A laser pulse traveling through a plasma can excite large amplitude plasma waves that can be used to accelerate relativistic electron beams in a very short distance—a technique called laser wakefield acceleration. Many wakefield acceleration experiments rely on the process of wave breaking, or self-injection, to inject electrons into the wave, while other injection techniques rely on operation without self-injection. We present an experimental study into the parameters, including the pulse energy, focal spot quality, and pulse power, that determine whether or not a wakefield accelerator will self-inject. By taking into account the processes of self-focusing and pulse compression we are able to extend a previously described theoretical model, where the minimum bubble size
k
p
r
b
required for trapping is not constant but varies slowly with density and find excellent agreement with this model.