Electron and proton acceleration by a super-Dreicer electric field is further investigated in a non-neutral reconnecting current sheet (RCS) with a variable plasma density. The tangential Bz and transverse magnetic field components Bx are assumed to vary with the distances x and z from the X nullpoint linearly and exponentially, respectively; the longitudinal component (a ‘guiding field’) is accepted constant. Particles are found to gain a bulk of their energy in a thin region close to the X nullpoint where the RCS density increases with z exponentially with the index λ and the tangential magnetic field Bx also increases with z exponentially with the index α. For the RCS with a constant density (λ = 0), the variations of the tangential magnetic field lead to particle power-law energy spectra with the spectral indices γ1 being dependent on the exponent α as: \documentclass[12pt]{minimal}
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\begin{document}$$\gamma_1 = 1 + \frac{1}{2\alpha}$$\end{document} for protons and \documentclass[12pt]{minimal}
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\begin{document}$$\gamma_1 = 1+ \frac{1}{\alpha}$$\end{document} for electrons in a strong guiding field (β > 10−2) and \documentclass[12pt]{minimal}
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\begin{document}$$\gamma_1 =\frac {1} 2 (1 +\frac{1}{\alpha})$$\end{document} for electrons in a moderate or weak guiding field (β > 10−4). For the RCS with an exponential density increase in the vicinity of the X nullpoint (λ≥ 0) there is a further increase of the resulting spectral indices γ that depends on the density exponent index λ as \documentclass[12pt]{minimal}
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\begin{document}$$\gamma = \gamma_1 +\frac{\lambda}{2\alpha}$$\end{document} for protons and for electrons in weaker guiding fields and as \documentclass[12pt]{minimal}
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\begin{document}$$\gamma = \gamma_1 + \frac{\lambda}{\alpha}$$\end{document} for electrons in stronger guiding fields. These dependencies can explain a wide variety (1.5–10) of particle spectral indices observed in solar flares by the variations of a magnetic field topology and physical conditions in a reconnecting region. This can be used as a diagnostic tool for the investigation of the RCS dynamics from the accelerated particle spectra found from hard X-ray and microwave emission.
