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A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data.

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported in arXiv:2007.14894v2: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement., Comment: 13 pages, 11 figures

We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufficient initial amplitude ($\ge(4.1\pm0.4)$ MV/m), the phase of the modulation along the bunch is reproducible from event to event, with 3 to 7% (of 2$\pi$) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated., Comment: Letter and Supplemental Material, 6 figures, 8 pages

Plasma wakefield dynamics over timescales up to 800 ps, approximately 100 plasma periods, are studied experimentally at the Advanced Wakefield Experiment (AWAKE). The development of the longitudinal wakefield amplitude driven by a self-modulated proton bunch is measured using the external injection of witness electrons that sample the fields. In simulation, resonant excitation of the wakefield causes plasma electron trajectory crossing, resulting in the development of a potential outside the plasma boundary as electrons are transversely ejected. Trends consistent with the presence of this potential are experimentally measured and their dependence on wakefield amplitude are studied via seed laser timing scans and electron injection delay scans., Comment: 11 pages, 8 figures

In 2017, AWAKE demonstrated the seeded self-modulation (SSM) of a 400 GeV proton beam from the Super Proton Synchrotron (SPS) at CERN. The angular distribution of the protons deflected due to SSM is a quantitative measure of the process, which agrees with simulations by the two-dimensional (axisymmetric) particle-in-cell code LCODE. Agreement is achieved for beam populations between $10^{11}$ and $3 \times 10^{11}$ particles, various plasma density gradients ($-20 \div 20\%$) and two plasma densities ($2\times 10^{14} \text{cm}^{-3}$ and $7 \times 10^{14} \text{cm}^{-3}$). The agreement is reached only in the case of a wide enough simulation box (at least five plasma wavelengths)., Comment: 8 pages, 9 figures, 1 table

The two currently largest all-sky photometric datasets, WISE and SuperCOSMOS, were cross-matched by Bilicki et al. (2016) (B16) to construct a novel photometric redshift catalogue on 70% of the sky. Galaxies were therein separated from stars and quasars through colour cuts, which may leave imperfections because of mixing different source types which overlap in colour space. The aim of the present work is to identify galaxies in the WISExSuperCOSMOS catalogue through an alternative approach of machine learning. This allows us to define more complex separations in the multi-colour space than possible with simple colour cuts, and should provide more reliable source classification. For the automatised classification we use the support vector machines learning algorithm, employing SDSS spectroscopic sources cross-matched with WISExSuperCOSMOS as the training and verification set. We perform a number of tests to examine the behaviour of the classifier (completeness, purity and accuracy) as a function of source apparent magnitude and Galactic latitude. We then apply the classifier to the full-sky data and analyse the resulting catalogue of candidate galaxies. We also compare thus produced dataset with the one presented in B16. The tests indicate very high accuracy, completeness and purity (>95%) of the classifier at the bright end, deteriorating for the faintest sources, but still retaining acceptable levels of 85%. No significant variation of classification quality with Galactic latitude is observed. Application of the classifier to all-sky WISExSuperCOSMOS data gives 15 million galaxies after masking problematic areas. The resulting sample is purer than the one in B16, at a price of lower completeness over the sky. The automatic classification gives a successful alternative approach to defining a reliable galaxy sample as compared to colour cuts., Comment: 12 pages, 15 figures, accepted for publication in A&A. Obtained catalogue will be included in the public release of the WISExSuperCOSMOS galaxy catalogue available from http://ssa.roe.ac.uk/WISExSCOS

The nature of dark energy, driving the accelerated expansion of the Universe, is one of the most important issues in modern astrophysics. In order to understand this phenomenon, we need precise astrophysical probes of the universal expansion spanning wide redshift ranges. Quasars have recently emerged as such a probe, thanks to their high intrinsic luminosities and, most importantly, our ability to measure their luminosity distances independently of redshifts. Here we report our ongoing work on observational reverberation mapping using the time delay of the Mg II line, performed with the South African Large Telescope (SALT)., Comment: 3 pages, 2 figures, submitted as PTA proceedings

