Several concepts for future linear colliders are dependent on very high gradient normal conducting RF cavities achieved by operation at cryogenic temperatures in order to reduce breakdown rates (BDR). These maximum fields are intended to be in excess of 200 MV/m. The concepts include the ultra compact Xray free electron laser and the C$^3$ collider. The theory involved with the complex physics of breakdown is a diverse and rich field of study. Most results are empirical so continued understanding of the phenomena becomes necessary. One contributing factor to the reduced BDR is the increased hardness at cryogenic temperatures of the copper. in order to test that assumption we can consider obtaining hardness improvements from the alloying of copper with silver. We will here present a preliminary theory of this alloy based improvement especially with respect to an improved understanding of the surface resistivity using our previously established theory improvements which go beyond the usual Reuter and Sondheimer explanation. We will compare this to quality factors measured in Cband pillbox cavities as a function of temperature.

Plasma wakefield acceleration (PWFA) is a burgeoning field, attracting much attention as an option to extend acceleration gradients from the present 100 MeV/m level to the TeV/m level. The effort will be expended to resolve the question of the long-term behaviour of the disturbances left behind in the plasma and the time it takes to reach equilibrium after the wakefield interaction occurs. The present limitations on gradient arise from material electromagnetic breakdown thresholds. Methods for exploring the beam's longitudinal and transverse phase space qualities have been developed in the context of an increasing worldwide effort. UCLA LAPD laboratory, with its diagnostics, permits the spatio-temporal resolution of electron density, magnetic field, and electro-magnetic signals in the plasma over long-time scales. We aim to explore intense electron beams for wake excitation available at the LAPD, commissioning the SAMURAI photoinjector and its electron beam production.

High brightness electron beams enable a wide spectrum of applications ranging from short wavelength radiation sources to high gradient wakefield acceleration. The rich dynamics that are intrinsic in charged particles accelerated in complex systems require a careful description in the analysis and design of a given machine, particularly regarding its stability. Numerous computer codes are in use by the accelerator community for such purposes. In particular, MILES is a simple tracking code we have developed that allows fast evaluations of collective effects in RF linacs. In this paper we extend the simple models previously developed to describe specific, diverse applications that can benefit from the fast simulation tools developed in MILES. Examples of this kind include particle driven acceleration schemes in a plasma where driver and witness beams propagate in the ``comb" pulse-train configuration. Specifically, we investigate the self-induced fields excited within both the rf-linac stage and the capillary. Further, we discuss additional advanced topics such as wakefield effects in planar FEL undulators and the emission of coherent synchrotron radiation in a magnetic chicane.