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Shu T. Lai is currently a visiting scientist at the Space Propulsion Laboratory, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology and a senior editor for "IEEE Transactions on Plasma Science". He is a fellow of the Institute of Electrical and Electronics Engineers. He was formerly a senior physicist at the Space Weather Center of Excellence, Space Vehicles Directorate, Air Force Research Laboratory (AFRL), Hanscom Air Force Base, Massachusetts.

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"Fundamentals of Spacecraft Charging is by a well-known leader in the field and provides a comprehensive, unique, and useful addition to the subject. Several sections, particularly the review and discussion of dielectric breakdown, are of particular interest. This book will be valuable as an introductory text or as a reference for those seeking details on specific aspects of charging."--Henry B. Garrett, coauthor ofSpacecraft-Environment Interactions

"Spacecraft charging has raised many interesting issues for engineers and scientists since the first observations in space. Accessible to a wide range of readers, Shu Lai's book offers a comprehensive survey of key materials on this multifaceted topic."--Alain Hilgers, European Space Research and Technology Centre

"Lai's compendium of surface and dielectric spacecraft charging ranges from the basic causes and controlling factors to the effects of secondary electron emission, and the formation of space charge potential wells and barriers. He considers the effects of charged particle beam emission from spacecraft, and the use of plasma sources as 'contactors' to limit charging. Finally, he shows the consequences, from discharges owing to differential charging, to resulting operational anomalies, and offers a suite of effective mitigation techniques."--Thomas E. Moore, NASA, Goddard Space Flight Center

"This book is by far and away the most comprehensive reference on the physics of spacecraft charging, which can be destructive for a spacecraft. The text is clear and straightforward and explores all the myriad facets of this phenomenon. I will use it in my teaching."--Daniel E. Hastings, Massachusetts Institute of Technology

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FUNDAMENTALS OF SPACECRAFT CHARGING

PRINCETON UNIVERSITY PRESS

Contents

Preface.......................................................................xiAcknowledgments...............................................................243Index.........................................................................245

Chapter One

We begin by asking four fundamental questions: What is spacecraft charging? What are the effects of spacecraft charging? How does spacecraft charging occur? Where and when does spacecraft charging occur?

1.1 What is Spacecraft Charging?

When a spacecraft has a net charge, positive or negative, the net charge generates an electric field according to Gauss's law. Space plasmas are assumed neutral. Although the plasma densities may fluctuate, their time scales (inverse of plasma frequencies) are much faster than spacecraft potential variations. Spacecraft charging takes a longer time than the ambient plasma fluctuations because it takes time to fill up capacitances. In the spacecraft charging community, the potential, f_p, of the ambient space plasma is traditionally defined as zero:

f_p = 0 (1.1)

Since potential is not absolute but relative, it is not surprising that in some other plasma sciences, the plasma potential is sometimes defined relative to that of a surface. In the field of spacecraft charging, the spacecraft potential is relative to the space plasma potential, which is defined as zero. The spacecraft potential is floating relative to the ambient plasma potential (figure 1.1). When a spacecraft potential, f_s, is nonzero relative to that of the ambient plasma, the spacecraft is charged:

f_p [not equal to] 0 (1.2)

The basic terminology of spacecraft charging is introduced here:

? For a conducting spacecraft, the charges are on the surfaces. This charging situation is called surface charging.

? A uniformly charged spacecraft has only one potential, f_s. This situation is called uniform charging or absolute charging.

? For a spacecraft composed of electrically separated surfaces, the potentials may be different on different surfaces. The potentials depend on the surface properties and on the environment, which may be nonisotropic. In this case, we have differential charging.

? If a spacecraft is covered with connected conducting surfaces (i.e., spacecraft ground or frame) and some unconnected or nonconducting surfaces, the charging of the frame is called frame charging.

? When the ambient electrons and ions are very energetic (MeV or higher), they can penetrate deep into dielectrics, which are nonconductors. This situation is called deep dielectric charging, or bulk charging.

