The sputtering of an oxygen thermosphere by energetic O

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. E1, PAGES , JANUARY 25, 2000 The sputtering of an oxygen thermosphere by energetic O R. E. Johnson, 1 D. Schnellenberger, and M. C. Wong 2 Department of Engineering Physics, University of Virginia, Charlottesville Abstract. Using two Monte Carlo models, we have calculated the ejection of O atoms from an atomic oxygen thermosphere which is bombarded by energetic O. In these calculations, incident oxygen ions strike atmospheric O, heating the atmosphere and setting O atoms on escape trajectories. For those ion fluxes most relevant to atmospheric sputtering at Mars, the full Monte Carlo model (DSMC model) is found to give the same sputtering yield as the Monte Carlo model in which the atmospheric structure is ignored and only the energetic atoms are tracked. In both models the sputtering yield is reduced by the electronic energy loss by the ions. The yield depends weakly on the details of the interaction potential if the relative amounts of forwardscattering to backscattering are realistic. The ejected atom energy spectra for the mean incident angle 55 are shown to be harder than the standard collision cascade distribution, close to the so-called incomplete cascade distribution. Yields for grazing incidence and for a thin atmosphere such as Europa s are given, and the analytic models used earlier are tested. Because the isotope ratios at Mars are likely to have been determined by atmospheric sputtering, Ar and Ne are included as constituents to verify the analytic models for the sputtering of trace species. The yields calculated here for an atomic O thermosphere can be used to estimate the sputtering of an atmosphere having molecules at the exobase. For Mars, ignoring feedback processes and using the ion fluxes listed by Johnson and Luhmann [1998], the loss is 0.45 bar, of which 0.15 bar is CO 2 with the largest uncertainty for atmospheric loss being the incident ion flux. 1. Introduction 1 Also at Goddard Institute for Space Studies, New York. 2 Also at AER Corp., Cambridge, Massachusetts. Copyright 2000 by the American Geophysical Union. Paper number 1999JE /00/1999JE001058$09.00 The heating and loss of atmosphere caused by plasma-ion bombardment is a problem of increasing interest in the physics of the atmospheres of planets and planetary satellites. The plasmas of interest at Mars and Venus are the local pickup ions, typically O [Luhmann and Koyzra, 1999]. When Titan is outside Saturn s magnetosphere, the solar plasma may have access to its atmosphere [Lammer and Bauer, 1993]. In addition, the trapped plasmas in planetary magnetospheres bombard Titan [Lammer et al., 1998], Tritan [Lammer, 1995], Io [Pospieszalska and Johnson, 1996], and Europa [Ip, 1998; Saur et al., 1998]. Even at the Earth, ring-current ion bombardment can affect the thermosphere [Bisikalo et al., 1995; Ishimoto et al., 1992; Koyzra et al., 1982; Torr et al., 1982], and enhanced solar activity can drive off atmosphere. Whereas sputtering yields have been suggested as being important for a number of these bodies, at Mars the isotope data [Pepin, 1994; Jakosky and Jones, 1997; Brain and Jakosky, 1998] indicate that a process like atmospheric sputtering has occurred and has removed significant amounts of atmosphere. In this paper we examine the sputtering process further. The plasma ions incident on the thermospheres of these bodies typically have energies of the order of hundreds of ev to tens of kev. Such particles lose their energy in a column of the order of a few times to atoms cm 2. This is roughly the same range of penetration depths for the absorbance of the short-wavelength photons that heat the Earth s thermosphere [e.g., Chamberlain and Hunten, 1987; Marov et al., 1997]. Therefore, even a relatively small energy flux that is deposited close to the nominal exobase can cause heating [Bisikalo et al., 1995; Ishimoto et al., 1992; Pospieszalska and Johnson, 1992] and drive flow [e.g., Bougher et al., 1990; Wong and Johnson, 1996; Lammer et al., 1998]. The high temperatures produced can lead to Jeans escape for the lightest components, which are, typically, H atoms [Lammer et al., 1998]. In addition, the momentum transfer to the atoms in the thermosphere by knock-on collisions can lead to enhanced loss of the heavier atoms and molecules, a process that has become known as atmospheric sputtering [Johnson, 1994]. For realistic atmospheres we have divided the sputtering into two parts: those incident particles which penetrate the nominal exobase and those which only pass through the corona. For the penetrating particles, which are studied here, a cascade of collisions is initiated in the atmosphere by the incident particle. For the other contribution, direct ejection can occur in single collisions of the incident particle with a coronal particle. The relative importance depends on the extent of the corona, the escape energy, and the escape depth of a struck atom [Johnson, 1990, 1994]. The composition of the thermosphere near the exobase for many objects is primarily atomic, often a mixture of O, N, or H atoms. When the composition is molecular, an energetic plasma ion transfers energy in close collisions with an individual atom in the molecule. These collisions produce dissociation and energetic fragments [Sieveka and Johnson, 1984]. Therefore, in both atomic and molecular thermospheres, energetic secondary atoms are set in motion. These atoms make further collisions with the constituents of the thermosphere. As the energy of the secondaries decreases, the primary energy trans- 1659

2 1660 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE fer events become direct momentum transfer to the whole molecule in a molecular thermosphere [Johnson and Liu, 1998]. The results presented here for an atomic atmosphere can be used to give a rough upper bound to the atmospheric sputtering rate for atmospheres having molecules at the exobase: for example, SO 2 at Io, O 2 at Europa, N 2 at Triton and Titan, and CO 2 at Mars in the present epoch. That is, for an atmosphere having molecules at the exobase, the exobase altitude for an escaping atom is roughly the same atomic column density as if the atmosphere were fully dissociated; for escaping molecules the exobase is higher and the escape energies are larger. On the other hand, the results obtained are directly applicable to the sputtering of the Martian atmosphere in earlier epochs, when the composition at the exobase was predominantly O. Feedback processes driven by plasma-ion impact act to enhance the O concentration. Because of these processes, the sputter contribution to the corona may be detectable at solar maximum [Johnson and Luhmann, 