
The process by which stellar explosions and remnants accelerate particles to cosmic ray energies.Cosmic ray acceleration is the process by which charged particles—mostly protons and atomic nuclei—are boosted to energies far beyond those achievable in human-made accelerators. These particles, arriving at Earth from space, carry energies up to 10^20 electronvolts, millions of times higher than the Large Hadron Collider can produce. The dominant sources are supernova remnants: when a massive star explodes, it drives a shock wave into the surrounding interstellar medium, and particles bouncing across this shock gain energy with each crossing—a mechanism known as diffusive shock acceleration.
The idea that supernova remnants could accelerate cosmic rays was proposed by Enrico Fermi in 1949, and the specific diffusive shock mechanism was developed in the late 1970s by Anthony Bell and others.
The key mechanism is repeated scattering by magnetic turbulence. A particle crossing a shock front from upstream to downstream and back gains a small energy boost each time, because the magnetic irregularities act as moving mirrors. Over thousands of crossings, the particle's energy grows exponentially. The process is self-limiting: once a particle's gyroradius becomes comparable to the size of the remnant, it escapes. This explains the observed power-law energy spectrum of cosmic rays, which extends over many orders of magnitude.
Understanding cosmic ray acceleration helps interpret data from gamma-ray observatories like Fermi-LAT and CTA, which detect the high-energy photons produced when accelerated particles interact with matter and radiation.
The most energetic cosmic rays, above 10^20 eV, are so fast that they would take only about 10 minutes to travel from the Sun to Earth, yet their sources remain mysterious because they are deflected by magnetic fields.
| ω | variable | angular frequency — angular frequency radian per second |
| k | variable | wave number — wave number radian per metre |
| c | variable | propagation speed — wave speed metre per second |
| | | | operator | returns the magnitude of a real number — absolute value operator |