The Mg II emission line is visible in the optical band for intermediate redshift quasars (0.4 < z < 1.6) and it is thus an extremely important tool to measure the black hole mass and to understand the structure of the Broad Line Region. We aim to determine the substructure and the variability of the Mg II line with the aim to identify which part of the line comes from a medium in Keplerian motion. Using the Southern African Large Telescope (SALT) with the Robert Stobie Spectrograph (RSS) we performed ten spectroscopic observations of quasar HE 0435-4312 (z = 1.2231) over a period of three years (Dec 23/24, 2012 to Dec 7/8, 2015). Both the Mg II line and the Fe II pseudo-continuum increase with time. We clearly detect the systematic shift of the Mg II line with respect to the Fe II over the years, corresponding to the acceleration of 104 pm 14 km/s/year in the quasar rest frame. The Mg II line shape is clearly non-Gaussian but single-component, and the increase in line equivalent width and line shift is not accompanied with significant evolution of the line shape. We analyse the conditions in the Mg II and Fe II formation region and we note that the very large difference in the covering factor and the turbulent velocity also support the conclusion that the two regions are spatially separated. The measured acceleration of the line systematic shift is too large to connect it with the orbital motion at a distance of the Broad Line Region (BLR) in this source. It may imply a precessing inner disk illuminating the BLR. Further monitoring is still needed to better constrain the variability mechanism., Comment: Astronomy and Astrophysics (in press)

The black hole mass measurement in active galaxies is a challenge, particularly in sources where the reverberation method cannot be applied. We aim to determine the black hole mass in a very special object, RE J1034+396, one of the two AGN with QPO oscillations detected in X-rays, and a single bright AGN with optical band totally dominated by starlight. We fit the stellar content using the code starlight, and the broad band disk contribution to optical/UV/X-ray emission is modeled with optxagnf. We also determine the black hole mass using several other independent methods. Various methods give contradictory results. Most measurements of the blacc hole mass are in the range 1.e6-1.e7 Msun, and the measurements based on dynamics give higher values than measurements based on Hbeta and Mg II emission lines., Comment: A&A, in press

We study canard solutions of the forced van der Pol (fvdP) equation in the relaxation limit for low-, intermediate-, and high-frequency periodic forcing. A central numerical observation is that there are two branches of canards in parameter space which extend across all positive forcing frequencies. For low-frequency forcing, we demonstrate the existence of primary maximal canards induced by folded saddle-nodes of type I, and establish explicit formulas for the parameter values at which the primary maximal canards and their folds exist. We then turn to the intermediate- and high-frequency forcing regimes, and show that the fvdP equation possesses torus canards instead. These torus canards consist of long segments near families of attracting and repelling limit cycles of the fast system, in alternation. We also derive explicit formulas for the parameter values at which the maximal torus canards and their folds exist. Primary maximal canards and maximal torus canards correspond geometrically to the situation in which the persistent manifolds near the family of attracting limit cycles coincide to all orders with the persistent manifolds that lie near the family of repelling limit cycles. The formulas derived for the folds of maximal canards in all three frequency regimes turn out to be representations of a single formula in the appropriate parameter regimes, and this unification confirms our numerical observation. In addition, we study the secondary canards induced by the folded singularities in the low-frequency regime and find that their fold curves turn around in the intermediate-frequency regime. We identify the mechanism responsible for this turning. Finally, we show that the fvdP equation is a normal form for a class of single-frequency periodically-driven slow/fast systems with two fast variables and one slow variable which possess a nondegenerate fold of limit cycles., Comment: 37 pages, 13 figures

Quasars, as the most luminous persistent sources in the Universe, have broad applications for cosmological studies. In particular, they can be employed to directly measure the expansion history of the Universe, similarly to SNe Ia. The advantage of quasars is that they are numerous, cover a broad range of redshifts, up to $z = 7$, and do not show significant evolution of metallicity with redshift. The idea is based on the relation between the time delay of an emission line and the continuum, and the absolute monochromatic luminosity of a quasar. For intermediate redshift quasars, the suitable line is Mg II. Between December 2012 and March 2014, we performed five spectroscopic observations of the QSO CTS C30.10 ($z = 0.900$) using the South African Large Telesope (SALT), supplemented with photometric monitoring, with the aim of determining the variability of the line shape, changes in the total line intensity and in the continuum. We show that the method is very promising., Comment: Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

