As far as chemical warfare goes, you could try something like Safer's soap. It's a potassium salt of fatty acids, and messes with the cell membranes of the targeted insects. The weakness is that it requires contact. Another alternative is a synthetic pyrethroid, like bifenthrin. It is a waxy solid, doesn't get absorbed through [your] skin, is a generally provided as a water dispersion (so no bad smell, either because of carrier or the compound itself, unlike acephate), and is about 1000 to 3000 times more effective against invertebrates than vertebrates.
Either way, you'll need multiple applications, to get any younglings that hatched from eggs, but both should work. Personally, I'd use bifrenthrin. Talstar-P is one formulation, and is available on Amazon. That particular formulation only needs about 2 teaspoons per gallon dilution, so you should buy the smallest possible quantity.
There are thousands of species. And thrips definably damage foliage.
