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The all-particle spectrum of cosmic rays measured at Earth has a knee-like feature around 4 PeV. A priori, it is not clear if this is a local feature specific to the Solar neighbourhood in the Milky Way, or if it is a generic property of the Galactic cosmic-ray spectrum. We argue that combining gamma-ray and cosmic-ray data of LHAASO indicates that the knee is a local feature. In order to demonstrate this, we derive a model for the local cosmic-ray spectrum and composition, consistent with the recent LHAASO measurements of the all-particle spectrum and the mean logarithmic mass in the knee region. We calculate the spectrum of diffuse gamma-ray emission based on this model and find that the expected spectral shape of the diffuse gamma-ray flux disagrees with the LHAASO measurements of the diffuse gamma-ray emission in the 10-100 TeV energy range in the inner and outer Galaxy. We determine the break energy in the CR spectrum expected from these gamma-ray data and find it an energy ten times lower than obtained from local measurements., Comment: 9 pages, 4 figures, 3 tables ; v2: accepted for publication, extended discussion, 1 figure added, conclusion unchanged

Time-dependent energy spectra of galactic cosmic rays (GCRs) carry fundamental information regarding their origin and propagation. When observed at the Earth, these spectra are significantly affected by the solar wind and the embedded solar magnetic field that permeates the heliosphere, changing significantly over an 11-year solar cycle. Energy spectra of GCRs measured during different epochs of solar activity provide crucial information for a thorough understanding of solar and heliospheric phenomena. The PAMELA experiment had collected data for almost ten years (15th June 2006 - 23rd January 2016), including the minimum phase of solar cycle 23 and the maximum phase of solar cycle 24. In this paper, we present new spectra for helium nuclei measured by the PAMELA instrument from January 2010 to September 2014 over a three Carrington rotation time basis. These data are compared to the PAMELA spectra measured during the previous solar minimum providing a picture of the time dependence of the helium nuclei fluxes over a nearly full solar cycle. Time and rigidity dependencies are observed in the proton-to-helium flux ratios. The force-field approximation of the solar modulation was used to relate these dependencies to the shapes of the local interstellar proton and helium-nuclei spectra., Comment: 9 pages, 5 figures

We compare the predictions of AAfrag for the spectra of secondary photons, neutrinos, electrons, and positrons produced in proton-proton collisions to those of the parameterisations of Kamae et al., Kelner et al., and Kafexhiu et al. We find that the differences in the normalisation of the photon energy spectra reach 20$-$50% at intermediate values of the transferred energy fraction $x$, growing up to a factor of two for $x\rightarrow\,$1, while the differences in the neutrino spectra are even larger. We argue that LHCf results on the forward production of photons favor the use of the QGSJET-II-04m model on which AAfrag is based. The differences in the normalisation have important implications in the context of multi-messenger astronomy, in particular, for the prediction of neutrino fluxes based on gamma-ray flux measurements, or regarding the inference of the cosmic ray spectrum, based on gamma-ray data. We note also that the positron-electron ratio from hadronic interactions increases with energy towards the cutoff, an effect which is missed using the average electron-positron spectrum from Kelner et al. Finally, we describe the publicly available python package aafragpy, which provides the secondary spectra of photons, neutrinos, electrons, and positrons. This package complements the AAfrag results for protons with energies above 4 GeV with previous analytical parameterizations of particle spectra for lower energy protons., Comment: 8 pages, 10 figures

We present a study of the solar-cycle variations of >80 MeV proton flux intensities in the lower edge of the inner radiation belt, based on the measurements of the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) mission. The analyzed data sample covers an ~8 year interval from 2006 July to 2014 September, thus spanning from the decaying phase of the 23rd solar cycle to the maximum of the 24th cycle. We explored the intensity temporal variations as a function of drift shell and proton energy, also providing an explicit investigation of the solar-modulation effects at different equatorial pitch angles. PAMELA observations offer new important constraints for the modeling of low-altitude particle radiation environment at the highest trapping energies., Comment: accepted for publication in the Astrophysical Journal Letters

Precise time-dependent measurements of the Z = 2 component in the cosmic radiation provide crucial information about the propagation of charged particles through the heliosphere. The PAMELA experiment, with its long flight duration (15th June 2006 - 23rd January 2016) and the low energy threshold (80 MeV/n) is an ideal detector for cosmic ray solar modulation studies. In this paper, the helium nuclei spectra measured by the PAMELA instrument from July 2006 to December 2009 over a Carrington rotation time basis are presented. A state-of-the-art three-dimensional model for cosmic-ray propagation inside the heliosphere was used to interpret the time-dependent measured fluxes. Proton-to-helium flux ratio time profiles at various rigidities are also presented in order to study any features which could result from the different masses and local interstellar spectra shapes.

