We develop a multi-scale computational model for studying tungsten fuzz formation under low-energy He irradiation. The molecular dynamics and kinetic Monte Carlo results show that the W fuzz growth mechanism is the following: the He atoms are trapped in W, forming bubbles and causing growth by loop punching. The bubbles close to the surface rupture. The balance between these processes leads to a stochastic surface growth, causing the surface roughness and fuzz thickness growth to scale as root t. The growth rates agree with the experimental results. Copyright (c) EPLA, 2014