1998]. In this paper, Monte Carlo calculations of the atmosphere near the exobase are carried out for the sputtering of an oxygen thermosphere by incident O in the energy range from 100 ev to 10 kev. We find that the sputtering efficiencies for O calculated by Luhmann et al. [1992] and Jakosky et al. [1994] in the earlier epochs are about 30% too large. The sputtering rates found by Kass and Yung [1995, 1996] for O incident on aco 2 O thermosphere are an order of magnitude overestimated. Further, the total carbon loss calculated by Kass and Yung [1996], corrected according to the results of Johnson and Liu [1996], is much larger than the upper bounds determined here owing to both the estimate of the yield and the use of a larger ion flux. The efficiency of removal of trace species, such as Ar and Ne, in such a thermosphere is also calculated since it is of interest for determining isotope ratios for Mars. 2. Calculations Two studies are reported in this paper. First, the atmosphere and the incident ions are described by a full Monte Carlo calculation [e.g., Pospieszalska and Johnson, 1992, 1996; Combi 1996]. Depending on the procedure used, this is often referred to as a direct simulation Monte Carlo calculation (DSMC) [Bird, 1994]. In this procedure the heating of the thermosphere near the exobase, the expansion of the corona, and the loss of atmosphere are treated self-consistently for a given plasma flux. In addition, a simpler Monte Carlo procedure was used, the type often employed in sputtering solids [Ziegler et al., 1985] and atmospheres [e.g., Haff et al., 1982]. In such calculations, only those energetic particles set in motion in the thermosphere are tracked until their energy decreases below the escape energy. These particles are presumed to move in a background of atoms at the ambient temperature and density. The second procedure is an enormous simplification, in that fewer particles are followed and the calculation is independent of both the ion flux and the thermospheric structure. The results can therefore be applied to a large variety of situations, but only sputtering efficiencies are calculated. Thermospheric heating and structure must be calculated separately [e.g., Johnson, 1989; Lammer et al., 1998]. We refer to these as the DSMC and the MC calculations below. We use the more complete DSMC model to test the validity of the MC calculation. Finally, because the analytic models of the sputtering efficiency are simple and useful, they are also tested here. Such a comparison was carried out earlier for an SO 2 atmosphere on Io [Pospieszalska and Johnson, 1996] using an oversimplified interaction of the ions with SO 2 and of energetic SO 2 with thermal SO 2 molecules. In that calculation no dissociation was allowed. Here a single component atomic oxygen thermosphere is bombarded by O, and the atomic ejection efficiencies are given as sputtering yields. The sputtering yield is defined as the average number of atoms ejected per ion incident. Because of the recent interest in loss of atmosphere from Mars, in both sets of calculations the escape energy U is assumed to be 2 ev, which is roughly the energy required by an O atom set in motion at the exobase of Mars. MC calculations have been carried out for the atmospheric sputtering of Mars: Haff et al. [1982] studied incident solar-wind protons; Luhmann and Koyzra [1991], Kass and Yung [1995, 1996], and Kass [1999] studied O pickup ions incident on an atmosphere having both atoms and molecules at the exobase. Cross sections used by in the latter calculations have been criticized [Johnson, 1992; Johnson and Liu, 1996]. Finally, analytic models for the sputtering have been used by Luhmann et al. [1992] and Jakosky et al. [1994]. The results presented here for an atomic exobase employ a realistic interaction cross section and are the first DSMC calculations relevant to Mars Model In this paper an oxygen thermosphere is bombarded by oxygen ions. Because the ions are efficiently neutralized by charge exchange well above the exobase [Luhmann and Koyzra, 1991], the incident particles are primarily neutral atoms. Although we will refer to the incident flux as ions, the universal potentials, discussed below, are roughly normalized to data for ion transmission through gases. In such a case the flux is a mix of ions and neutrals that depends on the incident ion energy. For the O O collision there are 16 separate ground state potential curves which describe the possible interactions between colliding ground state O( 3 P) atoms. These range from interactions that are attractive at long range to those that are repulsive at all separations. In addition, at the energies of interest here, excitations can occur which would expand the required basis set. However, for collisions involving significant energy transfer, the repulsive part of these potentials dominates, and the average deflection of colliding atoms is often described by scaling of the scattering data. A universal interaction potential, created by scaling cross section data [Ziegler et al., 1985], is used to describe the interacting O atoms: V R Z AZ B e 2 R R a U x exp ( 3.2x) exp ( x) exp ( x) exp ( x) a U a 0 / Z A 0.23 Z B (1) Here R is the distance between O atoms. We refer to this as the ZBL potential. For the principal problem of interest, Z A Z B 8 with masses M A M B 16 u. In (1), a 0 is the Bohr radius (a nm), and e is the electric charge (e ev a 0 ). In the DSMC calculations this potential is used for both the energetic O colliding with the atmospheric O and for collisions between O atoms in the thermosphere. This calculation gives baseline yields using a single potential. The clas-

3 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE 1661 these calculations we principally use the simple Firsov [1959] model, which applies at velocities much less than the Bohr velocity ( cm s 1 ): E e ev Z A Z B 5/ b Z A Z B 1/3 5 cm/s. (3) E e is the electronic energy loss for a collision with impact parameter b and relative velocity v. This expression overestimates the loss slightly. It is subtracted prior to the collision and reduces the atmospheric sputtering yield at 1 kev by 25%. Using the Ziegler et al. [1985] data from their TRIM code gives a 10% reduction in yield. At higher energies the electronic energy loss is more important and better estimates of E e are required [e.g., Eckstein, 1991], but at the lowest energies calculated here ( 0.1 kev) it is a small effect. Figure 1. The momentum transfer cross section (diffusion cross section) d plotted versus the O atom energy for the ZBL potential. sical diffusion cross section d obtained with this potential is given in Figure 1. It is also called the momentum transfer cross section. At the lowest energies of interest ( 10 ev) the cross section is smaller than the cross section obtained using the set of interaction potentials for a ground state O atom colliding with an O( 1 D) atom ( cm 2 [Yee and Dalgarno, 1987]) and that for O N( cm 2 [Kharchenko et al., 1997]). Eventually, a complete set of states should be used to determine the sputtering yield for this important system. Averaging the 16 O O interaction potentials can, in fact, give a single potential that is predominantly repulsive. However, such a procedure does not give a correct deflection function [Johnson et al., 1972]. Therefore a potential that is scaled to scattering data or direct use of the cross-section data is preferable. For comparison, we have used another universal potential, the Lenz-Jensen (LJ) potential. For the LJ potential the screening function above is replaced by LJ x 1 y y y y 4 exp y y 9.67x 0.5 x R/a TF a TF a 0 / Z A 2/3 Z B 2/3 1/ 2. (2) Here a TF is the Thomas-Fermi screening constant, and d is about 10% larger than that in Figure 1. The results obtained using these potentials are compared to those of Ishimoto et al. [1992], who used a semiempirical interaction based on O O 2 scattering data. In both the MC and DSMC calculations the electronic energy loss by the incident ion is included. That is, fast ions can also lose energy by electronic excitations and ionization of the atoms and molecules in the atmosphere. Such energy is like that deposited by UV photons. This can also contribute to heating, but unlike the energy given in momentum transfer collisions, the conversion to heat, after allowing for transport, UV emissions, etc., is typically 20% [e.g., Fox, 1993]. Therefore the effect on the temperature can be small. However, this energy loss competes with the loss to momentum transfer. In 2.2. DSMC Calculations Direct simulation by a Monte Carlo method (DSMC) has been widely applied to studies of nonequilibrium gas dynamics. Its validity in approximating the Boltzmann equation has been established, and the details of the method are given by Bird [1994]. This is similar to the procedure used by Pospieszalska and Johnson [1992, 1996] for the sputtering of Io s atmosphere. In this method one simulates the dynamics of a rarefied gas by tracking the motion of, and the collisions among, a large number of sample particles. Each sample particle, in turn, represents a large number of real molecules in the computation. In our calculation the particles are O atoms that move and collide in a constant gravitational field equivalent to that in the Martian thermosphere ( g 3.7 m s 2 ). The computational domain of interest is divided into a number of cells over which gas properties such as temperature and velocity are assembled. At each time step the number of collisions to be performed within each cell is determined according to the local density n, the effective collision cross section max, and the size of the time step t. The probability of a collision in a cell having a given density is equally likely at any point in its path and is independent of the time of the previous collision. Therefore pairs of particles are chosen within the cell randomly, and their collision probability is [(n v r max ) t], where v r is relative velocity. If, in the time interval of interest, a collision between a particular pair occurs, a binary collision calculation is performed, and each particle acquires a new velocity. At the end of each time step, when all the collision calculations have been performed in each of the cells, particles are then allowed to move ballistically under gravity for the period of t without encountering further collisions. That is, the collisions are uncoupled from the motion of the particles in the duration of a time step. Along their trajectories, particles are free to move across the boundaries between cells. In the calculations described here the one-dimensional (1-D) vertical atmospheric column is divided into 200 computational cells. Owing to the stratification of density over altitude, the sizes of the cells are chosen to vary logarithmically such that each cell contains roughly the same number of particles ( particles are used in each cell in our calculations). A particle is considered to have escaped if it moves across the top boundary from below with an energy larger than the escape energy (U es mgr, where R is that planet radius and m the particle mass). Non-escaping particles are allowed to return ballistically through the top surface. The velocity of every O atom escaping is stored, and

4 1662 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE Figure 2. Fraction f es of escaping particles produced at a depth N, given as a column density of O for 1 kev O incident at 0 and 55 (solid line) and 80 (dashed line). This can be roughly fit with es exp( es N) with es cm 2. The insert shows the yields versus atmospheric thickness, given here as the total column N max for 55 (circles) and 0 (squares). Lines are fits to Y[1 exp ( N max /N o )] with N o O/cm 2 being equivalent to a collision cross section cm 2. then a new O is added from the lower surface in a random direction and with its energy determined by the temperature of the surface. This procedure conserves the number of particles. The top boundary in this calculation has a column density above it equal to a fraction of ( max ) 1. At the lower boundary, which is the surface for a thin atmosphere or the base of the thermosphere for a thick atmosphere, we used T 200 K, and for every atom crossing this boundary a new one is emitted. A total column of Ocm 2 was used to describe the thermosphere near the exobase with 18,000 representative particles. Increasing this column did not change the results. After a sufficient time has elapsed, in which the atmosphere comes into equilibrium under the ion flux, and after a large number of particles have escaped, the calculation is terminated, and the sputtering yield and related quantities are determined MC Calculations In the simple Monte Carlo (MC) procedure used here, only the incident O and the struck (energized) O are tracked. These energetic atoms are treated as moving in a background gas of atmospheric O atoms. The thermal O atoms have velocities sufficiently smaller than the energetic particles that they can be ignored. Since the probability of a collision depends on the path length integrated over the density, only the column density through which an energetic O passes is calculated. Since uniform and nonuniform densities are equivalent in such a method, this calculation resembles that for the sputtering of solids [e.g., Johnson, 1990]. In addition, gravity is ignored in tracking the struck particles until they escape. If a particle that is set in motion crosses the exobase with sufficient energy