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1 Availabl onlin at ScincDirct Procdia Enginring 103 (2015 ) Th 13 th Hyprvlocity Impact Symposium Computational Modling of Elctrostatic Charg and Filds Producd by Hyprvlocity Impact David A. Crawford* Sandia National Laboratoris*, P. O. Box 5800, MS 0840, Albuqurqu, NM Abstract Following prior xprimntal vidnc of lctrostatic charg sparation, lctric and magntic filds producd by hyprvlocity impact, w hav dvlopd a modl of lctrostatic charg sparation basd on plasma shath thory and implmntd it into th CTH shock physics cod. Prliminary assssmnt of th modl shows good qualitativ and quantitativ agrmnt btwn th modl and prior xprimnts at last in th hyprvlocity rgim for th porous carbonat matrial tstd. Morovr, th modl agrs with th scaling analysis of xprimntal data prformd in th prior work, suggsting that lctric charg sparation and th rsulting lctric and magntic filds can b a substantial ffct at largr scals, highr impact vlocitis, or both Th Authors. Publishd by Elsvir Ltd. This is an opn accss articl undr th CC BY-NC-ND licns ( Publishd Elsvir Ltd. Slction and/or pr-rviw undr rsponsibility of th Hyprvlocity Impact Socity. Pr-rviw undr rsponsibility of th Curators of th Univrsity of Missouri On bhalf of th Missouri Univrsity of Scinc and Tchnology Kywords: magntic fild, lctric fild, plasma, hyprvlocity impact 1. Introduction Impacts in th hyprvlocity rgim oftn produc wakly ionizd vapor or plasma which has bn proposd to produc svral ffcts: (1) th plasma provids a significant prturbation to th ambint magntic fild and can produc spontanous magntic filds du to non-alignd lctron dnsity and tmpratur gradints [1-5]; (2) it supports th production of transint radiofrquncy lctromagntic filds [6-8]; and (3) it chargs jctd dbris which, bcaus of inrtial sparation, lads to significant lctrostatic and magntostatic fild production [9]. In prior work with xprimnts prformd at th NASA Ams Vrtical Gun Rang (AVGR), lctrostatic charg sparation during hyprvlocity impact was charactrizd for diffrnt impactor and targt gomtris [9]. Th xprimnts dirctly masurd th charg jctd at arly tim from cratrs producd by vrtical impacts. An array of aluminum plats dtctd charg arrival as a function of angl of jction from th targt surfac. Total charg sparation was found to vary narly linarly with mass (m) and possssd a vlocity (v) dpndnc of v (Fig. 1). Extrapolating ths obsrvations using a simpl dipol assumption with a charactristic lngth scal (x) and corrsponding tim scal (τ), Crawford and Schultz [9] showd th magnitud and duration of th lctric fild (E), lctric currnt (I) and magntic fild (B) for svral cass: 1) laboratory xprimnt (m=2x10-4 kg, x=0.5 m, v=5 km/s), 2) Lonid mtoroid (m=10-7 kg, x=1 m) striking a spaccraft at 72 km/s, 3) small mtoroid (m=1 kg, x=3 m) striking th Moon at 15 km/s and 4) 1 km astroid (m=10 12 kg, x=100 km) striking a plantary surfac at 20 km/s (Tabl 1). * David Crawford. Tl.: addrss:dacrawf@sandia.gov Th Authors. Publishd by Elsvir Ltd. This is an opn accss articl undr th CC BY-NC-ND licns ( Pr-rviw undr rsponsibility of th Curators of th Univrsity of Missouri On bhalf of th Missouri Univrsity of Scinc and Tchnology doi: /j.prong

2 90 David A. Crawford / Procdia Enginring 103 ( 2015 ) Slop = 2.6 +/- 0.1 Fig. 1. Ngativ charg pr unit projctil mass jctd by impacts of sphrical aluminum projctils into granular carbonat (dolomit) targts vs. impact vlocity, from [1]. Tabl 1. Elctromagntic proprtis of rprsntativ impacts, from [1]. τ (sc.) E (Volts/m) I (Amps) B (Tsla) 1) Laboratory 2x10-3 8x10 5 4x ) Lonid Mtoroid 3x ) Small Mtoroid 4x10-3 2x ) 1 km Astroid 100 4x x Modl In an attmpt to bttr undrstand th formativ mchanism of lctrostatic charg sparation during hyprvlocity impacts and provid a closr-to-first principls prdictiv capability, w hav dvlopd a modl basd on plasma shath thory which w hav incorporatd into th