We propose a new analytic scaling of the cut-off frequency of synchrotron radiation from active galactic nucleus ( AGN ) jets that are nonuniformly filled with many filaments .
The theoretical upper limit is provided independent of magnetic intensity , spectral index , coherence and correlation length of filamentary turbulence , etc. , such that \nu _ { c } \simeq 6 \times 10 ^ { 20 } \delta [ ( r - 1 ) / r ] ^ { 4 / 3 } ( b / 10 ^ { -4 } ) ~ { } { Hz } , where \delta , r and b are the Doppler beaming factor , shock-compression ratio and energy-density ratio of the perturbed/local mean magnetic field of the filaments , respectively .
Combining our results with observational data for 18 extragalactic sources , a constraint on the filament correlation length is found , in order to give the number scaling of filaments .
The results suggest that , in particular , the jets of compact BL Lacs possess a large number of filaments with transverse size scale smaller than the emission-region size .
The novel concept of the quantization of flowing plasma is suggested .