What exactly do you mean with "spike"? This word is used to describe q-switching or other related gain dynamics. Among all lasers that I know the HeNe laser is probably the least susceptible laser for q-switching dynamics. One of the reasons for this is an upperstate lifetime in the sub-microsecond range, which has to be compared with millisecond lifetimes of typical solid-state lasers. In a HeNe laser the photon lifetime in the cavity is comparable with the upperstate lifetime; in solid-state lasers photon lifetimes are at least a factor thousand shorter.