CTH shock physics cod [10]. Hyprvlocity impact producs wakly ionizd gas, solid and liquid (condnsd phas) fragmnts. As obsrvd by Langmuir [11], du to th substantial mass diffrnc btwn ions and much lightr lctrons, lctrons mor frquntly collid with and stick to condnsd phas surfacs until a ngativ potntial dvlops that impds furthr dposition of lctrons. Th rlativ motion of plasma and condnsd phass producs sparation of lctrostatic charg ovr macroscopic distancs lading to th gnration of lctrostatic and magntostatic filds. W now bliv ths filds to b th sourc of signals sn in arlir hyprvlocity impact xprimnts conductd at th AVGR [3-5]. In our modl, w track gas phass and condnsd phass sparatly using diffrnt CTH matrial IDs. Mass is xchangd btwn th gas and condnsd phass of a givn matrial whnvr th matrial tmpratur transitions abov or blow a vaporization tmpratur (T v ) providd for ach matrial by usr input. Evn at modst tmpratur (T) of just a fraction of an lctron volt (a fw thousand K), th gas phas will b a wakly ionizd gas containing fr lctrons (N ) and ions (N i ) constraind by th Saha Equation [12]: Ni N k Zi Z 1/ 2 3/ 4 2m kt Ei / 2kT 2 whr: N k (cm -3 ) is nutral numbr dnsity (N k =N 0 m, with m, th mass of substanc), E i (V) is ionization nrgy, Z i /Z ~o(1) is th ratio of partition functions, m is th mass of th lctron, and h and k ar th Planck and Boltzmann constants rspctivly. A mor rfind futur vrsion of our modl will us mor prcis stimats of fr lctrons and multipl ion spcis as dtrmind by numrical tchniqus [13] and summarizd in data tabls; howvr, calcit is a rlativly simpl ionizing systm with calcium th dominant ion which is wll rprsntd by th Saha quation. Initially, fr lctrons and ions ar in local quilibrium maintaining charg nutrality vn at microscopic scal. Howvr, th condnsd phas may collct charg from collision of ions and lctrons at th intrfac with ionizd gas phass. According to plasma lctrostatic shath thory, th initial charg sparation distanc is govrnd by th Dby h (1)

3 David A. Crawford / Procdia Enginring 103 ( 2015 ) Lngth, λ d =(ɛ 0 kt/n 2 ) 1/2 whr ɛ 0 is th prmittivity of fr spac and is th charg on th lctron [14]; howvr, hydrodynamic motion can sparat th phass, thrby lading to macroscopic charg sparation. Collision rats ar dtrmind by ion (J i ) and lctron (J ) thrmal currnts that in turn dpnd on gas phas tmpratur, ion and lctron concntrations: J N 4 Ni kt 4 J i mi kt m 1/ 2 1/ 2 xp 0 kt (2) (3) Whr N is th local lctron dnsity, m i is th mass of th dominant ion and ϕ 0 is th lctrostatic potntial on th surfac of th condnsd phas. W can dtrmin th quilibrium potntial (ϕ ) at th surfac of condnsd phas matrials by quating J i and J : which implis an quilibrium surfac charg (Q ) of: 1/ 2 kt m i 0 ln (4) m 2 Q A (5) whr A is th local surfac ara of th condnsd phas matrials. In our numrical modl, w calculat surfac charg (Q s ) by xplicitly intgrating Equations (2) and (3) in computational clls that contain an intrfac btwn condnsd phass and ionizd gass. In th prsnt vrsion of th modl, w considr only positiv singly chargd ions (always constraind by Equation 1) and fr lctrons. Undr ths circumstancs J i acts to incras Q s and J acts to dcras Q s. W limit th intgration to th quilibrium surfac charg (Q ) whn th thrmal currnts would othrwis driv Q s past th quilibrium valu. Howvr, charg can rach a frozn condition whn tmpratur and/or ion dnsity of th gas phas drops fastr than thrmal currnts can act to prsrv quilibrium, ithr by moving away from th quilibrium valu or not moving fast nough towards it. Ovrall charg nutrality is maintaind via constraint quations applid to th condnsd-phas bound charg and gas-phas fr lctrons. Th local ion dnsity is always in thrmodynamic quilibrium with th nutral gas atoms via Equation (1). Th surfac ara (A) of condnsd phass in a computational cll is approximatd by: 2 M min4 Lp, A A 4 3 rf min Lp, V 3 whr M is th mass of th