Fast radio bursts (FRB) — mysterious beacons of the Universe, emitting in milliseconds energy comparable to the Sun’s radiation over centuries. They are thought to originate from magnetars — super-magnetized remnants of neutron stars, predicted by Fritz Zwicky in the 1930s, where the magnetic field reaches monstrous $10^{11}$ T. In these extreme conditions, electromagnetic waves of such power are born that the surrounding plasma becomes an arena of nonlinear dances. The question of energy transfer from waves to particles long remained open: classical models claimed that for efficient acceleration the wave must literally overturn the background field. But a new study, based on the Hamiltonian approach and numerical simulation using the particle-in-cell method, has revealed a much more subtle and rich scenario.

Imagine a stormy ocean: the particles are swimmers, and the radio wave is a giant swell. It was previously thought that only a swell that exceeds the sea floor itself in height (δ ≥ 1) could overwhelm the swimmers. But it turns out that chaos sets in already at δ ≈ 0.25 — when the wave reaches only a quarter of the background magnetization. This threshold was determined using Chirikov’s resonance-overlap criterion: in phase space, islands of regular motion, like atolls, merge, destroying the last invariant tori.

The maximum Lyapunov exponent $λ_{max}$ ~ ln(a₀), which describes the rate at which trajectories diverge, begins to grow long before the wave overturns. But the most fascinating thing happens with further strengthening of the wave. Most swimmers remain in the foamy surf — their energy grows slowly, diffusively, proportionally to time. However, a small fraction, like virtuoso surfers, synchronize with the crest and shoot out into ballistic flight, reminiscent of Lévy jumps. The threshold for such ‘surfing’ is about four times higher than the chaos threshold, and the energy gain can be colossal. This explains the puzzle that plagued astrophysicists: why even in simulations with δ = 2, the dissipation of electromagnetic energy remains disappointingly low. The wave simply sweeps through the plasma, barely losing power, transferring it only to a tiny fraction of trapped particles. In essence, 99.99% of the energy goes nowhere — the magnetar screams into the void, and only one in a billion ‘passengers’ is carried away like a bullet into the vastness of the Galaxy.

These findings overturn established models of FRB radiation. Instead of simplified hydrodynamic approximations, one must take into account kinetic effects of phase synchronization and stochasticity. This opens the way to revising scenarios of radio wave escape from the magnetospheres of pulsars (the beacons discovered by Jocelyn Bell Burnell) and magnetars, as well as to explaining non-thermal tails in cosmic ray spectra. It is not excluded that surfing acceleration in waves from magnetic reconnection gives birth to particles with energies that baffle Earth's detectors — perhaps this is how the mysterious ultra-high-energy cosmic rays appear. Three-dimensional simulations with realistic geometry are already being planned, which will recreate this cosmic kitchen in detail — from wave generation to a relativistic surfer flying through the Galaxy.