1、, b95534 0003220 57T U Special Copvright Notice o I999 by the American Institute of Aeronautics and Astronautics. All rights reserved. AIAA G-083-1999 Guide to Modeling Earths Trapped Radiation Environment AIAA G-083-1999 Guide Guide To Modeling Earths Trapped Radiation Environment Sponsor American
2、Institute of Aeronautics and Astronautics Abstract This Guide serves as both an introduction to the phenomena of radiation in the space environment and the product engineering issues facing spacecraft designers. Emphasis is on the trapped radiation environment of the Earth which is known as the Van
3、Allen Belts. The leading empirical models are described and the problems in using them are identified. Current radiation modeling efforts are also discussed, along with shielding design and optimization. The Guide is intended for students, designers, mission planners, and others who need a ready und
4、erstanding of this critical issue affecting spacecraft performance in Earth orbit. AIAA G-083-1999 Library of Congress Cataloging-in-Publication AIAA guide to modeling earths trapped radiation environment/sponsor, American Institute of Aeronautics and Astronautics p. cm. “AIAA G-083-1999” Includes b
5、ibliographical references ISBN 1-56347-349-6 (softcover), 1-56347-367-4 (electronic) 1. Van Allen radiation belts-Mathematical models. 2. Magnetohydrodynamics-Mathematical models. I. American Institute of Aeronautics and Astronautics. QC809.V3G85 1999 538 ,766-dc21 99-35575 CI P Published by America
6、n Institute of Astronautics and Aeronautics 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191 Copyright O 1999 American Institute of Aeronautics and Astronautics All rights reserved. No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, witho
7、ut prior written permission of the publisher. Printed in the United States of America. II AIAA G-083-1999 Contents Foreword . v 1. Introduction 2. The Space Radiation Environment: Basic Concepts 2 3. The Trapped Radiation Environment 7 3.1 Overview . 7 3.2 Geomagnetic Field 3.3 Magnetic and 3.3.1 Ba
8、sic Particle Motion 3.3.2 Invariants of the Particle Motion 17 4. AE8 and AP8 Models . 20 5. Problems with AE and AP . 23 5.1 Solar Cycle E 5.2 Examples: Lo 5.3 Coverage Limitations 5.4 AE8/AP for shorter missions, factors approaching 10-1 O0 are easily possible). Even given an accurate ?average? de
9、scription of the environment, short-term variations of several orders of magnitude in dosage and single event upset (SEU) rates have been seen in the span of hours (e.g., the 1989 solar proton events). Complicating the practical application of the radiation environment to spacecraft design, radiatio
10、n transport codes and estimates of the effects of radiation damage are often inaccurate. Comparisons between ground tests and in situ measurements have shown significant disagreement. Furthermore, the parts used on the spacecraft can show variations in sensitivity of factors of 2-10, even within the
11、 same parts lot. Often, how a system is actually used can mask, or hopefully limit, the effects of radiation damage. Thus, to a degree, mitigating radiation effects is a black art and, increasingly, a very expensive art for which any imprecision in the knowledge of the trapped radiation environment
12、becomes a critical component. However, the ultimate solution is a comprehensive process that treats all uncertainties. 1 AIAA G-083-1999 2. The Space Radiation Environment: Basic Concepts This section provides an overview of the basic physical concepts and definitions that will be used throughout th
13、e guide. In particular, the concepts of energy, flux, fluence, and dosage will be briefly described. The reader is referred to the many excellent texts on space physics or astronomy for more detailed explanations. !2 First consider the concept of energy. In the case of particles that have a rest mas
14、s, the fundamental equation relating particle mass and velocity to kinetic energy is: E = (y - i)moc2 Relativistically (1 1 Non-Relativistically 1 2 = -moV2 where m = particle rest mass V = particle velocity c = speed of light E = particle kinetic energy For photons (which have no rest mass), the eq
15、uivalent equation is: E= hv where h = Plancks constant v = frequency of the light Closely coupled to the concept of energy is that of dose. Simply put, dose is the total energy accumulated in a given volume element of a specific material due to incident radiation. It is typically given in units of r
16、ads or “radiation absorbed dose” for a particular material (the material must be specified because energy absorption is dependent on the material). As an example, for silicon, 1 rad (Si) = lo- J/kg (Si). It must be emphasized that, for the same incident flux, different materials will be affected dif
17、ferently depending on the composition of the radiation and the composition of the absorbing material. In addition to the energy and composition of a particle or photon, it is also necessary to describe how many of them there are. This is usually done in terms of intensity or flux and, when speaking
