Available Models

All models inherit from PrimaryFlux and implement the same interface. They accept an optional geomagnetic_cutoff parameter (in GV) that zeros the flux below the corresponding rigidity for each nucleus.

Model Comparison

Nucleon Flux

All-nucleon flux (proton + neutron) scaled by \(E^{2.5}\) for visibility across the full energy range.

All-Particle Flux

Total flux of all nuclei (all-particle spectrum) scaled by \(E^{2.5}\).

Neutron Fraction

Fraction of neutrons in the nucleon flux, showing composition differences between models.

Mean Logarithmic Mass

\(\langle\ln A\rangle\) as a function of energy per particle. Higher values indicate heavier composition.

Parameterized Models

Class	Reference	Energy Range	Notes
HillasGaisser2012	Gaisser, Astropart. Phys. 35, 801 (2012)	Full range	Variants: H3a, H4a
H3a_polygonato	Modified Gaisser (2012)	Full range	Poly-gonato at low E
GaisserStanevTilav	Gaisser, Stanev, Tilav, arXiv:1303.3565 (2013)	Full range	Variants: 3-gen, 4-gen
CombinedGHandHG	Fedynitch et al., PRD 86, 114024 (2012)	Full range	GH at low E, HG at high E
PolyGonato	Hoerandel, Astropart. Phys. 19, 193 (2003)	Full range	11 mass groups
ZatsepinSokolskaya	Zatsepin & Sokolskaya, A&A 458, 1 (2006)	< 1-10 PeV	Variants: default, pamela
GaisserHonda	Gaisser & Honda, ARNPS 52, 153 (2002)	< 100 TeV	Tuned to balloon data
Thunman	Thunman et al., Astropart. Phys. 5, 309 (1996)	Full range	Proton-only broken power law
SimplePowerlaw27	Based on Thunman	Below knee	Proton-only \(E^{-2.7}\)
GlobalSplineFit	Fedynitch et al., arXiv:2609.32649 (2026)	1 GeV - \(10^{11}\) GeV	Via globalsplinefit (gsf extra); all species, versions 2026.1/2025/2019/2017
GlobalSplineFitReduced	Fedynitch et al., arXiv:2609.32649 (2026)	1 GeV - \(10^{11}\) GeV	Nucleon flux only, pivot uncertainty parameters
GlobalSplineFitBeta	Dembinski et al., PoS ICRC2017 533	10 GV - \(10^{11}\) GeV	Deprecated: GSF 2017 nucleon flux at φ = 554 MV

Nucleus ID Scheme (CORSIKA)

Protons have ID 14. Composite nuclei: ID = 100 * A + Z

Nucleus	A	Z	CORSIKA ID
Proton	1	1	14
Helium	4	2	402
Carbon	12	6	1206
Silicon	28	14	2814
Iron	54	26	5426

Geomagnetic Cutoff

All models accept geomagnetic_cutoff (in GV) as a constructor parameter. For a nucleus with charge \(Z\), the energy cutoff is \(E_\text{cut} = Z \times R_\text{cut}\) (GeV). Flux is zeroed below this energy.

import crflux.models as mods

# 7 GV cutoff (typical for mid-latitudes)
model = mods.HillasGaisser2012("H3a", geomagnetic_cutoff=7.0)

The plot below shows the effect of different cutoff values on the H3a nucleon flux:

Global Spline Fit (GSF)

GlobalSplineFit wraps globalsplinefit as a PrimaryFlux: per-nucleus fluxes for every species of the chosen version (CORSIKA ids, 201 = deuterium where carried) and exact proton/neutron nucleon fluxes. GlobalSplineFitReduced is its nucleon-only special case with the uncertainty as relative-flux parameters at pivot energies (ReducedGSF). Install with pip install "crflux[gsf]" (Python >= 3.10). Reference: A. Fedynitch, K. Fujisue, H. Dembinski, R. Engel, arXiv:2609.32649 (2026).

from crflux.models import GlobalSplineFit, GlobalSplineFitReduced
import numpy as np

gsf = GlobalSplineFit(version="2026.1")  # also "2025", "2019", "2017"
gsf.nucleus_flux(5626, 1e6)  # iron, total energy per nucleus
gsf.gsf.error(np.logspace(3, 6, 4), "Fe*")  # underlying globalsplinefit model

central = GlobalSplineFitReduced(version="2026.1")
red = central.reduction
theta = np.zeros(red.n_params)
theta[3] = red.sigma[3]  # +1 sigma on pivot 3
varied = GlobalSplineFitReduced(reduction=red, theta=theta)
fraction, proton, neutron = varied.p_and_n_flux(np.logspace(0, 8, 50))

Energies are total GeV (per nucleus for nucleus_flux, per nucleon for p_and_n_flux). time_interval selects the solar-modulation period (default Solar Cycle 24, "LIS" for none). geomagnetic_cutoff is applied by globalsplinefit per species in rigidity. Kinetic-energy reductions are rejected. GlobalSplineFitBeta is deprecated: its table is GSF 2017 at a fixed φ = 554 MV, i.e. GlobalSplineFit(version="2017", time_interval=(199807, 199808)).