condnsd phass in th cll, L p is th particl siz (provid as a constant by th usr for ach condnsd phas matrial), ρ rf is th rfrnc dnsity of th condnsd phas (STP conditions) and V cll is th cll volum, with A cll = V cll /Δx a rprsntativ cll cross-sction. Figur 2 shows a simulation of a 0.64 cm sphrical aluminum projctil vrtically striking a porous calcit targt at 5 km/s. Th simulation was prformd in two dimnsions assuming axial symmtry. Adaptiv msh rfinmnt was usd with th finst zon siz of Δx=Δy=0.024 cm tracking condnsd phass. For this simulation, w usd th lctrostatic charg sparation modl with proprtis shown in Tabl 2. Th projctil was modld as strngth-lss. W usd th ANEOS quation-of-stat (EOS) for aluminum, a SESAME calcit EOS with 26% porosity modld using th P-Alpha modl and a SESAME air EOS. Strngth of th porous calcit was modld as cohsion-lss using a prssur dpndnt yild surfac (slop of 0.8, ultimat yild of 1 kbar) and a Poisson ratio of Th rsidual air in th vacuatd impact chambr, although tnuous with prssur of only about 1 mbar, could still contribut ionization and so was includd in th simulation. Bcaus of th strong tmpratur dpndnc of Equation (1) us of a good EOS is critical. 0 D cll cll (6)

4 92 David A. Crawford / Procdia Enginring 103 ( 2015 ) μs. 10 μs. 1 ms. Fig. 2. CTH simulation of th vrtical impact of a 0.64-cm sphrical aluminum projctil into a calcit targt at 5 km/s using th lctrostatic charg sparation modl. Th calcit targt has a porosity of 26%. Evn though th xprimnt was conductd in a vacuum of approximatly 1 mbar, th rsidual air can still contribut ionization and must b accountd for. At this vlocity, aluminum nvr vaporizs. Som of th calcit dcomposs into CO 2 and CaO at approximatly 1,000 K. (Th CaO can r-condns yt th CO 2 rmains a gas.) Bottom squnc shows th nt lctrostatic charg dnsity (CQV) in numbr of protons (or lctrons) pr unit volum. Air and aluminum tnd to acquir positiv charg (rd) whras calcit tnds to acquir ngativ charg (blu). Currnts collctd on th charg snsor plats (indicatd by th arc at 55 cm radius) rflct th distribution sn hr (Fig. 3).

5 David A. Crawford / Procdia Enginring 103 ( 2015 ) Tabl 2. Paramtrs usd in th CTH lctrostatic charg modl. Aluminum Air Calcit N 0 (g -1 ) 2.23x x x10 21 E i (V) Z i / Z m i (amu) T v (V) L p (cm) 0.01 N/A Rsults Whil not in prfct agrmnt, CTH simulation rsults show good qualitativ agrmnt with th spatial and tmporal charg distribution sn during th impact xprimnts. Figur 3 shows an xprimnt conductd by Crawford and Schultz [9] to masur th lctric charg producd during a hyprvlocity impact into porous calcit. An array of 16 charg dtction plats wr placd to masur lctric charg arrival at 16 diffrnt jction angls. Th lctric currnts prdictd by th simulation show good qualitativ agrmnt with th xprimntally masurd valus, having similar bimodal signaturs and comparabl magnituds. Th lctric fild prdictd by th modl (Figur 4) shows good qualitativ agrmnt with th voltag masurd on horizontal plats in th xprimntal stup. A dtaild quantitativ match would rquir additional knowldg of th local nvironmnt (to dtrmin th capacitanc of th xprimntal systm) which, alas, was not rcordd at th tim of th xprimnts. Th magntic filds prdictd by th modl show good quantitativ agrmnt with th xprimntal valus (Figur 5). 53 ma Impact Tim (ms) Fig. 3. (Lft) Two movi frams from an xprimnt dsignd to masur charg jctd from an impact in a particulat carbonat targt, from [9]. Th projctil was a 0.48 cm aluminum sphr impacting at 5 km/s in an vacuatd targt chambr. Th uppr fram shows luminscnt matrial impinging on th uppr portion of an arc of 16 charg dtction plats. Th lowr fram, 2 ms latr, shows jcta hitting th arc at 35 dgrs. Th radius of th arc is 55 cm. (Cntr) Elctric currnt collctd by probs locatd on th arc. Each prob s jction angl is shown. (Right) CTH simulation of th currnts collctd at plats covring a similar rang in jction angls.

