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<h2>Enrico Camporeale</h2>
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<header class="major special">
<h2>Publications</h2>
</header>
<h2> Book and Chapters</h2>
<span>
<a href="https://www.sciencedirect.com/book/9780128117880/machine-learning-techniques-for-space-weather" target="_blank"><img src="./images/ML_book.jpg" width=15% align="left" alt="" style="margin:0px 50px 10px 0px"></a>
</span>
<h4><a href="https://www.sciencedirect.com/book/9780128117880/machine-learning-techniques-for-space-weather" target="_blank">Machine Learning Techniques for Space Weather</a></h4>
<h5>(eds.) <u>E. Camporeale</u>, S. Wing, J. Johnson</h5>
Elsevier (2017)
<p></p>
<br></br>
<p></p>
<li>A. Carè, <u>E. Camporeale</u> (2018)<br>
<b> Regression</b>, in <i> Machine Learning Techniques for Space Weather</i>
<br><br>
<li>S. Wing, J. Johnson, <u>E. Camporeale</u>, G. Reeves (2018)<br>
<b> Untangling the solar wind drivers of radiation belt: an information theoretical approach</b>, in <i> Machine Learning Techniques for Space Weather</i>
<br><br>
<li>M. Chandorkar, <u>E. Camporeale</u> (2018)<br>
<b> Probabilistic Forecasting of Geomagnetic Indices using Gaussian Process Models</b>, in <i> Machine Learning Techniques for Space Weather</i>
</p>
<h2> Manuscripts</h2>
<ul>
<span>
<a href="https://arxiv.org/pdf/2107.14322" target="_blank"><img src="./publications_files/PINN_RB.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Machine-learning based discovery of missing physical processes in radiation belt modeling <a href="https://arxiv.org/pdf/2107.14322" target="_blank" class="icon fa-download"></a></h4>
<h5><u>E. Camporeale</u>, G. J. Wilkie, A. Drozdov, J. Bortnik,
<i> under review</i> </h5>
Real-time prediction of the dynamics of energetic electrons in Earth's radiation belts incorporating incomplete observation data is important to protect valuable artificial satellites and to understand their physical processes. Traditionally, reduced models have employed a diffusion equation based on the quasilinear approximation. Using a Physics-Informed Neutral Network (PINN) framework, we train and test a model based on four years of Van Allen Probe data. We present a recipe for gleaning physical insight from solving the ill-posed inverse problem of inferring model coefficients from data using PINNs.
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With this, it is discovered that the dynamics of "killer electrons" is described more accurately instead by a drift-diffusion equation. A parameterization for the diffusion and drift coefficients, which is both simpler and more accurate than existing models, is presented.
</div>
<br><br>
<span>
<a href="https://arxiv.org/pdf/2108.06394" target="_blank"><img src="./publications_files/shneider.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>A Machine-Learning-Ready Dataset Prepared from the Solar and Heliospheric Observatory Mission <a href="https://arxiv.org/pdf/2108.06394" target="_blank" class="icon fa-download"></a></h4>
<h5>C. Shneider, A. Hu, A. K. Tiwari, M. G. Bobra, K. Battams, J. Teunissen, <u>E. Camporeale</u>,
<i> under review</i> </h5>
We present a Python tool to generate a standard dataset from solar images that allows for user-defined selection criteria and a range of pre-processing steps. Our Python tool works with all image products from both the Solar and Heliospheric Observatory (SoHO) and Solar Dynamics Observatory (SDO) missions. We discuss a dataset produced from the SoHO mission's multi-spectral images which is free of missing or corrupt data as well as planetary transits in coronagraph images, and is temporally synced making it ready for input to a machine learning system.
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Machine-learning-ready images are a valuable resource for the community because they can be used, for example, for forecasting space weather parameters. We illustrate the use of this data with a 3-5 day-ahead forecast of the north-south component of the interplanetary magnetic field (IMF) observed at Lagrange point one (L1). For this use case, we apply a deep convolutional neural network (CNN) to a subset of the full SoHO dataset and compare with baseline results from a Gaussian Naive Bayes classifier.
</div>
<br><br>
</ul>
<h2>Published (Peer-reviewed)</h2>
<h3>2022</h3>
<ol start=56; reversed>
<span>
<a href="" target="_blank"><img src="./publications_files/man.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Ensemble Modeling of Radiation Belt Electron Flux Decay Following a Geomagnetic Storm: Dependence on Key Input Parameters <a href="" target="_blank" class="icon fa-download"></a></h4>
<h5>M. Hua, J. Bortnik, A. Kellerman, <u>E. Camporeale</u>, Q. Ma (2022)
<i> Space Weather</i>, in press</h5>
We perform an ensemble of quasi-linear diffusion simulations of the radiation belt electron flux decay for ~6 days at L = 3.5 during the recovery phase of the storm on 7 November 2015, where plasmaspheric hiss dominantly drives the electron flux decay process. Based on Van Allen Probes measurements, we use percentiles to sample the distributions of the four key input parameters, which are the hiss wave amplitude Bw, hiss wave peak frequency fm, background magnetic field B0 and electron density Ne, with 11 points representing that range of each input, leading to 11^4 (~14,600) ensemble members.
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By developing a Lookup Table method to rapidly calculate the time-dependent diffusion coefficients, the changing wave environment at every time step is incorporated in our ensemble simulations. The comparison between the ensemble simulations and observation reveals the influence of uncertainties in the input parameters on the simulated electron fluxes. Our results demonstrate that the perturbations in Bw are the primary contributor for discrepancies between modeled and observed electron fluxes, while the simulation errors caused by variations in fm and Ne are strongly energy-dependent. The simulated electron flux using the wave parameters observed at the 50th percentile agrees with observations, and most of the simulation errors increase with decreasing observational probability density of the parameters, with the largest log accuracy ratio of ~14. Our physics-based ensemble modeling provides the essential information about the robustness of radiation belt simulation and forecast considering the uncertainties in the plasma wave measurement or parameterization.
</div>
<br><br>
<span>
<a href="https://doi.org/10.1029/2022SW003064" target="_blank"><img src="./publications_files/andong_dst.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Probabilistic prediction of Dst storms one-day-ahead using Full-Disk SoHO Images <a href="https://doi.org/10.1029/2022SW003064" target="_blank" class="icon fa-download"></a></h4>
<h5>A. Hu, C. Shneider, A. Tiwari, <u>E. Camporeale</u> (2022)
<i> Space Weather</i>, in press</h5>
We present a new model for the probability that the Disturbance storm time (Dst) index exceeds -100 nT, with a lead time between 1 and 3 days. Dst provides essential information about the strength of the ring current around the Earth caused by the protons and electrons from the solar wind, and it is routinely used as a proxy for geomagnetic storms. The model is developed using an ensemble of Convolutional Neural Networks (CNNs) that are trained using SoHO images (MDI, EIT and LASCO). The relationship between the SoHO images and the solar wind has been investigated by many researchers, but these studies have not explicitly considered using SoHO images to predict the Dst index.
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This work presents a novel methodology to train the individual models and to learn the optimal ensemble weights iteratively, by using a customized class-balanced mean square error (CB-MSE) loss function tied to a least-squares (LS) based ensemble.
The proposed model can predict the probability that Dst < − 100nT 24 hours ahead with a True Skill Statistic (TSS) of 0.62 and Matthews Correlation Coefficient (MCC) of 0.37. The weighted TSS and MCC from Guastavino et al. (2021) is 0.68 and 0.47, respectively. An additional validation during non-Earth-directed CME periods is also conducted which yields a good TSS and MCC score.
