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Historically, x-ray output of flash x-ray tubes was maximized empirically by changing the electrode geometry and varying the capacitance of the pulse generator. With the advent of high-voltage, low-impedance transmission lines, short-duration, high-current pulses could be generated with ease. An appropriate line scaling should assure that dose maximization is not reached at the expense of pulse prolongation which would reduce stop motion capability, but rather that dose rate should be maximized. Additionally, anode evaporation in the arc phase should be minimized to enhance tube life. Typically, the impedance of flash tubes changes during the discharge from infinity in the beginning to nearly zero in the arc phase and, either for field emission or high-vacuum discharge tubes, can well be modeled by a time-varying ohmic resistor Zx(t). Using a modification of Bergeron's method of travelling wave analysis, transient tube voltage and current can be determined out of a closed-form solution. This allows to calculate corresponding dose rate-time profiles of each spectrum. An ideal pulsed transmission line, charged up to a dc potential U0, has been assumed, characterized by its characteristic impedance Z0 and characteristic time T. Three typical examples illustrate the importance of optimum line scaling and K-series excitation voltage on tube performance such as dose, maximum dose rate, discharge delay time and pulse width. These examples encompass a transmission line with (a) constant initially stored energy E0 = UO2T/4Z0, but various combinations of Zo and T; (b) increasing energy E0 by decreasing Z0, but T = const; and (c) constant line parameters Z0 and T, but assumption of various Zx(t) profiles. Basic matching rules have been worked out in order to approach ideal operation for a given tube impedance time profile. A parametric analysis revealed that, with decreasing pulser impedance, there are increases in the bremsstrahlung and K-series radiation emissions, but that the pulse delay time and pulse width also increase, thus limiting applications to high-rate phenomena. A detailed description of the method and results which are also applicable to an ideal Blumlein line will be published elsewhere.
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