6 94 David A. Crawford / Procdia Enginring 103 ( 2015 ) b) Exprimntal masurmnts a) Photograph of xprimntal stup V cm 32 cm 44 cm 55 cm cm Impact Tim (ms) c) CTH simulation Fig. 4. Exprimnt to masur th lctrostatic fild producd by th impact of a 0.64 cm aluminum projctil into a particulat carbonat targt (impact vlocity: 5 km/s, vrtical), from [9]. a) Th impact cratr (10 cm diamtr) can b sn in th forground and svral of th plats locatd 20 and 32 cm from th impact ar shown in th background. b) Th voltag masurd on plats distributd radially from th impact point is shown with distanc from th cntr of th impact cratr indicatd. c) CTH simulation of th downward componnt of th lctric fild (V/m) at th sam xprimntal locations and shiftd in tim to corrspond to th xprimntal impact tim of ~0.5 ms. Furthrmor, th ovrall charg stat prdictd by th modl agrs quantitativly with th xprimntal data of Figur 1. Th modl matchs th linar mass dpndnc and th strong vlocity dpndnc of th xprimntal data at last in th carbonat vaporization/ionization rgim (Figur 6). Substantial disagrmnt btwn th modl and xprimntal data occurs blow impact vlocitis of about 2 km/s. Th caus of this is unknown. Th only ionization mchanism oprating in th modl in this vlocity rang is from air, with NO + th dominant ion. W can spculat that th P-Alpha modl is inadquat to dscrib calcit vaporization at low vlocitis. It wouldn t b too hard to imagin that hot spots formd from por collaps may b occurring in th calcit at th micro-scal (somthing not xpctd to b accuratly rprsntd by th P-Alpha modl). At vlocitis highr than about 8 km/s, th modl prdicts aluminum vaporization will bgin to contribut ions, producing a substantial incras in lctric charg production (Figur 6). This would b a rasonabl prdiction of th modl for futur xprimntal tsts.

7 David A. Crawford / Procdia Enginring 103 ( 2015 ) a) Magntic Fild (vrtical, 5.03 km/s) Y cm nt X 1 nt b) Fig. 5. a) Transint magntic fild obsrvd in a low initial magntic fild nvironmnt (500 nt orintd vrticallyup) ms aftr vrtical hyprvlocity (~5 km/s) impacts of 0.64 cm aluminum projctils into a powdrd dolomit targt, from [5]. Th plot is th avrag of svral impact xprimnts (75 masurmnt locations/orintations) with ach masurmnt locatd in a horizontal plan 9 cm blow th impact point. Shading rprsnts th vrtical componnt of th magntic fild whras vctors rprsnt th horizontal. Th cratr (whit circl) dfins th origin (whit cross) of th coordinat systm. b) Magntic fild strngth computd by CTH with modl dscribd in th txt. Th fild prdiction is for a location 9 cm blow and at a radius of 20 cm from th impact location. Th fild is toroidal, consistnt with bing gnratd by a vrtically orintd lctric currnt, initially orintd upward for th first 100 μs, followd by a wakr, but longr lasting downward currnt systm (i.. ngativ charg moving upward). Th avrag fild of about -2 nt from μs is consistnt with th xprimntal obsrvations shown on th lft. Fig. 6. Total ngativ charg pr unit mass jctd vs. impact vlocity. Exprimntal rsults from [9] ar shown with opn black circls. CTH simulation rsults using th modl dscribd in th txt ar shown with solid black squars. Good agrmnt btwn xprimnts and simulations is sn in th carbonat vaporization (and ionization) rgim. Th lack of agrmnt at low vlocitis, whr simulations prdict only air ionization to contribut, is discussd in th txt.

