Impact Vaporization and Ionization of Cosmic Dust Particles

IMPACT VAPORIZATION AND IONIZATION OF COSMIC DUSTPARTICLES

KLAUS HORNUNGUniversity B.W. Muenchen, Germany

E-mail: [email protected], Fax: 0049-89-6004-4092

YURI G. MALAMA and KHAIM S. KESTENBOIMInstitute for Problems in Mechanics RAS, Moscow, Russia

Abstract. We report on theoretical efforts to understand the process of vaporization and ion form-ation upon hypervelocity impact of small cosmic dust particles on a solid surface. Such collisionsoccur at the surface of solid bodies within the planetary system, which do not have an atmosphereas well as in various actual and upcoming space missions for in-situ measurements of interplanetary,interstellar and cometary dust. The investigation uses Godunov’s method to simulate the impact. Forthe very high velocitites investigated, the impacting dust particle as well as parts of the target vaporizeand some of the vapor cloud may change to partially ionized. Numerical results of the impact processare communicated for an 80 km s−1 impact of a slightly porous SiO2 particle on a compact SiO2surface. Values of the amount of vapor and liquid excavated from the target are given. Ionizationrates are calculated for the example investigated and an estimate is given how this extrapolates to thehighest conceivable velocities in the planetary system (above 100 km s−1).

1. Introduction

Cosmic dust is a subject of increasing interest in space investigations (Kissel, 1993;Grünet al., 1993). Dust such spectacular as in cometary tails, interplanetary dust ingeneral as well as also interstellar dust. Such particles often have a porous structurewith low mean density and submicron building blocks as the so called Brownleeparticles, collected near the earth (Brownlee, 1985). These dust particles in spaceare, as a rule, fast moving. Interplanetary dust particles at some 10 km s−1 andinterstellar dust faster, maybe even above 100 km s−1, relative to our solar system.If such a particle hits a solid surface, it gets completely vaporized and also someof the target. For the highest velocitites, some of the vapor is in ionized state. Suchhigh velocity impacts may occur at the surface of small planets, moons, asteroidsor at a spacecraft. For instance, around Jupiter’s moon Ganymede a cloud of ejectadebris has been found (Krügeret al., 1999), which could result from impacts. Inspace missions the impact ionization effect more specifically is used as a tool todetect and characterize dust particles (Table I). Measured quantitites are mass,velocity or chemical composition at impact velocitites from some to many km s−1.In view of this variety of applications, a detailed knowledge of the impact process

Astrophysics and Space Science274: 355–363, 2000.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

356 K. HORNUNG ET AL.

TABLE I

Missions with instruments using high velocity impact ionization

Mission Launch Object Velocity [km s−1]

VEGA 1,2 1984 Halley 79

GIOTTO 1985 Halley 69

GALILEO 1989 IP/IS dust 2 .. 70

ULYSSES 1990 IP/IS dust 2 .. 70

CASSINI 1997 IP/IS dust 1 .. 70

Saturn (2004)

STARDUST 1999 Wild 2 (2004) 6

IP/IS dust 20 .. 50

CONTOUR 2002 Encke (2003) 28

SW (2006) 14

d’Arrest (2008) 12

at cosmic velocitites is vital. The present paper reports on an effort to contributeto this understanding. It is especially dedicated to the correct consideration of thethermodynamic state in the ejecta’s volatile parts.

2. Basic Equations and Hydrocode

The effort is a numerical one and it starts from the gasdynamic conservation equa-tions of mass, momentum and energy in axisymmetrical form:

∂Efr∂t+ ∂Ear∂r+ ∂ Ebr∂z= Eh (1)

Ef =

ρ

ρu

ρv

e

, Ea=

ρu

p + ρu2

ρuv

u(e + p)

, Eb =

ρv

ρuv

p + ρv2

v(e + p)

, Eh =

0p

00

whereρ, u, v, andp are density, radial velocity, axial velocity, and pressure re-spectively,e = ρ(E + (u2+ v2)/2), E is the internal energy per mass unit.

In addition to (1) an equation of state is needed. We developed one for SiO2,which is chosen as model substance. It links known high pressure data to theThomas Fermi states at very high energy densities and accounts for the vaporiz-ation effect. For compressed states (ρ > ρ0) it uses the equation of Tillotson (seeAndersonet al., 1990),

p = (a + b

(E/E0)x2 + 1

)Eρ + Aµ+ Bµ2, (2)

IMPACT VAPORIZATION AND IONIZATION OF COSMIC DUST PARTICLES 357

wherex = ρ0/ρ, µ = (1− x)/x anda, b,A,B,E0 are constants, summarized inTable II.

