Cosmic Rays Research Articles

Explaining Muon Excess in Cosmic Rays Using the Gluon Condensation Model

Ultrahigh-energy cosmic rays are often characterized indirectly by analyzing the properties of secondary cosmic ray particles produced in the collisions with air nuclei. The particle number N μ of muon and the depth of shower maximum X max after air shower cascade are mostly studied to infer the energy and mass of the incident cosmic rays. Research has shown that there is a significant excess in the observed number of muons arriving at the ground from extensive air showers compared to the simulations using the existing cosmic ray hadronic interaction model. To explain this muon excess phenomenon, a new theoretical model, the gluon condensation model, is introduced in this paper and simulated by using the AIRES engine. We assume that the gluon condensation (GC) effect appears mainly in the first collision of the cascade, leading to a significant increase in the strangeness production, consequently, the production rate of kaons is increased, and n K /n π is greater than the value of the usual hadronic interaction process. In the calculation, the model assumes that only pions and kaons are produced in the GC state. The increase of strange particle yield would mean that the energy transferred from the hadronic cascade to the electromagnetic cascade through π 0 → 2γ decay is reduced. This would in turn increase the number of muons at the ground level due to meson decays. Our model provides a new theoretical possibility to explain the muon excess puzzle.

Origin of the break in the cosmic-ray electron plus positron spectrum at ∼1 TeV

Recent measurements of the cosmic-ray electron plus positron spectrum in several experiments have confirmed the presence of a break at ∼1 TeV. The origin of the break is still not clearly understood. In this work, we explored different possibilities for the origin, which include an electron source spectrum with a broken power law, a power law with an exponential or super-exponential cutoff, and the absence of potential nearby cosmic-ray sources. Based on the observed electron plus positron data from the DAMPE and the H.E.S.S experiments, and considering supernova remnants as the main sources of cosmic rays in the Galaxy, we find statistical evidence in favor of the scenario with a broken power-law source spectrum, with the best-fit source parameters obtained as Γ = 2.39 for the source spectral index, E0 ≈ 1.6 TeV for the break energy, and f = 1.59 × 1048 ergs for the amount of supernova kinetic energy injected into cosmic-ray electrons. This power-law break in the spectrum has been predicted for electrons confined inside supernova remnants after acceleration via diffusive shock acceleration process, and also indicated by the multi-wavelength study of supernova remnants. All of this evidence shows that the observed spectral break provides a strong indication of a direct link between cosmic-ray electrons and their sources. Our findings further show that electrons must undergo spectral changes while escaping the source region in order to reconcile the difference between the spectral index of electrons observed inside supernova remnants and that obtained from Galactic cosmic-ray propagation studies.

Galactic cosmic ray environment predictions for the NASA BioSentinel Mission, part 2:Post-mission validation

The BioSentinel CubeSat was deployed on the Artemis-I mission in November 2022 and has been continuously transmitting physical measurements of the space radiation environment since that time. Just before mission launch, we published computational model predictions of the galactic cosmic ray exposure expected inside BioSentinel for multiple locations and configurations. The predictions utilized models for the ambient galactic cosmic ray environment, radiation physics and transport, and BioSentinel geometry. Now that the nominal six-month BioSentinel mission has completed and some additional time has passed, those pre-launch predictions and additional model components can be validated. Dose-rate and linear energy transfer (LET) spectral measurements from the on-board dosimeter are presented along with a summary of the computational models used to calculate exposure quantities of interest. Sensitivity tests are performed to gauge the impact of various model choices on these quantities. Satellite data collected during the BioSentinel mission are used to provide some measure of independent validation for the galactic cosmic ray model used in the present calculations. It is shown that the combined models are in excellent agreement with the measured dose-rate. Model calculations agree well with measurement below ∼10 keV/µm and underpredict at higher LET. It is argued that the underprediction is likely due to detector response or low energy anomalous cosmic ray contributions able to reach the thinly shielded side of the on-board dosimeter.

