Highly energetic electrons are present in many different astrophysical systems, from solar flares and supernovae to planetary magnetospheres and the intra-cluster medium. Plasma turbulence is ubiquitous in these systems, and it is fundamental for the production of energetic particles and their transport properties.
The problem of particle acceleration in astrophysical turbulence was first considered by Fermi, who considered particles interacting with randomly moving scattering centres, thereby gaining energy stochastically . If the scattering centres have some coherent, large-scale motion, the energisation is more rapid . Since Fermi’s original ideas, the topic has been extensively investigated.
Using DiRAC we have studied the acceleration and transport properties of transrelativistic electrons in plasma turbulence  using hybrid PIC and test particle simulations. We have discovered that turbulence strength is a key parameter that controls electron acceleration, with rapid acceleration due to particle trapping happening when the turbulence level is high. Figure 1a shows two examples of open and trapped electron trajectories. Figure 1b shows a detail of electron trajectory with the trapped part highlighted in red. It can be seen, in the figure inset, that, when the electron is trapped, fast quasi-monotonic energisation is achieved. The fast energisation stage resembles a first-order Fermi process as observed by other authors in simulations of magnetic reconnection (see Ref  for further details).
The importance of turbulence strength to activate fast electron acceleration has important consequences for heliospheric and astrophysical plasmas, with implications for understanding, for example, the physics of solar flares and radio emission from galaxy clusters.
-  E. Fermi, On the origin of cosmic radiation, Physical Review 75:1169-1174 (1949)
-  E. Fermi, Galactic magnetic fields and the origin of cosmic radiation, The Astrophysical Journal 119:1 (1954)
-  D. Trotta, L. Franci, D. Burgess and P. Hellinger, Fast acceleration of transrelativistic electrons in astrophysical turbulence, The Astrophysical Journal, 894:2-136 (2020)