Normalization Constant

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N A Schwadron - One of the best experts on this subject based on the ideXlab platform.

  • spectral properties of large gradual solar energetic particle events ii systematic q m dependence of heavy ion spectral breaks
    The Astrophysical Journal, 2016
    Co-Authors: M I Desai, G M Mason, M A Dayeh, R W Ebert, D J Mccomas, C M S Cohen, R A Mewaldt, N A Schwadron
    Abstract:

    We fit ~0.1–500 MeV nucleon^(−1) H–Fe spectra in 46 large solar energetic particle (SEP) events with the double power-law Band function to obtain a Normalization Constant, low- and high-energy parameters γ_a and γ_b, and break energy E_ B, and derive the low-energy spectral slope γ_1. We find that: (1) γ_a, γ_1, and γ_b are species-independent and the spectra steepen with increasing energy; (2) E_B decreases systematically with decreasing Q/M scaling as (Q/M)^α ; (3) α varies between ~0.2–3 and is well correlated with the ~0.16–0.23 MeV nucleon^(−1) Fe/O; (4) in most events, α 3, and O E_B increases with γ_b–γ_a; and (5) in many extreme events (associated with faster coronal mass ejections (CMEs) and GLEs), Fe/O and ^3He/^4He ratios are enriched, α ⩾ 1.4, γ_b–γ_a < 3, and E B decreases with γ_b–γ_a. The species-independence of γ_a, γ_1, and γ_b and the Q/M dependence of E_B within an event and the α values suggest that double power-law SEP spectra occur due to diffusive acceleration by near-Sun CME shocks rather than scattering in interplanetary turbulence. Using γ_1, we infer that the average compression ratio for 33 near-Sun CME shocks is 2.49 ± 0.08. In most events, the Q/M dependence of E B is consistent with the equal diffusion coefficient condition and the variability in α is driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but weaker than the spectra for extreme events. In contrast, in extreme events, enhanced wave power enables faster CME shocks to accelerate impulsive suprathermal ions more efficiently than ambient coronal ions.

  • spectral properties of large gradual solar energetic particle events ii systematic q m dependence of heavy ion spectral breaks
    arXiv: Space Physics, 2016
    Co-Authors: M I Desai, G M Mason, M A Dayeh, R W Ebert, D J Mccomas, C M S Cohen, R A Mewaldt, N A Schwadron, C W Smith
    Abstract:

    We fit the $\sim$0.1-500 MeV/nucleon H-Fe spectra in 46 large SEP events surveyed by Desai et al. (2016) with the double power-law Band function to obtain a Normalization Constant, low- and high-energy parameters $\gamma_a$ and $\gamma_b$; and break energy $E_B$. We also calculate the low-energy power-law spectral slope $\gamma_1$. We find that: 1) $\gamma_a$, $\gamma_1$, and $\gamma_b$ are species-independent within a given SEP event, and the spectra steepen with increasing energy; 2) $E_B$'s are well ordered by Q/M ratio, and decrease systematically with decreasing Q/M, scaling as (Q/M)$^\alpha$ with $\alpha$ varying between $\sim$0.2-3; 3) $\alpha$ is well correlated with Fe/O at $\sim$0.16-0.23 MeV/nucleon and CME speed; 4) In most events: $\alpha $3; and 5) Seven out of 9 extreme SEP events (associated with faster CMEs and GLEs) are Fe-rich, have $\alpha >$1.4, have flatter spectra at low and high energies with $\gamma_b$-$\gamma_a <$3. The species-independence of $\gamma_a$, $\gamma_1$, and $\gamma_b$ and the systematic Q/M dependence of $E_B$ within an event, as well as the range of values for $\alpha$ suggest that the formation of double power-laws in SEP events occurs primarily due to diffusive acceleration at near-Sun CME shocks and not due to scattering in the interplanetary turbulence. In most events, the Q/M-dependence of $E_B$ is consistent with the equal diffusion coefficient condition while the event-to-event variations in $\alpha$ are probably driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but still weaker compared to that inferred for the extreme events.

M I Desai - One of the best experts on this subject based on the ideXlab platform.

