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Precision measurements by the Alpha Magnetic Spectrometer on the International Space Station of the primary cosmic-ray electron flux in the range 0.5 to 700 GeV and the positron flux in the range 0.5 to 500 GeV are presented. The electron flux and the positron flux each require a description beyond a single power-law spectrum. Both the electron flux and the positron flux change their behavior at $\sim 30\mathrm{GeV}$ but the fluxes are significantly different in their magnitude and energy dependence. Between 20 and 200 GeV the positron spectral index is significantly harder than the electron spectral index. The determination of the differing behavior of the spectral indices versus energy is a new observation and provides important information on the origins of cosmic-ray electrons and positrons.

A precision measurement by AMS of the antiproton flux and the antiproton-to-proton flux ratio in primary cosmic rays in the absolute rigidity range from 1 to 450 GV is presented based on $3.49\times 10^5$ antiproton events and $2.42\times 10^9$ proton events. The fluxes and flux ratios of charged elementary particles in cosmic rays are also presented. In the absolute rigidity range $\sim 60$ to $\sim 500\mathrm{GV}$, the antiproton $\overline{p}$, proton $p$, and positron $e^{+}$ fluxes are found to have nearly identical rigidity dependence and the electron $e^{-}$ flux exhibits a different rigidity dependence. Below 60 GV, the ($\overline{p}/p$), ($\overline{p}/e^{+}$), and ($p/e^{+}$) flux ratios each reaches a maximum. From $\sim 60$ to $\sim 500\mathrm{GV}$, the ($\overline{p}/p$), ($\overline{p}/e^{+}$), and ($p/e^{+}$) flux ratios show no rigidity dependence. These are new observations of the properties of elementary particles in the cosmos.

Precision measurements by the Alpha Magnetic Spectrometer (AMS) on the International Space Station of ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ fluxes are presented. The measurements are based on 100 million ${}^4\mathrm{He}$ nuclei in the rigidity range from 2.1 to 21 GV and 18 million ${}^3\mathrm{He}$ from 1.9 to 15 GV collected from May 2011 to November 2017. We observed that the ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ fluxes exhibit nearly identical variations with time. The relative magnitude of the variations decreases with increasing rigidity. The rigidity dependence of the ${}^3\mathrm{He}/{}^4\mathrm{He}$ flux ratio is measured for the first time. Below 4 GV, the ${}^3\mathrm{He}/{}^4\mathrm{He}$ flux ratio was found to have a significant long-term time dependence. Above 4 GV, the ${}^3\mathrm{He}/{}^4\mathrm{He}$ flux ratio was found to be time independent, and its rigidity dependence is well described by a single power law $\propto R^{\mathrm{\Delta }}$ with $\mathrm{\Delta }=-0.294\pm 0.004$. Unexpectedly, this value is in agreement with the B/O and B/C spectral indices at high energies.

Knowledge of the precise rigidity dependence of the helium flux is important in understanding the origin, acceleration, and propagation of cosmic rays. A precise measurement of the helium flux in primary cosmic rays with rigidity (momentum/charge) from 1.9 GV to 3 TV based on 50 million events is presented and compared to the proton flux. The detailed variation with rigidity of the helium flux spectral index is presented for the first time. The spectral index progressively hardens at rigidities larger than 100 GV. The rigidity dependence of the helium flux spectral index is similar to that of the proton spectral index though the magnitudes are different. Remarkably, the spectral index of the proton to helium flux ratio increases with rigidity up to 45 GV and then becomes constant; the flux ratio above 45 GV is well described by a single power law.

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.

We report the properties of sodium (Na) and aluminum (Al) cosmic rays in the rigidity range 2.15 GV to 3.0 TV based on 0.46 million sodium and 0.51 million aluminum nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. We found that Na and Al, together with nitrogen (N), belong to a distinct cosmic ray group. In this group, we observe that, similar to the N flux, both the Na flux and Al flux are well described by the sums of a primary cosmic ray component (proportional to the silicon flux) and a secondary cosmic ray component (proportional to the fluorine flux). The fraction of the primary component increases with rigidity for the N, Na, and Al fluxes and becomes dominant at the highest rigidities. The $\mathrm{Na}/\mathrm{Si}$ and $\mathrm{Al}/\mathrm{Si}$ abundance ratios at the source, $0.036\pm 0.003$ for $\mathrm{Na}/\mathrm{Si}$ and $0.103\pm 0.004$ for $\mathrm{Al}/\mathrm{Si}$, are determined independent of cosmic ray propagation.

