Ultrasonic imaging & NDE applications can greatly improve their signal-to-noise ratios (SNR) by driving each transducer (composing piezoelectric arrays) with a spike giving pulsed power of k-Watts, repetitively at a PRF = 5000 spikes/s, by using a HV capacitive-discharge generator. However very-high levels, of pulsed intensities (3-10 A) and voltages (300-700 V) must be considered for a rigorous spike modeling. Even though the consumed "average" power will be small, the intensity through each transducer achieves several amperes, so the pulsed powers delivered by each HV generator can attain levels higher than in CW high-power ultrasonic applications: e.g., up to 5 kW / spike. This is concluded here from a transient modeling of the loaded generator. Then, unforeseen phenomena rise: intense brief pulses of driving power & emitted force in transducers, and non-linearities in driver semiconductors, because their characteristic curves only include linear ranges. But fortunately, piezoelectric devices working in this intense regime do not show serious heating problems, because the average power remains being moderate. Intensity, power and voltage, driving a broadband transducer from a HV capacitive pulser, are calculated to drastically improve (in ≅ 40 dB) the ultrasonic net dynamic range available, with emitted forces ≅ 250 Newtons pp and E/R received pulses of 70 V pp.