Abstract
Context.
Particle acceleration at collisionless shocks, governed by Parker’s transport equation, is frequently characterized by a power-law energy spectrum with an exponential cutoff, typically taking the form ∼
E
−
γ
exp(−
E
/
E
0
). In high-energy astrophysics, the exponential decay is often generalized to ∼exp(−(
E
/
E
0
)
β
) to model both Galactic cosmic rays and gamma-ray spectra.
Aims.
We aim to propose a new spectral fitting formalism governed entirely by physically interpretable parameters, providing a comprehensive framework for interpreting observed energy spectra across space plasmas and high-energy astrophysics.
Methods.
Operating within the test-particle regime of diffusive shock acceleration, we derive a novel approximant for the energy spectrum of accelerated particles in the context of nonrelativistic piecewise shocks.
Results.
Our formulation reveals a previously uncharacterized transitional phase in the energy spectrum, situated between the canonical low-energy power-law distribution and the high-energy exponential decay asymptote. Furthermore, this approach demonstrates the emergence of robust spectral self-similarity across different ion species and temporal stages of the acceleration process.