**4. Discussion**

#### **4.1 Fluence dose relationship**

Dose distributed over a material results from a specific number of particles incident on a given material surface. Using the simplified equation of dose, *D* ¼ ∅*p*ð Þ *E S*pð Þ *E* , where *S*<sup>p</sup> corresponds to non-ionizing energy loss (NIEL) for DDD and stopping power for TID. The incident primary fluence interacts with the material through soft and hard knock-on collisions resulting in slowed down secondary charged particles. This develops a charged particle equilibrium with the absorption of the secondary fluence as the radiation energy escapes [45]. There exists a linear relationship existing between proton damage coefficients and determined NIEL for the case of GaAs cells [46]. The observable relationship results from the DDD increasing with the increase in proton fluence. Therefore, proton fluence at any energy level is an input to calculating degradation curves and or characteristic curves from which relative proton damage coefficients can be determined.

#### **4.2 Energy spectra dose relationship**

While the less energetic protons incident on the material is shielded off, the highly energetic protons (>100 MeV) are slowed down by the shielding of the material to low energies. The slowed-down protons initiate atomic and molecular collision; this process needs a build-up from low energies to exceed the threshold energy for atomic displacement to occur. Once the threshold energy is exceeded, the material properties start to degrade with absorption and particle production. Comparing the rate of energy loss, the NIEL peaks faster at much lower energies than the stopping power. While different materials have different threshold energies for atomic displacement, low proton energies (<1 MeV) are enough to build the threshold energies for atomic displacement for most shielding materials and this plays the largest contribution to damage production. The defining functional form of the energy spectrum below 1 MeV behaves as a reciprocal of stopping power calculated using the continuous slowing down approximation (CSDA) theory and is independent of the shield thickness. Theoretically, this is the range of the proton (Ra) which defines the mean distance a proton travels in the matter before it stops (Eq. (3)) below adopted from [6].

$$\mathbf{Ra} = \int\_{E\_{\rm min}}^{E\_{\rm max}} -\frac{\rho \mathbf{dx}}{\mathbf{d}E} \mathbf{d}E + \mathbf{Ra}(E\_{\rm min}) \tag{3}$$

Where Rað Þ *E*min is the measured range at minimum energy (*E*min) always taken at 1 MeV due to large enough data available for any proton event at the energy level.

Messenger et al. [47] found that 90% of the total dose to the shielded device was a contribution of relatively low proton energies up to about 12 MeV and only 10% was from proton energies from 12 to 500 MeV for an event on 19th October 1989. Extremely large SPEs associated with GLEs rarely occur, these contain high proton

#### *Solar Proton Activity over the Solar Cycle 24 and Associated Space Radiation Doses DOI: http://dx.doi.org/10.5772/intechopen.103832*

energies extending to GeV. The energy spectrum from such events is known to be 'hard' and it can penetrate deeper thicknesses of the shielding material. Mertens and Slaba [48] calculated the cumulative dose from a set of 65 historical SPEs associated with GLEs using the power-law function and noted that 25% of the peak total dose was contributed from energies >500 MeV corresponding to a spectrally hard SPE of February 1956. The double power law of the band distribution function has been recommended to best describe the energy spectrum of a GLE event over the broad energy ranges [18, 49]. Also, Xapsos et al. [50] found that the Weibull distribution describes the proton event energy spectra for the smallest values and is appropriate on broad energy ranges.

### **5. Summary**

The occurrence of solar proton and GLEs events follow solar cycle described by sunspot number. A least number of SPEs were recorded in solar cycle 24 with the least smoothed sunspot number compared to the previous three solar cycles. Every proton energy starting from the lowest to the highest energy level contributes to radiation dose and the slowed-down protons at low energies are critical in the assessment of space radiation damage. I also noted that the shield of a material is an important component to consider when evaluating proton damage effects. It's important to use the most appropriate distribution function that can describe the energy spectrum from low to high energy levels for any SPE event. However, this is a challenge with the GLE associated SPEs where there is an underestimation at high energies of GeV by most distribution functions. A further study regarding the probabilistic occurrence of SPEs, with the associated properties of solar flares, CMEs, GLE events, and energy spectrum is necessary, this is important to improve modeling and prediction capabilities of such events.
