  This paper discusses the trends and trade-offs between transverse sigma x and
longitudinal sigma z bunch dimensions, rf injector gradient, bunch charge, and
intrinsic electron mean transverse energy (MTE), where all can be chosen to be
independent, and the resulting effects on emittance and transverse brightness.
Using a practical example of a quarter wave normal conducting photoinjector, it
is computationally found that regardless of MTE and bunch charge, there is a
universal relation between the gradient E and the aspect ratio of the bunch
(sigma x /sigma z ) leading to the highest brightness. This computational
result is understood using an analytical formalism consisting of K J Kim's
emittance formulation and a two-dimensional space charge model. The results,
obtained computationally and interpreted in a robust physical framework, could
therefore provide the basis for an express mapping approach for emittance
forecasting when used with practical injector system design requirements and
limitations.
