Oreshkin V.I., Oreshkin E.V, Chaikovsky S.A., Artyomov A.P.

Transcription

1 Coulomb xploson of "hot spot". Orshkn V.., Orshkn E.V, Chakovsky S.A., Artyomov A.P. Th study prsntd n ths papr has shown that th gnraton of hard x rays d hghnrgy ons, whch ar dtctd n pnch mploson xprmnts, may b assocatd wth th Coulomb xploson of th hot spot that s formd du to th outflow of th matral from th pnch oss pont. Durng th procss of matral outflow, th tmpratur of th hot spot plasma nass, d condtons ars for th plasma lctrons to bcom contnuously acclratd. Th runaway of lctrons from th hot spot rgon rsults n th buldup of postv spac charg n ths rgon followd by a Coulomb xploson. Th condtons for th hot spot plasma lctrons to bcom contnuously acclratd hav bn rvald d stmats hav bn obtd for th kntc nrgy of th ons gnratd by th Coulomb xploson. A Z pnch s lctrcal dscharg n plasma, whch s comprssd undr th acton of th magntc prssur producd by th ntrnsc dscharg currnt [1-7]. Typcal of Z pnchs s th formaton of hot spots du to th dvlopmnt of larg-scal MHD nstablts [1,,8-10]. Th dscharg plasma column s dformd durng comprsson, whch s accompd by th formaton of ncks smallr n radus th th m column. Th magntc prssur n th nck rgon nass, rsultng, frst, n fastr comprsson d, scond, n matral outflow from th nck rgon n th axal drcton. Th fnal stag of th nckng s a hot spot. Apparntly, th axal jts wr frst dtctd n xprmntal study [11] whr th procss of comprsson of dutrum pnchs was nvstgatd. As ths jts wr accountd for by nas n nutron yld, th authors of Rf. [11] proposd a "noncylndrcal Z pnch" n whch th formaton of th hot spot was prdtrmnd by th gomtry of th dscharg. Subsquntly, ths confguraton was calld a plasma focus [1,13]. n subsqunt xprmnts on a dutrum plasma focus at currnts of about 1 MA, lctron bams, hard x rays, d "pthrmal" dutrons wth nrgs up to 8 MV wr dtctd [14]. Evn mor nrgtc dutrons wth nrgs of svral tns of mgalctron-volts wr dtctd n xprmnts wth dutrum lnrs mplodd at a currnt of.7 MA [15]. To xpl th gnraton of hgh-nrgy ons d hard x rays, th so-calld "targt" mchsm was proposd [16]. t s assumd that n th fnal stag of formaton of th hot spot, dsplacmnt currnts occur that gnrat strong lctrc flds n whch chargd partcls ar acclratd.

2 Although hot spots ar frquntly obsrvd n all varts of Z pnch, such as plasma focuss [1-14,17], plasma lnrs [10,14], d vacuum sparks [18], th procss of thr formaton n X pnch has rcvd th most study. An X pnch s a dvc consstng of two or mor ossd wrs (formng th lttr X ), d, lk th plasma focus, t was proposd [19] to produc hot spots. n contrast to a plasma focus, whr th plac of apparc of a hot spot s not known n advc, n X pnch t s prdtrmnd wll nough: ths s th wr oss pont. Ths fatur of X pnchs srvd as th ky to th succss of xprmntal studs of th voluton of th nck d th hot spot [0,1]. n X pnch, th hot spot s formd accordng to th followng scnaro [0-]. Wthn a short tm aftr th start of th currnt flow through th pnch, lctrc xploson of th wrs occurs. Thraftr, a nck s formd whos trsvrs dmnson s svral hundrds of momtrs, d thn a hot spot svral momtrs n sz s formd on th nck. Ths hot spot srvs as a sourc of soft x rays. At th nd, th hot spot xplods d at ths tm, hard x rays d hgh-nrgy ons ar gnratd. Th ons appar wth a slght dlay aftr th m puls of soft x rays [1]. Ths scnaro s llustratd by Fgs. 1 d that prsnt photographc mags of X pnch at dffrnt tms (Fg. 1) d th wavforms of th currnt flowng through th pnch d of th soft-x-ray puls (Fg. ). Th xprmnt was carrd out on a compact hgh-currnt gnrator [3], whch allowd swtchng a currnt of ampltud up to 30 ka d rs tm 180 ns n th short cut mod. Th dagnostc qupmnt of th gnrator consstd of Rogowsk cols usd to masur currnt wavforms; vacuum x-ray dods that allowd rcordng th puls wavform of soft x rays wth photon nrgs hv > 1 kv, d HSFC Pro optcal camra capabl of producng four frams n vsbl lght for ach shot. Th gnrator was loadd by X pnchs, ach consstng of two molybdnum wrs of damtr 1.7 mm nclnd at gl ϕ 3 to th X-pnch axs. Th xposur tm of ach of th mags shown n Fg. 1 was 3 ns. n Fg. 1a, whch prsnts mag of th X pnch takn at pak radaton ntnsty n th soft-x-ray rg (Fg. ), w c clarly s a nck of lngth 50 µm d a sgnfctly smallr hot spot. n th scond mag (s Fg. 1a), mad 0 ns latr, a cavty s sn at th nck plac that was formd obvously du to th xploson of th hot spot. Smlar pcturs wr obtd [0,1] for X pnchs also consstng of two molybdnum wrs of damtr 17 µm th currnt through whch at th tm of th xploson was ka. Ths mags, takn n soft x rays, clarly dmonstrat th xploson of th hot spot. Th caus of th xploson c b fast runaway of lctrons from th hot spot rgon, rsultng n th buldup of postv spac charg followd

