We continue our recent work to characterize the plasma content of high-redshift damped and sub-damped Lyman-alpha systems (DLAs/sub-DLAs), which represent multi-phase gaseous (proto)galactic disks and halos seen toward a background source. We survey N V absorption in a sample of 91 DLAs and 18 sub-DLAs in the redshift range 1.67<z<4.28 with unblended coverage of the N V doublet, using data from VLT/UVES, Keck/HIRES, and Keck/ESI. In DLAs, we find eight secure N V detections, four marginal detections, and 79 non-detections. The detection rate of N V in DLAs is therefore 13^{+5}_{-4}%. Two sub-DLA N V detections are found among a sample of 18, at a similar detection rate of 11^{+15}_{-7}%. We show that the N V detection rate is a strong function of metallicity, increasing by a factor of ~4 at [N/H]=[NI/HI]>-2.3. The N V and CIV component b-value distributions in DLAs are statistically similar, but the median b(N V) of 18 km/s is lower than the median b(O VI) of 25 km/s. Some ~20% of the N V components have b<10 km/s and thus arise in warm photoionized plasma at log (T/K)<4.92; local sources of ionizing radiation (as opposed to the extragalactic background) are required to keep the cloud sizes physically reasonable. The nature of the remaining ~80% of (broad) N V components is unclear; models of radiatively-cooling collisionally-ionized plasma at log(T/K)=5.2-5.4 are fairly successful in reproducing the observed integrated high-ion column density ratios and the component line widths, but we cannot rule out photoionization by local sources. Finally, we identify several unusual DLAs with extremely low metallicity (<0.01 solar) but strong high-ion absorption [log N(N V)>14 or log N(O VI)>14.2] that present challenges to either galactic inflow or outflow models.
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