Minimization of the external heating power to access self-ignition is advantageous to increase the reactor design flexibility and to reduce the capital and operating costs of the plasma heating device in a helical reactor. In this work we have discovered that a larger density limit leads to a smaller value of the required confinement enhancement factor, lower density limit margin reduces the external heating power, and over 300 s of the fusion power rise-up time makes it possible to reach a minimized heating power. While the fusion power rise-up time in a tokamak is limited by the OH transformer flux or the current drive capability, any fusion power rise-up time can be employed in a helical reactor for reducing the thermal stresses of the blanket and shields, because the confinement field is generated by the external helical coils.