8 96 David A. Crawford / Procdia Enginring 103 ( 2015 ) Conclusions and Futur Dirctions W hav dvlopd a modl of lctrostatic charg sparation basd on plasma shath thory and implmntd it into th CTH shock physics cod. Prliminary assssmnt of th modl shows good qualitativ and quantitativ agrmnt btwn th modl and prior xprimnts at last in th hyprvlocity rgim for th porous carbonat matrial tstd. Morovr, th modl agrs with th scaling analysis of xprimntal data prformd in prior work [9], suggsting that lctric charg sparation and th rsulting lctric and magntic filds can b a substantial ffct at largr scals, highr impact vlocitis, or both. In futur work, w will xplor th implications of this modl for th palomagntic rcord of cratrd plantary and small body surfacs in th solar systm. Acknowldgmnts Sandia is a multiprogram laboratory opratd by Sandia Corporation, a Lockhd Martin Company, for th Unitd Stats Dpartmnt of Enrgy undr Contract DE-AC04-94AL Rfrncs [1] Srnka, L. J., 1977, Spontanous magntic fild gnration in hyprvlocity impacts, Procdings of th Lunar Scinc Confrnc, 8, pp [2] Hood, L. L., Vickry, A., 1984, Magntic fild amplification and gnration in hyprvlocity mtoroid impacts with application to lunar palomagntism, Procdings of th Lunar and Plantary Scinc Confrnc 15, Journal of Gophysical Rsarch, 89 (supplmnt), C211-C223. [3] Crawford, D. A., Schultz, P. H., 1988, Laboratory obsrvations of impact gnratd magntic filds, Natur, 336, pp [4] Crawford, D. A., Schultz, P. H., 1991, Laboratory Invstigations of Impact-Gnratd Plasma, Journal of Gophysical Rsarch, Vol. 96, No. E3, pp. 18,807-18,817. [5] Crawford, D. A., Schultz, P. H., 1993, Th production and volution of impact-gnratd magntic filds, Intrnational Journal of Impact Enginring, 14, pp [6] Ditzl, H., Nukum, G. and Rausr, P., 1972, Micromtoroid Simulation Studis on Mtal Targts, Journal of Gophysical Rsarch, 77, pp [7] Bianchi, R., t al., 1984, Radiofrquncy missions obsrvd during macroscopic hyprvlocity impact xprimnts, Natur, 308, pp [8] L, N., t al., 2012, Masurmnts of Frly-Expanding Plasma from Hyprvlocity Impacts, Intrnational Journal of Impact Enginring, 44, pp [9] Crawford, D. A., Schultz, P. H., 1999, Elctromagntic Proprtis of Impact-Gnratd Plasma, Vapor and Dbris, Intrnational Journal of Impact Enginring, 23, pp [10] McGlaun, J. M, Thompson, S. L., Elrick, M. G., 1990, CTH - A Thr-Dimnsional Shock-Wav Physics Cod, Intrnational Journal of Impact Enginring, 10, p [11] Langmuir, I., 1923, Positiv Ion Currnts from th Positiv Column of Mrcury Arcs, Scinc, Vol. 58, No. 1502, [12] Saha, M. N., 1920, Ionisation in th Solar Chromosphr, Philosophical Magazin, 40, Octobr, [13] Li, J, Song, W., and Ning, J., 2014, Thortical and Numrical Prdictions of Hyprvlocity Impact-Gnratd Plasma, Physics of Plasmas, 21, [14] Swift, J.D., Schwar, M.J., 1970, Elctrical Probs for Plasma Diagnostics, Iliff, London.