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A precision measurement of the nitrogen flux with rigidity (momentum per unit charge) from 2.2 GV to 3.3 TV based on $2.2\times {10}^6$ events is presented. The detailed rigidity dependence of the nitrogen flux spectral index is presented for the first time. The spectral index rapidly hardens at high rigidities and becomes identical to the spectral indices of primary He, C, and O cosmic rays above $\sim 700\mathrm{GV}$. We observed that the nitrogen flux ${\mathrm{\Phi }}_{\mathrm{N}}$ can be presented as the sum of its primary component ${\mathrm{\Phi }}_{\mathrm{N}}^P$ and secondary component ${\mathrm{\Phi }}_{\mathrm{N}}^S$, ${\mathrm{\Phi }}_{\mathrm{N}}={\mathrm{\Phi }}_{\mathrm{N}}^P+{\mathrm{\Phi }}_{\mathrm{N}}^S$, and we found ${\mathrm{\Phi }}_{\mathrm{N}}$ is well described by the weighted sum of the oxygen flux ${\mathrm{\Phi }}_{\mathrm{O}}$ (primary cosmic rays) and the boron flux ${\mathrm{\Phi }}_{\mathrm{B}}$ (secondary cosmic rays), with ${\mathrm{\Phi }}_{\mathrm{N}}^P=(0.090\pm 0.002)\times {\mathrm{\Phi }}_{\mathrm{O}}$ and ${\mathrm{\Phi }}_{\mathrm{N}}^S=(0.62\pm 0.02)\times {\mathrm{\Phi }}_{\mathrm{B}}$ over the entire rigidity range. This corresponds to a change of the contribution of the secondary cosmic ray component in the nitrogen flux from 70% at a few GV to $<30\%$ above 1 TV.

A precision measurement by the Alpha Magnetic Spectrometer on the International Space Station of the positron fraction in primary cosmic rays in the energy range from 0.5 to 350 GeV based on $6.8\times {10}^6$ positron and electron events is presented. The very accurate data show that the positron fraction is steadily increasing from 10 to $\sim 250\mathrm{GeV}$, but, from 20 to 250 GeV, the slope decreases by an order of magnitude. The positron fraction spectrum shows no fine structure, and the positron to electron ratio shows no observable anisotropy. Together, these features show the existence of new physical phenomena.

We present high-statistics, precision measurements of the detailed time and energy dependence of the primary cosmic-ray electron flux and positron flux over 79 Bartels rotations from May 2011 to May 2017 in the energy range from 1 to 50 GeV. For the first time, the charge-sign dependent modulation during solar maximum has been investigated in detail by leptons alone. Based on $23.5\times {10}^6$ events, we report the observation of short-term structures on the timescale of months coincident in both the electron flux and the positron flux. These structures are not visible in the $e^{+}/e^{-}$ flux ratio. The precision measurements across the solar polarity reversal show that the ratio exhibits a smooth transition over $830\pm 30$ days from one value to another. The midpoint of the transition shows an energy dependent delay relative to the reversal and changes by $260\pm 30$ days from 1 to 6 GeV.

We present the precision measurement of the daily proton fluxes in cosmic rays from May 20, 2011 to October 29, 2019 (a total of 2824 days or 114 Bartels rotations) in the rigidity interval from 1 to 100 GV based on $5.5\times {10}^9$ protons collected with the Alpha Magnetic Spectrometer aboard the International Space Station. The proton fluxes exhibit variations on multiple timescales. From 2014 to 2018, we observed recurrent flux variations with a period of 27 days. Shorter periods of 9 days and 13.5 days are observed in 2016. The strength of all three periodicities changes with time and rigidity. The rigidity dependence of the 27-day periodicity is different from the rigidity dependences of 9-day and 13.5-day periods. Unexpectedly, the strength of 9-day and 13.5-day periodicities increases with increasing rigidities up to $\sim 10\mathrm{GV}$ and $\sim 20\mathrm{GV}$, respectively. Then the strength of the periodicities decreases with increasing rigidity up to 100 GV.

We report the observation of new properties of primary cosmic rays He, C, and O measured in the rigidity (momentum/charge) range 2 GV to 3 TV with $90\times {10}^6$ helium, $8.4\times {10}^6$ carbon, and $7.0\times {10}^6$ oxygen nuclei collected by the Alpha Magnetic Spectrometer (AMS) during the first five years of operation. Above 60 GV, these three spectra have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way.

