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We investigate the observability, by direct and indirect means, of a shockprecursor arising from magnetic field amplification by cosmic rays. We estimatethe depth of such a precursor under conditions of nonresonant amplification,which can provide magnetic field strengths comparable to those inferred forsupernova remnants. Magnetic field generation occurs as the streaming cosmicrays induce a plasma return current, and may be quenched either by nonresonantor resonant channels. In the case of nonresonant saturation, the cosmic raysbecome magnetized and amplification saturates at higher magnetic fields. Theprecursor can extend out to $10^{17} - 10^{18}$ cm and is potentiallydetectable. If resonant saturation occurs, the cosmic rays are scattered byturbulence and the precursor length will likely be much smaller.  The dependence of precursor length on shock velocity has implications forelectron heating. In the case of resonant saturation, this dependence issimilar to that in the more familiar resonantly generated shock precursor,which when expressed in terms of the cosmic ray diffusion coefficient$\varkappa $ and shock velocity $v_s$ is $\varkappa /v_s$. In the nonresonantlysaturated case, the precursor length declines less quickly with increasing$v_s$. Where precursor length proportional to $1/v_s$ gives constant electronheating, this increased precursor length could be expected to lead to higherelectron temperatures for nonresonant amplification. This should be expected atfaster supernova remnant shocks than studied by previous works. Existingresults and new data analysis of SN 1006 and Cas A suggest some observationalsupport for this idea.

Electron Heating, Magnetic Field Amplification, and Cosmic Ray Precursor Length at Supernova Remnant Shocks