1.2 What are Some Effects of Spacecraft Charging?

Spacecraft charging manifests itself in two types of effects: (1) damage to onboard electronic instruments and (2) interference with scientific measurements. The first type is very rare but may be harmful. The second type is very common. These effects are discussed in the following sections,

1.2.1 Damage to Onboard Electronic Instruments

Spacecraft charging affects telemetry and electronics on spacecraft. Logical circuits and computer chips are becoming smaller and less power consuming but are more delicate. Delicate electronics are susceptible to charging, anomalies, damage, or catastrophes. Undesirable currents entering circuits by conduction, through pinholes, or via electromagnetic waves through inadequate shielding may cause disturbances. Such disturbances often cause anomalies in the telemetry of the data of the measurements.

If neighboring surfaces are at very different potentials, there is a tendency for a sudden discharge to occur. A discharge may be small, large, frequent, or rare. The size of a discharge depends on the amount of charge built up in the electrostatic capacitances, and on the amount of neutral materials, such as gas, which may be ionized when a discharge is initiated. An avalanche ionization can lead to a large current. A small discharge may be simply a spark, generating electromagnetic waves that may disturb telemetry signals. A large discharge may cause damage. Damage to electronics may, in turn, affect operations, navigation, or even survivability of a spacecraft.

Two remarks: (1) A discharge on a spacecraft is often called an electrostatic discharge (ESD), because magnetic fields are almost not involved. In this context, discharge refers a harmful discharge. (2) The word discharge sometimes means "reduce the charging level." For example, suppose that a spacecraft charges to -10 kV, and the person in control suggests discharging the spacecraft to a lower voltage. In this context, to discharge means to mitigate.

If the incoming electrons or ions are of high energies (MeV or higher), they may be able to penetrate, pass through, or deposit inside materials. These high-energy electrons may stay inside nonconductors—i.e., dielectrics—for a long time. After a prolonged period of highenergy electron bombardment, the electrons inside may build up a high electric field. If the field is high enough, it may be sufficient to cause a local dielectric breakdown. When a local breakdown occurs, ionization channels develop extremely rapidly inside the dielectric, allowing currents to flow, which in turn generate more ionization and heat. As a result, internal instruments may be damaged. Fortunately, the densities of high-energy (MeV or higher) electrons and ions in space are low. Internal damage events are rare. However, when they occur, they may, in extreme cases, cause the loss of spacecraft.

1.2.2 Interference with Scientific Measurements

Spacecraft charging may affect scientific measurements on spacecraft. For example, when scientific measurements of space plasma properties such as the plasma density, mean energy, plasma distribution function, and electric fields are needed onboard, the measurements may be affected. The effects on each of these measurements are explained here.

We first examine the basic mechanism of how a charged object disturbs the ambient plasma. A charged spacecraft repels the plasma charges of the same sign and attracts those of the opposite sign (figure 1.1). As a result, a plasma sheath is formed in which the density of the repelled species is lower than that of the attracted species. The plasma density inside the sheath is different from that outside. The plasma in a sheath is nonneutral. Sheath formation occurs not only in space but also for charged objects in laboratory plasma.

Since the mean energy of the charged particles is shifted by repulsion or attraction, the mean energy of the electrons and that of the ions inside the sheath are different from their respective values outside. The amount of shift depends on the magnitude of repulsion or attraction.

The electron and ion energies of a plasma in equilibrium are in Maxwellian distributions:

f(E) = n(m/2pk T)^2/3 exp (-E/kT) (1.3)

A graph of the logarithm of the distribution, f(E), versus E would be a straight line with a slope equal to -1/kT, if f(E) is Maxwellian (figure 1.2).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.4)

If the distribution f(E) is measured on the surface of a spacecraft charged to a potential, f_s, the distribution measured would be shifted from that of the ambient plasma by an amount of energy ef_s. If the distribution is not Maxwellian, the graph f(E) will not be a straight line. No matter what the distribution is, the energy shift will be ef_s. In the following, we will examine Maxwellian distribution only.

For the attracted species, the energy shift is ef_s, forming a gap from 0 to ef_s in the distribution (figure 1.2). Physically, a charged particle initially at rest is attracted and would gain an energy ef_s when it arrives at the spacecraft surface. This size of the gap, which can be clearly identified, gives a measure of the spacecraft potential, f_s. The historical discovery of kilovolt-level charging of a spacecraft (ATS-5) at geosynchronous altitudes at night was made by using a method related to the idea described in this paragraph.

