Dual-Scale Waveform Optimization and Hysteretic-Fractal Resonant Stimulation (HFRS) for Minimizing Transport Resistance in Na-ion Lattices: Theory and Open Hardware Implementation

The transport of sodium ions (Na+) in intercalation battery materials is inherently limited by their larger ionic radius, leading to high activation energy (E_a) of diffusion and a non-linear increase in internal resistance (R_i) during fast-charging. This paper introduces a radical departure from macroscopic Constant Current/Constant Voltage (CC/CV) methodologies by proposing a Dual-Scale Waveform Optimization approach combined with Hysteretic-Fractal Resonant Stimulation (HFRS). Instead of relying on a static DC baseline, an 8-GPU computational cluster dynamically searches for the "ideal macroscopic shape" of the charging pulse, superimposed with high-frequency fractal excitations. This stimulation targets the resonant frequencies of crystal defects and oxygen vacancies to temporarily lower steric Peierls barriers, leading to a state approaching optimal collisionless ion transport. The paper details the anomaly detection methodology, the parallel search architecture, and proposes the design of an Open Hardware Wideband GaN PCB module for in-line dynamic charge control.