Energy-Dependent Fractal Fingerprinting of Electron Transport in Gaseous Media

Quantifying how electron trajectory geometry evolves with incident energy across chemically distinct media is central to radiation physics and electron microscopy, yet systematic energy-dependent fractal analysis remains scarce. Here, we report a Monte Carlo investigation of the energy dependence of the fractal dimension D(E) for six gaseous species (He, CH 4 , NH 3 , CO 2 , O 3 , Xe) at uniform density (5 g/cm 3 ) over 25-100-Kev, using the CASINO code combined with box-counting analysis validated against the Koch curve ([Formula: see text], relative error [Formula: see text]%). The parameters of the exponential model [Formula: see text] define species-specific spectral fingerprints. A reversibility efficiency [Formula: see text](E), defined analytically from these parameters, quantifies the degree of geometric complexity of the trajectories as a function of energy and serves as a complementary discriminating descriptor. Our findings suggest potential applications in atmospheric sensing and plasma diagnostics.