  • spectral properties of large gradual solar energetic particle events ii systematic q m dependence of heavy ion spectral breaks
    The Astrophysical Journal, 2016
    Co-Authors: M I Desai, G M Mason, M A Dayeh, R W Ebert, D J Mccomas, C M S Cohen, R A Mewaldt, N A Schwadron
    Abstract:

    We fit ~0.1–500 MeV nucleon^(−1) H–Fe spectra in 46 large solar energetic particle (SEP) events with the double power-law Band function to obtain a Normalization Constant, low- and high-energy parameters γ_a and γ_b, and break energy E_ B, and derive the low-energy spectral slope γ_1. We find that: (1) γ_a, γ_1, and γ_b are species-independent and the spectra steepen with increasing energy; (2) E_B decreases systematically with decreasing Q/M scaling as (Q/M)^α ; (3) α varies between ~0.2–3 and is well correlated with the ~0.16–0.23 MeV nucleon^(−1) Fe/O; (4) in most events, α 3, and O E_B increases with γ_b–γ_a; and (5) in many extreme events (associated with faster coronal mass ejections (CMEs) and GLEs), Fe/O and ^3He/^4He ratios are enriched, α ⩾ 1.4, γ_b–γ_a < 3, and E B decreases with γ_b–γ_a. The species-independence of γ_a, γ_1, and γ_b and the Q/M dependence of E_B within an event and the α values suggest that double power-law SEP spectra occur due to diffusive acceleration by near-Sun CME shocks rather than scattering in interplanetary turbulence. Using γ_1, we infer that the average compression ratio for 33 near-Sun CME shocks is 2.49 ± 0.08. In most events, the Q/M dependence of E B is consistent with the equal diffusion coefficient condition and the variability in α is driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but weaker than the spectra for extreme events. In contrast, in extreme events, enhanced wave power enables faster CME shocks to accelerate impulsive suprathermal ions more efficiently than ambient coronal ions.

  • spectral properties of large gradual solar energetic particle events ii systematic q m dependence of heavy ion spectral breaks
    arXiv: Space Physics, 2016
    Co-Authors: M I Desai, G M Mason, M A Dayeh, R W Ebert, D J Mccomas, C M S Cohen, R A Mewaldt, N A Schwadron, C W Smith
    Abstract:

    We fit the $\sim$0.1-500 MeV/nucleon H-Fe spectra in 46 large SEP events surveyed by Desai et al. (2016) with the double power-law Band function to obtain a Normalization Constant, low- and high-energy parameters $\gamma_a$ and $\gamma_b$; and break energy $E_B$. We also calculate the low-energy power-law spectral slope $\gamma_1$. We find that: 1) $\gamma_a$, $\gamma_1$, and $\gamma_b$ are species-independent within a given SEP event, and the spectra steepen with increasing energy; 2) $E_B$'s are well ordered by Q/M ratio, and decrease systematically with decreasing Q/M, scaling as (Q/M)$^\alpha$ with $\alpha$ varying between $\sim$0.2-3; 3) $\alpha$ is well correlated with Fe/O at $\sim$0.16-0.23 MeV/nucleon and CME speed; 4) In most events: $\alpha $3; and 5) Seven out of 9 extreme SEP events (associated with faster CMEs and GLEs) are Fe-rich, have $\alpha >$1.4, have flatter spectra at low and high energies with $\gamma_b$-$\gamma_a <$3. The species-independence of $\gamma_a$, $\gamma_1$, and $\gamma_b$ and the systematic Q/M dependence of $E_B$ within an event, as well as the range of values for $\alpha$ suggest that the formation of double power-laws in SEP events occurs primarily due to diffusive acceleration at near-Sun CME shocks and not due to scattering in the interplanetary turbulence. In most events, the Q/M-dependence of $E_B$ is consistent with the equal diffusion coefficient condition while the event-to-event variations in $\alpha$ are probably driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but still weaker compared to that inferred for the extreme events.

Hartmut Wittig - One of the best experts on this subject based on the ideXlab platform.

  • non perturbative determination of the axial current Normalization Constant in 0 a improved lattice qcd
    Nuclear Physics, 1997
    Co-Authors: Martin Lüscher, Stefan Sint, Rainer Sommer, Hartmut Wittig
    Abstract:

    Abstract A finite-size technique is employed to compute the Normalization Constant Z A of the isovector axial current in lattice QCD. The calculation is carried out in the quenched approximation for values of the bare gauge coupling g 0 ranging from 0 to 1. In the lattice action and the lattice expression for the axial current we include the counterterms required for O( a ) improvement, withaffe non-perturbatively determined coefficients. With little additional work the Normalization Constant Z V of the improved isospin current is also obtained.