Quiescent black hole X-ray binaries as multi-messenger sources

The origin of Galactic cosmic rays (CRs) is unknown even though they have traditionally been connected to supernovae based on energetic arguments. In the past decades, Galactic black holes in X-ray binaries (BHXBs) have been proposed as candidate sources of CRs, which revises the CR paradigm. BHXBs launch two relativistic jets during their outbursts, but recent observations suggested that these jets may be launched even during quiescence. A0620−00 is a well-studied object that shows indications of jet emission. We study the simultaneous radio-to-X-ray spectrum of this source that was detected while the source was in quiescence to better constrain the jet dynamics. Because most BHXBs spend their lifetimes in quiescence (qBHXBs), we used the jet dynamics of A0620−00 to study a population of 105 such sources distributed throughout the Galactic disc, and a further 104 sources that are located in the boxy bulge around the Galactic centre. While the contribution to the CR spectrum is suppressed, we find that the cumulative intrinsic emission of qBHXBs from both the boxy bulge and from the Galactic disc adds to the diffuse emission that various facilities detected from radio to TeV γ rays. We examined the contribution of qBHXBs to the Galactic diffuse emission and investigated the possibility of SKA, INTEGRAL, and CTAO to detect individual sources in the future. Finally, we compare the predicted neutrino flux to the recently presented Galactic diffuse neutrino emission by IceCube.

Variations in the Inferred Cosmic-Ray Spectral Index as Measured by Neutron Monitors in Antarctica

A technique has recently been developed for tracking short-term spectral variations in Galactic cosmic rays (GCRs) using data from a single neutron monitor (NM), by collecting histograms of the time delay between successive neutron counts and extracting the leader fraction L as a proxy of the spectral index. Here we analyze L from four Antarctic NMs from 2015 March to 2023 September. We have calibrated L from the South Pole NM with respect to a daily spectral index determined from published data of GCR proton fluxes during 2015–2019 from the Alpha Magnetic Spectrometer (AMS-02) on board the International Space Station. Our results demonstrate a robust correlation between the leader fraction and the spectral index fit over the rigidity range 2.97–16.6 GV for AMS-02 data, with uncertainty of 0.018 in the daily spectral index as inferred from L. In addition to the 11 yr solar activity cycle, a wavelet analysis confirms a 27 day periodicity in the GCR flux and spectral index corresponding to solar rotation, especially near sunspot minimum, while the flux occasionally exhibits a strong harmonic at 13.5 days. The magnetic field component along a nominal Parker spiral (i.e., the magnetic sector structure) is a strong determinant of such spectral and flux variations, with the solar wind speed exerting an additional, nearly rigidity-independent influence on flux variations. Our investigation affirms the capability of ground-based NM stations to accurately and continuously monitor cosmic-ray spectral variations over the long-term future.

Galactic outflows in different geometries

In the gravitational potential well of a galaxy, the behavior of outflows has been studied in different geometries i.e. constant flux tube, divergent and extreme divergent environments. First of all, we describe the hydrodynamic model by which we approach the outflows system. This model treats all the waves as fluids and applies fluid mechanics to them(cosmic rays, thermal plasma & Alfvén wave). Whereas outflows mean the gas regime above and below the center of the galactic disk, and we have taken it as a system where interaction between cosmic rays and plasma occurs. After discussing the hydrodynamic three-fluid model, we define three geometrical structures which can be acquired by outflows and relate these structures with thermal plasma, cosmic and Alfvén waves pressures, thus seeking for its behavior. The solution of the system is categorically divided into three branches, supersonic, subsonic and unphysical solutions.The most interesting of all is the transonic solution, a solution that evolves from subsonic to supersonic. First of all, we discuss only thermal plasma outflows and explain their evolution in three cases of outflows environments, followed by the addition of cosmic waves and Alfvén waves. After discussing three fluid outflows in different structures, we compared the results of thermal outflows with three fluid outflows and see how the addition of waves in the system affects the dynamics of the system. At last, the findings of this paper are discussed.

Proton Predominance At UHE Cosmic Rays Through Analysis Of Different Mass Composition Models

