Mathematical description of non-linear relaxating polarization in dielectrics with hydrogen bonds

Analytical investigating of the patterns of relaxation (volume-charge) polarization in dielectric materials class hydrogen bonded crystals (HBC) in the wide range of temperature (1–1500 K) and polarizing field strengths (100 kV/m–100 MV/m) in alternating field at frequencies of about 1 kHz–10 MHz is made. The generalized nonlinear by the polarizing field the semi-classical kinetic equation of proton relaxation, having (in this model) sense the protons current continuity equation solving by method of successive approximation by decomposition in infinite power series in comparison parameter is built. It is established that in the range of low fields (100–1000 kV/m) and high temperatures (100–250 K) the generalized kinetic equation is converted to the linearized Fokker–Planck equation and at low (70–100 K) and sufficiently high (250–450 K) temperatures are showed the nonlinear polarization effects caused respectively by proton tunneling and volume charge relaxation. With ultra-low (1–10 K) and ultra-high (500–1500 K) temperatures in the range of high fields (10 MV/m–100 MV/m) the contribution of such effects to the polarization is amplified. The influence of the non-linearities to relaxation times for microscopic acts of transitions protons through the potential barrier is studied.