to escape, U es, then escape is assumed to occur. The calculational exobase 1/ max is a smaller column than true exobase ( d ) 1 [Johnson, 1994]. We have already shown that the concept of a single exobase is imprecise. For energetic particles (mean escape energy 50 ev) the escape depth [Pospieszalska and Johnson, 1996; Johnson, 1994; Haff et al., 1982], as seen in Figure 2, differs from the escape depth for thermal atoms. In spite of this, the word exobase is used for convenience. The procedure used is the following: an O atom of energy E O is incident on the atmosphere at a given angle, varied from 0 to 80. This particle eventually strikes a background ( thermal ) O and sets it in motion. Such an atom is referred to as a secondary. If the energy of the struck particle (a secondary) is larger than the escape energy U es, it is tracked. It can set additional particles in motion until its energy is less than U es or it reaches a depth, given as a column N max, from which the production of additional secondaries no longer leads to ejection. The remaining motion of the incident particle is then followed to the next collision. In this way a cascade of collisions is described as being due to a series of particles set in motion, each of which is tracked until either it escapes or it has an energy U es. After the incident particle itself attains an energy U es or its depth in the atmosphere is N max, a new incident particle is sent into the atmosphere, and the procedure is repeated. The number of ejected O and their velocities are recorded until sufficient statistics are accumulated and an average yield is calculated. Although only the average yield is usually needed, the distribution in the yield is broad. Three random numbers describe each collision: R 1, R 2, and R 3. The first is used to calculate the distance to the next collision, and the other two are used to obtain the collision parameters. Using a Poisson distribution of path lengths, the column of gas through which an energized particle passes before it collides with a thermal particle is N 1 max ln 1 R 1. (4)

5 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE 1663 The cross section max is written in terms of the impact parameter b, the perpendicular distance between the particles 2 prior to the collision. Here max b max, where b max is the largest impact parameter considered. This is chosen so that the energy transfer to the struck particle is of the order of, or less than, the escape energy. Choosing a b max that is too small leads to an overestimate of the yield. Noting that equivalent areas are equally likely to produce collisions and the azimuthal angle is random, then R 2 b2 2 R b 3 (5) max 2 Having determined the collision parameters, the center of mass scattering angle and the velocities of the struck and incident particles are calculated [e.g., Johnson, 1990] from the interaction potential. Typically, the dependence of the scattering angle on the impact parameter is tabulated at a number of energies and is then interpolated. Alternatively, a magic formula is used. If the energy transfer cross section is available, then R 2 is used to determine the energy transfer to the stopped particle and, again, R 3 is used for the azimuthal angle. The MC calculation described differs from Monte Carlo calculations for the sputtering of amorphous solids [Eckstein, 1991] primarily in the treatment of escape [Johnson, 1994]. We tested our program using the escape conditions for a solid against the standard package program TRIM [Ziegler et al., 1985], which is typically used in ion beam laboratories [Schnellenberger, 1997]. We also verified that the sputtering yield for a solid with the same atomic composition and with the surface binding energy equal to U es is about half the atmospheric sputtering yield as predicted [Haff et al., 1982; Johnson, 1990]. By cutting the impact parameter off at b max, or the minimum energy transfer at U es, the energy loss due to soft collisions is ignored. Therefore we increased b max until the yield was independent of b max. A more efficient procedure is the following: choose a reasonable b max or U es emphasizing the hard collisions and calculate in advance the average missing softcollision energy loss accumulated between hard collisions (b b max or U U es ). Between collisions, subtract the softcollision energy loss and the electronic energy loss in (3) from the atom s energy. For a particle on an escape path, estimate the fraction of the exosphere through which the O travels and the soft-collision plus electronic energy loss prior to determining if escape occurs. Treating b max incorrectly can result in significant errors. For the ZBL potential the yield increases with decreasing b max for b max 3 Å. For instance, for a 1 kev O at normal incidence the average yield is Y 0.74 O ion 1 for b max 3Å. This becomes Y 1.0 if b max 2 Å and Y 5.0 if b max 1 Å. This large increase is due to the enhanced importance of hard collisions [Schnellenberger, 1997]. These results include the Firsov electronic energy loss in (3). Not including the electronic energy loss, the yield for b max 3 Å increases from 0.74 to 1.0. Using the electronic energy loss model in TRIM [Ziegler et al., 1985] gives 0.89 for the same b max. Using the Lenz-Jensen potential gives Y 1.0. Therefore uncertainties of 20% are expected due to uncertainties in the interactions. Because cascades initiated at depth contribute to the yield, we also calculated the yield versus column of atmosphere, N max. The yields are presented in the insert in Figure 2. It is seen that for a thin atmosphere such as that at Europa, the collision cascade sputtering described here is reduced. The results in Figure 2 are fit with Y(N max )/Y( ) 1 exp ( N max /N o ), N o cm 2. This is roughly the size of a collisionally thick atmosphere [Johnson, 1990]. Therefore the collision cascade contribution to the yield for Europa s atmosphere with a column density N o, as inferred by Hall et al. [1995], is about 70% of the full yield. Saur et al. [1998] calculate an atmosphere of 0.3N o, implying 30% of the cascade yield. 