Abstract: Methods, systems, and articles of manufacture consistent with the present invention determine an amount of energy required to bring a quartz workpiece to a fusion weldable condition. The fusion weldable condition is a state at which the quartz workpiece is in thermal balance while being substantially near but below a quartz sublimation point. Parameters of the quartz workpiece, such as thermal properties and dimensional data, are identified. Quantifiable parameters of a heat source (such as a laser's beam energy attributes and beam geometry) are also identified. Using these parameters, a relationship is generated representing a modeled state of thermal equilibrium for the weldable surface of the quartz workpiece. This relationship is used to determine the appropriate amount of energy to be applied to the quartz workpiece and associates a desired temperature of the workpiece with a transit time for applying the energy. Heat loss can be accounted for and adjusted as part of the determined amount of energy.