</div>
<br><br>
<span>
<a href="https://www.essoar.org/pdfjs/10.1002/essoar.10508063.3" target="_blank"><img src="./publications_files/iong.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>New Findings from Explainable SYM-H Forecasting using Gradient Boosting Machines <a href="https://www.essoar.org/pdfjs/10.1002/essoar.10508063.3" target="_blank" class="icon fa-download"></a></h4>
<h5>D. Iong, Y. Chen, G. Toth, S. Zou, T. Pulkkinen, J. Ren, <u>E. Camporeale</u>, T. Gombosi (2022)
<i> Space Weather</i>, in press</h5>
In this work, we develop gradient boosting machines (GBMs) for forecasting the SYM-H index multiple hours ahead using different combinations of solar wind and interplanetary magnetic field (IMF) parameters, derived parameters, and past SYM-H values. Using Shapley Additive Explanation (SHAP) values to quantify the contributions from each input to predictions of the SYM-H index from GBMs, we show that our predictions are consistent with physical understanding while also providing insight into the complex relationship between the solar wind and Earth's ring current.
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We also perform a direct comparison between GBMs and neural networks presented in prior publications for forecasting the SYM-H index by training, validating, and testing them on the same data. We find that the GBMs have a comparable root mean squared error as the best published black-box neural network schemes and GBMs have better Heidke Skill Scores at predicting strong storms.
</div>
<br><br>
<span>
<a href="https://www.frontiersin.org/articles/10.3389/fphy.2022.786639/pdf" target="_blank"><img src="./publications_files/kluth.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Machine Learning Methods Applied to the Global Modeling of Event-Driven Pitch Angle Diffusion Coefficients During High Speed Streams <a href="https://www.frontiersin.org/articles/10.3389/fphy.2022.786639/pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>G. Kluth, J.-F. Ripoll, S. Has, A. Fischer, M. Mougeot and <u>E. Camporeale</u> (2022)<i> Frontiers in Physics</i></h5>
Whistler-mode waves in the inner magnetosphere cause electron precipitation in the atmosphere through the physical process of pitch-angle diffusion. The computation of pitch-angle diffusion relies on quasi-linear theory and becomes time-consuming as soon as it is performed at high temporal resolution from satellite measurements of ambient wave and plasma properties. Such an effort is nevertheless required to capture accurately the variability and complexity of atmospheric electron precipitation, which are involved in various Earth’s ionosphere-magnetosphere coupled problems.
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In this work, we build a global machine-learning model of event-driven pitch-angle diffusion coefficients for storm conditions based on the data of a variety of storms observed by the NASA Van Allen Probes. We first proceed step-by-step by testing 8 nonparametric machine learning methods. With them, we derive machine learning based models of event-driven diffusion coefficients for the storm of March 2013 associated with high-speed streams. We define 3 diagnostics that allow highlighting of the properties of the selected model and selection of the best method. Three methods are retained for their accuracy/efficiency: spline interpolation, the radial basis method, and neural networks (DNN), the latter being selected for the second step of the study. We then use event-driven diffusion coefficients computed from 32 high-speed stream storms in order to build for the first time a statistical event-driven diffusion coefficient that is embedded within the retained DNN model. We achieve a global mean event-driven model in which we introduce a two-parameter dependence, with both the Kp-index and time kept as in an epoch analysis following the storm evolution. The DNN model does not entail any issue to reproduce quite perfectly its target, i.e., averaged diffusion coefficients, with rare exception in the Landau resonance region. The DNN mean model is then used to analyze how mean diffusion coefficients behave compared with individual ones. We find a poor performance of any mean models compared with individual events, with mean diffusion coefficients computing the general trend at best, due to their large variability. The DNN-based model allows simple and fast data exploration of pitch-angle diffusion among its multiple variables. We finally discuss how to conduct uncertainty quantification of Fokker-Planck simulations of storm conditions for space weather nowcasting and forecasting.
</div>
<br><br>
<span>
<a href="https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2021SW002925" target="_blank"><img src="./publications_files/napoletano.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Parameter Distributions for the Drag-Based Modeling of CME Propagation <a href="https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2021SW002925" target="_blank" class="icon fa-download"></a></h4>
<h5>G. Napoletano, R. Foldes, F. Berrilli, <u>E. Camporeale</u>, at al., (2022)<i> Space Weather</i>, in press </h5>
In recent years, ensemble modelling has been widely employed in space weather to estimate uncertainties in forecasts. We here focus on the ensemble modelling of CME arrival times and arrival velocities using a drag-based model, which is well-suited for this purpose due to its simplicity and low computational cost. Although ensemble techniques have previously been applied to the drag-based model, it is still not clear how to best determine distributions for its input parameters, namely the drag parameter and the solar wind speed.
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The aim of this work is to evaluate statistical distributions for these model parameters starting from a list of past CME-ICME events. We employ LASCO coronagraph observations to measure initial CME position and speed, and in situ data to associate them to arrival date and impact speed. For each event we ran a statistical procedure to invert the model equations producing the parameters distributions as the output.
Our results indicate that the distributions employed in previous works were appropriately selected, even though based on restricted samples and heuristic considerations.
</div>
<br><br>
</ol>
<h3>2021</h3>
<ol start=51; reversed>
<span>
<a href="./papers/epl20620-offprints.pdf" target="_blank"><img src="./publications_files/feraco.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Connecting Large-Scale Velocity and Temperature Bursts with Small-Scale Intermittency in Stratified Turbulence <a href="./papers/epl20620-offprints.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>F. Feraco, R. Marino, L. Primavera, A. Pumir, P. Mininni, D. Rosenberg, A. Pouquet, R. Foldes, E. Lévêque, <u>E. Camporeale</u>, et al. (2021),
<i> EPL</i> 135 14001 </h5>
Non-Gaussian statistics of large-scale fields are routinely observed in data from atmospheric and oceanic campaigns and global models. Recent direct numerical simulations (DNSs) showed that large-scale intermittency in stably stratified flows is due to the emergence of sporadic, extreme events in the form of bursts in the vertical velocity and the temperature. This phenomenon results from the interplay between waves and turbulent motions, affecting mixing. We provide evidence of the enhancement of the classical small-scale (or internal) intermittency due to the emergence of large-scale drafts, connecting large- and small-scale bursts.
<div onclick="openClose('a50')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a50" class="texter">
To this aim we analyze a large set of DNSs of the stably stratified Boussinesq equations over a wide range of values of the Froude number (Fr ~0.01-1). The variation of the buoyancy field kurtosis with Fr is similar to (though with smaller values than) the kurtosis of the vertical velocity, both showing a non-monotonic trend. We present a mechanism for the generation of extreme vertical drafts and vorticity enhancements which follows from the exact equations for field gradients.
</div>
<br><br>
<span>
<a href="./papers/IJUQ1104(5)-34623.pdf" target="_blank"><img src="./publications_files/ACCRUE.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>ACCRUE: Accurate and Reliable Uncertainty Estimate in Deterministic models <a href="./papers/IJUQ1104(5)-34623.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>E. Camporeale</u>, A. Carè (2021), <i> Int. J. Uncertainty Quantification </i>, 11(4). </h5>
In this paper we focus on the problem of assigning uncertainties to single-point predictions generated by a deterministic model that outputs a continuous variable. This problem applies to any state-of-the-art physics or engineering models that have a computational cost that does not readily allow running ensembles and estimating the uncertainty associated to single-point predictions. Essentially, we devise a method to easily transform a deterministic prediction into a probabilistic one. We show that for doing so, one has to compromise between the accuracy and the reliability (calibration) of such a probabilistic model. Hence, we introduce a cost function that encodes their trade-off, and we call this new method ACCRUE (ACCurate and Reliable Uncertainty Estimate).
