Modelling the Exposure of Satellites in Medium Earth Orbit to Proton Belt Radiation

Support from ESA applies to work undertaken in first year, and the resulting publication at https://doi.org/10.1029/2019SW002213 (included in the thesis).Geomagnetically trapped protons forming Earth's proton radiation belt pose a hazard to orbiting spacecraft. In particular, solar cells are prone to degradation caused by non-ionising collisions with protons in the energy range of several megaelectron volts, which can ultimately shorten the lifespan of a mission. Dynamic enhancements in trapped proton flux following solar energetic particle events have been observed to last several months, and there is a strong need for physics‐based modelling in order to predict the impact these changes may have on orbiting spacecraft. This thesis addresses the need for physics-based modelling by presenting an investigation into inner proton belt variability with a 3D numerical model created from scratch, and by quantifying the impact that variability has on the solar cell degradation of orbiting satellites. After a review of background concepts in Chapter 1, Chapter 2 presents a case study on satellites undergoing electric orbit raising to geostationary orbit. The increase in solar cell degradation that can occur during a period of proton belt enhancement is calculated for three example orbits. It is found that a large enhancement can cause an additional degradation in solar cell output power by up to ~5% over the course of orbit raising, and further changes of a few percent are shown to occur based on the choice of trajectory, or for a 50μm change in solar cell coverglass shielding thickness. In Chapter 3 a physics-based numerical model is constructed, solving for proton phase space density in terms of the first, second and third adiabatic invariants μ, K and L. This chapter demonstrates how key processes can be quantified, including transport via radial diffusion, the cosmic ray albedo neutron decay source and coulomb collisional loss. In Chapter 4, a 2D version of the model is applied to derive proton radial diffusion coefficients for a period of solar maximum. This is achieved by varying parameters controlling the rate of radial diffusion in order to optimise the fit between model and data from the CRRES satellite, under the assumption of steady state. Results are compared with diffusion coefficients derived in other literature, and the validity of the steady state assumption underlying this technique is discussed. In Chapter 5, the 3D numerical model is applied to investigate time variability at energies of 1-10 megaelectron volts, a crucial energy range for solar cell degradation. Three sets of diffusion coefficients from previous literature are applied to model the time evolution of proton phase space density over the four year period 2014-2018. The sensitivity of modelling results to the choice of diffusion coefficients is discussed, including the effect on the anisotropy of proton pitch angle distributions. In the final research chapter of this thesis, Chapter 6, these modelling results are then applied to calculate solar cell degradation over the modelling period for an example satellite in 1200km inclined circular orbit. This demonstrates the final step in an end-to-end physics-based calculation of solar cell degradation.Natural Environment Research Council (NERC) via Doctoral Training Programme NE/R009457/1; Additional support by the European Space Agency (ESA) through a CCN on ESA Contract 4000117974/16/NL/LF (VALIRENE

Modelling the Exposure of Satellites in Medium Earth Orbit to Proton Belt Radiation

Support from ESA applies to work undertaken in first year, and the resulting publication at https://doi.org/10.1029/2019SW002213 (included in the thesis).Geomagnetically trapped protons forming Earth's proton radiation belt pose a hazard to orbiting spacecraft. In particular, solar cells are prone to degradation caused by non-ionising collisions with protons in the energy range of several megaelectron volts, which can ultimately shorten the lifespan of a mission. Dynamic enhancements in trapped proton flux following solar energetic particle events have been observed to last several months, and there is a strong need for physics‐based modelling in order to predict the impact these changes may have on orbiting spacecraft. This thesis addresses the need for physics-based modelling by presenting an investigation into inner proton belt variability with a 3D numerical model created from scratch, and by quantifying the impact that variability has on the solar cell degradation of orbiting satellites. After a review of background concepts in Chapter 1, Chapter 2 presents a case study on satellites undergoing electric orbit raising to geostationary orbit. The increase in solar cell degradation that can occur during a period of proton belt enhancement is calculated for three example orbits. It is found that a large enhancement can cause an additional degradation in solar cell output power by up to ~5% over the course of orbit raising, and further changes of a few percent are shown to occur based on the choice of trajectory, or for a 50μm change in solar cell coverglass shielding thickness. In Chapter 3 a physics-based numerical model is constructed, solving for proton phase space density in terms of the first, second and third adiabatic invariants μ, K and L. This chapter demonstrates how key processes can be quantified, including transport via radial diffusion, the cosmic ray albedo neutron decay source and coulomb collisional loss. In Chapter 4, a 2D version of the model is applied to derive proton radial diffusion coefficients for a period of solar maximum. This is achieved by varying parameters controlling the rate of radial diffusion in order to optimise the fit between model and data from the CRRES satellite, under the assumption of steady state. Results are compared with diffusion coefficients derived in other literature, and the validity of the steady state assumption underlying this technique is discussed. In Chapter 5, the 3D numerical model is applied to investigate time variability at energies of 1-10 megaelectron volts, a crucial energy range for solar cell degradation. Three sets of diffusion coefficients from previous literature are applied to model the time evolution of proton phase space density over the four year period 2014-2018. The sensitivity of modelling results to the choice of diffusion coefficients is discussed, including the effect on the anisotropy of proton pitch angle distributions. In the final research chapter of this thesis, Chapter 6, these modelling results are then applied to calculate solar cell degradation over the modelling period for an example satellite in 1200km inclined circular orbit. This demonstrates the final step in an end-to-end physics-based calculation of solar cell degradation.Natural Environment Research Council (NERC) via Doctoral Training Programme NE/R009457/1; Additional support by the European Space Agency (ESA) through a CCN on ESA Contract 4000117974/16/NL/LF (VALIRENE