3. Results 3.1. DSMC Calculations The results of the DSMC depend on the incident ion flux, the total column of atmosphere represented, the temperature assigned at the base of that column, and the escape energy U es [e.g., Pospieszalska and Johnson, 1992, 1996]. If the flux of ions is very low, then large amounts of computer time are absorbed in tracking the atmospheric constituents between each new incident ion. If there is little or no escape (i.e., low ion flux or large U es ), then, as long as the spatial energy deposition profile for the incident particles [Ziegler et al., 1985] is described correctly, the heat can simply be deposited in the atmosphere [Pospieszalska and Johnson, 1992]. In such cases it is not necessary to use a DSMC model. As the ion flux increases, the heating and the escape rate also increase. Eventually, the atmospheric sputtering yield and the thermospheric temperature depend on the ion flux [Pospieszalzka and Johnson, 1996]. This general behavior is also seen here for O on an O thermosphere. For Mars the pickup ion flux estimated by Zhang et al. [1993] for mean solar conditions in the present epoch is low ( ions cm 2 s 1 ). Johnson and Luhmann [1998] indicate that the flux at solar maximum, including feedback, is significantly larger. In the DSMC calculations we used a flux of 10 9 ions cm 2 s 1 of 1 kev O, representative of the 3 EUV (2 Gyr) epoch of Zhang et al. [1993]. For this flux and a column of Ocm 2 the temperature and density versus altitude are given in Figure 3 for ions incident at 0 and 55 to the normal. (55 is a suggested mean incident angle for the pickup ion bombardment [Koyzra et al., 1982]). The temperature at the lower surface was set to 200 K, but the results are relatively insensitive to that temperature. The dependence of temperature on altitude is like that seen in works by Pospieszalska and Johnson [1992, 1996]. In Figure 4 the energy distribution of the O at the exobase is seen to fit a Maxwellian distribution but has an energetic tail associated with the cascade of energetic atoms set in motion [Johnson, 1994; Bisikalo et al., 1995]. The temperatures at the exobase are 845 K and 1050 K for 0 and 55, respectively, ignoring any horizontal flow [Bougher et al., 1990; Wong and Johnson, 1996]. Therefore ion heating can be important and will affect the structure of the corona [Johnson and Luhmann, 1998]. The atmospheric sputtering yields for these cases are 0.89 and 3.2, respectively, using the TRIM electronic loss. We also show the depth of origin of the escaping atoms in Figure 2 given as a column of atmosphere. For 0 and 80 the curves are roughly fit by es exp [ es N] with es 0.77 and cm 2, respectively. It is seen that escaping atoms can be set in motion relatively deep in the atmosphere (many mean free paths) and 1 es is 1.3/ d [Johnson, 1994]. Although Jeans escape due to ion heating of the thermosphere does occur at these temperatures, the loss of atmosphere is dominated by the nonthermal escape process studied here. Varying the flux, we find that the yield is independent of ion flux. It is also seen that the results agree with the MC

6 1664 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE Figure 5. The yield at normal incidence versus gravitational binding energy U es : the line is (U es ) (1 x), x 0.1. Figure 3. Calculated thermospheric temperature (top scale) and density (bottom scale) versus altitude above the reference altitude ( Ocm 2, where T 200 K) calculated using the direct simulation Monte Carlo (DSMC) model and a flux of 10 9 ions cm 2 s 1 of 1 kev ions at 0 (solid lines) and 55 (dashed lines). calculation for the same incident ion energy to within 5%. Therefore, for fluxes of 10 9 ions cm 2 s 1 and lower, the atmospheric structure is not important and Jeans escape can be ignored in determining the atmospheric sputtering yield. Hence the MC model can be used for most applications. Pospieszalska and Johnson [1996] explored higher energy deposition rates for which Jeans escape occurred. At those Martian fluxes suggested to be relevant to the 6 EUV epoch (1 Gyr) [Zhang et al., 1993], the ion heating will clearly give a Jeans contribution, enhancing the effective sputtering yield, as we confirmed in these calculations. However, the flux in this period may be overestimated since feedback processes will act to reduce the pickup ion flux onto the exobase [Johnson and Luhmann, 1998], and the magnetic field of Mars may have Figure 4. The energy distribution f x, normalized to unity, for the thermospheric O atoms near the nominal exobase (solid line) calculated in the DSMC model for 1 kev with a flux of 10 9 ions cm 2 s 1 incident at 0. The dashed line is the Maxwellian at T 845 K. been sufficient [Hutchins et al., 1997] to fully or partially stand off the ion flux MC Calculations and the Analytic Model The sputtering of refractory surfaces has a long history. Although no analytic model accurately describes the sputtering yields without using experimental parameters, the analytic expressions developed describe the principal aspects at intermediate ion energies. The standard expressions used for the solids, in which the barrier to escape is the surface binding energy, have been modified to describe atmospheric escape in which the barrier to escape is the gravitational energy. Using the notation of Johnson [1990, 1994], the atmospheric sputtering yield Y is written as Y i cs n E O c. (6) 2U es d E es cos p 1 Here E O is the incident energy of the O ion (atom), and U es is the gravitational escape energy. The quantity d is the diffusion cross section in Figure 1 evaluated at the escape energy E es ; is a transport coefficient for the energy deposited at the exobase, is a transport coefficient describing the energy spectra of the cascade of collisions, and i is the angle of incidence. Finally, the quantity S n is the energy loss cross section for elastic collisions evaluated at the incident energy E O. This is also related to the diffusion cross section in Figure 1: S n (E O ) [ E O /2] d (E O ), where is a mass factor, equal to 1 here. Therefore the interaction potential affects the yield primarily through the ratio d (E O )/ d (E es ), which is sensitive to the amount of forwardscattering in the potential. Here we test this model using the MC model with the ZBL interaction and the electronic energy loss in (3). In Figure 5 the yield is plotted versus U es for 1 kev O incident at 0 on an O thermosphere. This roughly follows U (1 x) ex with x 0.1, close to the simple model dependence in (6). Such a dependence is a result of the energy distribution of the cascade of recoils [Watson et al., 1980; Johnson, 1994] discussed below and allows the results here to be applied to the sputtering of other atmospheres. For sputtering of the Earth s O thermosphere with escape energy 10.4 ev at 55 the yield of 2.8 calculated here for U es 2 ev becomes Using