Despite the significant progress achieved in recent years, the physical mechanisms underlying the origin of solar energetic particles (SEPs) are still a matter of debate. The complex nature of both particle acceleration and transport poses challenges to developing a universal picture of SEP events that encompasses both the low-energy (from tens of keV to a few hundreds of MeV) observations made by space-based instruments and the GeV particles detected by the worldwide network of neutron monitors in ground-level enhancements (GLEs). The high-precision data collected by the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) satellite experiment offer a unique opportunity to study the SEP fluxes between $\sim$80 MeV and a few GeV, significantly improving the characterization of the most energetic events. In particular, PAMELA can measure for the first time with good accuracy the spectral features at moderate and high energies, providing important constraints for current SEP models. In addition, the PAMELA observations allow the relationship between low and high-energy particles to be investigated, enabling a clearer view of the SEP origin. No qualitative distinction between the spectral shapes of GLE, sub-GLE and non-GLE events is observed, suggesting that GLEs are not a separate class, but are the subset of a continuous distribution of SEP events that are more intense at high energies. While the spectral forms found are to be consistent with diffusive shock acceleration theory, which predicts spectral rollovers at high energies that are attributed to particles escaping the shock region during acceleration, further work is required to explore the relative influences of acceleration and transport processes on SEP spectra., Comment: 26 pages, 13 figures, 2 tables

The cosmic-ray lithium and beryllium ($^{6}$Li, $^{7}$Li, $^{7}$Be, $^{9}$Be, $^{10}$Be) isotopic composition has been measured with the satellite-borne experiment PAMELA, which was launched into low-Earth orbit on-board the Resurs-DK1 satellite on June 15th 2006. The rare lithium and beryllium isotopes in cosmic rays are believed to originate mainly from the interaction of high energy carbon, nitrogen and oxygen nuclei with the interstellar medium (ISM), but also on "tertiary" interactions in the ISM (i.e. produced by further fragmentation of secondary beryllium and boron). In this paper the isotopic ratios $^{7}$Li/$^{6}$Li and $^{7}$Be/($^{9}$Be + $^{10}$Be) measured between 150 and 1100 MeV/n using two different detector systems from July 2006 to September 2014 will be presented., Comment: 13 pages, 11 figures, accepted for publication in the Astrophysical Journal. arXiv admin note: text overlap with arXiv:1512.06535

New results on the short-term galactic cosmic ray (GCR) intensity variation (Forbush decrease) in December 2006 measured by the PAMELA instrument are presented. Forbush decreases are sudden suppressions of the GCR intensities which are associated with the passage of interplanetary transients such as shocks and interplanetary coronal mass ejections (ICMEs). Most of the past measurements of this phenomenon were carried out with ground-based detectors such as neutron monitors or muon telescopes. These techniques allow only the indirect detection of the overall GCR intensity over an integrated energy range. For the first time, thanks to the unique features of the PAMELA magnetic spectrometer, the Forbush decrease commencing on 2006 December 14, following a CME at the Sun on 2006 December 13 was studied in a wide rigidity range (0.4 - 20 GV) and for different species of GCRs detected directly in space. The daily averaged GCR proton intensity was used to investigate the rigidity dependence of the amplitude and the recovery time of the Forbush decrease. Additionally, for the first time, the temporal variations in the helium and electron intensities during a Forbush decrease were studied. Interestingly, the temporal evolutions of the helium and proton intensities during the Forbush decrease were found in good agreement, while the low rigidity electrons (< 2 GV) displayed a faster recovery. This difference in the electron recovery is interpreted as a charge-sign dependence introduced by drift motions experienced by the GCRs during their propagation through the heliosphere.

