Unless you use careful choice of materials for the lens and efforts to keep it very clean, you'd likely just destroy the lens if you used it as drawn.
You have the lens shown at the point where the light is already gathered into a small area (which is good from the standpoint of not needing a giant lens). The problem is the intense amount of energy contained in that small column of light. The lens will absorb a small fraction of it because the glass, quartz, whatever is not perfectly transmissive and all of that absorbed energy will turn into heat in the glass. Also, any speck of dirt will heat up to flame temperature and cause even more defects in the lens.
