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This paper develops a three level model for a continuous wave diode pumped alkali laser by creating rate equations based on a three level system. Differential equations for intra-gain pump attenuation and intra-gain laser growth are developed in the fashion done by Rigrod. Using Mathematica 7.0, these differential equations are solved numerically and a diode pumped alkali laser system is simulated. The results of the simulation are compared to previous experimental results and to previous computational results for similar systems. The absorption profile for the three level numerical model is shown to have excellent agreement with previous absorption models. The lineshapes of the three level numerical model are found to be nearly identical to previous developments excepting those models assumptions. The three level numerical model provides results closer to experimental results than previous systems and provides results which observe effects not previously modeled, such as the effects of lasing on pump attenuation. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the p