Energy dependence of reciprocal effective scattering lengths . The square points (∎) represent the IPTA experimental data (Ref. 5); the solid line the theoretical curve derived from Eq. (1). The dashed-dotted line with diamonds (◆) represents the electron-electron-scattering contribution to the reciprocal effective scattering length as reported in Ref. 5. The dashed line with crosses (×) provides the impact ionization contribution resulting from our fitting procedure [Eq. (1)].
Electronic multiplication rates as computed for crystalline polyethylene [Eq. (1)].
Electron-energy distribution function (normalized to one injected electron) for electrons inside the void, reported as a function of electric field in the void.
Values of the first Townsend coefficient of air at atmospheric pressure calculated according to Eq. (6) as a function of the applied electric field in the void, compared with semiempirical formulas in case that (a) attachment is neglected [semiempirical formula (7), after Ref. 24] and (b) attachment is considered [semiempirical formula (8), after Ref. 25].
Electronic energy states in PE as resulting from the LDA-DFT ab initio calculations (Refs. 12 and 13) and experimental results. The presence of surface states below the bottom of conduction band of polyethylene can be observed.
Number of electrons generated inside the void, starting from one single injected electron, as a function of electric field in the void and void height .
Fraction of electrons with energy values (hot electrons) striking PE surface as a function of electric field inside the void.
Reciprocal mean free path for impact ionization and DEA scattering as a function of electron energy in polyethylene.
Effective fraction of hot electrons (with energy values ) produced inside the void and inducing a chemical damage (through DEA) upon polyethylene surface, as a function of electric field in the void.
Damage growth rates vs poling field, computed by Eq. (16) (, void size ) for three different data sets of the values, i.e., (1) the values calculated by means of Eq. (6) (considering attachment), (2) the values derived from Eq. (8) (Ref. 25) that considers attachment, and (3) the values derived from Eq. (7) (Ref. 24) that neglects attachment.
Damage growth rate as a function of void height in PE at 10, 15, and (poling field) and temperature of .
Damage growth rate as a function of temperature in XLPE (poling field equal to , void height equal to ).
Damage growth rate as a function of poling field in PE at , for several different void heights. The dashed lines delimit regions of low field (LF), high field (HF), and ultrahigh field (UHF) as quoted in the figure.
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