Effectiveness of Problem-Based Learning Prior to Lectures on Learning and Retention

In the mandatory tutorial sections of an introductory probability and statistics course of just over 70 students in the Arts and Science undergraduate program, students were randomly assigned to small groups to work on accessible problems from upcoming material without any prior instruction on how to solve them. Solutions were ungraded, and marks were assigned for participation only. A multiyear study was conducted to test students for their level of retention one year later, comparing them to a previous control group. The test question concerned Bayes’ Theorem. Results suggest that the strategy improves student reasoning and retention of concepts while, as expected, a formula is long forgotten. However, low participation rates in the survey post-test produced a p-value of 20%, precluding a claim of statistical significance. Nonetheless, qualitative student feedback on surveys during the course showed a very strong positive response to the approach. Students reported the approach helped their thinking and reasoning, and assisted in their learning. They appreciated the informal, low-pressure environment of the problem-based learning (PBL) sessions, and reported that the sessions were beneficial for developing their own understanding of the concepts before going to lecture. Notwithstanding their positive feedback on PBL activities, students still expressed a preference for traditional instructional approaches where the teaching assistant leads them through solution procedures

Solar Cell Degradation due to Proton Belt Enhancements During Electric Orbit Raising to GEO

The recent introduction of all‐electric propulsion on geosynchronous satellites enables lower‐cost access to space by replacing chemical propellant. However, the time period required to initially raise the satellite to geostationary orbit (GEO) is around 200 days. During this time the satellite can be exposed to dynamic increases in trapped flux which are challenging to model. To understand the potential penalty of this new technique in terms of radiation exposure, the influence of several key parameters on solar cell degradation during the electric orbit raising period has been investigated. This is achieved by calculating the accumulation of non‐ionising dose through time for a range of approaches. We demonstrate the changes in degradation caused by launching during a long‐lived (100s of days) enhancement in MeV trapped proton flux for three different electric orbit raising scenarios and three different thicknesses of coverglass. Results show that launching in an active environment can increase solar cell degradation due to trapped protons by ~5% before start of service compared with a quiet environment. The crucial energy range for such enhancements in proton flux is 3‐10MeV (depending on shielding). Further changes of a few percent can occur between different trajectories, or when a 50μm change in coverglass thickness is applied

Modelling inner proton belt variability at energies 1 to 10MeV using BAS‐PRO

Geomagnetically trapped protons forming Earth’s proton radiation belt pose a hazard to orbiting spacecraft. In particular, solar cell degradation is caused by non-ionising collisions with protons at energies of several megaelectron volts (MeV), which can shorten mission lifespan. Dynamic enhancements in trapped proton flux following solar energetic particle events have been observed to last several months, and there is a strong need for physics-based modelling to predict the impact on spacecraft. However, modelling proton belt variability at this energy is challenging because radial diffusion coefficients are not well constrained. We address this by using the British Antarctic Survey proton belt model BAS-PRO to perform 3D simulations of the proton belt in the region 1.15 ≤ L ≤ 2 from 2014 to 2018. The model is driven by measurements from the RBSPICE and MagEIS instruments carried by the Van Allen Probe satellites. To investigate sensitivity, simulations are repeated for three different sets of proton radial diffusion coefficients DLL taken from previous literature. Comparing the time evolution of each result, we find that solar cycle variability can drive up to a ∼75% increase in 7.5MeV flux at L = 1.3 over four years due to the increased importance of collisional loss at low energies. We also show how the anisotropy of proton pitch angle distributions varies with L and energy, depending on DLL. However we find that phase space density can vary by three orders of magnitude at L = 1.4 and μ = 20MeV/G due to uncertainty in DLL, highlighting the need to better constrain proton DLL at low energy