Design of single mesh flashlamp driving circuits with resistive losses

The normalized nonlinear equation
(dI/d\tau) \pm [\alpha + \beta|I|^{1/2}] + \int\min{0}\max{\tau}I d\bar{\tau}= 1
describing current evolution in a single mesh flashlamp driving circuit has been solved using numerical methods for the case of a critically damped pulse (
\alpha \simeq 0.84) and \beta = r/Z_{0} \neq 0
. Normalized current, power, and energy waveforms for values of β in the range
0 \leq \beta \leq 0.5
are obtained. The energy efficiency η
E
, which is numerically equal to the flashlamp dissipated energy di-Vided by the energy stored in the driving circuit, is also shown as a function of β. Increased numerical accuracy has improved the previously used value of α for critical damping and leads to a slightly different form for the curve representing the locus of values (α β) to obtain critically damped pulses in the presence of restrictive losses.