Recently, detection of giant (1017 to 1020eV ) and super giant ( Ep >1020 eV ) air showers is gaining importance as the investigation of EAS in these energy ranges is expected to give necessary information on characteristics of high energy nuclear interactions in one hand and for solving the astrophysical problem of Cosmic Ray origin , beyond the Greisen-Zatsepin-Kuzmin cut-off energy near 1020 eV. Due to the very low Cosmic Ray flux in the UHE range ( > 1017 eV ) direct measurement by balloons or satellites are not possible. The experimental approach realized conventionally uses extended ground-based installations catching data of the induced air showers . An alternative approach is to use a low cost particle detector array called mini-array for detecting UHE cosmic rays by Linsley’s method of arrival time measurement. The miniarray consist of eight plastic scintillation counters covering an area of 2m2 operating for detecting EAS particles of primary energy 1017 -1018 eV based on Linsley’s method of arrival time measurement. An optical detector (5 inch diameter PMT) has been installed at the centre of the miniarray to record the associated optical Cerenkov pulse produced by the ultra-relativistic shower particles in the atmosphere with an aim to derive primary mass composition above 1017 eV. Optical pulses are recorded in one channel of the DSO and the stored data in the wave form memory are transferred to the computer via GPIB interface. The particle detector pulses are triggered with the help of trigger circuit and recorded through other channel of the DSO and transferred to the same DSO. However, the data are subjected to large fluctuation both in particle detection and optical photon detection. Primary energy is estimated through the parameter shower size which is also indirectly measured from a small sample of shower front using miniarray data. Mass composition estimated indirectly relies on simulation model. On the basis of pulse height distribution measurement, the inferred mass composition is predominantly protons, with a tendency of mass composition becoming lighter at the highest energies.

A new analytic approach to infer the cosmic-ray ionization rate in hot molecular cores from HCO+, N2H+, and CO observations

Context. The cosmic-ray ionization rate (ζ2) is one of the key parameters in star formation, since it regulates the chemical and dynamical evolution of molecular clouds by ionizing molecules and determining the coupling between the magnetic field and gas. Aims. However, measurements of ζ2 in dense clouds (e.g., nH ≥ 104 cm−3) are difficult and sensitive to the model assumptions. The aim is to find a convenient analytic approach that can be used in high-mass star-forming regions (HMSFRs), especially for warm gas environments such as hot molecular cores (HMCs). Methods. We propose a new analytic approach to calculate ζ2 through HCO+, N2H+, and CO measurements. By comparing our method with various astrochemical models and with observations found in the literature, we identify the parameter space for which the analytic approach is applicable. Results. Our method gives a good approximation, to within 50%, of ζ2 in dense and warm gas (e.g., nH ≥ 104 cm−3, T = 50, 100 K) for AV ≥ 4 mag and t ≥ 2 × 104 yr at Solar metallicity. The analytic approach gives better results for higher densities. However, it starts to underestimate ζ2 at low metallicity (Z = 0.1 Z⊙) when the value is too high (ζ2 ≥ 3 × 10−15 s−1). By applying our method to the OMC-2 FIR4 envelope and the L1157-B1 shock region, we find ζ2 values of (1.0 ± 0.3) × 10−14 s−1 and (2.2 ± 0.4) × 10−16 s−1, consistent with those previously reported. Conclusions. We calculate ζ2 toward a total of 82 samples in HMSFRs, finding that the average value of ζ2 toward all HMC samples (ζ2 = (7.4±5.0)×10−16 s−1) is more than an order of magnitude higher than the theoretical prediction of cosmic-ray attenuation models, favoring the scenario that locally accelerated cosmic rays in embedded protostars should be responsible for the observed high ζ2.

A Yebes W-band Line Survey towards an Unshocked Molecular Cloud of Supernova Remnant 3C 391: Evidence of Cosmic-Ray-Induced Chemistry

Cosmic rays (CRs) have strong influences on the chemistry of dense molecular clouds (MCs). To study the detailed chemistry induced by CRs, we conducted a Yebes W-band line survey towards an unshocked MC (which we named 3C391:NML) associated with supernova remnant 3C 391. We detected emission lines of 18 molecular species in total and estimated their column densities with local thermodynamic equilibrium (LTE) and non-LTE analysis. Using the abundance ratio N(HCO+)/N(CO) and an upper limit of N(DCO+)/N(HCO+), we estimated that the CR ionization rate of 3C391:NML is ζ ≳ 2.7 × 10−14 s−1 with an analytic method. However, we caution against adopting this value because chemical equilibrium, which is a prerequisite of using the equations, is not necessarily reached in 3C391:NML. We observed lower N(HCO+)/N(HOC+), higher N(HCS+)/N(CS), and higher X(l-C3H+) by an order of magnitude in 3C391:NML than the typical values in quiescent dense MCs. We found that an enhanced CR ionization rate (of order ∼10−15 or ∼10−14 s−1) is needed to reproduce the observation with a chemical model. This is higher than the values found in typical MCs by 2–3 orders of magnitude.

