1 Order of Magnitude Scaling of the Cathode Region in an Axisymmetric Transferred Electric Arc P. F. Mendez, M. A. Ramirez, G. Trapaga, T. W. Eagar Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 ABSTRACT A new technique of order of magnitude scaling (OMS) [1] has been applied to the mathematical modeling of the cathode region of a long gas tungsten arc (GTA). The estimations obtained are combined with numerical calculations, thus important features of both techniques are considered simultaneously: the high precision of numerical modeling, and the generality and simplicity of algebraic expressions. Power-law expressions for the estimations of characteristic unknowns such as maximum pressure in the cathode spot and maximum plasma velocity are obtained and are consistent with previous analytical or asymptotic work. Dimensional analysis is used to identify dimensionless groups governing the system, and asymptotic considerations are used to identify two dimensionless groups (the Reynolds number and the dimensionless arc length) as the most significant ones governing momentum transfer in the cathode region. The estimations obtained are calibrated with functions that depend only on these two most significant dimensionless groups. It is suggested that the numerical results for different cases can be reduced to a single general map. Accepted for publication in Metallurgical Transactions-B