For the repelled species, the shift is -ef_s. This forms no gap but results in the loss of the negative energy portion of the distribution (figure 1.2). Physically, the repelled ambient species of energy between 0 and ef_s are repelled by the charged spacecraft. They cannot reach the spacecraft surface and the instrument on the surface and therefore cannot be measured.

Electric fields are important in governing the flow of electrons and ions in space plasmas. Measurements of electric fields in space are commonly carried out by means of the double probe method. The addition of an artificial potential gradient by a charged spacecraft may affect the measurements. Typical electric fields measured in the ionosphere are of the order of mV/m, which is easily overwhelmed by strong electric fields near the spacecraft surfaces charged to, for example, hundreds of volts.

Spacecraft charging may also affect measurements of magnetic pitch angles of incoming charged particles since charged particles drift in the presence of both electric and magnetic fields. The trajectories of the charged particles are disturbed and therefore are different from those without spacecraft charging.

1.3 How Does Spacecraft Charging Occur?

The cause of surface charging is due to the difference between ambient electron and ion fluxes. Electrons are faster than (all kinds of) ions because of their mass difference. As a result, we have the following theorem:

Theorem: The ambient electron flux is much greater than that of the ambient ions.

To illustrate this point, let us consider hydrogen ions whose mass m_i is about 1837m_e, where m_e is the electron mass. The electron and ion number densities are equal. Equipartition of energy gives the equality:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.5)

where the ion energy kT_i equals the electron energy kT_e, where k is the Boltzmann constant. Equation (1.5) yields a ratio of the electron to ion velocities: v_e [approximately equal to]. 43v_i.

The equality, equation (1.5), is only approximately valid. If the ion energy kT_i fluctuates and deviates, equation (1.5) would change accordingly. As long as the energies, kT_i and kT_e, are of the same order of magnitude, the preceding equality remains valid as a good approximation, viz, the ambient electron flux is much greater than that of the ambient ions. If some of the ions are heavier than H⁺, the velocity difference would be greater.

Therefore, the electron flux, n_eev_e, is greater than the ion flux, n_eev_i. As a corollary of this property of relative velocities, we conclude that surface charging is usually negative, because the surface intercepts more electrons than ions.

It takes a finite time to charge a surface because its capacitance is finite. For typical surfaces at geosynchronous altitudes, it takes a few milliseconds to come to a charging equilibrium. At equilibrium, Kirchhoff's circuital law applies because the surface is a node in a circuit in space.

Kirchhoff's law states that at every node in equilibrium, the sum of all currents coming in equals the sum of all currents going out. Therefore, the surface potential, f, must be such that the sum of all currents must add up to zero. These currents, I₁, I₂, ..., I_k, account for incoming electrons, incoming ions, outgoing secondary electrons, outgoing backscattered electrons, and other currents if present. The current balance equation, equation (1.6), determines the surface potential f at equilibrium:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.6)

1.4 Capacitance Charging

With a steady ambient current, I, the time, t, for charging a surface is given by

tI = Cf (1.7)

where ITLITL is the capacitance, and f is the surface potential. For a simple example, the surface capacitance ITLITL of a spherical object of radius R = 1 m is given by ITLITL = e_o4pR [approximately equal to] 10^-10 farad/m. Let us take the ambient current I = JpR², where J is the ambient flux. The object in a space environment of flux density J = 0.5 nA/cm² would charge from 0 to 1 kV in t [approximately equal to] 2 ms, which is a short time for many applications. The charging time, x, increases directly with the charging level, f, and inversely with the radius, R, and the current density, J:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.8)

Capacitance charging is analogous to the filling of a tub with water; the water flow rate and the hose size (the cross section of flow) control the time of filling (figure 1.3). During filling, the water level is rising, and therefore the incoming current exceeds the outgoing current. This means that Kirchhoff's law, viz, steady state current balance, is not applicable during capacitance charging; one needs to include a time-dependent term. Once the tub is filled, the water level remains constant, and therefore the incoming and outgoing currents balance each other. The current balance equation, equation (1.6), is not applicable for our simple example during the first 2 ms but is a valid approximation thereafter. (Note that it takes infinite time to charge a capacitance asymptotically, but, for our purpose, we do not need exact values because the space plasma is not measured with high accuracy and varies very much in space and time.)