<div onclick="openClose('a49')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a49" class="texter">
We use the continuous rank probability score to measure accuracy and we derive an analytic formula for the reliability, in the case of forecasts of continuous scalar variables expressed in terms of Gaussian distributions. The new ACCRUE cost function is then used to estimate the input-dependent variance, given a black-box "oracle" mean function, by solving a two-objective optimization problem. The simple philosophy behind this strategy is that predictions based on the estimated variances should not only be accurate, but also reliable (i.e., statistically consistent with observations). Conversely, early works based on the minimization of classical cost functions, such as the negative log probability density, cannot simultaneously enforce both accuracy and reliability. We show several examples both with synthetic data, where the underlying hidden noise can accurately be recovered, and with large real-world datasets.
</div>
<br><br>
<span>
<a href="https://agupubs.onlinelibrary.wiley.com/doi/pdfdirect/10.1029/2020SW002684" target="_blank"><img src="./publications_files/precipnet.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Toward a next generation particle precipitation model: Mesoscale prediction through machine learning (a case study and framework for progress) <a href="https://agupubs.onlinelibrary.wiley.com/doi/pdfdirect/10.1029/2020SW002684" target="_blank" class="icon fa-download"></a></h4>
<h5>R. McGranaghan, J. Ziegler, T. Bloch, S. Hatch, <u>E. Camporeale</u>, K. Lynch, M. Owens, J. Gjerloev, B. Zhang, S.H. Skone (2021), <i> Space Weather </i>, 19, e2020SW002684. </h5>
We advance the modeling capability of electron particle precipitation from the magnetosphere to the ionosphere through a new database and use of machine learning tools to gain utility from those data. We have compiled, curated, analyzed, and made available a new and more capable database of particle precipitation data that includes 51 satellite years of Defense Meteorological Satellite Program (DMSP) observations temporally aligned with solar wind and geomagnetic activity data. The new total electron energy flux particle precipitation nowcast model, a neural network called PrecipNet, takes advantage of increased expressive power afforded by machine learning approaches to appropriately utilize diverse information from the solar wind and geomagnetic activity and, importantly, their time histories. <div onclick="openClose('a48')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a48" class="texter">
With a more capable representation of the organizing parameters and the target electron energy flux observations, PrecipNet achieves a >50% reduction in errors from a current state-of-the-art model (OVATION Prime), better captures the dynamic changes of the auroral flux, and provides evidence that it can capably reconstruct mesoscale phenomena. We create and apply a new framework for space weather model evaluation that culminates previous guidance from across the solar-terrestrial research community. The research approach and results are representative of the `new frontier' of space weather research at the intersection of traditional and data science-driven discovery and provides a foundation for future efforts.</br></br>
</div>
<br><br>
<span>
<a href="https://www.swsc-journal.org/articles/swsc/pdf/2021/01/swsc210064.pdf" target="_blank"><img src="./publications_files/specialissue_JSWSC.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Space Weather research in the Digital Age and across the full data lifecycle: Introduction to the Topical Issue <a href="https://www.swsc-journal.org/articles/swsc/pdf/2021/01/swsc210064.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>R. McGranaghan, <u>E. Camporeale</u>, M. Georgoulis, A. Anastasiadis (2021), <i> J. Space Weather Space Clim.</i>, 11(50). </h5>
The onset and rapid advance of the Digital Age have brought challenges and opportunities for scientific research characterized by a continuously evolving data landscape reflected in the four V’s of big data: volume, variety, veracity, and velocity. The big data landscape supersedes traditional means of storage, processing, management, and exploration, and requires adaptation and innovation across the full data lifecycle (i.e., collection, storage and processing, analytics, and representation). The Topical Issue, “Space Weather research in the Digital Age and across the full data lifecycle”, collects research from across the full data lifecycle (collection, management, analysis, and communication; collectively “Data Science”) and offers a tractable compendium that illustrates the latest computational and data science trends, tools, and advances for Space Weather research.
<div onclick="openClose('a47')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a47" class="texter">
We introduce the paradigm shift in Space Weather and the articles in the Topical Issue. We create a network view of the research that highlights the contribution to the change of paradigm and reveals the trends that will guide it hereafter.
</div>
<br><br>
</ol>
<h3>2020</h3>
<ol start=47; reversed>
<span>
<a href="./papers/Hu_2020_ApJ_900_86.pdf" target="_blank"><img src="./publications_files/CNN_reconnection.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Identifying Magnetic Reconnection in 2D Hybrid Vlasov Maxwell Simulations with Convolutional Neural Networks <a href="./papers/Hu_2020_ApJ_900_86.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>A. Hu, M. Sisti, F. Finelli, F. Califano, J. Dargent, M. Faganello, <u>E. Camporeale</u> , J. Teunissen (2020)</u> <i>Astrophys. J.</i>, 900, 1, 86</h5>
Magnetic reconnection is a fundamental process that quickly releases magnetic energy stored in a plasma. Identifying from simulation outputs where reconnection is taking place is nontrivial and, in general, has to be performed by human experts. Hence, it would be valuable if such an identification process could be automated. Here, we demonstrate that a machine-learning algorithm can help to identify reconnection in 2D simulations of collisionless plasma turbulence.
<div onclick="openClose('a46')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a46" class="texter">
Using a Hybrid Vlasov Maxwell model, a data set containing over 2000 potential reconnection events was generated and subsequently labeled by human experts. We test and compare two machine-learning approaches with different configurations on this data set. The best results are obtained with a convolutional neural network combined with an "image cropping" step that zooms in on potential reconnection sites. With this method, more than 70% of reconnection events can be identified correctly. The importance of different physical variables is evaluated by studying how they affect the accuracy of predictions. Finally, we also discuss various possible causes for wrong predictions from the proposed model.<p></p>
</br></br>
</div>
</br>
<span>
<a href="./papers/cerri2020.pdf" target="_blank"><img src="./publications_files/NHK.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Space-filter techniques for quasi-neutral hybrid-kinetic models <a href="./papers/cerri2020.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>S.S. Cerri, <u>E. Camporeale</u> (2020)</u> <i>Phys. Plasmas</i>, 27, 082102</h5>
The space-filter approach has been proved as a fundamental tool in studying turbulence in neutral fluids, providing the ability to analyze scale-to-scale energy transfer in configuration space. It is well known that turbulence in plasma presents challenges different from neutral fluids, especially when the scale of interest includes kinetic effects. The space-filter approach is still largely unexplored for kinetic plasma.
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<div id="a45" class="texter">
Here, we derive the space-filtered (or equivalently “coarse-grained”) equations in configuration space for a quasi-neutral hybrid-kinetic plasma model, in which ions are fully kinetic and electrons are a neutralizing fluid. Different models and closures for the electron fluid are considered, including finite electron-inertia effects and full electrons' pressure-tensor dynamics. Implications for the cascade of turbulent fluctuations in real space depending on different approximations are discussed.
<p></p>
</br></br>
</div>
</br>
<span>
<a href="./papers/16921113.pdf" target="_blank"><img src="./publications_files/dBdt.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>A gray-box model for a probabilistic estimate of regional ground magnetic perturbations: Enhancing the NOAA operational Geospace model with machine learning. <a href="./papers/16921113.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>E. Camporeale</u>, M.D. Cash, H. J. Singer, C. C. Balch, Z. Huang, G. Toth (2020)</u> <i> J. Geophys. Res.</i>, 125, e2019JA027684</h5>
We present a novel algorithm that predicts the probability that the time derivative of the
horizontal component of the ground magnetic field dB/dt exceeds a specified threshold at a given
location. This quantity provides important information that is physically relevant to geomagnetically
induced currents (GICs), which are electric currents associated with sudden changes in the Earth's magnetic
field due to space weather events.
