Step 2: Searching for a solution
But the cusps did not concentrate much while the winston concentrators might be suitable for a box oven but not for what I had in mind. They concentrate in an area behind the compound parabola.
Eventually I decided that if I rotated a parabola round its focus by a certain number of degrees and joined the 2 inside curves It might work for me.
Using that shape focuses the light in an area at or below the focal point of the combined parabolas.
I have added image notes to the 2 pictures below to explain it a bit. Shape 1 is the parabola for a parabolic dish.
Shape 2 shows how to turn it to make a 45 degree compound parabolic dish (suitable for up to 3 hours of solar cooking without moving the dish!)