A precision measurement by AMS of the positron fraction in primary cosmic rays in the energy range from 0.5 to 500 GeV based on 10.9 million positron and electron events is presented. This measurement extends the energy range of our previous observation and increases its precision. The new results show, for the first time, that above $\sim 200\mathrm{GeV}$ the positron fraction no longer exhibits an increase with energy.

We report the properties of primary cosmic-ray sulfur (S) in the rigidity range 2.15 GV to 3.0 TV based on $0.38\times {10}^6$ sulfur nuclei collected by the Alpha Magnetic Spectrometer experiment (AMS). We observed that above 90 GV the rigidity dependence of the S flux is identical to the rigidity dependence of Ne-Mg-Si fluxes, which is different from the rigidity dependence of the He-C-O-Fe fluxes. We found that, similar to N, Na, and Al cosmic rays, over the entire rigidity range, the traditional primary cosmic rays S, Ne, Mg, and C all have sizeable secondary components, and the S, Ne, and Mg fluxes are well described by the weighted sum of the primary silicon flux and the secondary fluorine flux, and the C flux is well described by the weighted sum of the primary oxygen flux and the secondary boron flux. The primary and secondary contributions of the traditional primary cosmic-ray fluxes of C, Ne, Mg, and S (even $Z$ elements) are distinctly different from the primary and secondary contributions of the N, Na, and Al (odd $Z$ elements) fluxes. The abundance ratio at the source for $\mathrm{S}/\mathrm{Si}$ is $0.167\pm 0.006$, for $\mathrm{Ne}/\mathrm{Si}$ is $0.833\pm 0.025$, for $\mathrm{Mg}/\mathrm{Si}$ is $0.994\pm 0.029$, and for $\mathrm{C}/\mathrm{O}$ is $0.836\pm 0.025$. These values are determined independent of cosmic-ray propagation.

We report the observation of new properties of primary cosmic rays, neon (Ne), magnesium (Mg), and silicon (Si), measured in the rigidity range 2.15 GV to 3.0 TV with $1.8\times {10}^6\mathrm{Ne}$, $2.2\times {10}^6\mathrm{Mg}$, and $1.6\times {10}^6\mathrm{Si}$ nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. The Ne and Mg spectra have identical rigidity dependence above 3.65 GV. The three spectra have identical rigidity dependence above 86.5 GV, deviate from a single power law above 200 GV, and harden in an identical way. Unexpectedly, above 86.5 GV the rigidity dependence of primary cosmic rays Ne, Mg, and Si spectra is different from the rigidity dependence of primary cosmic rays He, C, and O. This shows that the Ne, Mg, and Si and He, C, and O are two different classes of primary cosmic rays.

We present the precision measurement of 2824 daily helium fluxes in cosmic rays from May 20, 2011 to October 29, 2019 in the rigidity interval from 1.71 to 100 GV based on $7.6\times {10}^8$ helium nuclei collected with the Alpha Magnetic Spectrometer (AMS) aboard the International Space Station. The helium flux and the helium to proton flux ratio exhibit variations on multiple timescales. In nearly all the time intervals from 2014 to 2018, we observed recurrent helium flux variations with a period of 27 days. Shorter periods of 9 days and 13.5 days are observed in 2016. The strength of all three periodicities changes with time and rigidity. In the entire time period, we found that below $\sim 7\mathrm{GV}$ the helium flux exhibits larger time variations than the proton flux, and above $\sim 7\mathrm{GV}$ the helium to proton flux ratio is time independent. Remarkably, below 2.4 GV a hysteresis between the helium to proton flux ratio and the helium flux was observed at greater than the $7\sigma$ level. This shows that at low rigidity the modulation of the helium to proton flux ratio is different before and after the solar maximum in 2014.

Precision measurements of cosmic ray positrons are presented up to 1 TeV based on 1.9 million positrons collected by the Alpha Magnetic Spectrometer on the International Space Station. The positron flux exhibits complex energy dependence. Its distinctive properties are (a) a significant excess starting from $25.2\pm 1.8\mathrm{GeV}$ compared to the lower-energy, power-law trend, (b) a sharp dropoff above $284_{-64}^{+91}\mathrm{GeV}$, (c) in the entire energy range the positron flux is well described by the sum of a term associated with the positrons produced in the collision of cosmic rays, which dominates at low energies, and a new source term of positrons, which dominates at high energies, and (d) a finite energy cutoff of the source term of $E_s=810_{-180}^{+310}\mathrm{GeV}$ is established with a significance of more than $4\sigma$. These experimental data on cosmic ray positrons show that, at high energies, they predominantly originate either from dark matter annihilation or from other astrophysical sources.

