Step 1: 1: The "Main Part of the Explosion".
2. Go to Effects>Render>Clouds. Click OK when a window pops up showing properties for the 'cloud' thing.
3. Duplicate Layer. (Shown on picture below)
4.Go to top layer, then Effects>Distort>Bulge. Make the value 100.
5.Go to bottom layer, then ffects>Distort>Buldge. Make the value -200.
6.Go to the top layer, then go to Properties (on picture below), then change the blend form to "XoR".
7. Flatten the layers. (Below)
Step 1: Done, should look like image below.