18、in terms of a time interval, fluence. Confusion arises over the concepts of intensity/flux and fluence because there are many different ways to define these quantities. Here, we will define the quantity “unidirectional differential intensity” j( E, O, t) as : The flux (number of particles or photons
19、 per unit time) of a given energy per unit energy interval dE in a unit solid angle (di2 =27ccos OdOd) about the direction of observation (in the O,direction), incident on unit of surface area (dA) perpendicular to the direction of observation. 2 AIAA G-083-1999 This is illustrated in Fig. 1 .2 Typi
20、cal units are particlescm-2si .sri .keV-l for protons or electrons and particles.m-2si .sri .(MeVp-l)-l for heavy ions (where ,u is nucleon). A typical spectrum for iron cosmic rays is presented in Fig. 2.3 In the figure, the solid curves are for solar maximum (lower) and solar minimum (upper). The
21、dashed curve is the 90% worst case iron spectrum, which is implied by comparison with the cosmic ray helium spectrum. The “unidirectional integral intensity” (or flux) is defined as the intensity of all particles with energy greater than or equal to a threshold energy E: (4) with units of particles
22、cm-2s-isri. We define the “omnidirectional flux” Jas: J=/jdQ 4z Fluence / is the integral of the flux over a given time interval (e.g., one hour, one year): I =/jdt (5) 6t Here, when we refer to omnidirectional fluence /(E), we will normally mean the “omnidirectional integral (in energy) fluence” su
23、ch that: I, = jrn E dE/dQ/ 4z 6t jdt The units of this quantity are particlescm-2 for some specified (6) threshold energy E (typically 1 MeV or higher for radiation effects) and for a specified time interval (often one year). FLUX Figure 1 - The flux of a given energy per unit energy interval din a
24、unit solid angle about the direction of observation (Copyright by and used by permission of Springer-Verlag, New York) 3 AIAA G-083-1999 10 n 3 % 10 I -1 UJ 10-71 I I I IlIlII I I I 11111I 10-8“ , 10 IO2 io3 u io4 io5 KINETIC ENERGY (MeV/u) Figure 2- The iron cosmic ray spectrum To allow comparisons
25、 among different energies, particle types, and dosages, it is common practice to talk in terms of “1 -MeV equivalent“ (typically 1 -MeV electrons or 1 -MeV neutrons in silicon). First, the energy dependence of the damage and energy content of the spectra for the environment to be considered are used
26、 to determine what fluence of 1-MeV particles (electrons or neutrons) would produce the same amount of damage or dose in the material (typically silicon or aluminum). A curve for neutrons, in units of MeV-mb (where b is a barn or cm2 and the relative displacement damage is defined in terms of the cr
27、oss section times the energy of the incident particle), is given in Fig. 3.4 As an illustration, for 14 MeV neutrons, the 1-MeV neutron dose damage equivalent is given by multiplying the 14 MeV dose by 2.5 (obtained from Ref. 4). (Note: because of variations in the damage parameter with material and
28、 property, it should always be kept in mind that the use of a damage equivalent is not exact but an approximation for comparison purposes.) 4 AIAA G-083-1999 n E 1 o-1 1 oo 1 o1 IO2 INCIDENT NEUTRON ENERGY (MeV) Figure 3- Neutron displacement damage equivalence curve (Copyright by and used by permis
29、sion of Institute of Electrical and Electronics Engineers) A final quantity related to energy absorption and flux is the Linear Energy Transfer (LET). The LET is the energy transferred by radiation per unit length of absorbing material. That is, LET is proportional to dE/dx (note: there is in fact a
30、 slight difference between “energy transferred” and “energy lost per unit length” but that will be ignored here). For ionization and excitation effects, LET is often expressed in MeV/pm of the primary particle track length or, if the density of the material is known, MeVcm2.rng-l (this is typically
31、the unit when the reference is to an LET between 1 and 30 and is given by: -). 1 dE PdX The concept of LET is particularly important when discussing single event upsets (SEUS) or “soft errors.” These occur when a particle, typically an ionized, high energy atomic nucleus, deposits enough energy in t
32、he sensitive region of an electronic device to cause a change in the logic state of the device. Upsets occur only when the energy deposited exceeds a critical level in the sensitive region of the device. This is often computed in terms of LET. When viewed as a function of LET, the probability of ups
33、et is, in its simplest form, a threshold phenomenon: any particle with a minimum LET of Lo or greater will cause an upset. This behavior is illustrated in Fig. 4 where the energy deposited per unit length (LET) is plotted vs incident particle energy-note how the curve has a peak rate. Lo corresponds
