Synergy between laser linewidth and frequency chirp in mesospheric magnetometry based on the sodium laser guide star

Mesospheric sodium magnetometry with a laser guide star measures the geomagnetic field near 90~km. Its sensitivity hinges on laser linewidth and chirp, yet prior work optimized these two parameters only separately. We use velocity-resolved density-matrix simulations of Larmor-synchronous pulsed Na D$_2$ pumping to scan both parameters jointly. Linewidth and chirp exhibit a synergy: when chirping carries the recoil-mitigation role, the return flux stays within 1\% of its peak across linewidths of 2--10~MHz. The flux-optimal chirp is $0.19~\mathrm{MHz/\upmu s}$, one fifth of the continuous-wave rate; this synergy guides high-sensitivity mesospheric magnetometer design.