Robust Betatron-Tune Measurement from Schottky Spectra: Complementary Classical and Deep-Learning Paradigms

Schottky spectra provide key beam diagnostics, with betatron sidebands encoding the fractional tune.

Reliable tune measurement is particularly important for third-order resonance slow extraction in compact medical proton synchrotrons, where low signal-to-noise ratios and limited frequency resolution can compromise conventional peak-detection and curve-fitting methods.

This work develops two complementary tune estimators with a shared spectral front-end but different temporal representations.

The classical estimator coherently pools motion-compensated spectra, detects the sideband using a multi-width matched-filter bank, and performs sub-bin estimation through local argmax and an adaptive MAD-gated centroid.

The deep-learning estimator converts each spectrum into a tune-likelihood map using a convolutional neural network with FFT-based global convolutions, then propagates the posterior with a discrete two-dimensional (q,v) Bayesian tracker under a Gaussian motion model while also reporting posterior uncertainty.

On a synthetic dynamic-tune benchmark, the deep-learning estimator outperforms published baselines across the operating range, while the classical estimator exceeds the latency-compensated baseline and requires neither training data nor GPU acceleration.

On near-stationary SAPT beam data, both methods operate end-to-end, with the deep-learning model requiring no retraining.

Median per-frame latency remains below 1 ms on commodity hardware, supporting real-time-capable tune measurement in compact medical synchrotrons.