Constraining the Primordial Intergalactic Magnetic Field in Cosmic Voids with the Density-Weighted Ariza Length

We introduce the density-weighted Ariza length, a line-of-sight integral over cosmic voids weighted by their dynamical depth, as a target-selection criterion for searches of the primordial intergalactic magnetic field and axion-like particles. Deeper voids host less dynamo activity, allowing the intergalactic magnetic field to retain its primordial value and providing longer coherent paths for photon-ALP conversion, which is the physical motivation for weighting by the nonlinear density contrast. We compute this length for six BL Lac objects at redshift under 0.7 using void catalogues from Tully et al. and the all-sky 2MRS reconstruction. Fermi-LAT spatial profiles over 18 years from 2008 to 2026 at energies between 10 and 100 GeV show no extended emission consistent with a cascade halo. The tightest PSF-based intergalactic magnetic field limit is below 0.016 femtogauss from Mrk 421 at energies above 100 GeV. The object 4FGL J1442.0+4348 at a redshift of 0.673 passes 12 Mpc from the centre of the Boötes Void, with an Ariza length of 376 Mpc, a chord length of 260 Mpc, and a density contrast of 0.95, making it among the highest-priority targets identified in this work for both Cherenkov Telescope Array intergalactic magnetic field and axion-like particle searches. From the non-detection of spectral modulation in 417 photons, we derive a model-dependent upper limit on the axion-photon coupling below 7.8 times 10 to the power of minus 11 per GeV at 95% confidence level, numerically comparable to the CAST helioscope bound within the adopted assumptions. Cascade simulations indicate that Cherenkov Telescope Array North at energies above 1 TeV could probe couplings above 2 times 10 to the power of minus 12 per GeV and magnetic fields above 0.18 femtogauss for J1442.