The AMS-02 Cosmic-Ray Deuteron Flux is Consistent with a Secondary Origin

The recent measurements of cosmic-ray (CR) deuteron fluxes by AMS-02 show that the rigidity dependence of deuterons is similar with that of protons but flatter than 3He, which has been attributed to the existence of primary deuterons with abundance much higher than that from the Big Bang nucleosynthesis. The requirement of highly deuteron-abundant sources imposes a serious challenge to modern astrophysics since there is no known process to produce a large amount of deuterons without violating other constraints. In this work we demonstrate that the fragmentation of heavy nuclei up to nickel plays a crucial role in shaping/enhancing the spectrum/flux of the CR deuterons. Based on the latest CR data, the predicted secondary fluxes of deuterons and 3He are found to be reasonably consistent with the AMS-02 measurements, and a primary deuteron component is not needed. The observed differences between the spectra of D and 3He, as well as those between the D/4He (D/p) and 3He/4He (3He/p) flux ratios, measured in the rigidity space, is probably due to the kinetic-energy-to-rigidity conversion and the solar modulation, given different charge-to-mass ratios of D and 3He. More precise measurements of the fragmentation cross sections of various nuclei to produce deuterons, tritons, and 3He in a wide energy range will be very helpful in further testing the secondary origin of cosmic-ray deuterons.

Detection of carbon dioxide and hydrogen peroxide on the stratified surface of Charon with JWST

Charon, Pluto’s largest moon, has been extensively studied, with research focusing on its primitive composition and changes due to radiation and photolysis. However, spectral data have so far been limited to wavelengths below 2.5 μm, leaving key aspects unresolved. Here we present the detection of carbon dioxide (CO2) and hydrogen peroxide (H2O2) on the surface of Charon’s northern hemisphere, using JWST data. These detections add to the known chemical inventory that includes crystalline water ice, ammonia-bearing species, and tholin-like darkening constituents previously revealed by ground- and space-based observations. The H2O2 presence indicates active radiolytic/photolytic processing of the water ice-rich surface by solar ultraviolet and interplanetary medium Lyman-α photons, solar wind, and galactic cosmic rays. Through spectral modeling of the surface, we show that the CO2 is present in pure crystalline form and, possibly, in intimately mixed states on the surface. Endogenically sourced subsurface CO2 exposed on the surface is likely the primary source of this component, with possible contributions from irradiation of hydrocarbons mixed with water ice, interfacial radiolysis between carbon deposits and water ice, and the implantation of energetic carbon ions from the solar wind and solar energetic particles.

Influence of magnetosphere disturbances on particle fluxes measured by ground-based detectors

This study examines how the Earth's surface particle fluxes are modulated by the interplanetary magnetic field (IMF) carried by coronal mass ejections (ICME). Our findings underscore the role of magnetic reconnection in allowing low-energy galactic cosmic rays (GCRs) to penetrate the magnetosphere, leading to enhanced secondary particle fluxes through reduced cutoff rigidity —a phenomenon known as the magnetospheric effect (ME). In contrast, the Forbush decrease (FD) driven by the scalar magnetic field strength results in significant particle flux reductions. On May 10–11, 2024, the FD, directly linked to the enormous geomagnetic storm (GMS), was complicated by the simultaneous registration of secondary particles from the solar energetic particle (SEP) event, which was energetic enough to generate secondary particles in space and on the ground, leading to increases in detector count rates, known as ground-level enhancements (GLEs). Using new experimental facilities, we reveal that secondary particles during ME events release up to 10 MeV energy (maximum energy of approximately 10 MeV), whereas, during FD and GLE events, the energy release extends to 100 MeV (maximum energy of approximately 100 MeV). These insights contribute to refining event classification schemes and predictive models of space weather.