The PAMELA cosmic ray detector was launched on June 15th 2006 on board the Russian Resurs-DK1 satellite, and during ten years of nearly continuous data-taking it has observed new interesting features in cosmic rays (CRs). In a decade of operation it has provided plenty of scientific data, covering different issues related to cosmic ray physics. Its discoveries might change our basic vision of the mechanisms of production, acceleration and propagation of cosmic rays in the Galaxy. The antimatter measurements, focus of the experiment, have set strong constraints to the nature of Dark Matter. Search for signatures of more exotic processes (such as the ones involving Strange Quark Matter) was also pursued. Furthermore, the long-term operation of the instrument had allowed a constant monitoring of the solar activity during its maximum and a detailed and prolonged study of the solar modulation, improving the comprehension of the heliosphere mechanisms. PAMELA had also measured the radiation environment around the Earth, and it detected for the first time the presence of an antiproton radiation belt surrounding our planet. The operation of Resurs-DK1 was terminated in 2016. In this article we will review the main features of the PAMELA instrument and its constructing phases. Main part of the article will be dedicated to the summary of the most relevant PAMELA results over a decade of observation

Protons detected by the PAMELA experiment in the period 2006-2014 have been analyzed in the energy range between 0.40-50 GV to explore possible periodicities besides the well known solar undecennial modulation. An unexpected clear and regular feature has been found at rigidities below 15 GV, with a quasi-periodicity of $\sim$450 days. A possible Jovian origin of this periodicity has been investigated in different ways. The results seem to favor a small but not negligible contribution to cosmic rays from the Jovian magnetosphere, even if other explanations cannot be excluded., Comment: article 4 figures, 1 table

Precise measurements of the time-dependent intensity of the low energy ($<50$ GeV) galactic cosmic rays are fundamental to test and improve the models which describe their propagation inside the heliosphere. Especially, data spanning different solar activity periods, i.e. from minimum to maximum, are needed to achieve comprehensive understanding of such physical phenomenon. The minimum phase between the 23$^{rd}$ and the 24$^{th}$ solar cycles was peculiarly long, extending up to the beginning of 2010 and followed by the maximum phase, reached during early 2014. In this paper, we present proton differential spectra measured from January 2010 to February 2014 by the PAMELA experiment. For the first time the galactic cosmic ray proton intensity was studied over a wide energy range (0.08-50 GeV) by a single apparatus from a minimum to a maximum period of solar activity. The large statistics allowed the time variation to be investigated on a nearly monthly basis. Data were compared and interpreted in the context of a state-of-the-art three-dimensional model describing the galactic cosmic rays propagation through the heliosphere., Comment: article, 4 figures. Accepted for publication on The Astrophysical Journal Letters (January 2018)

The PAMELA satellite experiment is providing comprehensive observations of the interplanetary and magnetospheric radiation in the near-Earth environment. Thanks to its identification capabilities and the semi-polar orbit, PAMELA is able to precisely measure the energetic spectra and the angular distributions of the different cosmic-ray populations over a wide latitude region, including geomagnetically trapped and albedo particles. Its observations comprise the solar energetic particle events between solar cycles 23 and 24, and the geomagnetic cutoff variations during magnetospheric storms. PAMELA's measurements are supported by an accurate analysis of particle trajectories in the Earth's magnetosphere based on a realistic geomagnetic field modeling, which allows the classification of particle populations of different origin and the investigation of the asymptotic directions of arrival., Comment: Accepted for publication in Advances in Space Research, 2016. 21 pages, 7 figures

Cosmic-ray electrons and positrons are a unique probe of the propagation of cosmic rays as well as of the nature and distribution of particle sources in our Galaxy. Recent measurements of these particles are challenging our basic understanding of the mechanisms of production, acceleration and propagation of cosmic rays. Particularly striking are the differences between the low energy results collected by the space-borne PAMELA and AMS-02 experiments and older measurements pointing to sign-charge dependence of the solar modulation of cosmic-ray spectra. The PAMELA experiment has been measuring the time variation of the positron and electron intensity at Earth from July 2006 to December 2015 covering the period for the minimum of solar cycle 23 (2006-2009) till the middle of the maximum of solar cycle 24, through the polarity reversal of the heliospheric magnetic field which took place between 2013 and 2014. The positron to electron ratio measured in this time period clearly shows a sign-charge dependence of the solar modulation introduced by particle drifts. These results provide the first clear and continuous observation of how drift effects on solar modulation have unfolded with time from solar minimum to solar maximum and their dependence on the particle rigidity and the cyclic polarity of the solar magnetic field., Comment: 11 pages, 2 figures

