CHAPTER DEEP DIELECTRIC CHARGING AND SPACECRAFT ANOMALIES 16 Shu T. Lai*,†, Kerri Cahoy‡, Whitney Lohmeyer‡, Ashley Carlton‡, Raichelle Aniceto‡, Joseph Minow§ MIT Space Propulsion Laboratory, Cambridge, MA, United States* Boston College, Newton, MA, United States† MIT Space Systems Laboratory, Cambridge, MA, United States‡ NASA Marshall Space Flight Center, Huntsville, AL, § United States CHAPTER OUTLINE 1 Introduction ................................................................................................................................. 419 2 What Is Deep Dielectric Charging? ................................................................................................ 420 2.1 The Roles of Ions ........................................................................................................422 3 Space Environments ..................................................................................................................... 423 3.1 Trapped Radiation ......................................................................................................423 3.2 Temporal Variation of the Radiation Belts .....................................................................423 3.3 Relative Role of Electrons and Ions ..............................................................................424 4 Deep Dielectric Charging and Discharging ..................................................................................... 426 5 Dependence from Geomagnetic Indices: Dst and Kp Index ............................................................... 428 6 Delay Time ................................................................................................................................... 428 7 Discharge Event Parameters .......................................................................................................... 429 8 Spacecraft Design Guidelines ........................................................................................................ 429 9 Conclusion ................................................................................................................................... 431 Acknowledgment ................................................................................................................................ 431 References ........................................................................................................................................ 431 1 INTRODUCTION The space radiation environment presents hazards to satellites and the services they provide by causing internal and surface charging, displacement damage, accumulated dose effects, etc., which have led to many documented satellite anomalies (e.g., Baker, 2000; Fennell et al., 2001; Frederickson, 1996). This chapter focuses on internal charging, which is one of the main causes of space environment- related anomalies (Koons et al., 1999). We present the physical mechanisms and environments that may lead to internal charging, an overview of some notable on-orbit spacecraft anomalies that are at- tributed to internal charging, and conclude with spacecraft design guidelines that can be used to mit- igate internal charging threats. Extreme Events in Geospace. https://doi.org/10.1016/B978-0-12-812700-1.00016-9 419 # 2018 Elsevier Inc. All rights reserved. 420 CHAPTER 16 DEEP DIELECTRIC CHARGING AND SPACECRAFT ANOMALIES 2 WHAT IS DEEP DIELECTRIC CHARGING? Deep dielectric charging (also called internal, or bulk charging) occurs when high-energy electrons and ions (MeV and higher) penetrate satellite shielding materials and deposit charge on internal spacecraft components. The terms “deep dielectric” or “bulk” charging refer to charge densities that accumulate within insulating (or dielectric) materials when exposed to penetration radiation. The more generic term “internal charging” includes charge densities that accumulate on the surfaces of conducting materials within the shielding afforded by the outer structure of a spacecraft. Both processes result in electric fields within spacecraft structures and materials and represent a threat to arcing which can damage spacecraft components. The physics of internal charging for an insulator exposed to radiation environments is described by a set of two equations (Sessler, 1987; Sessler et al., 2004) ρ rE ¼r2Φ ¼ (1) κε0 ∂ρ ¼rÁðÞJ + J (2) ∂t R C where the Eq. (1) is Poisson’s equation that relates the electric field, E, and electric potential, Φ, to the charge density, ρ, within the material. The continuity equation in Eq. (2) relates the charge density accumulating in the material to the incident radiation (electron) current density, JR, and the conduction current density, JC. The parameters κ and ε0 are the dielectric constant for material