<div onclick="openClose('a44')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a44" class="texter">
The model follows a “gray‐box” approach by combining the output of a
physics‐based model with machine learning. Specifically, we combine the University of Michigan's
Geospace model that is operational at the National Oceanic and Atmospheric Administration (NOAA) Space
Weather Prediction Center, with a boosted ensemble of classification trees. We discuss the problem of
recalibrating the output of the decision tree to obtain reliable probabilities. The performance of the model is
assessed by typical metrics for probabilistic forecasts: Probability of Detection and False Detection, True
Skill Statistic, Heidke Skill Score, and Receiver Operating Characteristic curve. We show that the
ML‐enhanced algorithm consistently improves all the metrics considered.
<p></p>
</br></br>
</div>
</br>
<span>
<a href="./papers/2019JA027618.pdf" target="_blank"><img src="./publications_files/Bayesian_VAP.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Bayesian inference of quasi-linear radial diffusion parameters using Van Allen Probes <a href="./papers/2019JA027618.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>R. Sarma, M. Chandorkar, I. Zhelavskaya, Y. Shprits, A. Drozdov, <u>E. Camporeale</u><i> J. Geophys. Res.</i>, 125, e2019JA027618. </h5>
The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is based on a quasi-linear approach with prescribed inner and outer boundary conditions. The 1-d diffusion model requires the knowledge of a diffusion coefficient and an electron loss timescale, which are typically parameterized in terms of various quantities such as the spatial (L) coordinate or a geomagnetic index (for example, Kp).
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<div id="a43" class="texter">
These terms are empirically derived, not directly measurable, and hence are not known precisely, due to the inherent non-linearity of the process and the variable boundary conditions. In this work, we demonstrate a probabilistic approach by inferring the values of the diffusion and loss term parameters, along with their uncertainty, in a Bayesian framework, where identification is obtained using the Van Allen Probe measurements. Our results show that the probabilistic approach statistically improves the performance of the model, compared to the parameterization employed in the literature.
<p></p>
</br></br>
</div>
<p></p>
<span>
<a href="./papers/Chandorkar_2020.pdf" target="_blank"><img src="./publications_files/mandar.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>DYNAMIC TIME LAG REGRESSION: PREDICTING WHAT AND WHEN. <a href="./papers/Chandorkar_2020.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>M. Chandorkar,<u> Camporeale, E.</u>, C. Furthlener, B. Poduval, M. Sebag (2020)</u> <i> International Conference on Learning Representations 2020</i></h5>
This paper tackles a new regression problem, called Dynamic Time-Lag Regression
(DTLR), where a cause signal drives an effect signal with an unknown time delay.
The motivating application, pertaining to space weather modelling, aims to predict
the near-Earth solar wind speed based on estimates of the Sun’s coronal magnetic
field. <div onclick="openClose('a42')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a42" class="texter">
DTLR differs from mainstream regression and from sequence-to-sequence
learning in two respects: firstly, no ground truth (e.g., pairs of associated sub-
sequences) is available; secondly, the cause signal contains much information
irrelevant to the effect signal (the solar magnetic field governs the solar wind prop-
agation in the heliosphere, of which the Earth’s magnetosphere is but a minuscule
region).
A Bayesian approach is presented to tackle the specifics of the DTLR problem,
with theoretical justifications based on linear stability analysis. A proof of concept
on synthetic problems is presented. Finally, the empirical results on the solar wind
modelling task improve on the state of the art in solar wind forecasting.
<p></p>
</br></br>
</div>
</ol>
<h3>2019</h3>
<ol start=42; reversed>
<span>
<a href="./papers/vida.pdf" target="_blank"><img src="./publications_files/vida.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>ViDA: a Vlasov-DArwin solver for plasma physics at electron scales. <a href="./papers/vida.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>O. Pezzi, Cozzani, G., Califano, F., Valentini, F., Guarrasi, M.,<u> Camporeale, E.</u>, ... & Veltri, P. (2019)</u> <i> Journal of Plasma Physics</i>, 85,5 </h5>
We present a Vlasov–DArwin numerical code (ViDA) specifically designed to
address plasma physics problems, where small-scale high accuracy is requested
even during the nonlinear regime to guarantee a clean description of the plasma
dynamics at fine spatial scales. <div onclick="openClose('a41')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a41" class="texter">
The algorithm provides a low-noise description of
proton and electron kinetic dynamics, by splitting in time the multi-advection Vlasov
equation in phase space. Maxwell equations for the electric and magnetic fields are
reorganized according to the Darwin approximation to remove light waves. Several
numerical tests show that ViDA successfully reproduces the propagation of linear and
nonlinear waves and captures the physics of magnetic reconnection. We also discuss
preliminary tests of the parallelization algorithm efficiency, performed at CINECA
on the Marconi-KNL cluster. ViDA will allow the running of Eulerian simulations
of a non-relativistic fully kinetic collisionless plasma and it is expected to provide
relevant insights into important problems of plasma astrophysics such as, for instance,
the development of the turbulent cascade at electron scales and the structure and
dynamics of electron-scale magnetic reconnection, such as the electron diffusion
region.
<p></p>
</br></br>
</div>
</br></br>
<span>
<a href="./papers/Camporeale-2019-Space_Weather.pdf" target="_blank"><img src="./publications_files/Grandchallenge.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>The challenge of machine learning in space weather nowcasting and forecasting. <a href="./papers/Camporeale-2019-Space_Weather.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>E. Camporeale </u> <i> Reviews of Geophysics, Grand Challenges in the Earth and Space Sciences</i></h5>
The numerous recent breakthroughs in machine learning make imperative to carefully
ponder how the scientific community can benefit from a technology that, although not necessarily new, is
today living its golden age. This Grand Challenge review paper is focused on the present and future role
of machine learning in Space Weather. The purpose is twofold. <div onclick="openClose('a40')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a40" class="texter">
On one hand, we will discuss previous
works that use machine learning for Space Weather forecasting, focusing in particular on the few
areas that have seen most activity: the forecasting of geomagnetic indices, of relativistic electrons at
geosynchronous orbits, of solar flares occurrence, of coronal mass ejection propagation time, and of solar
wind speed. On the other hand, this paper serves as a gentle introduction to the field of machine learning
tailored to the Space Weather community and as a pointer to a number of open challenges that we believe
the community should undertake in the next decade. The recurring themes throughout the review are
the need to shift our forecasting paradigm to a probabilistic approach focused on the reliable assessment of
uncertainties, and the combination of physics-based and machine learning approaches, known as gray box.
<p></p>
</br></br>
</div>
</br></br>
<span>
<a href="./papers/2018SW002026.pdf" target="_blank"><img src="./publications_files/reliability.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>On the Generation of Probabilistic Forecasts From Deterministic Models. <a href="./papers/2018SW002026.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>E. Camporeale </u>, Chu, X., Agapitov, O. V., Bortnik, J.<i> Space Weather</i>,17(3), 455-475 </h5>
Most of the methods that produce space weather forecasts are based on deterministic models.
In order to generate a probabilistic forecast, a model needs to be run several times sampling the input
parameter space, in order to generate an ensemble from which the distribution of outputs can be inferred.
