Kaur, M. Gupta, D.N. JACoW Publishing Geneva, Switzerland 978-3-95450-184-7 10.18429/JACoW-IPAC2018-THPML052 English 4752-4754 THPML052 Contribution to a conference proceedings 2018 2018-06 https://doi.org/10.18429/JACoW-IPAC2018-THPML052 http://jacow.org/ipac2018/papers/thpml052.pdf Excitation of plasma wave by two lasers beating in a collisional dominated relativistic plasma is investigated. We study the energy exchange between a plasma wave and two co-propagating lasers in plasma including the effect of relativistic mass change and electron-ion collisions. Two lasers, having frequency difference equal to the plasma frequency, excite a plasma beat wave resonantly by the ponderomotive force, which obeys the energy and momentum conservation*. The relativistic effect and the electron-ion collision both contribute in energy exchange between the interacting waves in the beat-wave acceleration mechanism. Our study shows that the initial phase difference between interacting waves generates a phase mismatch between lasers and plasma wave, which alters the rate of amplitude variations of the interacting waves and, hence, affects the energy exchange between the interacting waves**. This study may be crucial to design a compact plasma accelerator in low-intensity regime***.