Energy spectrum of Solar energetic particles (SEP's) I would like to know if we have obtained any observations regarding the energy spectrum of solar energetic particles. Something like the following histogram :

And if so, what is the index of the power-law. Thank you!
 A: 
I would like to know if we have obtained any observations regarding the energy spectrum of solar energetic particles.

Yes, there are several decades (>30 years) worth of observations of solar energetic particles (SEP) [e.g., Desai et al., 2016a,b; Reames, 2017].

And if so, what is the index of the power-law. Thank you!

There is not one, but two for each mass-per-charge chemical abundance.  The solar wind already contains multiple heavy ions above protons, including but not limited to alpha-particles (i.e., helium nuclei), carbon, nitrogen, oxygen, neon, magnesium, silicon, sulpher, calcium, and iron [e.g., Desai et al., 2016b; Reames, 2017].
The spectra, in terms of particle fluence $j(E)$, are described by a double- or broken-power-law [e.g., Desai et al., 2016a], given by:
$$
\begin{align}
  j\left( E \right) & = C \ E^{-\gamma_{a}} \ e^{-E/E_{B}} \text{  for  } E \leq \left( \gamma_{b} - \gamma_{a} \right) \ E_{B} \tag{0a} \\
  j\left( E \right) & = C \ E^{-\gamma_{b}} \ \left[ \left( \gamma_{b} - \gamma_{a} \right) \ E_{B} \right]^{\gamma_{b} - \gamma_{a}} \ e^{-\left( \gamma_{b} - \gamma_{a} \right)} \text{  for  } E > \left( \gamma_{b} - \gamma_{a} \right) \ E_{B} \tag{0b}
\end{align}
$$
It turns out that the type of solar event (e.g., solar flare) that causes the SEP also matters in regards to the slopes and the flux vs time profile [e.g., Reames, 2017].
References


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*Desai, M.I., et al., "Spectral Properties of Large Gradual Solar Energetic Particle Events. I. Fe, O, and Seed Material," Astrophys. J. 816(2), pp. 68, doi:10.3847/0004-637X/816/2/68, 2016a

*Desai, M.I., et al., "Spectral Properties of Large Gradual Solar Energetic Particle Events. II. Systematic Q/M Dependence of Heavy Ion Spectral Breaks," Astrophys. J. 828(2), pp. 106, doi:10.3847/0004-637X/828/2/106, 2016b.

*Reames, D.V. "Solar Energetic Particles," Lecture Notes in Physics 932, doi:10.1007/978-3-319-50871-9, 2017.