A Magnetized Strongly Turbulent Corona as the Source of Neutrinos from NGC 1068

The cores of active galactic nuclei are potential accelerators of 10–100 TeV cosmic rays, in turn producing high-energy neutrinos. This picture was confirmed by the compelling evidence of a TeV neutrino signal from the nearby active galaxy NGC 1068, leaving open the question of what is the site and mechanism of cosmic-ray acceleration. One candidate is the magnetized turbulence surrounding the central supermassive black hole. Recent particle-in-cell simulations of magnetized turbulence indicate that stochastic cosmic-ray acceleration is nonresonant, in contrast to the assumptions of previous studies. We show that this has important consequences on a self-consistent theory of neutrino production in the corona, leading to a more rapid cosmic-ray acceleration than previously considered. The turbulent magnetic-field fluctuations needed to explain the neutrino signal are consistent with a magnetically powered corona. We find that strong turbulence, with turbulent magnetic energy density higher than 1% of the rest-mass energy density, naturally explains the normalization of the IceCube neutrino flux, in addition to the neutrino spectral shape. Only a fraction of the protons in the corona, which can be directly inferred from the neutrino signal, are accelerated to high energies. Thus, in this framework, the neutrino signal from NGC 1068 provides a testbed for particle acceleration in magnetized turbulence.

Production and test of BI-RPC detectors for ATLAS Phase-2 upgrade

The current Resistive Plate Chamber (RPC) system is undergoing a major upgrade (ATL (2017)), consisting in the installation of approximately 1000 RPC detector units in the innermost barrel layer of the ATLAS Muon Spectrometer. The goal of the project is to increase the detector coverage, currently limited to approximately 80%, and improve the trigger robustness and efficiency. The production of the gas volumes takes place in Italy, in Germany and China, while the readout panels in Cosenza (Italy) and Hefei (China). The Italian collaboration is taking care of the construction and test of the chambers located in the large sectors of the ATLAS barrel (BIL). Here we present the state of the art of the production, certification and logistics related to all the components produced at the Italian sites, as well as the assembly line and characterization of the BIL chambers at CERN with cosmic rays. The certification results of the components produced are analyzed and discussed.

Lateral Distribution Function Estimation of Electrons and Muons using Nishimura-Kamata-Greisen Function

Abstract The density of charged particles in extensive air showers reaching the surface of the Earth was calculated by estimating the lateral distribution function (LDF) of different primary particles at high energies. LDF simulation was performed using the AIRES system (version 19.04.10), a set of programs and subroutines designed to simulate ultra-high-energy air showers resulting from the interaction of cosmic rays with the Earth’s atmosphere. This system includes algorithms for fast simulation and output data management, and can simulate particle showers realistically and manage the related data efficiently. Its aim is to contribute to research on high-energy cosmic ray interactions for two charged particles, like muons and electrons, at very high energies (1016, 1018, and 1019 eV) and taking into account the effect of particles, such as protons, helium nuclei, and iron nuclei, and primary energies and zenith angles (0°, 20°, and 40°). The LDF was also calculated using the Nishimura–Kamata–Greisen function, and good agreement was found with the results produced by the AIRES system for high-energy muons and electrons created by primary particles.

Nonthermal Signatures of Radiative Supernova Remnants

The end of supernova remnant (SNR) evolution is characterized by a so-called “radiative” stage, in which efficient cooling of the hot bubble inside the forward shock slows expansion, leading to eventual shock breakup. Understanding SNR evolution at this stage is vital for predicting feedback in galaxies, since SNRs are expected to deposit their energy and momentum into the interstellar medium at the ends of their lives. A key prediction of SNR evolutionary models is the formation at the onset of the radiative stage of a cold, dense shell behind the forward shock. However, searches for these shells via their neutral hydrogen emission have had limited success. We instead introduce an independent observational signal of shell formation arising from the interaction between nonthermal particles accelerated by the SNR forward shock (cosmic rays) and the dense shell. Using a semi-analytic model of particle acceleration based on state-of-the-art simulations coupled with a high-resolution hydrodynamic model of SNR evolution, we predict the nonthermal emission that arises from this interaction. We demonstrate that the onset of the radiative stage leads to nonthermal signatures from radio to gamma rays, including radio and gamma-ray brightening by nearly 2 orders of magnitude. Such a signature may be detectable with current instruments, and will be resolvable with the next generation of gamma-ray telescopes (namely, the Cherenkov Telescope Array).