We present the precision measurements of 11 years of daily cosmic positron fluxes in the rigidity range from 1.00 to 41.9 GV based on $3.4\times {10}^6$ positrons collected with the Alpha Magnetic Spectrometer (AMS) aboard the International Space Station. The positron fluxes show distinctly different time variations from the electron fluxes at short and long timescales. A hysteresis between the electron fluxes and the positron fluxes is observed with a significance greater than $5\sigma$ at rigidities below 8.5 GV. On the contrary, the positron fluxes and the proton fluxes show similar time variation. Remarkably, we found that positron fluxes are modulated more than proton fluxes with a significance greater than $5\sigma$ for rigidities below 7 GV. These continuous daily positron fluxes, together with AMS daily electron, proton, and helium fluxes over an 11-year solar cycle, provide unique input to the understanding of both the charge-sign and mass dependencies of cosmic rays in the heliosphere.

A precise measurement of the proton flux in primary cosmic rays with rigidity (momentum/charge) from 1 GV to 1.8 TV is presented based on 300 million events. Knowledge of the rigidity dependence of the proton flux is important in understanding the origin, acceleration, and propagation of cosmic rays. We present the detailed variation with rigidity of the flux spectral index for the first time. The spectral index progressively hardens at high rigidities.

Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of the deuteron ($D$) flux are presented. The measurements are based on $21\times {10}^6$ $D$ nuclei in the rigidity range from 1.9 to 21 GV collected from May 2011 to April 2021. We observe that over the entire rigidity range the $D$ flux exhibits nearly identical time variations with the $p$, ${}^3\mathrm{He}$, and ${}^4\mathrm{He}$ fluxes. Above 4.5 GV, the $D/{}^4\mathrm{He}$ flux ratio is time independent and its rigidity dependence is well described by a single power law $\propto R^{\mathrm{\Delta }}$ with ${\mathrm{\Delta }}_{D/{}^4\mathrm{He}}=-0.108\pm 0.005$. This is in contrast with the ${}^3\mathrm{He}/{}^4\mathrm{He}$ flux ratio for which we find ${\mathrm{\Delta }}_{{}^3\mathrm{He}/{}^4\mathrm{He}}=-0.289\pm 0.003$. Above $\sim 13\mathrm{GV}$ we find a nearly identical rigidity dependence of the $D$ and $p$ fluxes with a $D/p$ flux ratio of $0.027\pm 0.001$. These unexpected observations indicate that cosmic deuterons have a sizable primarylike component. With a method independent of cosmic ray propagation, we obtain the primary component of the $D$ flux equal to $9.4\pm 0.5\%$ of the ${}^4\mathrm{He}$ flux and the secondary component of the $D$ flux equal to $58\pm 5\%$ of the ${}^3\mathrm{He}$ flux.

We report the observation of new properties of primary iron (Fe) cosmic rays in the rigidity range 2.65 GV to 3.0 TV with $0.62\times {10}^6$ iron nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. Above 80.5 GV the rigidity dependence of the cosmic ray Fe flux is identical to the rigidity dependence of the primary cosmic ray He, C, and O fluxes, with the $\mathrm{Fe}/\mathrm{O}$ flux ratio being constant at $0.155\pm 0.006$. This shows that unexpectedly Fe and He, C, and O belong to the same class of primary cosmic rays which is different from the primary cosmic rays Ne, Mg, and Si class.

We report on the observation of new properties of secondary cosmic rays Li, Be, and B measured in the rigidity (momentum per unit charge) range 1.9 GV to 3.3 TV with a total of $5.4\times {10}^6$ nuclei collected by AMS during the first five years of operation aboard the International Space Station. The Li and B fluxes have an identical rigidity dependence above 7 GV and all three fluxes have an identical rigidity dependence above 30 GV with the $\mathrm{Li}/\mathrm{Be}$ flux ratio of $2.0\pm 0.1$. The three fluxes deviate from a single power law above 200 GV in an identical way. This behavior of secondary cosmic rays has also been observed in the AMS measurement of primary cosmic rays He, C, and O but the rigidity dependences of primary cosmic rays and of secondary cosmic rays are distinctly different. In particular, above 200 GV, the secondary cosmic rays harden more than the primary cosmic rays.

