Universality of the scaling law for particle energization in collisionless plasmas

Particles are energized—heated and accelerated to nonthermal energies—in laboratory, space, solar, and astrophysical plasmas. In collisionless plasmas, ion and electron temperatures are often unequal and cannot be fully understood within the framework of magnetohydrodynamics (MHD). In this context, a relation, Δε_s = q_sVBL_s, for each species can be useful, where Δε_s is the energy gain for species s, measured in the plasma rest frame, relative to the upstream region of shocks and magnetic reconnection; q_s is the charge; V is the plasma bulk flow speed; B is the magnetic field strength; and L_s is a characteristic length scale of energization. From this relation, we recently derived semiempirical scalings for ion and electron temperature increases across shocks and magnetic reconnection in Earth’s plasma environment. However, it remains unclear how broadly these scalings apply. Here we show that the same scalings explain temperature increases in other plasma environments such as laboratory experiments, planetary magnetospheres, solar flares, and supernova remnant shocks. Combined with another recent report that the maximum energy of particles in various plasma environments follows the same relation when L_s is taken as the system size, our results indicate that Δε_s = q_sVBL_s provides a novel framework that universally captures particle energization—both heating and acceleration to nonthermal energies. Additionally, the scaling captures the essential MHD trends while revealing systematic deviations that point to kinetic effects beyond fluid models, highlighting promising directions for theoretical and simulation studies.