7 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE 1665 Figure 6. Atmospheric sputtering yield versus incident angle i (zenith angle) divided by the yield at normal incidence ( i 0 ), shown for three energies: 0.1 (squares), 1.0 (circles), and 10.0 kev (diamonds). The line is [cos i ] p ; p 1.6 is roughly valid at high energies. The insert shows the probability of the incident O scattering out of the atmosphere versus angle of incidence. different interaction potentials and a two-stream method, Koyzra et al. [1982] obtain 0.15, whereas Ishimoto et al. [1992] obtain 0.7 using a semiempirical cross section. Both ignored electronic energy loss. The inclusion of the electronic loss described in (3) would reduce the Ishimoto et al. yield to a value roughly consistent with our yield. This agreement suggests that the yields are only weakly dependent on the potential. The principal issue is the forwardscattering versus backscattering ratio, which is too large in the Koyzra et al. [1982] result, accounting for a factor of 4 in the yield. Also, Kass and Yung [1995, 1996] used an interaction potential that gives far too much backscattering, resulting in a yield at 55 of 9, a factor of 3 larger [Kass, 1999]. It is also useful to note that the standard TRIM package program for 1 kev O on solid O with sublimation energy of 2 ev, multiplied by 2 [Johnson, 1992, 1994], gives Y 0.7 and Y 3.9 for 0 and 55. These are reasonably close to our values using the TRIM electronic energy loss 0.89 and 3.2, so this code can provide a reasonable estimate for the sputtering of an atomic thermosphere. At high ion energies the model predicts that the exponent p in (6) is about 1.6. This dependence applies when the incident particle is not deflected significantly as it penetrates the gas. The dependence of the MC yield on incident angle is shown in Figure 6 for three energies (0.1, 1.0, and 10 kev). It is seen that such an exponent cannot represent the low-energy calculations. As the ion energy increases, the dependence approaches p 1.6 below 70. At large angles of incidence ( 70 ) the yield levels off or even decreases as the incident particle and the energetic secondaries are scattered out of the atmosphere prior to initiating the full collision cascades. The probability of backscattering on the incident angle is shown at three energies in the insert of Figure 6. At 55 incidence, 10% of the incident particles are scattered out of the atmosphere at all energies with each carrying, on the average, 20% of its initial energy. Grazing collisions appear to dominate the loss processes at Io. In Figure 7 the yield is fit to Y cs n (E O ) and Y c [S n (E O )/ d (E es )] from Eq. 6. These are compared to the calculated sputtering yield versus incident O energy. It is seen that the yields obtained using the ZBL potential and (3) are roughly proportional to S n at intermediate energies. At the lower energies displayed it is seen that the proportionality to S n fails and the yield decreases more rapidly than S n. In this region the energy dependence of the cross section [ d (E es )] for the escaping particles is important. Because the transport quantities and describe the energetic atomic cascades, their values extracted from the data for solids should roughly apply to the energetic atomic cascades in a gas. Using the results of Johnson [1994, Figure 4], the value of [ / d ] extracted from laboratory data is cm 2 when the incident and target atoms have equal masses. At normal incidence this gives c ev 1 cm 2 in (6). However, the Y(0)/S n calculated here for a 1 kev O using the universal potential and the electronic energy loss in (3) gives c about half this value. At 55, using p 1.6, the MC result is 70% of the model estimate. Using the TRIM electronic energy loss, the differences are smaller. The analytic model in (6) is based on a solution to the Boltzmann transport equation for the energy distribution of the cascade of recoils produced by an energetic atom setting in motion atoms of equal mass. It is well established that independent of the interaction potential, the lognormal distribution applies [Johnson, 1994]. The lead term in spectra of recoils set in motion with initial energy E is /E 2 x, with x small. This

8 1666 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE Figure 7. The calculated yield versus ion energy at 0 (solid circles) and 55 (squares) zenith angles. The solid line is a fit: Y cs n (E O ), with c ev 1 cm 2 for 0 and c ev 1 cm 2 for 55. Also shown is a fit appropriate at low energies: Y c S n (E O )/ d (E es ) (dashed line), with c 2.4/keV at 0 and 8.2/keV at 55. accounts for the in (6). The energy distribution of the escaping species [e.g., Johnson, 1994] becomes 1 dy 1 x U 1 x es Y de es E es U es 2 x. (7) For the MC calculation of the yield for normal incidence over the energy range studied, this result is obtained with x 0.2. Such a result was also found here using DSMC and by Pospieszalska and Johnson [1996]. That is, when ions penetrate the atmosphere, the flux of atoms across the exobase is represented by a Maxwellian at the temperature of the exobase and a roughly E 2 tail. Using this dependence, Johnson and Luhmann [1998] modeled the sputter-produced component of the Martian corona. When the angle of incidence is large, the energetic secondaries are scattered out of the atmosphere and the distribution changes. This is the grazing incidence case discussed in reference to Figure 6. For angles of incidence equal to 55 and 80, the distributions exhibit a slower decay at large E es. In Figure 8 the result for i 80 is shown to be fit at large E es using x 0.6 in (7). This approaches the dependence of the singlecollision contribution [Sieveka and Johnson, 1984]. A dependence of E 1.4 es was inferred by Smyth and Combi [1997] from the morphology of the Na cloud at Io. They referred to this as the incomplete cascade distribution. The changing character of the sputtered atom energy distribution is also seen in the average energy of the ejecta. Integrating the distribution above out to some maximum energy (a E O ), the lead term is proportional to E x o. The quantity a truncates the distribution in (7), and is a mass factor equal to 1 for O O [e.g., Johnson, 1994]. The values of the mean escape energy in Figure 9a exhibit a dependence ( E 0.6 O )at 55 consistent with the incomplete cascade. From Figure 9b, E es is seen to increase with increasing angle of incidence, owing to scattering out of energetic primary recoils. Because the exiting particles are very nonthermal, they escape from depth with the column determined by d (E es )[Johnson, 1994]. For 1 kev ions incident at 55 we find E es 23 ev; hence Figure 1 gives d (E es ) cm 2. Mean escape depths are found to be 1.3/ d [Johnson, 1994], giving an exobase column of N x Ocm 2, consistent with what we have used in the past ( ( cm 2 ) 1 [Johnson, 1990, 1992]). Not surprisingly, this is also close to N o in Figure 2. The exit angular distribution for normal incidence is typically modeled by Figure 8. Sputter particle energy distribution versus the energy of escaping atom for i 80 (solid line). The dashed line is [ /E 2 x ], with x 0.6. The insert shows the ejected O atom angle distribution at normal incidence. The line is 3cos 2 es.

