High-voltage generation system for a traveling-wave Stark decelerator

In this paper we describe the high-voltage generation system we have developed for a traveling-wave Stark decelerator (TWSD). The TWSD can reduce the forward velocity of a molecular beam of heavy neutral polar molecules such as strontium monofluoride (SrF) and barium monofluoride (BaF) from $\sim$ 200 m/s down to $\sim$ 6 m/s. The main motivation for the development of this device is the increased sensitivity from precision spectroscopy of the decelerated molecules to test fundamental physics. The high-voltage generation system can produce eight pulsed sinusoidal waveforms with a maximum amplitude of 10 kV and a linear frequency sweep from 16.7 kHz down to 500 Hz over the span of 40 ms at a repetition rate of 10 Hz. The eight waveforms are phase-offset to each other by 45 degrees. To slow down the heavy molecules, the decelerator is required to have a length of $\sim$ 4 m, which results in a significant capacitive coupling between adjacent channels of $\sim$ 160 pF. As a consequence, the control and stability of the waveforms is extra challenging. We designed a method that compensates for the frequency-dependent coupling between the eight channels. Allowing for amplitude and phase-offsets that do not deviate more than 1% and 2 degrees, respectively, from their design values during the frequency sweep. The system outperforms commercially available options in terms of stability, output voltage amplitude, cost and ease of maintenance. This approach is also relevant for other fields where precise control of high-voltage waveforms is required, such as particle accelerator physics, plasma physics and mass spectroscopy.

💡 Research Summary

The paper presents a complete design, implementation, and characterization of a high‑voltage generation system tailored for a traveling‑wave Stark decelerator (TWSD) intended to slow heavy neutral polar molecules such as SrF and BaF from ~200 m/s to a few m/s. The decelerator consists of eight parallel electrode channels arranged in an octagonal geometry, each requiring a sinusoidal voltage up to 10 kV peak with a 45° phase offset relative to its neighbours. The required voltage waveform must sweep linearly in frequency from 16.7 kHz down to 500 Hz over a 40 ms interval, repeated at 10 Hz. Because the decelerator is 3–4.5 m long, the inter‑channel capacitance (~160 pF) and the capacitance to ground (~57 pF) produce an effective load of about 151 pF. This large reactive load creates strong frequency‑dependent amplitude and phase distortions, making precise waveform control a major technical challenge.

To meet these requirements the authors adopt a transformer‑based architecture rather than commercial high‑voltage amplifiers. Eight arbitrary waveform generators (Moku Pro devices) produce low‑power baseband signals that feed eight Behringer NX3000D audio amplifiers, each capable of 3 kW peak power. The amplifiers operate in bridge mode to double the output voltage, and a series resistor protects the amplifiers and stabilises the load. Custom‑wound step‑up transformers then boost the audio‑amplifier output to the required 10 kV. The transformers are engineered so that their two intrinsic resonances (parallel and series) lie outside the 2–20 kHz operating band, thereby minimising resonance‑induced amplitude and phase excursions.

The core innovation is a digital feedback and predistortion scheme. The complete transfer function of each channel (including amplifier, transformer, and capacitive load) is measured across the sweep range. The arbitrary waveform generators then apply a calculated inverse distortion to the input signals so that, after passing through the hardware, the output voltage follows the ideal sinusoid with the prescribed amplitude and phase. The feedback also compensates for the ≈600 µs channel‑to‑channel delay variations of the audio amplifiers, ensuring that the 45° phase relationship is maintained throughout the sweep. With this approach the authors achieve amplitude errors below 1 % and phase errors below 2°, well within the tolerances required to avoid significant molecular loss.

Performance is validated on a 200 pF dummy load and on a 3 m section of the actual decelerator (effective load 101 pF). Waveforms are tested at 1 kV, 5 kV, and the full 10 kV. Total harmonic distortion (THD) remains under 0.25 % across the entire frequency sweep, a substantial improvement over the commercial Trek amplifiers (THD <2 %). The system reliably delivers the required voltage at the full 10 Hz repetition rate, with stable ramp‑up and ramp‑down periods that suppress current spikes caused by the capacitive load.

Cost analysis shows that the transformer‑plus‑audio‑amplifier solution is roughly 60 % cheaper than buying a comparable high‑voltage solid‑state amplifier, and the modular design simplifies maintenance and part replacement. The ability to reach 10 kV enables operation in the BaF N=2 rotational state, where a deeper electric trap (≈10 kV) increases the phase‑space acceptance by a factor of four compared with the 5 kV limit of the N=1 state. Consequently, the number of molecules transmitted through the decelerator can be dramatically increased, and final velocities as low as 30 m/s (or even 800 Hz sweep for <10 m/s) become accessible, allowing direct loading into electric or optical traps for precision spectroscopy experiments such as the NL‑eEDM measurement.

Beyond molecular beam deceleration, the authors note that the presented high‑voltage waveform generation technique—combining custom transformers, high‑power audio amplifiers, and digital predistortion feedback—has broader relevance to fields requiring precise, high‑voltage, multi‑channel waveforms, including particle accelerator components, plasma heating systems, and advanced mass‑spectrometry instrumentation.

In summary, the paper delivers a cost‑effective, high‑performance, and highly controllable high‑voltage generation platform that meets the stringent demands of a long‑baseline traveling‑wave Stark decelerator, thereby advancing the capability to produce ultra‑slow, high‑flux beams of heavy polar molecules for next‑generation precision measurements.