Elastic rethermalization of a trapped atomic gas (${\Gamma }_{\mathrm{el}}\sim n{\sigma }_{\mathrm{el}}\bar{v}$)

After energy-selective loss, elastic collisions redistribute energy and refill the escaping tail. This restores a nearly thermal distribution when redistribution is fast compared with the changing cutoff and unwanted atom loss. The collision rate depends on number density, cross section, and relative speed; slowing atoms alone does not guarantee continued equilibration.

Runaway evaporative cooling is an evaporation regime in which cooling makes subsequent elastic rethermalization of a trapped atomic gas faster rather than slower. In a sufficiently confining trap, the cooling sample can become denser enough that the increasing number density outweighs the decreasing collision speed in ${\Gamma }_{\mathrm{el}}\sim n{\sigma }_{\mathrm{el}}\bar{v}$.

The growing collision rate helps replenish the high-energy tail removed by forced evaporative cooling. It is not automatic: trap weakening, unfavorable cross section changes or unwanted particle loss can instead reduce the rate. Measuring atom number, cloud size and temperature during the ramp tests whether the favorable regime is actually maintained.