However, ensemble simulations are costly and often preclude the possibility of real-time forecasting. We
introduce a simple and robust method to generate uncertainties from deterministic models, that does
not require ensemble simulations. <div onclick="openClose('a39')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a39" class="texter">The method is based on the simple consideration that a probabilistic
forecast needs to be both accurate and well calibrated (reliable). We argue that these two requirements are
equally important, and we introduce the Accuracy-Reliability cost function that quantitatively measures
the trade-off between accuracy and reliability. We then define the optimal uncertainties as the standard
deviation of the Gaussian distribution that minimizes the cost function. We demonstrate that this simple
strategy, implemented here by means of a deep neural network, produces accurate and well-calibrated
forecasts, showing examples both on synthetic and real-world space weather data.
<br><br>
<p></p>
</br></br>
</div>
</br></br>
<span>
<a href="./papers/Pezzi_Fourier_Hermite.pdf" target="_blank"><img src="./publications_files/Pezzi_hermite.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4> Fourier–Hermite decomposition of the collisional Vlasov–Maxwell system: implications for the velocity-space cascade.
<a href="./papers/Pezzi_Fourier_Hermite.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>Pezzi, O., Valentini, F., Servidio, S.,<u> Camporeale, E. </u>, & Veltri, P.<i> Plasma Physics and Controlled Fusion</i>, 61(5), 054005.</h5>
</br>
Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both
space and laboratory plasmas. Recently, new theories, in situ spacecraft observations and
numerical simulations suggest a novel scenario for turbulence, characterized by a so-called
phase-space cascade—the formation of fine structures, both in physical and velocity-space. <div onclick="openClose('a38')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a38" class="texter">
This
new concept is here extended by directly taking into account the role of inter-particle collisions,
modeled through the nonlinear Landau operator or the simplified Dougherty operator. The
characteristic times, associated with inter-particle correlations, are derived in the above cases.
The implications of introducing collisions on the phase-space cascade are finally discussed.
<br><br>
<p></p>
</br></br>
</div>
</ol>
<h3>2018</h3>
<ol start=38; reversed>
<span>
<a href="./papers/gruet_et_al_sw2018.pdf" target="_blank"><img src="./publications_files/lstm.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Multiple hours ahead forecast of the Dst index using a combination of Long Short-Term Memory neural network and Gaussian Process
<a href="./papers/gruet_et_al_sw2018.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>M. Gruet, M. Chandorkar, A. Sicard, <u>E. Camporeale</u> (2018), <i> Space Weather, </i> 16, 11 </h5>
</br>
In this study, we present a method that combines a Long Short-Term Memory (LSTM) recurrent
neural network with a Gaussian Process (GP) model to provide up to 6-hour ahead probabilistic
forecasts of the Dst geomagnetic index. The proposed approach brings together the sequence
modelling capabilities of a recurrent neural network with the error bars and confidence bounds
provided by a Gaussian process. <div onclick="openClose('a37')" style="cursor:hand; cursor:pointer"><font size="2.5"><u>More/Less</u> </font></div>
<div id="a37" class="texter">
Our model is trained using the hourly OMNI and GPS databases,
both of which are publicly available.We first develop a Long Short-Term Memory network to get a
single point prediction of Dst. This model yields great accuracy in forecasting the Dst index from 1h
ahead to 6h ahead, with a correlation coefficient always higher than 0.873 and a root mean square
error lower than 9.86. However, even if global metrics show excellent performance, it remains poor in
predicting intense storms (Dst<-250 nT) 6 hours in advance. To improve it and to obtain probabilistic
forecasts, we combine the LSTM model obtained with a Gaussian process, and evaluate the hybrid
predictor using the Receiver Operating Characteristic curve and the reliability diagram. We conclude
that this hybrid methodology provides improvements in the forecast of geomagnetic storms, from 1
hour to 6 hours ahead.
<br><br>
<p></p>
</br></br>
</div>
</br></br>
<span>
<a href="https://www.ann-geophys-discuss.net/angeo-2018-7/angeo-2018-7.pdf" target="_blank"><img src="./publications_files/cumulant.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Transfer entropy and cumulant based cost as measures of nonlinear causal relationships in space plasmas: applications to Dst
<a href="https://www.ann-geophys-discuss.net/angeo-2018-7/angeo-2018-7.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>J. Johnson, S. Wing, <u>E. Camporeale</u> (2018), <i> Ann. Geophys. </i> in press</h5>
</br>
It is well known that the magnetospheric response to the solar wind is nonlinear. Information theoretical tools such as mutual information, transfer entropy, and cumulant based analysis are able to characterize the nonlinearities in the system. Using cumulant based cost, we show that nonlinear significance of Dst peaks at 3 − 12 hours lags that can be attributed to V Bs, which also exhibit similar behavior. However, the nonlinear significance that peaks at lags 25, 50, and 90 hours can be attributed to internal dynamics, which may be related to the relaxation of the ring current.
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<div id="a36" class="texter">
These peaks are absent in the linear and nonlinear self-significance of V Bs. Our analysis with mutual information and transfer entropy show that both methods can establish that there are a strong correlation and transfer of information from Vsw to Dst at a time scale that is consistent with that obtained
from the cumulant based analysis. However, mutual information also shows that there is a strong correlation in the backward direction, from Dst to Vsw,
which is counterintuitive. In contrast, transfer entropy shows that there is no or little transfer of information from Dst to Vsw, as expected because it
is the solar wind that drives the magnetosphere, not the other way around. Our case study demonstrates that these information theoretical tools are quite
useful for space physics studies because these tools can uncover nonlinear dynamics that cannot be seen with the traditional analyses and models that
assume linear relationships.
<br><br>
<p></p>
</br></br>
</div>
</br></br>
<span>
<a href="https://arxiv.org/pdf/1711.00291" target="_blank"><img src="./publications_files/SW_turbulence.jpg" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Coherent structures and spectral energy transfer in turbulent plasma: a space-filter approach
<a href="https://arxiv.org/pdf/1711.00291" target="_blank" class="icon fa-download"></a></h4>
<h5><u>E. Camporeale</u>, L. Sorriso-Valvo, F. Califano, A. Retinò (2018), <i> Phys. Rev. Lett. </i> 120,125101</h5>
</br>
Plasma turbulence at scales of the order of the ion inertial length is mediated by several mechanisms, including linear wave damping, magnetic reconnection, the formation and dissipation of thin current sheets, and stochastic heating. It is now understood that the presence of localized coherent structures enhances the dissipation channels and the kinetic features of the plasma. However, no formal way of quantifying the relationship between scale-to-scale energy transfer and the presence of spatial structures has been presented so far. In the Letter we quantify such a relationship analyzing the results of a two-dimensional high-resolution Hall magnetohydrodynamic simulation. In particular, we employ the technique of space filtering to derive a spectral energy flux term which defines, in any point of the computational domain, the signed flux of spectral energy across a given wave number. The characterization of coherent structures is performed by means of a traditional two-dimensional wavelet transformation.
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<div id="a35" class="texter">
By studying the correlation between the spectral energy flux and the wavelet amplitude, we demonstrate the strong relationship between scale-to-scale transfer and coherent structures. Furthermore, by conditioning one quantity with respect to the other, we are able for the first time to quantify the inhomogeneity of the turbulence cascade induced by topological structures in the magnetic field. Taking into account the low space-filling factor of coherent structures (i.e., they cover a small portion of space), it emerges that 80% of the spectral energy transfer (both in the direct and inverse cascade directions) is localized in about 50% of space, and 50% of the energy transfer is localized in only 25% of space.