We present results over an 11-year Solar cycle of cosmic antiprotons based on $1.1\times {10}^6$ events in the rigidity range from 1.00 to 41.9 GV. The $\overline{p}$ fluxes exhibit distinct properties. The magnitude of the $\overline{p}$ flux temporal variation is significantly smaller than those of $p$, $e^{-}$, and $e^{+}$. A hysteresis between the $\overline{p}$ fluxes and the $p$ fluxes is observed, whereas the $\overline{p}$ and $e^{-}$ fluxes show a linear correlation. With a model-independent analysis, we found a universal relation between the shape of the rigidity spectrum and the magnitude of flux temporal variation over an 11-year Solar cycle for both positively and negatively charged particles. The simultaneous results on $\overline{p}$ and $p$, $e^{-}$, and $e^{+}$ provide unique information for understanding particle transport in the Solar System as a function of mass, charge, and spectral shape.

Precision results on cosmic-ray electrons are presented in the energy range from 0.5 GeV to 1.4 TeV based on $28.1\times {10}^6$ electrons collected by the Alpha Magnetic Spectrometer on the International Space Station. In the entire energy range the electron and positron spectra have distinctly different magnitudes and energy dependences. The electron flux exhibits a significant excess starting from $42.1_{-5.2}^{+5.4}\mathrm{GeV}$ compared to the lower energy trends, but the nature of this excess is different from the positron flux excess above $25.2\pm 1.8\mathrm{GeV}$. Contrary to the positron flux, which has an exponential energy cutoff of $810_{-180}^{+310}\mathrm{GeV}$, at the $5\sigma$ level the electron flux does not have an energy cutoff below 1.9 TeV. In the entire energy range the electron flux is well described by the sum of two power law components. The different behavior of the cosmic-ray electrons and positrons measured by the Alpha Magnetic Spectrometer is clear evidence that most high energy electrons originate from different sources than high energy positrons.

We present the precision measurement from May 2011 to May 2017 (79 Bartels rotations) of the proton fluxes at rigidities from 1 to 60 GV and the helium fluxes from 1.9 to 60 GV based on a total of $1\times {10}^9$ events collected with the Alpha Magnetic Spectrometer aboard the International Space Station. This measurement is in solar cycle 24, which has the solar maximum in April 2014. We observed that, below 40 GV, the proton flux and the helium flux show nearly identical fine structures in both time and relative amplitude. The amplitudes of the flux structures decrease with increasing rigidity and vanish above 40 GV. The amplitudes of the structures are reduced during the time period, which started one year after solar maximum, when the proton and helium fluxes steadily increase. Above $\sim 3\mathrm{GV}$ the $p/\mathrm{He}$ flux ratio is time independent. We observed that below $\sim 3\mathrm{GV}$ the ratio has a long-term decrease coinciding with the period during which the fluxes start to rise.

We report the properties of precision time structures of cosmic nuclei He, Li, Be, B, C, N, and O fluxes over an 11-year solar cycle from May 2011 to November 2022 in the rigidity range from 1.92 to 60.3 GV. The nuclei fluxes show similar but not identical time variations with amplitudes decreasing with increasing rigidity. In particular, below 3.64 GV the Li, Be, and B fluxes, and below 2.15 GV the C, N, and O fluxes, are significantly less affected by solar modulation than the He flux. We observe that these differences in solar modulation are linearly correlated with the differences in the spectral indices of the cosmic nuclei fluxes. This shows, in a model-independent way, that solar modulation of galactic cosmic nuclei depends on their spectral shape. In addition, solar modulation differences due to nuclei velocity dependence on the mass-to-charge ratio ($A/Z$) are not observed.

Precise knowledge of the charge and rigidity dependence of the secondary cosmic ray fluxes and the secondary-to-primary flux ratios is essential in the understanding of cosmic ray propagation. We report the properties of heavy secondary cosmic ray fluorine F in the rigidity $R$ range 2.15 GV to 2.9 TV based on 0.29 million events collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. The fluorine spectrum deviates from a single power law above 200 GV. The heavier secondary-to-primary F/Si flux ratio rigidity dependence is distinctly different from the lighter B/O (or B/C) rigidity dependence. In particular, above 10 GV, the $\frac{\mathrm{F}/\mathrm{Si}}{\mathrm{B}/\mathrm{O}}$ ratio can be described by a power law $R^{\delta }$ with $\delta =0.052\pm 0.007$. This shows that the propagation properties of heavy cosmic rays, from F to Si, are different from those of light cosmic rays, from He to O, and that the secondary cosmic rays have two classes.