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

TL;DR

The paper presents a 105 GHz heterodyne interferometer designed for MAP to deliver fast, high-precision, line-integrated plasma density measurements in a high RF-noise environment. By using a single fixed-frequency microwave source with an upconverter, and embedding a high-speed mixed-signal front-end and FPGA-based fringe counting, the system avoids drift-prone dual-supply configurations and expensive master oscillators, while enabling real-time density updates at $5\ \mu s$ and a fractional fringe resolution of $0.01$. The quasioptical path with four elliptical mirrors allows tight focusing and flexible positioning, with independently movable source and return arms to probe different axial locations. The architecture achieves line-averaged density resolutions down to $1.5\times 10^{17}\ \mathrm{m^{-3}}$ and operates up to mid-$10^{19}\ \mathrm{m^{-3}}$, providing a robust, modular diagnostic capable of validating and calibrating complementary density measurements (e.g., LIF) and supporting automated experimental campaigns. The design’s modularity also permits swapping in Terahertz or FIR capabilities without major changes to the interferometer, enhancing its applicability for future plasma diagnostic needs.

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 $5\;\mathrm{μs}$ up into the mid $\mathrm{10^{19}\; m^{-3}}$ density range with a noise level of $1.0\mathrm{\cdot 10^{17}\; m^{-3}}$.

Figures (9)

• Figure 1: Simplified CAD render showing a top view of MAP with the 2.6 m long vacuum vessel and the microwave interferometer. The probe beam is sent out from the enclosure on the top and passes through the plasma as indicated by the green beam. The beam is sent back to the enclosure by the mirror system on the bottom. Both parts of the interferometer can be moved horizontally and vertically using independent computer-controlled motion platforms.
• Figure 2: Example of heterodyne interferometer AC signal with $f = 1\mathrm{\; MHz}$ and a rapid phase shift. Top: The measurement signal with phase shift (blue), the expected signal without phase shift (orange dotted), and the phase shift itself (green). Bottom: Conversion of the measurement signal into logic (blue), indicating whether the signal is above or below 0 V, along with the logic reference (orange).
• Figure 3: Flow chart of the density measurement process.
• Figure 4: Photograph of the entire interferometer system, except for two of the mirrors, with tape measure for scale. The enclosure's top and front side panels have been removed to show the FPGA, microwave components, connecting cables, power supplies, alignment laser, and two elliptical mirrors. The configuration shown is the one for alignment in which the green laser matches the microwave beam's divergence and focal point distance to the first mirror. During measurement, the small flip mirror is rotated 90 degrees up to allow the microwave beam to pass into the focusing elliptical mirror unobstructed.
• Figure 5: View of the signal and power carrying layers of the mixed signal circuit board with a penny for scale. To improve signal integrity, different kinds of signals are separated into different layers and separated by two continuous ground planes. Analog signals are on the top layer (red) and rarely the first inner layer (purple). Digital signals are on the bottom layers (blue) and rarely the second inner layer (green). Power rails, supplying seven different voltage levels, are shown in purple and green.