detail. We show explicitly that SHARP-1D can overcome a number of the limitations of existing PIC algorithms. Using SHARP-1D, we demonstrate a number of points that are important to correctly simulate the full evolution of beam-plasma instabilities. We show that convergence for PIC algorithms requires increasing both spatial resolution and the number of particles per cell concurrently. For a beam-plasma system, we show that the spectral resolution is another important resolution criteria and under-resolved simulations can lead to erroneous physical conclusions. We quantify the required box sizes to faithfully resolve the spectral support of the instabilities. When the background plasmas contain structure, we show that a significant fraction of beam energy (similar to that in uniform plasma simulations; $\sim 20$\%) is, still, lost during the linear evolution of the electrostatic unstable modes. Compared to uniform plasma growth rates, we find lower growth rates, however, the non-uniform systems stay longer in the linear regime. Therefore, the IGM inhomogeneities are unlikely to affect the efficiency of beam-plasma instabilities to cool the blazar-induced pair beams

SHARP: A Spatially Higher-order, Relativistic Particle-in-Cell Code

Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher-order accurate relativistic PIC algorithm in one spatial dimension, which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher-order interpolation functions to achieve a spatially higher-order accurate algorithm (up to fifth order). We validate our algorithm against several test problems -- thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutions of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second-order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., those that lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables us to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.Comment: 26 pages, 19 figures, discussion about performance is added, published in Ap

Growth of beam-plasma instabilities in the presence of background inhomogeneity

We explore how inhomogeneity in the background plasma number density alters the growth of electrostatic unstable wavemodes of beam plasma systems. This is particularly interesting for blazar-driven beam-plasma instabilities, which may be suppressed by inhomogeneities in the intergalactic medium as was recently claimed in the literature. Using high resolution Particle-In-Cell simulations with the SHARP code, we show that the growth of the instability is local, i.e., regions with almost homogeneous background density will support the growth of the Langmuir waves, even when they are separated by strongly inhomogeneous regions, resulting in an overall slower growth of the instability. We also show that if the background density is continuously varying, the growth rate of the instability is lower; though in all cases, the system remains within the linear regime longer and the instability is not extinguished. In all cases, the beam loses approximately the same fraction of its initial kinetic energy in comparison to the uniform case at non-linear saturation. Thus, inhomogeneities in the intergalactic medium are unlikely to suppress the growth of blazar-driven beam-plasma instabilities.Comment: 10 pages, 6 figures, Accepted by ApJ, comments welcom

Importance of resolving the spectral support of beam-plasma instabilities in simulations

Many astrophysical plasmas are prone to beam-plasma instabilities. For relativistic and dilute beams, the {\it spectral} support of the beam-plasma instabilities is narrow, i.e., the linearly unstable modes that grow with rates comparable to the maximum growth rate occupy a narrow range of wave numbers. This places stringent requirements on the box-sizes when simulating the evolution of the instabilities. We identify the implied lower limits on the box size imposed by the longitudinal beam plasma instability, i.e., typically the most stringent condition required to correctly capture the linear evolution of the instabilities in multidimensional simulations. We find that sizes many orders of magnitude larger than the resonant wavelength are typically required. Using one-dimensional particle-in-cell simulations, we show that the failure to sufficiently resolve the spectral support of the longitudinal instability yields slower growth and lower levels of saturation, potentially leading to erroneous physical conclusion.Comment: 7 pages, 9 figures, accepted by Ap

Coupling multi-fluid dynamics equipped with Landau closures to the particle-in-cell method

The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run-times and often to setups in less than three spatial dimensions. Traditionally, this is circumvented either via hybrid-PIC methods (adopting massless electrons) or via magneto-hydrodynamic-PIC methods (modelling the background plasma as a single charge-neutral magneto-hydrodynamical fluid). Because both methods preclude modelling important plasma-kinetic effects, we introduce a new fluid-PIC code that couples a fully explicit and charge-conservative multi-fluid solver to the PIC code SHARP through a current-coupling scheme and solve the full set of Maxwell's equations. This avoids simplifications typically adopted for Ohm's Law and enables us to fully resolve the electron temporal and spatial scales while retaining the versatility of initializing any number of ion, electron, or neutral species with arbitrary velocity distributions. The fluid solver includes closures emulating Landau damping so that we can account for this important kinetic process in our fluid species. Our fluid-PIC code is second-order accurate in space and time. The code is successfully validated against several test problems, including the stability and accuracy of shocks and the dispersion relation and damping rates of waves in unmagnetized and magnetized plasmas. It also matches growth rates and saturation levels of the gyro-scale and intermediate-scale instabilities driven by drifting charged particles in magnetized thermal background plasmas in comparison to linear theory and PIC simulations. This new fluid-SHARP code is specially designed for studying high-energy cosmic rays interacting with thermal plasmas over macroscopic timescales.Comment: 35 pages, 11 figures, submitted to JPP. Comments are welcom

Deciphering the physical basis of the intermediate-scale instability

We study the underlying physics of cosmic-ray (CR) driven instabilities that play a crucial role for CR transport across a wide range of scales, from interstellar to galaxy cluster environments. By examining the linear dispersion relation of CR-driven instabilities in a magnetised electron-ion background plasma, we establish that both, the intermediate and gyroscale instabilities have a resonant origin and show that these resonances can be understood via a simple graphical interpretation. These instabilities destabilise wave modes parallel to the large-scale background magnetic field at significantly distinct scales and with very different phase speeds. Furthermore, we show that approximating the electron-ion background plasma with either magnetohydrodynamics (MHD) or Hall-MHD fails to capture the fastest growing instability in the linear regime, namely the intermediate-scale instability. This finding highlights the importance of accurately characterising the background plasma for resolving the most unstable wave modes. Finally, we discuss the implications of the different phase speeds of unstable modes on particle-wave scattering. Further work is needed to investigate the relative importance of these two instabilities in the non-linear, saturated regime and to develop a physical understanding of the effective CR transport coefficients in large-scale CR hydrodynamics theories.Comment: 14 pages, 3 figures, submitted to JPP Letters, comments welcom

Reliability of hypertrophy of the contralateral testis in prediction of the status of impalpable testis

Background: The hypertrophied testis can predict the status of the impalpable contralateral one. The aim of this study was to assess the accuracy of contralateral testicular hypertrophy for predicting the presence or absence of impalpable undescended testis (UDT) in Egyptian boys.Patients and methods: This study was carried out on 204 patients with unilateral impalpable UDT who presented to the Pediatric Surgery Department, Al-Azhar University Hospitals, from July 2014 to April 2016. Only 40 patients with unilateral impalpable UDT and hypertrophy of the contralateral testes were included in this study. They were subjected to routine laboratory investigations, ultrasonography measurement of the volume of the hypertrophied testis, and diagnostic laparoscopy for the impalpable intra-abdominal testis (IAT). Both ultrasonography and laparoscopic findings were reported.Results: Out of 204 patients with unilateral impalpable UDT, only 40 patients fulfilled the inclusion criteria. Their ages ranged from 1 to 5 years, with a mean of 2.3±1.18 years. Testicular volume ranged from 0.94 to 6.33 cm3, with amean of 3.12±1.41 cm3. Diagnostic laparoscopy indicated 30 patients with vanishing testis, four patients with low IAT, and three patients with high IAT and three patients with testicular vessels and vas passing internal inguinal ring, where inguinal exploration indicated atrophic testes.Conclusion: Hypertrophied testis can predict the absence of other contralateral impalpable testis when its volume is 1.85 cm3.Keywords: hypertrophy, impalpable undescended testis, laparoscopy, reliabilit