We present the first measurement of cosmic-ray fluxes of ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ isotopes in the rigidity range from 1.9 to 25 GV. The measurements are based on $9.7\times {10}^5$ ${}^6\mathrm{Li}$ and $1.04\times {10}^6$ ${}^7\mathrm{Li}$ nuclei collected by the Alpha Magnetic Spectrometer on the International Space Station from May 2011 to October 2023. We observe that over the entire rigidity range the ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ fluxes exhibit nearly identical time variations and, above $\sim 4\mathrm{GV}$, the time variations of ${}^6\mathrm{Li}$, ${}^7\mathrm{Li}$, He, Be, B, C, N, and O fluxes are identical. Above $\sim 7\mathrm{GV}$, we find an identical rigidity dependence of the ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ fluxes. This shows that they are both produced by collisions of heavier cosmic-ray nuclei with the interstellar medium and, in particular, excludes the existence of a sizable primary component in the ${}^7\mathrm{Li}$ flux.

Knowledge of the rigidity dependence of the boron to carbon flux ratio (B/C) is important in understanding the propagation of cosmic rays. The precise measurement of the $\mathrm{B}/\mathrm{C}$ ratio from 1.9 GV to 2.6 TV, based on 2.3 million boron and 8.3 million carbon nuclei collected by AMS during the first 5 years of operation, is presented. The detailed variation with rigidity of the $\mathrm{B}/\mathrm{C}$ spectral index is reported for the first time. The $\mathrm{B}/\mathrm{C}$ ratio does not show any significant structures in contrast to many cosmic ray models that require such structures at high rigidities. Remarkably, above 65 GV, the $\mathrm{B}/\mathrm{C}$ ratio is well described by a single power law $R^{\mathrm{\Delta }}$ with index $\mathrm{\Delta }=-0.333\pm 0.014(\text{fit})\pm 0.005(\text{syst})$, in good agreement with the Kolmogorov theory of turbulence which predicts $\mathrm{\Delta }=-1/3$ asymptotically.

We report the unique properties of cosmic phosphorus (P), chlorine (Cl), argon (Ar), potassium (K), and calcium (Ca) fluxes in the GV to TV rigidity range collected by the Alpha Magnetic Spectrometer (AMS) on the International Space Station. With a total of one million events collected over 13.5 years, we observed that the rigidity dependencies of the five fluxes are well described by the sums of a primary cosmic ray component and a secondary cosmic ray component. The abundance ratios of all five elements to Si at the source are accurately determined independent of cosmic ray propagation. The source abundance of Ar and Ca (even-$Z$ elements) is larger than P, Cl, and K (odd-$Z$ elements). The secondary components of the P and the Cl fluxes are each $\sim 1/3$ of the F flux, and the secondary components of the Ar, K, and Ca fluxes are each $\sim 1/2$ of the F flux. The twenty elements measured by AMS, from He to Ca and Fe, can be categorized into four classes, two primary and two secondary, based on their rigidity dependence.

We present a measurement of the cosmic ray $(e^{+}+e^{-})$ flux in the range 0.5 GeV to 1 TeV based on the analysis of 10.6 million $(e^{+}+e^{-})$ events collected by AMS. The statistics and the resolution of AMS provide a precision measurement of the flux. The flux is smooth and reveals new and distinct information. Above 30.2 GeV, the flux can be described by a single power law with a spectral index $\gamma =-3.170\pm 0.008(\text{stat}+\text{syst})\pm 0.008(\text{energy}\text{scale})$.

We present the precision measurements of 11 years of daily cosmic electron fluxes in the rigidity interval from 1.00 to 41.9 GV based on $2.0\times {10}^8$ electrons collected with the Alpha Magnetic Spectrometer (AMS) aboard the International Space Station. The electron fluxes exhibit variations on multiple timescales. Recurrent electron flux variations with periods of 27 days, 13.5 days, and 9 days are observed. We find that the electron fluxes show distinctly different time variations from the proton fluxes. Remarkably, a hysteresis between the electron flux and the proton flux is observed with a significance of greater than $6\sigma$ at rigidities below 8.5 GV. Furthermore, significant structures in the electron-proton hysteresis are observed corresponding to sharp structures in both fluxes. This continuous daily electron data provide unique input to the understanding of the charge sign dependence of cosmic rays over an 11-year solar cycle.

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.