</div>
</ol>
<h3>2017</h3>
<ol start=35; reversed>
<span>
<a href="./papers/camporeale_JGR_2017.pdf" target="_blank"><img src="./publications_files/classification._GP.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Classification of Solar Wind with Machine Learning
<a href="./papers/camporeale_JGR_2017.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>E. Camporeale</u>, A. Carè, J. Borovsky (2017), <i> J. Geophys. Res.</i> </h5>
</br>
We present a four-category classification algorithm for the solar wind, based on Gaussian Process. The four categories are the ones previously adopted in Xu and Borovsky [2015]: ejecta, coronal hole origin plasma,
streamer belt origin plasma, and sector reversal origin plasma. The algorithm is trained and tested on a labeled portion of the OMNI dataset. It uses seven
inputs: the solar wind speed V sw , the temperature standard deviation σ T , the sunspot number R, the f 10.7 index, the Alfven speed v A , the proton specific
entropy Sp and the proton temperature Tp compared to a velocity-dependent expected temperature. The output of the Gaussian Process classifier is a four
element vector containing the probabilities that an event (one reading from the hourly-averaged OMNI database) belongs to each category.
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<div id="a34" class="texter">
The probabilistic nature of the prediction allows for a more informative and flexible interpretation of the results, for instance being able to classify events as ’undecided’. The new method has a median accuracy larger than 90% for all categories, even using a small set of data for training. The Receiver Operating Characteristic curve and the reliability diagram also demonstrate the excellent quality of this new method. Finally, we use the algorithm to classify a large portion of the OMNI dataset, and we present for the first time transition probabilities between different solar wind categories. Such probabilities represent the ’climatological’ statistics that determine the solar wind baseline.
<br><br>
</div>
<p></p>
<span>
<a href="./papers/swe20479.pdf" target="_blank"><img src="./publications_files/DST_GP.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Probabilistic Forecasting of the Disturbance Storm Time Index: An Autoregressive Gaussian Process approach
<a href="./papers/swe20479.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>M. Chandorkar, <u>E. Camporeale</u>, S. Wing (2017), <i> Space Weather</i>, 15, 1004 </h5>
</br>
We present a methodology for generating probabilistic predictions for the Disturbance Storm Time(Dst) geomagnetic activity index. We focus on the One Step Ahead prediction task and use the OMNI hourly resolution data to build our models. Our proposed methodology is based on the technique of Gaussian Process Regression. Within this framework we develop two models; Gaussian Process Autoregressive (GP-AR) and Gaussian Process Autoregressive with eXogenous inputs (GP-ARX).
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<div id="a33" class="texter">
We also propose a criterion to aid model selection with respect to the order of autoregressive inputs. Finally, we test the performance of the GP-AR and GP-ARX models on a set of 63 geomagnetic storms between 1998 and 2006 and illustrate sample predictions with error bars for some of these events.
<br><br>
</div>
<p></p>
<span>
<a href="./papers/1612.07827.pdf" target="_blank"><img src="./publications_files/UQ_1D.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Adaptive selection of sampling points for uncertainty quantification
<a href="./papers/1612.07827.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>Camporeale, E. </u>, Agnihotri, A., Rutjes, C. (2017), <i> Int. J. Uncertainty Quant.</i>, </h5>
We present a simple and robust strategy for the selection of sampling points in Uncertainty Quantification. The goal
is to achieve the fastest possible convergence in the cumulative distribution function of a stochastic output of interest.
We assume that the output of interest is the outcome of a computationally expensive nonlinear mapping of an input
random variable, whose probability density function is known. We use a radial function basis to construct an accurate
interpolant of the mapping. This strategy enables adding new sampling points one at a time, adaptively. This takes
into full account the previous evaluations of the target nonlinear function.
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<div id="a32" class="texter">
We present comparisons with a stochastic
collocation method based on the Clenshaw-Curtis quadrature rule, and with an adaptive method based on hierarchical
surplus, showing that the new method often results in a large computational saving
<br><br>
</div>
<p></p>
<span>
<a href="./papers/electron_inertia_and_quasineutrality_in_the_weibel_instability.pdf" target="_blank"><img src="./publications_files/weibel.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Electron inertia and quasi-neutrality in the Weibel instability
<a href="./papers/electron_inertia_and_quasineutrality_in_the_weibel_instability.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>E. Camporeale</u>, C. Tronci (2017), <i> J. Plasma Phys.,</i> 83</h5>
While electron kinetic effects are well known to be of fundamental importance in
several situations, the electron mean-flow inertia is often neglected when length scales
below the electron skin depth become irrelevant. This has led to the formulation of
different reduced models, where electron inertia terms are discarded while retaining
some or all kinetic effects. Upon considering general full-orbit particle trajectories, this
paper compares the dispersion relations emerging from such models in the case of the
Weibel instability. As a result, the question of how length scales below the electron
skin depth can be neglected in a kinetic treatment emerges as an unsolved problem,
since all current theories suffer from drawbacks of different nature.
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<div id="a31" class="texter">
Alternatively,
we discuss fully kinetic theories that remove all these drawbacks by restricting to
frequencies well below the plasma frequency of both ions and electrons. By giving
up on the length scale restrictions appearing in previous works, these models are
obtained by assuming quasi-neutrality in the full Vlasov–Maxwell system.
<br><br>
</div>
<p></p>
<span>
<a href="./papers/comparison_of_linear_modes_in_kinetic_plasma_models.pdf" target="_blank"><img src="./publications_files/linear_theory.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Comparison of linear modes in kinetic plasma models
<a href="./papers/comparison_of_linear_modes_in_kinetic_plasma_models.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>Camporeale, E. </u> & Burgess, D (2017), <i> J. Plasma Phys.</i>, 83</h5>
We compare, in an extensive and systematic way, linear theory results obtained
with the hybrid (ion kinetic and electron fluid), the gyrokinetic and the fully kinetic
plasma models. We present a test case with parameters that are relevant for solar
wind turbulence at small scales, which is a topic now recognized to need a kinetic
treatment, to a certain extent.
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<div id="a30" class="texter">
We comment on the comparison of low-frequency
single modes (Alfvén/ion-cyclotron, ion-acoustic and fast modes) for a wide range of
propagation angles, and on the overall spectral properties of the linear operators, for
quasi-perpendicular propagation. The methodology and the results presented in this
paper will be valuable when choosing which model should be used in regimes where
the assumptions of each model are not trivially satisfied.
<br><br>
</div>
<p></p>
<span>
<a href="./papers/dawn-dusk.pdf" target="_blank"><img src="./publications_files/dawn-dusk.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Dawn-dusk asymmetries in the auroral particle precipitation and their modulations by substorms
<a href="./papers/dawn-dusk.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>Wing, S., Johnson, J.,<u> Camporeale, E.</u> (2017), <i> AGU Monograph</i>, in press</h5>
</ol>
<h3>2016</h3>
<ol start=29; reversed>
<span>
<a href="./papers/camporeale_SW16_for_arxiv.pdf" target="_blank"><img src="./publications_files/UQ_VERB.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>On the propagation of uncertainties in radiation belt simulations
<a href="./papers/camporeale_SW16_for_arxiv.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>Camporeale, E.</u>, Y. Shprits, M. Chandorkar, A. Drozdov, S. Wing (2016),<i> Space Weather</i></h5>
We present the first study of the uncertainties associated with radiation belt
simulations, performed in the standard quasi-linear diffusion framework. In particular,
we estimate how uncertainties of some input parameters propagate through the nonlinear simulation, producing a distribution of outputs that can be quite broad.
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<div id="a29" class="texter">
Here, we restrict our focus on two-dimensional simulations (in energy and pitch angle space) of
parallel-propagating chorus waves only, and we study as stochastic input parameters the
geomagnetic index K p (that characterizes the time dependency of an idealized storm),
the latitudinal extent of waves, and the average electron density. We employ a colloca-
tion method, thus performing an ensemble of simulations. The results of this work point
to the necessity of shifting to a probabilistic interpretation of radiation belt simulation
results, and suggest that an accurate specification of a time-dependent density model
is crucial for modeling the radiation environment.