Pressure and energy in (2) are made up from cold and termal components:p =pc + pt , E = Ec + Et . For expanded states (ρ < ρ0) the description starts from apower law for the cold part of pressure and energy and continues with a modifiedGrueneisen approximation for the thermal part:

p = pc + γ E − EcV

, V = x

ρ0, pc = ζ( 1

xn1− 1

xn2), Ec = −

∫pcdV, (3)

where the volume- and energy dependent Grueneisen coefficientγ is given by

γ = as + bs

E/E0+ 1

as = ah1 + bh1s + ch1s2 (4)

bs = ah2 + bh2s + ch2s2, s = log10(

xmax

x)

The constantsn1, n2, ζ , ah1, bh1, ch1, ah2, bh2, ch2 are listed in Table II. The de-scription reaches from 7.5 fold compression up to relative volumes of (V/V0)max=xmax= 105, i.e. up to very large expansions, which is needed to correctly describethe gaseous states. With the constants of Table II, pressure and energy follow inMbar and 1012 erg g−1 respectively. Figure I shows a plot of the isochores (lines ofconstant density) of this equation of state (1 TPa= 10 Mbar, 1 TPa m3/Mg = 1013 ergg−1) together with the isochores and isotherms from the Thomas-Fermi model ofKalitkin and Kuz’mina (1975). The sharp pressure drop is due to vaporization andat higher energies the isochores smoothly merge into the TF values. The additionallines, marked with squares are the cold compression curve (lower) and the shockHugoniot curve of the compact material (upper). Our EOS has a good overallagreement (i.e. within the experimental uncertainties) with the tables of Ree (1976).

This EOS (2-4) is now used in the simulation of the impact process. The numer-ical method is Godunov’s scheme (see Godunovet al., 1976; Roe, 1981; Colellaand Glaz, 1985; Baranov and Malama, 1993). We choose this method, because itgives more reliable values for the thermodynamic parameters within the fluid ele-ment than any other hydrocode. It extends previous work on high velocity impact(Malama, 1982; Malama, 1984; Hornunget al., 1996) by introducing a secondorder scheme. The technique applied here treats as Langrangian boundaries thefollowing lines (see Figure 2): the shock waves in dust particle and target (Sd ,St ),an outer vacuum boundary as the limit of the calculational region, the dust/targetinterface (Idt ) and an additional gas/condenced phases interface (Igc) in the target.Elsewise the grid is Eulerian which means that there is mass flow across its meshboundaries. The architecture of this grid is adapted to the characteristics of the flowand is changed during the calculation if necessary. This helps to avoid extremedeformation of the cells for the rapidly expanding gaseous products. In additionthe transport of Lagrangian marker particles through the velocity field is integrated.


TABLE II

Constants for the SiO2 equation of state

ρ0 a b A

2.65 0.5 1.5 0.0649

B E0 n1 n2

0.0169 415E − 5 9 1.421875

ζ ah1 bh1 ch1

8.568297E − 3 0.23 −1.98E − 2 1.476E − 2

ah2 bh2 ch2 xmax

0.437 −7.79778E − 2 5.812889E − 2 105

Details of the numerical method will be published elsewhere. With respect to plan-etary and space science applications an important characteristic of the technique is,that it conserves entropy very accurately in the Lagrangian frame of reference. Thisis needed for a correct characterization of the thermodynamic state of the gaseousproducts. Many other hydrocodes have difficultites at this point.

3. An Example at 80 km s−1

As an example we discuss the 80 km s−1 impact of a cylindrical SiO2 particle ofequal radius and height with lower initial density than normal (ρ = 1.5 g cm−3)onto a compact SiO2 surface (ρ = 2.65 g cm−3). SiO2 is chosen, since it formsa fair chemical model for a cosmic dust particle as well as for planetary surfaces.This is because its mean atomic mass and atom numbers are close to typical dust,rocky planetary surfaces as well as Al which is frequently used in spaceship struc-tures. Also it contains components of low (Si) and high (O) ionization potential inreasonable proportions. Figure 2 shows a plot in radial and axial coordinates withthe Lagrangian boundaries Sd,Idt , St , and Igc and the positions of 1000 dust and4000 target marker particles. All these markers have equal mass. The left 4 plotsare early stages of the impact up to times of 0.3, which corresponds to about 4 psec(the time unit depends on the dust’s size and for a height of 1µm it is 12.5 psec).At this stage a shock travels through the particle (a faint horizontal line visible inframe 2) and the target shock begins to form. A first gasous cloudlet is generated atthe edge. The right 4 plots are late stages from time 1 to 16, corresponding to 12.5to 200 psec. Now the dust is completely vaporized and the gas can expand freely.Here we can see also the development of the crater hole. The light grey area is the


Figure 1. Isochores for the SiO2 Equation of State compared with Thomas Fermi isochores andisotherms.