  • Non-perturbative determination of the axial current Normalization Constant in O(a) improved lattice QCD
    Nuclear Physics B, 1997
    Co-Authors: Martin Lüscher, Stefan Sint, Rainer Sommer, Hartmut Wittig
    Abstract:

    A finite-size technique is employed to compute the Normalization Constant $Z_A$ of the isovector axial current in lattice QCD. The calculation is carried out in the quenched approximation for values of the bare gauge coupling $g_0$ ranging from 0 to 1. In the lattice action and the lattice expression for the axial current we include the counterterms required for O(a) improvement, with non-perturbatively determined coefficients. With little additional work the Normalization Constant $Z_V$ of the improved isospin current is also obtained.

R W Ebert - One of the best experts on this subject based on the ideXlab platform.

  • spectral properties of large gradual solar energetic particle events ii systematic q m dependence of heavy ion spectral breaks
    The Astrophysical Journal, 2016
    Co-Authors: M I Desai, G M Mason, M A Dayeh, R W Ebert, D J Mccomas, C M S Cohen, R A Mewaldt, N A Schwadron
    Abstract:

    We fit ~0.1–500 MeV nucleon^(−1) H–Fe spectra in 46 large solar energetic particle (SEP) events with the double power-law Band function to obtain a Normalization Constant, low- and high-energy parameters γ_a and γ_b, and break energy E_ B, and derive the low-energy spectral slope γ_1. We find that: (1) γ_a, γ_1, and γ_b are species-independent and the spectra steepen with increasing energy; (2) E_B decreases systematically with decreasing Q/M scaling as (Q/M)^α ; (3) α varies between ~0.2–3 and is well correlated with the ~0.16–0.23 MeV nucleon^(−1) Fe/O; (4) in most events, α 3, and O E_B increases with γ_b–γ_a; and (5) in many extreme events (associated with faster coronal mass ejections (CMEs) and GLEs), Fe/O and ^3He/^4He ratios are enriched, α ⩾ 1.4, γ_b–γ_a < 3, and E B decreases with γ_b–γ_a. The species-independence of γ_a, γ_1, and γ_b and the Q/M dependence of E_B within an event and the α values suggest that double power-law SEP spectra occur due to diffusive acceleration by near-Sun CME shocks rather than scattering in interplanetary turbulence. Using γ_1, we infer that the average compression ratio for 33 near-Sun CME shocks is 2.49 ± 0.08. In most events, the Q/M dependence of E B is consistent with the equal diffusion coefficient condition and the variability in α is driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but weaker than the spectra for extreme events. In contrast, in extreme events, enhanced wave power enables faster CME shocks to accelerate impulsive suprathermal ions more efficiently than ambient coronal ions.

  • spectral properties of large gradual solar energetic particle events ii systematic q m dependence of heavy ion spectral breaks
    arXiv: Space Physics, 2016
    Co-Authors: M I Desai, G M Mason, M A Dayeh, R W Ebert, D J Mccomas, C M S Cohen, R A Mewaldt, N A Schwadron, C W Smith
    Abstract:

    We fit the $\sim$0.1-500 MeV/nucleon H-Fe spectra in 46 large SEP events surveyed by Desai et al. (2016) with the double power-law Band function to obtain a Normalization Constant, low- and high-energy parameters $\gamma_a$ and $\gamma_b$; and break energy $E_B$. We also calculate the low-energy power-law spectral slope $\gamma_1$. We find that: 1) $\gamma_a$, $\gamma_1$, and $\gamma_b$ are species-independent within a given SEP event, and the spectra steepen with increasing energy; 2) $E_B$'s are well ordered by Q/M ratio, and decrease systematically with decreasing Q/M, scaling as (Q/M)$^\alpha$ with $\alpha$ varying between $\sim$0.2-3; 3) $\alpha$ is well correlated with Fe/O at $\sim$0.16-0.23 MeV/nucleon and CME speed; 4) In most events: $\alpha $3; and 5) Seven out of 9 extreme SEP events (associated with faster CMEs and GLEs) are Fe-rich, have $\alpha >$1.4, have flatter spectra at low and high energies with $\gamma_b$-$\gamma_a <$3. The species-independence of $\gamma_a$, $\gamma_1$, and $\gamma_b$ and the systematic Q/M dependence of $E_B$ within an event, as well as the range of values for $\alpha$ suggest that the formation of double power-laws in SEP events occurs primarily due to diffusive acceleration at near-Sun CME shocks and not due to scattering in the interplanetary turbulence. In most events, the Q/M-dependence of $E_B$ is consistent with the equal diffusion coefficient condition while the event-to-event variations in $\alpha$ are probably driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but still weaker compared to that inferred for the extreme events.

