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Fluctuations in atmospheric pressure arc plasma devices play important role in plasma processing applications. A full knowledge and control over such fluctuations can effectively lengthen lifetime and drastically improve performance and reliability. Dynamical analyses of associated experimental fluctuating signals established existence of chaotic dynamics in such devices. However, the origin of such fluctuations remained unexplained so far and no theoretical investigation is carried out to explore underlying physics behind such phenomena. This work addresses development of a general theory for such fluctuations in atmospheric pressure arc plasma devices in terms of various nondimensional parameters using basic governing equations and presents the result of application of the theory to various important experiments reported in literature. Various aspects of dynamic behavior have been investigated through the study of coefficients appearing in the nonlinear amplitude equation. It has been shown that the theory supports arc current and gas flow rate as the major externally available controlling parameters in agreement with experiment. Theory exhibits period doubling route to chaos under variation of control parameter as observed experimentally. System includes catastrophic behavior for some operating range. The whole work is divided into two parts. This paper presents part I: development of theory for such fluctuations using basic equations of the dynamics and study of system behavior.