liquid shocked target material. The pictures show a clear layering of the gaseousproducts. First the outer parts of the dust of the original dust particle (dark markersabove the Idt -line), then the inner parts (light markers above the Idt -line) and thenthe vaporized target atoms (markers below the Idt -line). Our calculations do notinclude effects of elastic-plastic properities of the solid at small pressures, sincefor the investigation of the vaporization effect these are of minor importance. Theydo contribute to the final shape of the crater, but by the time of its final formationthe vapor has escaped far from the target. The total amount of vapor released fromthe target material is about 46 times the mass of the impacting particle. This isa rather high value caused by the fact that dust and target materials are not toomuch different in density. The total amount of liquid SiO2 produced is about 1300times the particles’ mass. The total momentum in z-direction (normal to target)of the condensed target material is 2.6 times the momentum of the incoming dustparticle, a number which can be of interest for spacecrafts. The liquid part of thetarget material will certainly desintegrate into small droplets, as experimentallyverified in former shock wave vaporization studies, due to the strong shear forcesduring high pressure unloading (Hornung and Michel, 1972). However an inclusionof this process is outside the possibilities of any hydrocode. It is sufficient to keepin mind that part of the liquid leaves the crater hole in form of a spray of liquid


Figure 2.Impact of aρ = 1.5 g cm−3 SiO2 cylindrical dust particle onto aρ = 2.65 g cm−3 SiO2surface. Time unit ish/v, h being the cylinder’s height (see also http://windoms.sitek.net/∼comet).

droplets with some further partial vaporization upon expansion (see also O’Keefeand Ahrens, 1987 for large scale impacts).

4. Ionization in the Expanding Gaseous Cloud

The ionization state in the gaseous products is calculated following the ideas of Ra-izer (1959) within the frame of reference of the moving Lagrangian test particles.It turned out that the states of those particles, which undergo substantial ionizationare entirely located in the Thomas Fermi region, such that we can use the TF tem-perature information. Spectroscopic data and resulting partition functions are usedas long as there is LTE. After its end we can assume the ionization to be frozen, due


TABLE III

Ionization of the dust particle material

v [km s−1] Ts [eV] Si+ [%] Si++ [%] O+ [%] O++ [%]

40 11.7 2.3 0 0 0

60 19.6 14 0 0.01 0

80 28.6 51 0.003 0.3 0

100 39 83 0.4 9.6 0

150 68 54 46 89 0.12

to the very rapid expansion (see Drapatz and Michel, 1972; Hornung and Kissel,1994). Here the size of the dust becomes important, since it determines the timescale of expansion cooling. We choose a value of 1µm for radius and height.Table III contains mean values for ionization of the dust particle for the examplechosen (impact of a 1µm sizedρ = 1.5 g cm−3 dust particle onto aρ = 2.65 SiO2

surface, Ts is the temperature behind the initial particle shock wave). It follows thatonly Si ionizes to a substantial amount, whereas O very little, due to its much higherionization potential. One might be interested, how this depends on impact velocityand especially how it extrapolates to higher velocitites in view of the very highvelocity particle streams from interstellar space. We have performed 1-D estimatesand the result (included in Table III) is that the lower threshold lies at about 40 kms−1 for the combination of materials chosen as well as much higher ionization de-grees and also doubly ionized states for impact velocitites above 100 km s−1. Thusan observation of doubly ionized states in in-situ impact ionization measurementsof cosmic dust may be used to recognize such extremely high velocitites. How-ever one should be careful in taking these values as universal. They depend verymuch on the density ratio dust/target. At lower dust densities and/or higher targetdensitites such large ionization degrees may appear already at lower velocities. Forexample, if the impact instead of on SiO2 would be on Ag, which is used in somein-situ experiments, the values for 100 km s−1 in Table III would show up alreadyat 80 km s−1. The example chosen in these calculations is thought to be reasonablefor a dust/planetary body interaction. Ionization from the target is much less, due toits higher density and because the target shock wave quickly weakens. An averagevalue is about 0.3%. This, however, is not a negligible amount, since the total targetvapor is 46 times the dust’s mass. Thus total ionization (dust+target) sums up to avalue of 65%, normalized to the mass of the impacting dust particle.

The above method to calculate ionization does not give an answer, how upon im-pact at velocities much less than 40 km s−1 ions may be produced. From laboratoryexperiments (Knabe and Krueger, 1982; Krueger, 1996) it is known that already at afew km s−1 there is a certain charge production from the impacting particle as wellas from the target. The underlying physical process, however, is not understood at


present. It might be connected with surface disturbances, when the shock waves indust and target exit from a free surface as mentionned in an earlier review on thesubject (Hornunget al., 1996). Former experiments of Anisimovet al.(1970) withlaser impacts point in this direction. Those surface effects, however, may also bethe ionization mechanism at very high velocitites, if the dust particles are extremelysmall. It is thought that this begins at about 100 nm particle radius and is clearlypresent at 10 nm. The time scale of the impact process is then below 1 psec andthere may not be enough time to form ions from thermal excitation. There is anindication in the impact mass spectra of the HALLEY measurements that suchatogram dust particles may exist in the neighbourhood of comets (Utterback andKissel, 1990; Sagdeevet al., 1989) and an interesting question might be whetherthey also exist in the interstellar medium as part of its mass inventory.

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Impact Vaporization and Ionization of Cosmic Dust Particles