Method for Approximating Electron Beam Currents Accelerated by a Piezoelectric Transformer

Abstract

Piezoelectric transformers (PTs) are currently used to accelerate charged-particle beams for various applications. Beam interactions at the output of the PT can be treated as a parallel RC electrical load. The impedance of the load can affect the output voltage because of the small, finite amount of charge available in the PT; therefore, high-impedance diagnostics are required to characterize the PT. A thermionic electron emitter was used to provide a controllable beam current for testing the effects of electrical loading on the PT. The electron beam was operated in vacuum at pressures of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> -10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> torr. The input mechanical quality factor and the effective output electrical quality factor were used to approximate the electron beam current on the basis on the PTs equivalent electromechanical circuit. The output voltage needed for the output electrical quality factor was measured via bremsstrahlung interactions at the output electrode of the PT. Optical techniques for finding internal operating parameters such as electric field and stress were used to determine the load with curve fitting as a comparison with the quality factor diagnostic. Approximating the electron beam current with such methods will help determining the output power that such PTs can generate for future applications.