34、 to a constant value of LET. As illustrated, there can be multiple values of energy (E, and E, here) that correspond to the same value of LET. A useful way of presenting the environment in terms of LET is the Heinrich curve. The Heinrich curve gives the integral flux as a function of LET rather than
35、 particle energy. The Heinrich flux FH is the flux of particles for a single species with a (threshold) LET of LETo or greater: E, AIAA G-083-1999 where fi is the particle flux for the species i as a function of energy and E, and E2 are the energies between which the LET is greater than or equal to
36、the threshold LET, (a representative integral Heinrich curve for iron is plotted in Fig. 55). The LET depends not only on particle energy, but on the target material as well because the LET vs energy curve will be different for all particle species. Experiments have shown, however, that to the first
37、 order it is the LET that is important for determining upsets and not the particle energy or its species. The Heinrich flux vs LET plot is the principal means of presenting radiation data for use in SEU calculations just as the particle flux vs energy is the main means of presenting radiation data f
38、or use in dosage calculations. Energy Figure 4- Linear Energy Transfer Function (LET) vs Energy lo2J t IRON I I I I IIIII I I I IIIII 1 o5 1 o-6 lo3 lo4 MeV cm /g Figure 5- Heinrich curves for iron cosmic rays 6 AIAA G-083-1999 To summarize, this section has defined the basic terminology used to des
39、cribe the radiation environment-dose, flux/intensity, fluence, LET, and 1 -MeV equivalent. The reader is referred to books and articles by Roederer2 and others for more complete descriptions of these concepts. 3. The Trapped Radiation Environment 3.1 Overview By definition, the high energy particle
40、radiation environment in space consists of electrons with energies greater than 40 KeV, protons or neutrons with energies greater than 1 MeV, and heavy ions with energies above 1 MeV/nucleon. Lower energy electrons, protons, and ions are ubiquitous but are considered as plasma. The populations are c
41、haracterized in terms of their kinetic energy, charge state (or lack thereof), and composition. Unlike photons, which travel uniformly at the speed of light, particles can vary in velocity from a few m/s to a sizable fraction of the speed of light as in the case of cosmic rays. The high energy radia
42、tion population can be roughly divided into four families based on these characteristics: 1) Galactic cosmic rays, which consist of interplanetary protons, electrons, and ionized heavy nuclei. 2) Trapped radiation (for the Earth, the Van Allen belts). 3) Protons and heavy nuclei associated with sola
43、r proton events. 4) Neutrons (primarily cosmic ray albedo neutrons CRAN particles). The first population changes relatively slowly (cyclically with the solar cycle). It is included here because it is believed to contribute to the CRAN and the trapped heavy ion population (see Section 6.2). The secon
44、d population, the Earths trapped radiation environment, can be divided into zones. Typically, the inner zone is populated with very high energy protons produced by CRAN decay and lower energy electrons, which also vary on a solar cycle timescale. The outer zone consists primarily of more energetic e
45、lectrons and lower energy protons, which vary rapidly on a timescale that can be as short as one day, or less, in response to magnetic storms. The third population is highly time dependent, being associated with infrequent coronal mass ejections (CMEs). The fourth is a secondary population because t
46、he relatively short lifetime of neutrons severely limits any solar-produced fluxes at 1 AU or beyond. Each type of radiation has a characteristic spectrum and preferred interaction mode with matter that supports this simple division. Here, the discussion will focus primarily on the trapped radiation
47、 environment, the Van Allen belts. First discovered by James Van Allen and his collaborators on Explorer I, trapped radiation at the Earth consists principally of energetic protons and electrons, with lesser percentages of heavy ions such as O+, contained by the Earths magnetic field in toroidal bel
48、ts. Commonly known as the “Van Allen belts,”6 these toroidal regions consist of (at least) two zones or belts. The inner belt extends from approximately hundreds of kilometers to -6000 km in altitude and is populated by high energy (approximately tens of mega electronvolts) protons and medium energy
49、 (50-1000 keV) electrons, while the outer belt, up to 60,000 km in altitude, is predominately populated by high energy electrons. Schematics of the radiation flux contours for the Van Allen belts are illustrated in Fig. 6 where the average omnidirectional integral fluxes above energy thresholds are shown for 1-MeV electrons and 10-MeV pro ton. The detailed mechanism by which particles are entrapped in the belt regions is not well understood nor is the primary source clearly identified (albedo neutrons are considered an important source of the intense proton and electron
