produce ions having kinetic energy in the 1-100 kV range that may be collected to give a signature of ion motion. In conclusion, we have identified a compelling opportunity, based on the emergence of low charge, low emittance, few fs, high energy electron beams, to investigate an array of topics in high field physics. The primary motivation here is production of TV/m plasma wakefields, thus pushing the state-of-the-art by well over an order of magnitude, with dra- matic implications on the size of future high-energy frontier accelerators. In analyzing the practical implementation of such an experiment at the LCLS, we find many aspects of the scenario that strongly add to its appeal. Most importantly, beams having peak space-charge fields on the order of a TV/m give an unprecedented tool for investigating the behavior of atomic systems under ultra-fast application of unipolar, very large amplitude electric fields. These fields also may allow exploration of potentially critical ion motion effects in a PWFA. Further, beams with these self-fields can yield prompt, coherent electromagnetic emission through a variety of mechanisms such as edge radiation, thus creating a novel, high power source of half-cycle IR radiation not accessible by other means. This radiation thus serves as both a unique source and as a means of bunch length diagnosis. We have also discussed innovative approaches to diagnosis of σ$_{x}$ , as well as beam transport and focusing and found that an experiment at the LCLS, having an appropriately small footprint in the post-undulator region, seems to be realizable. A collaboration based on the authorship of this Letter is now preparing a proposal to perform such an experiment. [1] J. Rosenzweig, et al. , Nucl. Instrum. Methods Phys. Res. A 593 , 39 (2008). [2] R. Bonifacio, C. Pellegrini, and L. Narducci, Opt. Commun. 50 , 373 (1984). [3] R. Neutze et al. , Nature 406 , 752 (2000). [4] Y. Ding et al. , Phys. Rev. Lett. 102 , 254801 (2009). [5] M. Hogan et al. , Phys. Rev. Lett. 95 , 054802 (2005). [6] I. Blumenfeld, et al. , Nature 445 , 7129 (2007). [7] J.B. Rosenzweig, N. Barov, M.C. Thompson, R.B. Yoder, Phys. Rev. ST Accel. Beams 7 , 061302 (2004). [8] J.B. Rosenzweig, B. Breizman, T. Katsouleas and J.J. Su, Phys. Rev. A 44 , R6189 (1991). 9