3 by a Coulomb xploson. Ths scnaro s supportd by th prsnc of lctron bam, ndcatng th prsnc of runaway lctrons n th pnch plasma [4,5]. t should b notd that th runaway lctrons n gas dschargs [6,7] ar probably gnratd also du to a Coulomb xploson. Howvr, n ths cas, th Coulomb xploson occurs as a consqunc of th formaton of a ngatv charg at th had of th od-drctd stramr [8,9]. xt, w show that condtons for th runaway of lctrons ars durng th voluton of th hot spot. Th formaton of th nck n a Z pnch was studd n dtal [8], d a smpl modl of ths procss was proposd. Accordng to ths modl, th nck s formd durng comprsson of th pnch wrs, whch s accompd by th matral outflow from th nck rgon along th axs (n both th postv d th ngatv drcton). Ths taks plac n condtons clos to th Bnntt qulbrum [30], that s, whn th magntc prssur of th plasma s approxmatly qual to ts thrmal prssur. t was shown [31] that for y currnt dnsty dstrbuton nsd a pnch, th Bnntt qulbrum condton s gvn by kt = c ( 1 z) +, (1) whr s th currnt through th pnch, s th numbr of ons pr unt lngth, z s th m on charg, T s th pnch tmpratur, k s Boltzmn s constt, d c s th vlocty of lght n vacuum. n X pnch, th Bnntt qulbrum condton (1) sams to hold up to hgh dgrs of comprsson. For alumnum X pnch, th paramtrs of th hot spot wr dtrmnd for th tm of formaton of th soft-x-ray puls, d t was shown that at ths tm, condton (1) was fulflld wth good prcson [3]. As th matral flows out from th nck rgon, th plasma tmpratur nass, n accordc wth (1), d condtons may ars for th onst of contnuous acclraton of th plasma lctrons, such that lctron, bng n lctrostatc fld, gs mor nrgy wthn th m fr path th loss t n nlastc collsons. Th tcal lctrostatc fld strngth, E, at whch th frcton forc fals to balc th lctrc forc at y valu of th drctd lctron vlocty s dtrmnd by th Dr tron [4] E Λ 0., () D whr s th lctron charg, Λ s th Coulomb logarthm, d D s th Dby snng radus, whch, for multcharg plasma, c b wrttn as [33]

4 D = kt ( z ) 4π n + z, (3) whr n s th on dnsty n th pnch plasma d z z s th RMS on charg. Blow, w assum that n πr hs, whr Rhs s th radus of th hot spot. Th runaway lctron bam s formd n a pnch whn th lctrc fld strngth n th hot spot, Ehs, producd by th currnt flowng through th pnch bcoms hghr th E,.. E < E =, (4) hs πr hsσ whr σ s th conductvty of th hot spot plasma. Th wll-known d oftn usd xprsson for th conductvty of compltly onzd plasma aoss th magntc fld was obtd by Bragnsky [34]; t rads ( kt ) 3 σ Brag =, (5) 4 πm Λz 3 / whr m s th lctron mass. Howvr, formula (5) taks nto account only lastc lctron-on collsons, d, as notd by Bragnsky [34], th actual conductvty of th plasma should b lowr du to plasma wavs, moturbulnc, nlastc collsons, tc. Th causs for omalous rsstvty n pnchs wr dscussd, for nstc, n Rf. 8; howvr, thr s no commonly opnon on ths problm. t was supposd [8] that th das n plasma conductvty du to omalous ffcts bcoms sgnfct whn th currnt lctron vlocty u = bcoms z gratr th th thrmal vlocty of th ons, u kt =, whr m s th atomc mass of th m pnch matral,.. whn condton for th numbr of ons pr unt lngth: ( + z) u < u. n vw of (1), th last nqualty c b rducd to th m c 1 <. (6) z