exposed to the charging environment and permittivity of free space, respectively. Eqs. (1), (2) together describe the magnitude and direction of a time and spatially dependent electric field within a material due to the accumulation of charge from an external radiation source and loss of charge from the material through conduction. Typically, only electron currents are considered for internal charging because ions at similar energies as the electrons don’t penetrate deeply into materials. Ions with sufficient energy to penetrate deep into the materials typically exhibit very low flux compared to the electrons with the same penetration depth. Thus, ions are not a significant contributor for internal charging currents in most internal charging environments. The role of ions will be considered in Section 2.1. Electron cur- rents are given by hi γ α J ¼ σE ¼ σ + k d E (3) C dark p dt where the bulk conductivity of the insulator σ is divided into the σdark conductivity (in the absence of exposure to photons or charged particles) and a radiation induced conductivity that depends on the dose rate (dγ/dt) generated by interaction of the radiation field with the dielectric material. The parameter kp is the coefficient of radiation-induced conductivity and the exponent 0.5<α<1 depends on the energy distribution of electron trapping states in the insulating material. Evaluation of internal charging re- quires solving both a radiation transport problem to compute the charge deposition and radiation dose rates within the material and the electrostatic problem to obtain the electrostatic fields and potentials due to the accumulating charge density. The propagation of the high-energy particles is governed by the Bethe-Bloch equation (Garrett and Whittlesey, 2012; Ziegler, 1999): 2 WHAT IS DEEP DIELECTRIC CHARGING? 421 dE 4πZ2n 2mv2 SEðÞ¼À ¼ e α2 log À β2 À logI (4) dx mv2 1 À β2 where S(E) is the stopping power, which is the energy loss per unit distance of particle penetration into matter. dE SEðÞ¼À (5) dx The range R, which means the depth, of penetration by a charged particle of initial energy Ep is given by Z Ep ¼ 1 R ðÞdE (6) 0 SE Using Eqs.(4)–(6), one can plot the range, or penetration depth, for a given projectile and a given material. Fig. 1 shows that the penetration depth of electrons is about two orders of magnitude as ions of about the same energy. For a typical spacecraft wall with a thickness of 100 mils (2.54 mm) of aluminum, electrons need energies in the range 0.5–5 MeV to penetrate, and protons need energies of 10–100 MeV. For a more in depth discussion, see (Ziegler, 1999). One of the key characteristics of deep dielectric charging is the time it takes to build up electric fields within an insulating material or on a conductor compared to the time it takes for charge to leak mil metric 100,000 Al <~1 m 10,000 (g/cm2) e-mil <~0.1 m p-mil 1000 <~10 <~10 mm 100 <~1 <~1 mm (mil) 10 <~0.1 <~0.1 mm 1 Depth in aluminium, (electrons and protons) <~10 um 0.1 <~10 kÅ 0.01 0.01 0.1 1 10 100 1000 Energy (MeV) FIG. 1 Electron (solid) and proton (dashed) penetration depth in aluminum (in mils on the left y-axis and in meters on the right y-axis) for a range of energies (0.01–1000 MeV). For 100 mils (2.54 mm) of aluminum, protons need to have energies above about 20 MeV and electrons need to have energies above 1 MeV to pass through.Reprinted with permission from Garrett, H., Whittlesey, A., 2012. Guide to mitigating spacecraft charging effects. In: JPL Space Science and Technology Series, Inc. John Wiley & Sons, Pasadena, CA. 422 CHAPTER 16 DEEP DIELECTRIC CHARGING AND SPACECRAFT ANOMALIES off the material. An estimate of this time constant can be obtained from a simple one dimensional, planar model for internal charging of an insulator where the electric field E at a depth X in a dielectric is given by Garrett and Whittlesey (2000). εðÞdE=dt + σE ¼ JR (7) The parameters E, JR, and ε, and σ are the electric field, radiation current density, absolute permittivity of the material, and σ the volume conductivity of the insulating material described in Eq. (3). A solution to this equation assuming that JR and σ are independent of time is E ¼ E0 expðÞÀσt=ε + ðÞJR=σ ðÞ1 À expðÞÀσt=ε (8) where E0 is the electric field at t¼0. The absolute permittivity of the material is related to the permit- tivity in a vacuum ε0 by the dielectric constant κ ¼ε/ε0. Using this definition in Eq. (8), the time con- stant for charging of the material is estimated by τ ¼ε/σ or τ ¼κε0/σ. The charges deposited inside the dielectrics can stay inside for hours, days, or weeks (Rodgers and Sorenson, 2012; Bodeau, 2010). If the dielectric’s resistivity is high, the rate of charge build up can overcome the leakage rate of the material and large charge