Data from the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) satellite experiment were used to measure the geomagnetic cutoff for high-energy (>80 MeV) protons during the 14 December 2006 geomagnetic storm. The variations of the cutoff latitude as a function of rigidity were studied on relatively short timescales, corresponding to spacecraft orbital periods (94 min). Estimated cutoff values were compared with those obtained by means of a trajectory tracing approach based on a dynamical empirical modeling of the Earth's magnetosphere. We found significant variations in the cutoff latitude, with a maximum suppression of about 7 deg at lowest rigidities during the main phase of the storm. The observed reduction in the geomagnetic shielding and its temporal evolution were related to the changes in the magnetospheric configuration, investigating the role of interplanetary magnetic field, solar wind and geomagnetic parameters. PAMELA's results represent the first direct measurement of geomagnetic cutoffs for protons with kinetic energies in the sub-GeV and GeV region., Comment: 26 pages, 6 figures and 1 table. Accepted for publication in Space Weather

The cosmic-ray hydrogen and helium ($^1$H, $^2$H, $^3$He, $^4$He) isotopic composition has been measured with the satellite-borne experiment PAMELA, which was launched into low-Earth orbit on-board the Resurs-DK1 satellite on June 15th 2006. The rare isotopes $^2$H and $^3$He in cosmic rays are believed to originate mainly from the interaction of high energy protons and helium with the galactic interstellar medium. The isotopic composition was measured between 100 and 1100 MeV/n for hydrogen and between 100 and 1400 MeV/n for helium isotopes using two different detector systems over the 23rd solar minimum from July 2006 to December 2007., Comment: 22 pages, 17 figures, Accepted for publication on the Astrophysical Journal

Precision measurements of the electron component in the cosmic radiation provide important information about the origin and propagation of cosmic rays in the Galaxy not accessible from the study of the cosmic-ray nuclear components due to their differing diffusion and energy-loss processes. However, when measured near Earth, the effects of propagation and modulation of galactic cosmic rays in the heliosphere, particularly significant for energies up to at least 30 GeV, must be properly taken into account. In this paper the electron (e^-) spectra measured by PAMELA down to 70 MeV from July 2006 to December 2009 over six-months time intervals are presented. Fluxes are compared with a state-of-the-art three-dimensional model of solar modulation that reproduces the observations remarkably well., Comment: 40 pages, 18 figures, 1 table

Data from the PAMELA satellite experiment were used to measure the geomagnetic cutoff for high-energy ($\gtrsim$ 80 MeV) protons during the solar particle events on 2006 December 13 and 14. The variations of the cutoff latitude as a function of rigidity were studied on relatively short timescales, corresponding to single spacecraft orbits (about 94 minutes). Estimated cutoff values were cross-checked with those obtained by means of a trajectory tracing approach based on dynamical empirical modeling of the Earth's magnetosphere. We find significant variations in the cutoff latitude, with a maximum suppression of about 6 deg for $\sim$80 MeV protons during the main phase of the storm. The observed reduction in the geomagnetic shielding and its temporal evolution were compared with the changes in the magnetosphere configuration, investigating the role of IMF, solar wind and geomagnetic (Kp, Dst and Sym-H indexes) variables and their correlation with PAMELA cutoff results., Comment: Conference: The 34th International Cosmic Ray Conference (ICRC2015), 30 July - 6 August, 2015, The Hague, The Netherlands, Volume: PoS(ICRC2015)287

Data from the PAMELA satellite experiment were used to perform a detailed measurement of under-cutoff protons at low Earth orbits. On the basis of a trajectory tracing approach using a realistic description of the magnetosphere, protons were classified into geomagnetically trapped and re-entrant albedo. The former include stably-trapped protons in the South Atlantic Anomaly, which were analyzed in the framework of the adiabatic theory, investigating energy spectra, spatial and angular distributions; results were compared with the predictions of the AP8 and the PSB97 empirical trapped models. The albedo protons were classified into quasi-trapped, concentrating in the magnetic equatorial region, and un-trapped, spreading over all latitudes and including both short-lived (precipitating) and long-lived (pseudo-trapped) components. Features of the penumbra region around the geomagnetic cutoff were investigated as well. PAMELA observations significantly improve the characterization of the high energy proton populations in near Earth orbits., Comment: Conference: The 34th International Cosmic Ray Conference (ICRC2015), 30 July - 6 August, 2015, The Hague, The Netherlands, Volume: PoS(ICRC2015)288