Note that coupled capacitances take a longer time to charge and thin dielectric layers have larger capacitances than surfaces. For simplicity, we will not consider these complications.

1.5 Other Currents

In sunlight, the photoemission current emitted from a spacecraft surface has to be taken into account. In quiet periods (without severe magnetic storms), the photoemission current often exceeds the ambient currents, thus charging a typical spacecraft surface positively. Since photoelectrons generated by sunlight in the geosynchronous environment have typically a few eV in energy, they cannot leave if the surface potential exceeds a few volts positive. Thus, sunlight charging is typically at only a few volts positive.

Secondary and backscattered electrons are of central importance in spacecraft charging. They will be discussed in detail in chapter 4.

For spacecraft charging induced by charged beam emission, the beam current must be included in the current balance equation. Depending on the properties of the beam and the charging condition of the spacecraft, a fraction f of the beam may leave the spacecraft, while the rest of the beam current returns to the spacecraft. The net current leaving the spacecraft may be very different from that leaving the exit point of the beam,—i.e., the fraction f may be <<1. If the net beam current leaving the spacecraft exceeds the ambient current arriving at the spacecraft, the beam controls the spacecraft potential.

1.6 Where Does Spacecraft Charging Occur?

Natural surface charging depends on the location of the spacecraft, the material of the surface, the local time, and the space weather. It is customary to delineate four types of locations: geosynchronous altitudes, low Earth orbit altitudes, the auroral latitudes, and the radiation belts.

1.6.1 Geosynchronous Altitudes

The most important region of surface charging is at or near geosynchronous altitudes. This region is important for two reasons: (1) Even though the plasma density is often low, the energy is sometimes high. (2) There are many communication satellites in this region.

The geosynchronous region is sometimes inside the plasmasphere (figure 1.4). During very quiet days, the entire region can be inside the plasmasphere, while during extremely disturbed days, the entire region can be outside it. Most often, the dusk side is inside while the rest of the region is outside. Although the plasmasphere corotates to some extent with the Earth, the protruding part on the dusk side often persists. The shape of the plasmasphere is not corotating. The plasmasphere usually has relatively high plasma density (> 1 cm^-3) and low plasma energy (< 100 eV). Within the plasmasphere, charging of spacecraft surfaces is at zero or low level (usually a few eV negative without sunlight) and is not of concern. In sunlight, the level is at most a few eV positive, which is also not of concern. Occasionally, the spacecraft is outside the plasmasphere and in a low-density (< 1 cm^-3), high-energy (keV) plasma region. There, high-level spacecraft surface charging may occur if there is a surge of high-energy electrons and the surface is in eclipse. The high-energy (many keVs and higher) electron cloud typically arrives sunward from the geomagnetic tail.

The initial disturbance usually comes from the Sun in the form of solar wind, high-energy electron and ion clouds, and also x rays. The electrons and ions, upon arrival, compress the dayside magnetosphere and then elongate the nightside magnetosphere to hundreds of Earth radii, forming a long magnetospheric tail (figure 1.5). The elongation is analogous to the stretching of a rubber band. An elongated rubber band eventually snaps back. After hours of stretching, magnetic reconnection occurs somewhere in the geomagnetic tail followed by a snap-back. As a result, an energized electron and ion cloud travels toward the Earth from the tail. This describes the process of a geomagnetic substorm, or simply substorm. It can occur more than once in a night—that is, a storm may consist of a series of substorms.

The energetic electrons and ions enter the Earth's geosynchronous altitudes at about midnight. There, the energetic electrons travel eastward due to the Earth's magnetic field curvature, while the energetic ions travel westward (appendix 1). Since the high-energy electrons are often the cause of spacecraft charging, spacecraft charging at or near the geosynchronous altitude region occurs most probably near midnight and the morning hours. Typically, the charging levels in this region reach hundreds of volts or even several kV, if the spacecraft surface is not in sunlight.

(Continues...)

Excerpted from FUNDAMENTALS OF SPACECRAFT CHARGINGby SHU T. LAI Copyright © 2012 by Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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