Radiation Panel

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Description

The Radiation Panel calculates the radiation that a surface is exposed to from the Sun whilst also modelling the affects of any configured shielding. The panel takes in Solar Model information, based on whether the panel is naturally shielded behind a planet from the sun. The Radiation Panel is designed to be used in partnership with the Radiation Model.

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Example Use Cases

• Radiation Modelling: Determining the radiation exposure of shielded and unshielded components onboard a spacecraft as a form of risk analysis.

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Module Implementation

The Radiation Panel determines the external Solar Flux $F_{\mathrm{external}}$ upon a surface at a time based on the relative angle between the sun direction vector $\hat{\text{s}}$ and the component normal up vector $\hat{\text{n}}$ of the panel. The final external flux equation is calculated as follows:

$$F_{\mathrm{external}}=F\times C_e\times C_p\times (\hat{\text{n}}\cdot \hat{\text{s}})\times A$$

In this equation, $A$ is the area of the panel defined in squared meters, and $C$ denotes the eclipsing visibility factor. $C_e$ is the eclipse factor caused by the celestial bodies blocking the sun, where $1$ would be perfect visibility and $0$ is entirely in eclipse. $C_p$ is the panel eclipse factor. This is calculated from an external integration such as Unreal and uses ray casts to determine if part of the spacecraft is blocking the solar panel’s area. Without Unreal, this value defaults to $1$.

The solar flux and eclipse data are pulled from the solar flux and eclipse message on the spacecraft. This is automatically fetched and added to the panel’s software definition. If the albedo model is applied to the orbiting body, and the spacecraft has been set up to read albedo data, then the total flux $F$ can be summed to be:

$$F=F_{\odot }+F_e(\hat{\text{n}}\cdot \hat{\text{e}})$$

where $\hat{\text{n}}$ is the component normal up vector, $\hat{\text{e}}$ is the earth direction vector, $F_{\odot }$ is the solar flux at that location and $F_e$ is the albedo value at the spacecraft’s location in orbit.

From the External Flux value, the panel applies a simple shielding calculation to determine the Internal Flux value. These Flux values are used by the Radiation Model in it’s calculations, with the Internal Flux values used if the Radiation Model is configured for a shielded component. The internal flux is calculated using an exponential attenuation model and is as follows:

$$F_{\mathrm{internal}}=F_{\mathrm{external}}\times e^{-\mu x}$$

where $\mu$ is the Linear Attenuation Coefficient for the shielding material and $x$ is the thickness of the material. If the shielding material thickness is set to 0, the internal Flux value is set to the external value.

On each tick of the simulation, the Total Ionizing Dose (TID) for the model is incremented based on one of the following formulas. The first is for when the panel is incorporating the effects of each panels shielding, with the change in TID:

$$\Delta \mathrm{TID}=\frac{F_{\mathrm{internal}}\times (\hat{\text{n}}\cdot \hat{\text{s}})\times A\times \Delta t}{\rho \times x}\times E$$

Where $F_{\mathrm{internal}}$ , $\hat{\text{n}}$ , $\hat{\text{s}}$ , $A$ covered above. The Shielding Density, $\rho$ , and Shielding Thickness, $x$, of the panel are also considered as well as $\Delta t$ which is the simulation time step. The Energy to Dose Conversion Efficiency, $E$, relates the translation of absorbed energy to dose for the shielding material.

If the model isn’t shielded, the change in TID is simply:

$$\Delta \mathrm{TID}=F_{\mathrm{external}}\times (\hat{\text{n}}\cdot \hat{\text{s}})\times A\times \Delta t\times E$$

The Single Event Effect (SEE) Probability for the panel is then also calculated from the following:

$$\mathrm{SEE}=1-e^{-\lambda }$$

\lambda = (\hat{\textbf{n}}\cdot \hat{\textbf{s}}) \times A \times \frac{F}{E_\mathrm{avg}} $$Where $F$ is the external or shielded flux from above and $E_{\mathrm{avg}}$ is the Average Particle Energy of the solar particles and is used to convert the Flux.

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Assumptions/Limitations

• If multiple Radiation Panels are stacked in front of each other towards the Sun, each panel will return the same value as if it had direct exposure.
• Additional sources of radiation (such as Van Allen Belt Radiation or Galactic Cosmic Rays) are not modelled.
• Radiation panels are defined as a 2D square. As such, the entire panel is treated as a uniform system, with complex geometries needing to be build from multiple instances of the radiation panel.
• Unconventionally, the External and Internal Flux values are measured in Watts per Square Meter. The Radiation Model converts this via an Average Particle Energy value.
• The SEE Probability calculation approach is designed for conceptual or early phase modelling.