The PAMELA satellite experiment is providing first direct measurements of Solar Energetic Particles (SEPs) with energies from about 80 MeV to several GeV in near-Earth space, bridging the low energy data by other space-based instruments and the Ground Level Enhancement (GLE) data by the worldwide network of neutron monitors. Its unique observational capabilities include the possibility of measuring the flux angular distribution and thus investigating possible anisotropies. This work reports the analysis methods developed to estimate the SEP energy spectra as a function of the particle pitch-angle with respect to the Interplanetary Magnetic Field (IMF) direction. The crucial ingredient is provided by an accurate simulation of the asymptotic exposition of the PAMELA apparatus, based on a realistic reconstruction of particle trajectories in the Earth's magnetosphere. As case study, the results for the May 17, 2012 event are presented., Comment: Conference: The 34th International Cosmic Ray Conference (ICRC2015), 30 July - 6 August, 2015, The Hague, The Netherlands, Volume: PoS(ICRC2015)085

The PAMELA detector was launched on board of the Russian Resurs-DK1 satellite on June 15, 2006. Data collected during the first four years have been used to search for large-scale anisotropies in the arrival directions of cosmic-ray positrons. The PAMELA experiment allows for a full sky investigation, with sensitivity to global anisotropies in any angular window of the celestial sphere. Data samples of positrons in the rigidity range 10 GV $\leq$ R $\leq$ 200 GV were analyzed. This article discusses the method and the results of the search for possible local sources through analysis of anisotropy in positron data compared to the proton background. The resulting distributions of arrival directions are found to be isotropic. Starting from the angular power spectrum, a dipole anisotropy upper limit \delta = 0.166 at 95% C.L. is determined. Additional search is carried out around the Sun. No evidence of an excess correlated with that direction was found., Comment: The value of the dipole anisotropy upper limit has been changed. The method is correct but there was a miscalculation in the relative formula

We present a precise measurement of downward-going albedo proton fluxes for kinetic energy above $\sim$ 70 MeV performed by the PAMELA experiment at an altitude between 350 and 610 km. On the basis of a trajectory tracing simulation, the analyzed protons were classified into quasi-trapped, concentrating in the magnetic equatorial region, and un-trapped spreading over all latitudes, including both short-lived (precipitating) and long-lived (pseudo-trapped) components. In addition, features of the penumbra region around the geomagnetic cutoff were investigated in detail. PAMELA results significantly improve the characterization of the high energy albedo proton populations at low Earth orbits., Comment: 28 pages, 8 figures. Accepted for publication in Journal of Geophysical Research - Space Physics

The nature of particle acceleration at the Sun, whether through flare reconnection processes or through shocks driven by coronal mass ejections (CMEs), is still under scrutiny despite decades of research. The measured properties of solar energetic particles (SEPs) have long been modeled in different particle-acceleration scenarios. The challenge has been to disentangle to the effects of transport from those of acceleration. The Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) instrument, enables unique observations of SEPs including composition and the angular distribution of the particles about the magnetic field, i.e. pitch angle distribution, over a broad energy range (>80 MeV) -- bridging a critical gap between space-based measurements and ground-based. We present high-energy SEP data from PAMELA acquired during the 2012 May 17 SEP event. These data exhibit differential anisotropies and thus transport features over the instrument rigidity range. SEP protons exhibit two distinct pitch angle distributions; a low-energy population that extends to 90{\deg} and a population that is beamed at high energies (>1 GeV), consistent with neutron monitor measurements. To explain a low-energy SEP population that exhibits significant scattering or redistribution accompanied by a high-energy population that reaches the Earth relatively unaffected by dispersive transport effects, we postulate that the scattering or redistribution takes place locally. We believe these are the first comprehensive measurements of the effects of solar energetic particle transport in the Earth's magnetosheath., Comment: 21 pages, 4 figures. Accepted for publication in The Astrophysical Journal Letters

