Geophysical Research Letters
Simulations of relativistic runaway breakdown (RRB) are performed as functions of both time and space, resulting in explicit calculations of e-folding lengths (λ) and times (τ). The ratio of λ to τ agrees well with the speed of the avalanche, which ranges from 2.61 × 108 m sˉ¹ to 2.72 × 108 m sˉ¹. Thus, using the speed of light, c, for the ratio of λ to τ can cause a 10% error when estimating λ from τ. A 10% error in λ will cause a factor of three error in the predicted number of runaway electrons for every ten estimated e-foldings. In addition, previous models that predict peak radiated electric fields from RRB have used avalanche speeds of 0.987c and higher. Using a propagation speed of 0.89c causes a dramatic change in the predicted beaming pattern of electromagnetic radiation caused by RRB in these models.
Coleman, Lee M. and Dwyer, Joseph R., "Propagation Speed Of Runaway Electron Avalanches" (2006). Aerospace, Physics, and Space Science Faculty Publications. 498.