Can you be more specific? Which aphid species are you interested in? The species will determine which host plant you need to grow in order to feed them, and you would match the growing season conditions of wherever that species normally lives.
If you just want any species, I might recommend the green peach aphid (Myzus persicae) because it's a generalist (has quite a few host plants). 25°C and 14 hr daylight or so would probably be fine.
E.g. Article Arabidopsis-Green Peach Aphid Interaction: Rearing the Insec...
You can also rear cereal aphid (Rhopalosiphum padi or Rhopalosiphum
maidis) on barley (which is easy and quick to grow). Same temp and photoperiod.
E.g. Article Intraguild predation of the aphid parasitoid Aphelinus certu...
The adult stage of cotton aphid Aphis gossypii (Glover), bean aphid Aphis craccivora (Kock) and corn aphid Rhopalosiphum maidis (Fitch) (Homoptera: Aphididae), were collected from okra, faba beans, and corn plants, respectively from different farms at El-Gharbia Governorate. The aphid cultures were maintained under laboratory conditions for six months. Kenaf plants Hibiscus cannabinus, broad bean Vicia faba and corn Zea mays (L.) Wliczek seedlings were used for rearing aphids' Aphis gossypii, Aphis craccivora and Rhopalosiphum maidis, respectively according to Zein, et al. (1982). After 7-15 days aphids were transferred from infested to healthy seedlings by cutting the heavily infested leaves and placed on the healthy seedlings.
Contamination between cultures was prevented by placing the seedlings in special chambers 50×50×60 cm covered with muslin on their sides. These cultures were kept in a breeding room under the temperature of 25±2°C, 65±5 relative humidity (R.H) and 12 hours daily illumination by using two fluorescent bulbs of 40 watts each .
Zein, A. A.; A. H. Masoud; R. Salam and A. H. Hosny (1982). Studies on some factors affecting susceptibility of Aphis gossypii (Glov.) to some insecticides. J. Agric. Res. Tanta Univ, 8 (2) : 308-318.
I have observed that if you keep plants under water stress, aphids population increases fast, and if you give optimum water to plants their population don't grow much. consider this factor also in your experiment.
The aphid should be reared on the host plant they were collected from, or should be reared for multiple generations on a new host plant before testing. The issue is that you do not want host plant stresses to influence bioassay outcomes. The number of generations depends on how great the move. If you collect A. gossypii from cotton and insist on rearing it on wheat you may need 40 or more generations.
Most artificial diets only keep the adults alive. Reproduction is better on a natural host. So the question is then what is the effect of dietary stress on the insect, and how does this interact with the effect of the insecticide.
Consistency is often more important than specifics. You could test all the insects in the laboratory at 28C and 42% relative humidity with a 16:8 light:dark cycle, or you could treat all the insects outside and see what happens. Sometimes one uses augmentative release of pests to insure that all treatments have (roughly) the same pest pressure at the start of the experiment. The choice made should be determined by the questions asked.
The laboratory experiment is more controlled, but the results are less relevant to field conditions. It is not reasonable to expect a grower to carefully dip each plant in his 10 acre field, yet we routinely apply an even coating to a petri dish as part of a bioassay. More commonly the grower will spray the field and some leaves will be missed, many will have discrete deposits leaving other areas untreated. While the patter looks uniform to people, an aphid views the entire field on a very different spatial scale.
2- Daily checking for any potential natural enemy attack
3- Once a week or every two weeks (max.), refresh your rearing by providing new healthy plants
4- If you see winged individuals in you rearing cage, so you have problem need to be solved : high density, natural enemy presence, high temperature (> 23C°), host quality, lighting instability.
To rear aphids you need to take care of the following factors .To chose the suitable host is an important factor.Temperature ,is effective to have a good culture ; it must suit the aphid. Photo-period is also needed to fit the aphid .Crowded of the reared aphid should be avoided .Adding healthy host regularly is required .