Active Galactic Nucleus Jet-inflated Bubbles as Possible Origin of Odd Radio Circles

Odd radio circles (ORCs) are newly discovered extragalactic radio objects with an unknown origin. In this work, we carry out three-dimensional cosmic-ray (CR) magnetohydrodynamic simulations using the FLASH code and predict the radio morphology of end-on active galactic nucleus (AGN) jet-inflated bubbles considering hadronic emission. We consider CR proton (CRp)-dominated jets as they tend to inflate oblate bubbles, promising to reproduce the large inferred sizes of the ORCs when viewed end-on. We find that powerful and long-duration CRp-dominated jets can create bubbles with similar sizes (∼300–600 kpc) and radio morphology (circular and edge-brightened) to the observed ORCs in low-mass (M vir ∼ 8 × 1012 − 8 × 1013 M ⊙) halos. Given the same amount of input jet energy, longer-duration (thus lower-power) jets tend to create larger bubbles since high-power jets generate strong shocks that carry away a significant portion of the jet energy. The edge-brightened feature of the observed ORCs is naturally reproduced due to efficient hadronic collisions at the interface between the bubbles and the ambient medium. We further discuss the radio luminosity, X-ray detectability, and the possible origin of such strong AGN jets in the context of galaxy evolution. We conclude that end-on CR-dominated AGN bubbles could be a plausible scenario for the formation of ORCs.

Full inverse Compton Scattering: Total transfer of energy and momentum from electrons to photons

In this article we discuss a peculiar regime of Compton Scattering that assures the maximum transfer of energy and momentum from free electrons propagating in vacuum to the scattered photons. We name this regime Full Inverse Compton Scattering (FICS) because it is characterized by the maximum and full energy loss of the electrons in collision with photons: up to 100% of the electron kinetic energy is indeed transferred to the photon. In the case of relativistic electrons, characterized by a large Lorentz factor (γ≫1), FICS regime corresponds to an incident photon energy equal to mec22, i.e. approximately 255.5 keV. We interpret such an astonishing result as FICS being the time reversal of direct Compton Scattering of very energetic photons (of energy much greater than mec2) onto atomic electrons. Although the cross section of Compton scattering is decreasing with the energy of the incident photon, making the process less probable with respect to other reactions (pair production, nuclear reactions, etc.) when high energetic photons are bombarding a target, the kinematics straightforwardly implies that the back-scattered photons would have an energy reaching asymptotically mec22. FICS is instead the unique suitable working point in Compton scattering for achieving the total transfer of (kinetic) energy exactly from the electron to the photon. Experiencing transitions from the initial momentum to zero in the laboratory system, in FICS the electron is also subject to very large negative acceleration; this fact can lead to possible experiments of sensing the Unruh temperature and related photon bath. On the other side of the energy dynamic range, low relativistic electrons can be completely stopped by moderate energy photons (tens of keV), leading to full exchange of temperature between electron clouds and photon baths. Cosmic gamma ray sources can be affected in their evolution by this peculiar FICS regime of Compton scattering.

The Big Bang versus the Steady State: Gamow, Hoyle and Ryle, rivals in cosmology

Abstract This account of the controversy concerning the Big Bang and Steady State theories contrasts the different approaches to science of George Gamow, Fred Hoyle and Martin Ryle. Einstein’s general relativity offered theoretical physicists an indispensable tool kit for making mathematical models of the Universe. Georges Lemaître made an astonishing impact in 1927 with his proposal that the expanding Universe started from a decaying super-radioactive primeval atom. Gamow refined Lemaître’s model by proposing that primordial nucleosynthesis in the early expanding Universe had formed the chemical elements. Hoyle, who by contrast had discovered the conditions under which stellar nucleosynthesis could occur via the evolution and explosion of massive stars, publicly dismissed Gamow’s cosmology as an unnecessary speculation. Hoyle, Hermann Bondi and Thomas Gold proposed the alternative steady state theory in 1948. In 1950 Ryle constructed the first radio telescope with the sensitivity to discriminate between the rival models of the Universe. Steady state cosmology survived Ryle’s first surveys of cosmic radio sources because Ryle’s data was inadequate. However results from the much improved Third and Fourth Cambridge Surveys demonstrated that our Universe had evolved. The Ryle-Hoyle debates became intensely passionate and personal. In 1965 the discovery of the cosmic microwave background radiation settled the argument in favour of the Lemaître Big Bang evolving Universe.

Multi-fractal Analysis of Cosmic Rays over Mid- and High-Latitude Stations During Severe Geomagnetic Storms

Multi-fractal Analysis of Cosmic Rays over Mid- and High-Latitude Stations During Severe Geomagnetic Storms