An Innovative Heterodyne Microwave Interferometer for Plasma Density Measurements on the Madison AWAKE Prototype

Abstract: The Madison AWAKE Prototype (MAP) is a high-power, high-density helicon plasma experiment. The project's main goal is to develop a scalable plasma source for use in a beam-driven plasma wakefield accelerator as part of the AWAKE project. We measure the plasma density with a new heterodyne microwave interferometer that features several improvements over traditional approaches. The design uses a single microwave source combined with an upconverter to avoid frequency drift and reduce overall cost. Elliptical mirrors focus the probe beam into the plasma and guide it back to the receiver. The transmitter and receiver along with the measurement electronics are co-located in a small enclosure and are assisted by two small mirrors on the opposite side of MAP. Both halves of the system move independently on computer-controlled motion platforms. This setup enables fast repositioning of the interferometer to measure at any axial location despite the magnets, wiring and structural supports that would block movement of a waveguide-based system. A high-speed, high-precision mixed signal circuit and FPGA analyze the probe signal directly in the enclosure which obviates the need for a digitizer or oscilloscope. The interferometer resolves phase shifts down to one hundredth of a fringe, resulting in a line-averaged resolution of $1.5\mathrm{\cdot 10^{17}\; m^{-3}}$. The system provides a real-time measurement every $5\;\mathrm{\mu s}$ up into the mid $\mathrm{10^{19}\; m^{-3}}$ density range with a noise level of $1.0\mathrm{\cdot 10^{17}\; m^{-3}}$.