when i grew aeroponic vegetables for a family at their house i used Azamax by GH you can use it systemically or as a foiliar spray but it tends to clog spray bottles so you dont need much. certainly not full strength. id use it with a drop of dawn dish soap. the insturctions for use are also vague. it works the same on insects as it does on plants. it clogs cells and suffocates the organism. So if you use too much you can kill a plant, but you know that.
You can also do the same thing with vegetable oil and dish soap. the thing about it is you will need to apply it more than once.
I grew indoors so outdoors growing is probably a whole 'nother ballgame