# Presentation: 742521

## ESP Model for Solar Particle Risk Assessment

***Mike Xapsos***
***NASA/GSFC, Code 561***
***Greenbelt, MD 20771***

## ACKNOWLEDGMENTS

**Co-Investigators:**
**Janet Barth and E.G. Stassinopoulos, Code 561**
**Robert McGuire, Code 632**
**Craig Stauffer and George Gee, SGT Inc.**
**Ed Burke, Consultant**
**Sponsors:**
**MSFC Space Environments and Effects Program**
**GSFC R&TD**

## OUTLINE

**Introduction**
**Data Base**
**Initial Distribution of Solar Proton Event (SPE) Magnitudes**
**Worst Case Event Distributions**
**Cumulative Fluence Distributions**
**Ongoing Work**

## INTRODUCTION

**Long-term models of solar particle radiation exposure are useful for spacecraft subsystem and instrument design**
**especially critical for missions to the moon or Mars**
**The**** E****mission of ****S****olar ****P****rotons (****ESP****) model predicts for user specified confidence level and mission time period:**
**omnidirectional fluences and fluxes at 1 AU**
**>1 to >300 MeV protons**
**Model based on advanced statistical methods:**
**Maximum Entropy Theory**
**Extreme Value Theory**
**Compound Poisson Process Theory**

## DATA BASE

**Our model is based primarily on the IMP-8 Goddard Medium Energy (GME) Instrument data**
**Nearly continuous coverage since 1973**
**IMP-8 near circular orbit at ~35 Earth radii suitable for determining fluxes at 1 AU**
**30 energy bins of proton differential flux ranging from 0.88 to 485 MeV.**
**Main problem: occasional detector saturation observed during largest events and occasional gaps in data**
**Supplement GME data with:**
**IMP-8 CPME data**
**GOES SEM data**

## October – November 1989 “Episode”

## INITIAL DISTRIBUTION OF SOLAR PARTICLE EVENT MAGNITUDES

**Determine probability distributions using ****maximum entropy theory:**
**Method for determining probability distribution when data are incomplete**
**Maximize the distribution’s entropy (uncertainty) subject to known constraints**
**Results in least biased distribution in the face of missing information**
**Distribution turns out to be truncated power law in event magnitude (fluence or flux).**

## ESP MODEL: INITIAL DISTRIBUTIONSMaximum Entropy Approach

## WORST CASE EVENT DISTRIBUTIONS

**Determine probability distributions using**
**     ****extreme value statistics:**
**Well established for modeling environmental phenomena such as earthquakes, floods, etc.**
**In contrast to central value statistics, extreme value theory ****focuses on the distribution of largest (or smallest) values**
**Results for worst case events are obtained from initial distribution as function of confidence level and mission duration.**

## ESP MODEL: WORST CASE DISTRIBUTIONSExtreme Value Theory Approach

**3**

## CUMULATIVE FLUENCE DISTRIBUTIONS

**Determine probability distributions using**
**    ****maximum entropy and compound Poisson process theory:**
**Maximum entropy approach indicates cumulative distribution is lognormal and has time dependent parameters.**
**Compound Poisson process theory predicts evolution of lognormal parameters over time.**
**Results are consistent with Monte Carlo type simulations using initial distribution of SPE fluences.**

## ESP MODEL: CUMULATIVE DISTRIBUTIONMaximum Entropy Approach

**.50**

**.80**

## Cumulative Fluences for Solar Max and Solar Min

## ONGOING WORK

**Apply what we have learned about solar proton event models to construct models of solar heavy ion exposures.**
**Currently funded by MSFC to add IMP-8 GME heavy ion data to existing models (long-term, mainly low energy data)**
**Will require support to expand efforts to include higher energy data obtained with more modern instrumentation**
**Also need to integrate abundance model to be used with ion species present in small amounts.**
**Incorporate Langley HZETRN code for shielding.**