R A Mewaldt - One of the best experts on this subject based on the ideXlab platform.

  • spectral properties of large gradual solar energetic particle events ii systematic q m dependence of heavy ion spectral breaks
    The Astrophysical Journal, 2016
    Co-Authors: M I Desai, G M Mason, M A Dayeh, R W Ebert, D J Mccomas, C M S Cohen, R A Mewaldt, N A Schwadron
    Abstract:

    We fit ~0.1–500 MeV nucleon^(−1) H–Fe spectra in 46 large solar energetic particle (SEP) events with the double power-law Band function to obtain a Normalization Constant, low- and high-energy parameters γ_a and γ_b, and break energy E_ B, and derive the low-energy spectral slope γ_1. We find that: (1) γ_a, γ_1, and γ_b are species-independent and the spectra steepen with increasing energy; (2) E_B decreases systematically with decreasing Q/M scaling as (Q/M)^α ; (3) α varies between ~0.2–3 and is well correlated with the ~0.16–0.23 MeV nucleon^(−1) Fe/O; (4) in most events, α 3, and O E_B increases with γ_b–γ_a; and (5) in many extreme events (associated with faster coronal mass ejections (CMEs) and GLEs), Fe/O and ^3He/^4He ratios are enriched, α ⩾ 1.4, γ_b–γ_a < 3, and E B decreases with γ_b–γ_a. The species-independence of γ_a, γ_1, and γ_b and the Q/M dependence of E_B within an event and the α values suggest that double power-law SEP spectra occur due to diffusive acceleration by near-Sun CME shocks rather than scattering in interplanetary turbulence. Using γ_1, we infer that the average compression ratio for 33 near-Sun CME shocks is 2.49 ± 0.08. In most events, the Q/M dependence of E B is consistent with the equal diffusion coefficient condition and the variability in α is driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but weaker than the spectra for extreme events. In contrast, in extreme events, enhanced wave power enables faster CME shocks to accelerate impulsive suprathermal ions more efficiently than ambient coronal ions.

  • spectral properties of large gradual solar energetic particle events ii systematic q m dependence of heavy ion spectral breaks
    arXiv: Space Physics, 2016
    Co-Authors: M I Desai, G M Mason, M A Dayeh, R W Ebert, D J Mccomas, C M S Cohen, R A Mewaldt, N A Schwadron, C W Smith
    Abstract:

    We fit the $\sim$0.1-500 MeV/nucleon H-Fe spectra in 46 large SEP events surveyed by Desai et al. (2016) with the double power-law Band function to obtain a Normalization Constant, low- and high-energy parameters $\gamma_a$ and $\gamma_b$; and break energy $E_B$. We also calculate the low-energy power-law spectral slope $\gamma_1$. We find that: 1) $\gamma_a$, $\gamma_1$, and $\gamma_b$ are species-independent within a given SEP event, and the spectra steepen with increasing energy; 2) $E_B$'s are well ordered by Q/M ratio, and decrease systematically with decreasing Q/M, scaling as (Q/M)$^\alpha$ with $\alpha$ varying between $\sim$0.2-3; 3) $\alpha$ is well correlated with Fe/O at $\sim$0.16-0.23 MeV/nucleon and CME speed; 4) In most events: $\alpha $3; and 5) Seven out of 9 extreme SEP events (associated with faster CMEs and GLEs) are Fe-rich, have $\alpha >$1.4, have flatter spectra at low and high energies with $\gamma_b$-$\gamma_a <$3. The species-independence of $\gamma_a$, $\gamma_1$, and $\gamma_b$ and the systematic Q/M dependence of $E_B$ within an event, as well as the range of values for $\alpha$ suggest that the formation of double power-laws in SEP events occurs primarily due to diffusive acceleration at near-Sun CME shocks and not due to scattering in the interplanetary turbulence. In most events, the Q/M-dependence of $E_B$ is consistent with the equal diffusion coefficient condition while the event-to-event variations in $\alpha$ are probably driven by differences in the near-shock wave intensity spectra, which are flatter than the Kolmogorov turbulence spectrum but still weaker compared to that inferred for the extreme events.