Pulsed-power driven x-ray radiographic systems are being developed to operate at higher power in an effort to increase source brightness and penetration power. Essential to the design of these systems is a thorough understanding of electron power flow in the transmission line that couples the pulsed-power driver to the load. In this paper, analytic theory and fully relativistic particle-in-cell simulations are used to model power flow in several experimental transmission-line geometries fielded on Sandia National Laboratories' upgraded Radiographic Integrated Test Stand [IEEE Trans. Plasma Sci. 28, 1653 (2000)]. Good agreement with measured electrical currents is demonstrated on a shot-by-shot basis for simulations which include detailed models accounting for space-charge-limited electron emission, surface heating, and stimulated particle emission. Resonant cavity modes related to the transmission-line impedance transitions are also shown to be excited by electron power flow. These modes can drive oscillations in the output power of the system, degrading radiographic resolution.
An approximate solution for electron trajectories in a space sinusoidal electric field with a slowly changing amplitude is constructed by varying the modulus of the Jacobi elliptic functions representing electron trajectories in a constant amplitude field. This solution is used, together with energy conservation, to obtain the time behavior of the amplitude of nonlinear longitudinal oscillations in a collisionless plasma. The resulting integrodifferential equation for the amplitude depends on the ratio γ/α0, where γ is the Landau damping constant, and α0 is the initial value of the frequency of oscillations of trapped electrons in the potential trough of the wave. Numerical solutions are carried out for several values of this ratio. For γ/α0 → 0 (constant amplitude limit) O'Neil's results are recovered. For small but finite values of the ratio γ/α0, the present method shows the effect of the energy exchange between resonant electrons and the decaying electric field. The time of regrowth and the corresponding minimum amplitude are evaluated and compared with the results of O'Neil.
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