Quasars can be used as a complementary tool to SN Ia to probe the distribution of dark energy in the Universe by measuring the time delay of the emission line with respect to the continuum. The understanding of the Mg II emission line structure is important for cosmological application and for the black hole mass measurements of intermediate redshift quasars. The knowledge of the shape of Mg II line and its variability allows to determine which part of the line should be used to measure the time delay and the black hole mass. We thus aim at determination of the structure and the variability of the Mg II line as well as of the underlying Fe II pseudo-continuum. We performed five spectroscopic observations of a quasar CTS C30.10 (z = 0.9000) with the SALT telescope between December 2012 and March 2014, and we studied the variations of the spectral shape in the 2700 - 2900 A rest frame. We showed that the Mg II line in this source consists of two kinematic components, which makes the source representative of type B quasars. Both components were well modeled with a Lorentzian shape. Both components vary in a similar way. The Fe II contribution seems to be related only to the first (blue) Mg II component}. Broad band spectral fitting rather favor the use of the whole line profile. The contribution of the Narrow Line Region to Mg II is very low, below 2%. The Mg II variability is lower than the variability of the continuum, which is consistent with the simple reprocessing scenario. The variability level of CTS C30.10 and the measurement accuracy of the line and continuum is high enough to expect that further monitoring will allow to measure the time delay between the Mg II line and continuum., Comment: accepted to Astronomy & Astrophysics; no language corrections

The Mg II line is of extreme importance in intermediate redshift quasars since it allows us to measure the black hole mass in these sources and to use these sources as probes of the distribution of dark energy in the Universe, as a complementary tool to SN Ia. Reliable use of Mg II requires a good understanding of all the systematic effects involved in the measurement of the line properties, including the contamination by Fe II UV emission. We performed three spectroscopic observations of a quasar LBQS 2113-4538 (z = 0.956) with the SALT telescope separated in time by several months and we analyze in detail the mean spectrum and the variability in the spectral shape. We show that even in our good-quality spectra the Mg II doublet is well fit by a single Lorentzian shape. We tested several models of the Fe II pseudo-continuum and showed that one of them well represents all the data. The amplitudes of both components vary in time, but the shapes do not change significantly. The measured line width of LBQS 2113-4538 identifies this object as a class A quasar. The upper limit of $3\%$ for the contribution of the Narrow Line Region (NLR) to Mg II may suggest that the separation of the Broad Line Region (BLR) and NLR disappears in this class of objects., Comment: 10 pages, 8 figures, accepted to A&A

We study Mixed Mode Oscillations (MMOs) in systems of two weakly coupled slow/fast oscillators. We focus on the existence and properties of a folded singularity called FSN II that allows the emergence of MMOs in the presence of a suitable global return mechanism. As FSN II corresponds to a transcritical bifurcation for a desingularized reduced system, we prove that, under certain non-degeneracy conditions, such a transcritical bifurcation exists. We then apply this result to the case of two coupled systems of FitzHugh- Nagumo type. This leads to a non trivial condition on the coupling that enables the existence of MMOs.

We examine a simple, fuel-air, model of combustion in a spark ignition (si) engine with indirect injection. In our two fluid model, variations of fuel mass burned in cycle sequences appear due to stochastic fluctuations of a fuel feed amount. We have shown that a small amplitude of these fluctuations affects considerably the stability of a combustion process strongly depending on the quality of air-fuel mixture. The largest influence was found in the limit of a lean combustion. The possible effect of nonlinearities in the combustion process has been also discussed., Comment: 10 pages, 6 figures

We examine a simple, fuel-air, model of combustion in spark ignition (si) engine with indirect injection. In our two fluid model, variations of fuel mass burned in cycle sequences appear due to stochastic fluctuations of a fuel feed amount. We have shown that a small amplitude of these fluctuations affects considerably the stability of a combustion process strongly depending on the quality of air-fulel mixture. The largest influence was found in the limit of a lean combustion. The possible effect of nonlinearities in the combustion process were also discussed., Comment: 9 pages, 3 figures, submitted to Journal of Vibration and Control