The PAMELA satellite-borne experiment is providing first direct measurements of Solar Energetic Particles (SEPs) with energies from $\sim$80 MeV to several GeV in near-Earth space. Its unique observational capabilities include the possibility of measuring the flux angular distribution and thus investigating possible anisotropies related to SEP events. This paper focuses on the analysis methods developed to estimate SEP energy spectra as a function of the particle pitch angle with respect to the Interplanetary Magnetic Field (IMF). The crucial ingredient is provided by an accurate simulation of the asymptotic exposition of the PAMELA apparatus, based on a realistic reconstruction of particle trajectories in the Earth's magnetosphere. As case study, the results of the calculation for the May 17, 2012 event are reported., Comment: 25 pages, 9 figures

We report an accurate measurement of the geomagnetically trapped proton fluxes for kinetic energy above > 70 MeV performed by the PAMELA mission at low Earth orbits (350-610 km). Data were analyzed in the frame of the adiabatic theory of charged particle motion in the geomagnetic field. Flux properties were investigated in detail, providing a full characterization of the particle radiation in the South Atlantic Anomaly region, including locations, energy spectra and pitch angle distributions. PAMELA results significantly improve the description of the Earth's radiation environment at low altitudes placing important constraints on the trapping and interaction processes, and can be used to validate current trapped particle radiation models., Comment: 22 pages, 5 figures

The propagation of cosmic rays inside our galaxy plays a fundamental role in shaping their injection spectra into those observed at Earth. One of the best tools to investigate this issue is the ratio of fluxes for secondary and primary species. The boron-to-carbon (B/C) ratio, in particular, is a sensitive probe to investigate propagation mechanisms. This paper presents new measurements of the absolute fluxes of boron and carbon nuclei, as well as the B/C ratio, from the PAMELA space experiment. The results span the range 0.44 - 129 GeV/n in kinetic energy for data taken in the period July 2006 - March 2008.

Precision measurements of the positron component in the cosmic radiation provide important information about the propagation of cosmic rays and the nature of particle sources in our Galaxy. The satellite-borne experiment PAMELA has been used to make a new measurement of the cosmic-ray positron flux and fraction that extends previously published measurements up to 300 GeV in kinetic energy. The combined measurements of the cosmic-ray positron energy spectrum and fraction provide a unique tool to constrain interpretation models. During the recent solar minimum activity period from July 2006 to December 2009 approximately 24500 positrons were observed. The results cannot be easily reconciled with purely secondary production and additional sources of either astrophysical or exotic origin may be required., Comment: 14 pages, 4 figures, 1 table. Accepted for publication in Physical Review Letters. Corrected a typo in the flux units of Table 1

The PAMELA satellite borne experiment is designed to study cosmic rays with great accuracy in a wide energy range. One of PAMELA's main goal is the study of the antimatter component of cosmic rays. The experiment, housed on board the Russian satellite Resurs-DK1, was launched on June 15th 2006 and it is still taking data. In this work we present the measurement of galactic positron energy spectrum in the energy range between 500 MeV and few hundred GeV., Comment: 4 pages, 4 figures, v2: MLP variable description added, bibliography updated. A revised version will appear in proc. 33rd International Cosmic Ray Conference, Rio de Janeiro 2013

The satellite-borne experiment PAMELA has been used to make new measurements of cosmic ray H and He isotopes. The isotopic composition was measured between 100 and 600 MeV/n for hydrogen and between 100 and 900 MeV/n for helium isotopes over the 23rd solar minimum from July 2006 to December 2007. The energy spectrum of these components carries fundamental information regarding the propagation of cosmic rays in the galaxy which are competitive with those obtained from other secondary to primary measurements such as B/C., Comment: 11 pages, 11 figures, 5 tables. To appear in Astrophysical Journal

The energy spectra of galactic cosmic rays carry fundamental information regarding their origin and propagation. These spectra, when measured near Earth, are significantly affected by the solar magnetic field. A comprehensive description of the cosmic radiation must therefore include the transport and modulation of cosmic rays inside the heliosphere. During the end of the last decade the Sun underwent a peculiarly long quiet phase well suited to study modulation processes. In this paper we present proton spectra measured from July 2006 to December 2009 by PAMELA. The large collected statistics of protons allowed the time variation to be followed on a nearly monthly basis down to 400 MV. Data are compared with a state-of-the-art three-dimensional model of solar modulation., Comment: 17 pages, 5 figures, 1 table, to appear in Astrophysical Journal. Corrected two elements of Table 1