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The size distribution of solar energetic particle (SEP) events, which represent a more energetic subset than flare events, is mostly found to follow power law distribution functions, rather than Poissonian random distribution functions. However, the numerical value of the power law slope is generally flatter than the slopes of the flare size distributions in hard X-rays, soft X-rays, and EUV (Hudson 1978), which can be explained in at least four different ways: (i) normal flares and proton flares are produced by two fundamentally different acceleration mechanisms; (ii) proton flares behave differently than normal flares; (iii) the fractal dimensionality of SEP events is different from normal flares; (iv) proton flares are subject to a selection bias toward the most energetic events and thus are not a representative sample of large flares. Nevertheless, the standard fractal-diffusive SOC model can explain the observed slopes of SEP size distributions, but observations reveal deviations from straight power law functions, or broken power law slopes, and thus are not unique and need to be modeled in more detail.
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