<br><br>
</div>
<p></p>
<span>
<a href="./papers/thor.pdf" target="_blank"><img src="./publications_files/thor.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Turbulence Heating ObserveR – satellite mission proposal
<a href="./papers/thor.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>A. Vaivads et al. (2016), <i> J. Plasma Phys.</i>, 82</h5>
The Universe is permeated by hot, turbulent, magnetized plasmas. Turbulent plasma is
a major constituent of active galactic nuclei, supernova remnants, the intergalactic and
interstellar medium, the solar corona, the solar wind and the Earth’s magnetosphere,
just to mention a few examples. Energy dissipation of turbulent fluctuations plays
a key role in plasma heating and energization, yet we still do not understand the
underlying physical mechanisms involved.
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<div id="a28" class="texter">
THOR is a mission designed to answer
the questions of how turbulent plasma is heated and particles accelerated, how the
dissipated energy is partitioned and how dissipation operates in different regimes of
turbulence. THOR is a single-spacecraft mission with an orbit tuned to maximize
data return from regions in near-Earth space – magnetosheath, shock, foreshock and
pristine solar wind – featuring different kinds of turbulence. Here we summarize the
THOR proposal submitted on 15 January 2015 to the ‘Call for a Medium-size mission
opportunity in ESAs Science Programme for a launch in 2025 (M4)’. THOR has been
selected by European Space Agency (ESA) for the study phase.
<br><br>
</div>
<p></p>
<span>
<a href="./papers/wing2016.pdf" target="_blank"><img src="./publications_files/wing.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Information theoretical approach to discovering solar wind drivers of the outer radiation belt
<a href="./papers/wing2016.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>Wing, S., Johnson, J., <u>Camporeale, E.</u>, Reeves, G. (2016), <i> J. Geophys. Res.</i>, 121 </h5>
The solar wind-magnetosphere system is nonlinear. The solar wind drivers of geosynchronous electrons with energy range of 1.8–3.5 MeV are investigated using mutual information, conditional mutual information (CMI), and transfer entropy (TE). These information theoretical tools can establish linear and nonlinear relationships as well as information transfer.
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<div id="a27" class="texter">
The information transfer from solar wind velocity (Vsw) to geosynchronous MeV electron flux (Je) peaks with a lag time of 2 days. As previously reported, Je is anticorrelated with solar wind density (nsw) with a lag of 1 day. However, this lag time and anticorrelation can be attributed at least partly to the Je(t + 2 days) correlation with Vsw(t) and nsw(t + 1 day) anticorrelation with Vsw(t). Analyses of solar wind driving of the magnetosphere need to consider the large lag times, up to 3 days, in the (Vsw, nsw) anticorrelation. Using CMI to remove the effects of Vsw, the response of Je to nsw is 30% smaller and has a lag time < 24 h, suggesting that the MeV electron loss mechanism due to nsw or solar wind dynamic pressure has to start operating in < 24 h. nsw transfers about 36% as much information as Vsw (the primary driver) to Je. Nonstationarity in the system dynamics is investigated using windowed TE. When the data are ordered according to transfer entropy value, it is possible to understand details of the triangle distribution that has been identified between Je(t + 2 days) versus Vsw(t).
<br><br>
</div>
<p></p>
<span>
<a href="./papers/1.4940963.pdf" target="_blank"><img src="./publications_files/recurrence.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Collisional effects on the numerical recurrence in Vlasov-Poisson simulations
<a href="./papers/1.4940963.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>Pezzi, O., <u>E. Camporeale</u>, F. Valentini (2016), <i> Phys. Plasmas</i>, 23, 022103</h5>
The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. {\bf 112}, 1456--1459 (1958)]. By decomposing the linear
Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability.
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<div id="a26" class="texter">
The analysis is then confirmed and extended to the nonlinear regime through a Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used, an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales, can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.
<br><br>
</div>
<p></p>
<span>
<a href="./papers/camporeale_cpc_15.pdf" target="_blank"><img src="./publications_files/hermite.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>On the velocity space discretization for the
Vlasov-Poisson system: comparison between implicit
Hermite spectral and Particle-in-Cell methods
<a href="./papers/camporeale_cpc_15.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>Camporeale, E.</u>, G.L. Delzanno, B.K Bergen, J.D. Moulton (2016), <i>Comp. Phys. Comm.</i>, 198, 47-58</h5>
We describe a spectral method for the numerical solution of the Vlasov-
Poisson system where the velocity space is decomposed by means of an Hermite
basis, and the configuration space is discretized via a Fourier decomposition.
The novelty of our approach is an implicit time discretization that
allows exact conservation of charge, momentum and energy.
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<div id="a25" class="texter">
The computational
efficiency and the cost-effectiveness of this method are compared to the
fully-implicit PIC method recently introduced by Markidis and Lapenta [52]
and Chen et al. [15]. The following examples are discussed: Langmuir wave,
Landau damping, ion-acoustic wave, two-stream instability. The Fourier-
Hermite spectral method can achieve solutions that are several orders of
magnitude more accurate at a fraction of the cost with respect to PIC. <br><br>
</div>
<p></p>
</ol>
<h3>2015</h3>
<ol start=24; reversed>
<p></p>
<span>
<a href="./papers/1.4929853.pdf" target="_blank"><img src="./publications_files/zimbardo.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Wave-particle interactions with parallel whistler waves: nonlinear and time-dependent effects revealed by Particle-in-Cell simulations
<a href="./papers/1.4929853.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>Camporeale, E.</u> & Zimbardo, G. (2015), <i> Phys. Plasmas</i> <b>22</b>, 092104</h5>
We present self-consistent Particle-in-Cell simulations of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earth's radiation belt.
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<div id="a2" class="texter">
By tracking PIC particles, and comparing with test-particles simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi-linear theory routinely used in radiation belt studies. In particular we show that pitch angle diffusion is enhanced during the linear growth phase, and it rapidly saturates. We discuss how the saturation is related to the fact that the domain in which the particles' pitch angle diffuse is bounded, and to the well-known problem of 90∘ diffusion barrier. <br><br>
</div>
<p></p>
<span>
<a href="./papers/10.1002_2015GL063874.pdf" target="_blank"><img src="./publications_files/resonant.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Resonant and non-resonant whistlers-particle interaction in the radiation belts
<a href="./papers/10.1002_2015GL063874.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>Camporeale, E.</u> (2015), <i> Geophys. Res. Lett., 42</i>, 3114-3121,</h5>
We study the wave-particle interactions between lower band chorus whistlers and an anisotropic tenuous population of
relativistic electrons.
We present the first direct comparison of first-principle Particle-in-Cell (PIC) simulations with a quasi-linear diffusion code.
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<div id="a1" class="texter">
In the PIC approach, the waves are self-consistently generated by the temperature anisotropy instability that quickly
saturates and relaxes the system towards marginal stability.
We show that the quasi-linear diffusion and PIC results have significant quantitative mismatch
in regions of energy/pitch angle where the resonance condition is not satisfied.
Moreover, for pitch angles close to the loss cone the diffusion code overestimates the scattering, particularly
at low energies.
This suggests that higher order nonlinear theories should be taken in consideration
in order to capture non-resonant interactions, resonance broadening, and to account for scattering at angles close to 90 degress. <br><br>
</div>
<p></p>
<span>
<a href="./papers/1.4907665.pdf" target="_blank"><img src="./publications_files/tronci.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Neutral Vlasov kinetic theory of magnetized plasmas
<a href="./papers/1.4907665.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>Tronci, C. & <u>Camporeale, E.</u> (2015), <i> Phys. Plasmas., </i> 22, 020704</h5>
The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects.