9 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE 1667 Table 1. Yields for a Two-Component Atmosphere Species (1 kev O Incident) 0 Incidence* 55 Incidence* (100% O) Y O (100% Ne) Y Ne (100% Ar) Y Ar (10% Ne) Y Ne /Y O [0.089] [0.089] (5% Ne) Y Ne /Y O [0.042] [0.042] (10% Ar) Y Ar /Y O [0.044] [0.044] (5% Ar) Y Ar /Y O [0.021] [0.021] *Results are for the MC calculation using the larger electronic energy loss (equation (3)). Square brackets are analytic model (equation (9)). Figure 9. Mean energy of the escaping atoms, E es, versus (a) incident energy of the O atom/ion, E O, for 0 (squares) and 55 (circles) and (b) incident angle i for 0.1 (squares), 1.0 (circles), and 10.0 kev (diamonds). Lines are to guide the eye. 1 dy 2 cos Y d cos es. (8) es Although this result is roughly applicable for the fastest ions, it is seen from the insert in Figure 8 not to apply at normal incidence for 1 kev O ions. In addition, at the lower energies studied here there is a splash effect [Pospieszalska and Johnson, 1996]. For the angular ejecta distribution for nonnormal incidence no simple model applies. As the incident angle becomes more grazing, more of the ion s momentum is directly transferred to exiting atoms, so that Monte Carlo calculations are needed. In the limit of grazing incidence, for an ion passing through a spherical, planetary corona, ejection by single collisions dominates [Sieveka and Johnson, 1984]. On the basis of the comparisons above, the expression for the yield, used by Johnson [1992] for sputtering of Mars and Venus (equation (6)), is not accurate in detail but can give guidance over a broad range of energies Rare Gas Atoms That the atmosphere of Mars may be lost in part by atmospheric sputtering is suggested by the isotope ratios for rare gas atoms (RGA) [Jakosky et al., 1994]. Here we mix Ar and Ne into the O thermosphere to determine the relative loss rate of these trace species as compared to the dominant species. We use the MC model and the ZBL potential both for collisions between RGAs and for collisions between an RGA and an O atom. The convenient electronic energy loss expression in (3) is also used. Calculations are carried out for Ne or Ar mixed at 5 and 10% for both normal incidence and 55. Such fractions are much larger than expected but are required here to obtain sufficient statistics. Since the change in the yields scaled to concentration is small, the 5% results apply when the RGA concentrations are lower. The atmospheric sputtering yields for the pure atmosphere and the ratio of the RGA to O ejected for mixed atmospheres are given in Table 1. Because the energy distribution in (7) was roughly independent of cross section, in analytic models, one typically assumes that this distribution applies to both species. Using the MC model, we verified that this assumption is correct. Therefore it is the relative concentrations at the exobase and the escape energy that, to first order, determines the relative yields. Because the dependence of the sputtering yield on the interaction potential is weak, the ratio of the yields can be simply written [e.g., Sigmund, 1981]. Applying this to an atmosphere [e.g., Johnson, 1990, 1994] gives Y 1 c 1 U es,2. (9) Y 2 c 2 U es,1 Using the result above, the yield for an individual species is roughly [e.g., Sigmund, 1981] c j U es, j Y j. (10) Y 1 c 1 U es,1 Here Y j is the yield from the mix, and Y j is the yield for the single component atmosphere. The result in (9) (square brackets in Table 1) is compared to the ratios obtained from the MC calculations in Table 1. For 1 kev incident O, (9) compares well with the MC calculation except for Ar at normal incidence. This is because of the splash effect, which is more important for the heavier species. Hence, at much lower energies the model is less successful. However, the use of (9) by Jakosky et al. [1994] to obtain the relative yield for Ar isotopes for 1 kev O incident at 55 is justified. That is, calling r the ratio in the atmosphere for a particular isotopic pair (r is the column for species 1 over column for species 2) and using the initial ratio r o, an estimate of the net loss of this species can be obtained. If the principal loss process is sputtering, then one can write f the fraction remaining as f 1/ R 1 r r 1 r o R m 2 2 m 1 r o 1 exp m 2 m 1 g z. kt

10 1668 JOHNSON ET AL.: SPUTTERING OF AN O ATMOSPHERE The quantity R for sputtering is based on the analytic expression in (9), where z is height of the exobase above the homopause, T is the average temperature in this region, and g is the gravitational acceleration Application to Mars and Europa The above results can now be used to constrain the sputtering rate of the atmosphere of Mars. It has become customary to calculate the yields for a 1 kev O incident at 55 as being a representative incident particle. This energy and angle are at the peak of the ion flux distributions calculated by Zhang et al. [1993] for three epochs: 1 EUV, based on the EUV intensity at solar minimum in the present epoch; 3 EUV, an epoch 3 Gyr after formation; and 6 EUV, an epoch 1 Gyr after formation. Therefore we averaged our calculated yields (using ZBL (3)) over the published flux distributions to test the validity of using a representive ion of 1 kev and 55. Using an incident angle of 55 but averaging the calculated yields over the energy distributions determined by Zhang et al. [1993], we obtain averaged yields of 2.4, 2.6, and 3.0 in the three epochs. Assuming an energy of 1 kev O and averaging the calculated yields over the incident angle distributions of Zhang et al., we obtain averaged yields of 2.6, 2.9, and 3.0 in the three epochs. These averaged yields compare reasonably well with the yield for 1 kev and