Ludwig's hand sent out all the mana in his body, unlike what he had hoped for to create a fireball and shoot it inside the Lizardman's mouth, he forgot to ask Thomas for an important thing. How do mages usually shoot out spells?
Unwilling to spend time to think of the how's, Ludwig simply acted on instinct.
Van Dijk had mentioned to him that magic is about one's will, imagination, and emotion. Right now, Ludwig's imagination was that of a flaming fireball that was to blow up and turn his enemy to cinders, in that regard he had things worked out. As for his emotions, he borrowed Thomas's rage. While the final and most important part, the will, was simply Ludwig's own intention of not wanting to die a dog's death, and fueled all his power and rage into his arm, disregarding any measures of safety and care.