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<div id="a3" class="texter">
Euler-Poincare' reduction theory is used to show that the neutral Vlasov kinetic theory possesses a variational formulation in both Lagrangian and Eulerian coordinates. By construction, the model recovers all collisionless neutral models employed in plasma simulations. Then, comparisons between the neutral Vlasov system and hybrid kinetic-fluid models are presented in the linear regime. <br><br>
</div>
<p></p>
<span>
<a href="./papers/0963-0252_24_2_025014.pdf" target="_blank"><img src="./publications_files/plume.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Approximate semi-analytical solutions for the steady-state expansion of a contactor plasma
<a href="./papers/0963-0252_24_2_025014.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5><u>Camporeale, E.</u>, E. Hogan, E. MacDonald (2015)<i> Plasma Sources Sci. Technol.</i>, <b> 24 </b>, 025014</h5>
We study the steady-state expansion of a collisionless, electrostatic, quasi-
neutral plasma plume into vacuum, with a fluid model. We analyze approximate
semi-analytical solutions, that can be used in lieu of much more expensive numerical
solutions.
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<div id="a24" class="texter">
In particular, we focus on the earlier studies presented in Parks and Katz
(1979) [1], Korsun and Tverdokhlebova (1997) [2], and Ashkenazy and Fruchtman
(2001) [3]. By calculating the error with respect to the numerical solution, we can
judge the range of validity for each solution. Moreover, we introduce a generalization
of earlier models that has a wider range of applicability, in terms of plasma injection
profiles. We conclude by showing a straightforward way to extend the discussed
solutions to the case of a plasma plume injected with non-null azimuthal velocity.
<br><br>
</div>
<p></p>
<span>
<a href="./papers/Haynes_PoP_2015.pdf" target="_blank"><img src="./publications_files/hole.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
</span>
<li>
<h4>Electron vortex magnetic holes: a nonlinear coherent plasma structure
<a href="./papers/Haynes_PoP_2015.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>Haynes, C. T., Burgess, D., <u>Camporeale, E.</u>, & Sundberg, T. (2015), <i>Phys. Plasmas</i> 22, 012309</h5>
We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional PIC simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits.
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The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas. <br><br>
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<h3>2014</h3>
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<a href="./papers/1.4901583.pdf" target="_blank"><img src="./publications_files/kaw.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
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<h4>Vlasov simulations of kinetic Alfven waves at proton kinetic scales
<a href="./papers/1.4901583.pdf" target="_blank" class="icon fa-download"></a></h4>
<h5>Vasconez, C. L., Valentini, F., <u>Camporeale, E.</u>, & Veltri, P. (2014), <i>Phys. Plasmas</i>, 21(11), 112107</h5>
Kinetic Alfvén waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton gyro radius ρp and/or inertial length dp and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems.
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In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfvén waves at proton kinetic scales, in typical conditions of the solar wind environment (proton plasma beta βp = 1). In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to dp and βp ≃ 1 (for which ρp ≃ dp ) the kinetic Alfvén waves have small phase speed compared to the proton thermal velocity, wave-particle interaction processes produce significant deformations in the core of the particle velocity distribution, appearing as phase space vortices and resulting in flat-top velocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithm allows for a clean almost noise-free description of the velocity space, three-dimensional plots of the proton velocity distribution help to emphasize how the plasma departs from the Maxwellian configuration of thermodynamic equilibrium due to nonlinear kinetic effects. <br><br>
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<a href="http://arxiv.org/pdf/1403.2773v2" target="_blank"><img src="./publications_files/hybrid_MHD.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
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<h4>Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian
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<h5>Tronci, C., Tassi, E., <u>Camporeale, E.</u>, & Morrison, P. J. (2014), <i>Plasma Phys. and Controlled Fusion </i> 56 095008</h5>
This paper investigates hybrid kinetic-magnetohydrodynamic (MHD) models, where a hot plasma (governed by a kinetic theory) interacts with a fluid bulk (governed by MHD). Different nonlinear coupling schemes are reviewed, including the pressure-coupling scheme (PCS) used in modern hybrid simulations.
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This latter scheme suffers from being non-Hamiltonian and is unable to exactly conserve total energy. Upon adopting the Vlasov description for the hot component, the non-Hamiltonian PCS and a Hamiltonian variant are compared. Special emphasis is given to the linear stability of Alfvén waves, for which it is shown that a spurious instability appears at high frequency in the non-Hamiltonian version. This instability is removed in the Hamiltonian version.<br><br>
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<a href="./papers/Haynes_ApJ2014.pdf" target="_blank"><img src="./publications_files/haynes.png" width=10% align="left" alt="" style="margin:0px 50px 10px 0px; border-radius: 15%;"></a>
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<h4>Reconnection and electron temperature anisotropy in sub-proton scale plasma turbulence
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<h5>Haynes, C. T., Burgess, D., & <u>Camporeale, E.</u> (2014), <i>Astrophys. J. </i> 783(1), 38</h5>
Knowledge of turbulent behavior at sub-proton scales in magnetized plasmas is important for a full understanding of the energetics of astrophysical flows such as the solar wind. We study the formation of electron temperature anisotropy due to reconnection in the turbulent decay of sub-proton scale fluctuations using two-dimensional, particle-in-cell plasma simulations with a realistic electron-proton mass ratio and a guide field perpendicular to the simulation plane.
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A power spectrum fluctuation with approximately power-law form is created down to scales of the order of the electron gyroradius. We identify the signatures of collisionless reconnection at sites of X-point field geometry in the dynamic magnetic field topology, which gradually relaxes in complexity. The reconnection sites are generally associated with regions of strong parallel electron temperature anisotropy. The evolving topology of magnetic field lines connected to a reconnection site allows for the spatial mixing of electrons accelerated at multiple, spatially separated reconnection regions. This leads to the formation of multi-peaked velocity distribution functions with strong parallel temperature anisotropy. In a three-dimensional system that can support the appropriate wave vectors, the multi-peaked distribution functions would be expected to be unstable to kinetic instabilities, contributing to dissipation. The proposed mechanism of anisotropy formation is also relevant to space and astrophysical systems where the evolution of the plasma is constrained by linear temperature anisotropy instability thresholds. The presence of reconnection sites leads to electron energy gain, nonlocal velocity space mixing, and the formation of strong temperature anisotropy; this is evidence of an important role for reconnection in the dissipation of turbulent fluctuations. <br><br>
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<h3>2013 and before</h3>
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</li><li>Delzanno, G. L., <u>Camporeale, E.</u>, Moulton, J. D., Borovsky, J. E., MacDonald, E. A., & Thomsen, M. F. (2013)<br>
<b>CPIC: A Curvilinear Particle-in-Cell Code for Plasma--Material Interaction Studies.</b><br>
<i> IEEE Transactions on Plasma Science</i>, 41, 12, 3577
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We describe a new electrostatic particle-in-cell (PIC) code in curvilinear geometry called curvilinear PIC (CPIC). The code models the microscopic (kinetic) evolution of a plasma with the PIC method, coupled with an adaptive computational grid that can conform to arbitrarily shaped domains. CPIC is particularly suited for multiscale problems associated with the interaction of complex objects with plasmas. A map is introduced between the physical space and the logical space, where the grid is uniform and Cartesian. In CPIC, most of the operations are performed in logical space. CPIC was designed following criteria of versatility, robustness, and performance. Its main features are the use of structured meshes, a scalable field solver based on the black box multigrid algorithm and a hybrid mover, where particles' position is in logical space while the velocity is in physical space. Test examples involving the interaction of a plasma with material boundaries are presented. <br><br>
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