5 Th lowr thrshold of blow whch th omalous ffcts bcom sgnfct s of th ordr of cm 1. Th tmpratur at whch th nqualty u < u holds s gvn by 1 m z kt = m c 1, (7) m + z A whr A mc = 3 17 ka s th Alfvn currnt. n th xprmnt wth a molybdnum pnch th rsults of whch ar prsntd n Fgs. 1 d, th tmpratur kt was about 30 V. Th mpact of omalous ffcts c b takn nto account [8,35] by prsntng th plasma conductvty as σ = σ Brag / a, whr a s a dmnsonlss factor; ts valu dpnds on th typ of moturbulnc structurs that scattr lctrons [35]. Early n th procss, whn >, th factor a s clos to unty. Howvr, as mor d mor matral lavs th nck rgon, so that th numbr of ons n th oss-scton of th plasma column dass to <, th factor a nass. Onc ths taks plac, th plasma starts rapdly hatng up, ts radal comprsson slows down [8,17], d th vlocty of outflow along th z-axs nass. Approxmatly at ths pont n tm, th hot spot s formd. As a rsult of th nas n tmpratur, th Dby snng radus D nass, th tcal lctrc fld strngth E dass, d nqualty (4) s fulflld; that s, w hav E < E. Usng th Bnntt condton (1) for th tmpratur d hs takng nto account rlatons (), (3), d (5), w c rwrt nqualty (4) as mc < 3.5 a 1+ z, (8) whr s th thrshold numbr of ons pr unt lngth of th pnch at whch condtons ars for lctrons to bcom contnuously acclratd (for z = 0 d a =10, w hav cm 1 ). Comparng nqualts (6) d (8), w fnd that m / 0.3 a, whnc w obt m th rg for th dmnsonlss factor a: m 1 < a << A, whr A s th atomc m wght of th pnch matral masurd n atomc mass unts. Th runaway lctron bam formd n th hot spot rgon f condton (8) s fulflld s rsponsbl for th buldup of postv spac charg n th pnch plasma. Th Coulomb xploson

6 probably occurs approxmatly at th tm whn th lctrostatc nrgy of th ons whos lctrc charg s not balcd by th charg of th lctrons bcoms gratr th th magntc nrgy,.. Ε lc E mag H = dv Ε = dv, whr E d H ar, rspctvly, th lctrc d 8π 8π th magntc fld strngth at th hot spot (th ntgral s valuatd ovr th volum n whch th postv spac charg s bult up). Th lctrostatc nrgy of th ons n th Coulomb xploson c b stmatd usng Maxwll's quaton dve πzn + = 4, whr + n s th dnsty of th ons whos lctrc charg s not balcd by th charg of th lctrons. For th cas whr th radal d th axal dmnson of th hot spot ar approxmatly qual to ach othr,.. Rhs L hs, th followng stmat s vald: ( z ) Lhs 1 lc Ε +. (9) 4 + whr s th numbr of unbalcd ons pr unt lngth. For a unform currnt dstrbuton, th magntc nrgy concntratd n th spac occupd by th hot spot s gvn by 1 4 c mag Ε = L hs. (10) Hnc, th numbr of unbalcd ons pr unt lngth should b m c + z A. (11) As th xploson occurs, th lctrostatc nrgy s convrtd nto th kntc nrgy of th hot spot ons, d th avrag kntc nrgy pr on s gvn by Ε kn x Ε L hs ( + z) 0.07m 1 c a A. (1) n th xprmnt wth a molybdnum X pnch th rsults of whch ar prsntd n Fgs. 1 d, th avrag kntc nrgy of ons n th Coulomb xploson should b about 00 kv (for a = 10 d z = 0). n th xprmnt [15] wth dutrum Z pnchs mplodd at a currnt of.7 MA, n whch, as mntond, th nrgy spctrum of fast ons was masurd, dutrons wth nrgs of up to MV wr dtctd. Supposng that th avrag kntc nrgy of dutrons kn Ε was about 0 MV, w obt that, accordng to (1), th dmnsonlss factor a for ths xprmnt was about 10.

7 Thus, th hard x rays, th lctron bam, d th hgh nrgy ons obsrvd n pnch mploson xprmnts may b rlatd to th Coulomb xploson of th hot spot. Th hot spot s formd du to th outflow of th pnch matral n th axal drcton. As mor d mor matral lavs th hot spot rgon, th tmpratur of th hot spot plasma nass, d thr ars condtons for th plasma lctrons to bcom contnuously acclratd. Th lctron runaway from th hot spot rgon rsults n th buldup of postv spac charg that s followd by a Coulomb xploson. Th work was supportd by th Russ Scnc Foundaton, grt numbr , work Orshkn E.V. supportd by grt RFBR

8 Fg. 1 mags of X pnch (two molybdnum wrs of damtr 1.7 µm) takn wth HSFC- Pro four-fram optcal camra at t1 = 68 ns (a) d t = 88 ns (b); x-ray puls was dtctd at t = 67 ± ns t 1 t 5, ka x XRD sgnal, V t, ns Fg. Wavforms of th currnt through th X pnch d of th x-ray puls gnratd by th pnch. t x

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