incident angle 55 (2.8 O ion 1 ). The estimates for the yield used by Jakosky et al. [1994] and Luhmann and Johnson [1998] included both the collision cascade contribution, described here, and the single-collision ejection contribution [Sieveka and Johnson, 1984]. The latter was estimated to be 1.3 for O on an O thermosphere [Johnson, 1992]. Therefore, on the basis of the two electronic stopping estimates and the single-collision contribution, we suggest an average yield of ejected/ion incident, compared to the value of 6. estimated earlier [Johnson, 1992] and used recently by Johnson and Luhmann [1998]. If we assume that the atmosphere is fully dissociated and, on the basis of (9), the sputtering of C is 1.3 times that of O, then a rough upper estimate to the net atomic loss rate is s [ i (2 R 2 x )Y ]. Here Y is the mean atomic yield per ion, i is the ion flux, and R x is the radius at the exobase. We use Y O 4.5 and Y C 6, with the exobase concentrations and the ion flux for the three epochs used by Luhmann et al. [1992] and given in Table 1 of Johnson and Luhmann [1998]. The number of bars of atmosphere lost in each of the two periods studied, t Gyr and t Gyr from formation, is [ s tmg], where s is the sputter flux averaged over the planet s surface ( s /4 R 2 x ), m is the mass of O, and g is the gravitational acceleration. This gives an integrated loss of 0.45 bar, of which CO 2 would comprise 0.15 bar. For only O and CO 2 at the exobase, the remainder is atomic O, presumably from dissociated CO 2 or H 2 O. The above estimate ignores the feedback processes discussed by Johnson and Luhmann [1998]. These act to enhance the ion flux and hence increase the sputtering rate. However, the feedback processes may reduce the loss rate estimate for the earliest epoch (1 Gyr) examined by Zhang et al. [1993]. The result above also ignores the possibility of an early magnetic field [Hutchins et al., 1997]. Assuming the potentials and the electronic energy loss used here are correct, the poorest constrained component is the yield for single-collision ejection from the corona of a curved atmosphere. This contribution is obtained by direct knock-on collisions that transfer energy larger than the escape energy in a direction outward to atoms above the nominal exobase [e.g., Johnson, 1990, 1992]. The atmospheric loss estimated here is far below the total loss suggested recently [Kass and Yung, 1995, 1996]. That estimate, although large, did not include the single-collision ejection from the corona and did not include electronic energy loss. These effects act in opposite directions. However, they used ion fluxes that are about twice the values used here in the early epochs. It is these early epochs that dominate the net loss. In addition, as pointed out earlier, the cross section for CO 2 used was initially overestimated [Johnson and Liu, 1996, 1998]. Finally, their potential for O O gives a yield of 9 for a pure O thermosphere versus that of 3 estimated here. Recently, Kass [1999] modified the interaction cross sections on the basis of the work of Johnson and Liu [1998] and included electronic energy loss reducing the total loss. For the range of incident ion energies that is important for atmospheric sputtering at Europa, 1 10 kev O, the cascade contribution to the atmospheric sputtering yield is fairly constant, as seen in Figure 7. For an incident angle of 55 we can scale the yields using U 0.9 es, as seen in Figure 5. This gives Y O 10 O/O for a thick Europan atmosphere. For an atmosphere O 2 cm 2 [Johnson et al., 1982; Hall et al., 1995] the yield is reduced to 70% of this value on the basis of the results in Figure 2. The single collision contribution for Europa is 2.3 O 2 /O, using the procedure of Johnson [1992]. This gives a net yield for a fully dissociated atmosphere of 9 O ejected per incident O. An incident S would sputter more efficiently, and H would sputter much less efficiently. Using the atomic O yield, we can estimate a rough upper bound of about 4.5 O 2 /O. Johnson [1990] gave an estimate for a molecular atmosphere: 1/4 the yield from a fully dissociated atmosphere, or 2.2 O 2 /O. The size of the yield is such that atmospheric sputtering can limit the atmospheric content of oxygen, as suggested by Saur et al. [1998]. 4. Conclusions We have carried out a set of Monte Carlo calculations of the collision cascade contribution to atmospheric sputtering by energetic O ions or atoms incident on an atomic oxygen thermosphere. An average interaction potential was used, derived from atomic collision data [Ziegler et al., 1985], and electronic energy loss was included. These Monte Carlo results are now available to estimate yields for more complex thermospheres. With appropriate scaling the yields can be applied, for example, to the Earth s geocorona and to N incident on an N thermosphere. In this paper we compared a full Monte Carlo model (DSMC) of the atmosphere with a simpler restricted model (MC). In the DSMC calculation the thermosphere developed a structure determined by the ion flux, whereas in the MC model, in which the thermal motion of the atmospheric particles is ignored, we did not include structure. By comparing yields at a number of ion fluxes for the DSMC with the yield for our MC calculation, we showed that this structure is not important for the collision cascade contribution to the sputtering yield as long as sputtering dominates plasma-ion-induced Jeans escape. Therefore the simpler MC calculations are useful. A simple O thermosphere was studied to test analytic models of sputtering and to place rough constraints on sputtering rates from a more complex thermosphere. Such constraints are needed since collision cross sections are not available to carry