The first step is to identify which part of the bug we’re looking at, and I think it should be recognizable as portions of the compound eyes with thousands of tiny lenses, or ommatidia, producing that geometrically speckled look. The fact that these compound eyes meet at a long seam (the almost vertical black line) narrows down the possibilities to just one family out of all dragonflies and damselflies in North America: the darners, Aeshnidae. The eyes of all damselflies are separated by a gap; at most, the eyes of the other dragonflies meet at a very short seam, but some are separated by a gap or just meet at a point.
The next thing you might notice is the pair of black tooth-like projections at the bottom of the image. Considering that we appear to be looking at portions of both compound eyes and the seam where they meet, it makes sense that those projections are on the rear of the head (the front being out of view beyond the top of the image). The roughly triangular pale area at the end of the black seam is the occiput and the teeth are projections on its rear margin.
So we have a North American aeshnid (darner) with a pair of toothy projections on the occiput’s rear margin. There is only one species, and one sex of that species, which possesses such cranial armature: the female Common Green Darner (Anax junius)—a common species across the continent from southern Canada to northern Mexico and the West Indies (it is even on Hawaii and easternmost Asia, and has strayed to the United Kingdom). This is such a distinctive structural feature on female Common Green Darners that it is illustrated in Dragonflies of North America (Needham, Westfall, and May, 2000). See Figure 80 on page 159. Males of the species lack those projections, and the rear margin of their occiput is smooth and slightly concave—quite unremarkable, actually. Because of that, if we had the same limited view of a male Common Green Darner, we would not be able to identify it to species.
Below is a more expansive view of our mystery subject, so you can put all of this into perspective. The undeniably green thorax and blue-and-black bull’s eye pattern on the frons (just in front of the eyes) scream Common Green Darner. Even the lanky Giant Darner (Anax walsinghami) of the southwestern US—basically a stretched version of the Common Green Darner with similar frons and thoracic coloration, is ruled out by those occipital projections (both males and females).
I implied that there was more to glean from our challenge . . . Did you notice the damage to the ommatidia (lenses) on both eyes just forward of the occiput? Just left of the occiput, there’s a small darkened spot that looks almost like a puncture, and to the right there appears to be a depression with a scratch across the middle. This is proof positive that a male has “grabbed” her with his abdominal appendages. The male’s epiproct (lower abdominal appendage) would have landed right over the occiput, and that thing has some serious toothy projections of its own which caused the damage to the eyes. That well-armed epiproct must make it difficult for the female to simply shake him off. Naturally, copulation was the male’s goal, but we can’t tell if they actually copulated or not—there are limits to what we can divine from images!
I leave you with a final full-body view of our mystery subject (same individual, different angle). This female Common Green Darner (Anax junius) was photographed in Colusa, California, on 28 May 2013.