arXiv:1710.00149v2 [physics.plasm-ph] 30 Nov 2017 123 456 7 SUBMITTEDTOIEEETRANS.PLASMASCI. 1 SUBMITTEDTOIEEETRANS.PLASMASCI. 2 Experiment to Form and Characterize a Section of a Spherically Imploding Plasma Liner S. C. Hsu, S. J. Langendorf, K. C. Yates, J. P. Dunn, S. Brockington, A. Case, E. Cruz, F. D. Witherspoon, M. A. Gilmore, J. T. Cassibry, R. Samulyak, P. Stoltz, K. Schillo, W. Shih, K. Beckwith, and Y. C. F. Thio (Invited Paper) Abstract—Wedescribeanexperimenttoformandcharacterize experiments, with the aide of associated numerical modeling a section of a spherically imploding plasma liner by merging [14], [17], led to the following key results of relevance to the six supersonic plasma jets that are launched by newly designed physicsofplasma-linerformation:(1)confirmationofplasma- contoured-gapcoaxialplasmaguns.Thisexperimentisaprelude jetparameters,andcharacterizationoftheirevolutionandpro- to forming a fully spherical imploding plasma liner using many dozensofplasmaguns,asastandoffdriverforplasma-jet-driven files, during approximately1 m of jet propagationaway from magneto-inertialfusion.Theobjectivesofthesix-jetexperiments the railgun nozzle [13], (2) identification and characterization are to assess the evolution and scalings of liner Mach number of collisional-plasma-shock formation between two obliquely and uniformity, which are important metrics for spherically mergingplasma jets [14], [15], largely consistent with hydro- imploding plasma liners to compress magnetized target plasmas dynamicobliqueshocktheory,and(3)theroleofrisingmean- tofusionconditions.Thispaperdescribesthedesignofthecoaxial plasma guns, experimental characterization of the plasma jets, charge-stateZ¯ in keeping the dynamics between merging jets six-jetexperimentalsetupanddiagnostics,initialdiagnosticdata in a collisional regime (because of the Z¯−4 dependence of fromthree-andsix-jetexperiments,andthehigh-levelobjectives thecounterstreamingion–ionmeanfreepath)[16].Inparallel, of associated numerical modeling. additionaltheory and modeling efforts examined plasma-liner Index Terms—Plasma applications, Plasmas radial convergence and scalings in one dimension (1D) [18]– [22], and the effects of discrete jet merging on plasma-liner I. INTRODUCTION convergencein 3D [23]–[25]. Collectively,these priorstudiessetthe stage forthepresent SPHERICALLY implodingplasma liners formedby merg- PLX-α project, which is named after the Accelerating Low- ing supersonic plasma jets are a proposed low-cost, cost Plasma Heating and Assembly (ALPHA) program of the high-shot-rate, standoff driver for plasma-jet-driven magneto- Advanced Research Projects Agency–Energy (ARPA-E) that inertialfusion(PJMIF)[1]–[3].Magneto-inertialfusion(MIF) sponsorstheongoingresearch.TheprimaryobjectiveofPLX- [4]–[6] seeks to achieve fusion at ion densities intermediate α by the end of the ALPHA program is to form and study a between those of magnetic and inertial fusion, by combining fully spherical imploding plasma liner with at least 36 and attributesofboththelatterapproaches.Theprimarynear-term up to 60 merging plasma jets (Fig. 1) that are launched by objective of the Plasma Liner Experiment(PLX) [2], [7] is to newly designed coaxial plasma guns fabricated by HyperV demonstrate the formation of spherically imploding plasma Technologies Corp., which is now owned by new fusion liners by merging dozens of supersonic plasma jets, and startup HyperJet Fusion Corporation. Development of novel, to demonstrate their viability and scalability toward reactor- β > 1 (where β is the ratio of thermal-to-magnetic pressure) relevant energies and scales. magnetizedplasmatargets[26]forPJMIFisatanascentstage The PLX facility was built in 2010–2011 at Los Alamos and discussed elsewhere [2], [27], [28]. In future experiments National Laboratory (LANL) to study plasma-liner formation involving plasma-liner compression of magnetized plasma via mergingsupersonicplasmajets [2],[8]. From2011–2014, targets, we envision using a subset of the same coaxial guns PLX utilized parallel-plate mini-railguns [9]–[12], designed (that form the liner) to form an inertially confined dense andbuiltbyHyperVTechnologiesCorp.,inaseriesofexperi- plasmatarget(∼1018cm−3),andtopotentiallymagnetizethe ments[7] to studysingle-jetpropagation[13], two-jetoblique target (β > 1, ωτ & 1, where ωτ is the Hall magnetization merging [14], [15], and two-jet head-on merging [16]. These parameter) using laser beat-wave current drive [27], [28]. S.C.Hsu,S.J.Langendorf,andJ.P.DunnarewithPhysicsDivision,Los The remainder of this paper is organized as follows. Sec- AlamosNational Laboratory,LosAlamos,NM;email:[email protected]. tion II describesthe design of the new PLX-α coaxialplasma K. C. Yates and M. A. Gilmore are with the Electrical and Computer gunsandexperimentaldatacharacterizingtheplasmajetsthat Engineering Department, University ofNewMexico, Albuquerque, NM. S.Brockington,A.Case,E.Cruz,andF.D.WitherspoonarewithHyperV they launch. Section III describes the motivation, experimen- Technologies Corp.andHyperJetFusionCorporation, bothinChantilly, VA. tal/diagnosticsetups,andinitialdiagnosticresultsofthree-and J. T. Cassibry and K. Schillo are with the Propulsion Research Center, six-gun experiments (a predecessor to the spherical plasma- University ofAlabamainHuntsville, Huntsville, AL. R.SamulyakandW.ShiharewiththeDepartmentofAppliedMathematics liner-formation experiments using 36–60 guns). Section IV andStatistics, StonyBrookUniversity, StonyBrook,NY. provides a brief overview of the PLX-α numerical-modeling P.Stoltz is andK.Beckwith was with Tech-X Corporation, Boulder, CO; objectives.Finally,Sec.Vprovidesasummaryanddescription K.Beckwith isnowwithSandiaNational Laboratories, Albuquerque, NM. Y.C.F.ThioiswithHyperJetFusionCorporation, Chantilly, VA. of future plans. SUBMITTEDTOIEEETRANS.PLASMASCI. 3 TABLEI REQUIREDANDACHIEVEDARGONPLASMA-JETPARAMETERSOFTHE NEWPLX-αCOAXIALPLASMAGUNS.DETAILSREGARDINGTHE MEASUREMENTOFJETPARAMETERSAREGIVENINSEC.II-C. Parameter Required Achieved Density ≈2×1016 cm−3 >2×1016 cm−3 Mass >1mg 0.47±0.11mg Velocity ≥50km/s 52.5±5.1km/s Length ≤10cm 16±5.7cm ofthePLX-αguns.Furtherdiscussionoftheachievedplasma- jet parameters is presented in Sec. II-C. B. Coaxial-gun design To fulfill these requirements, we exploited prior HyperV gun-development efforts that had already led to (1) linear railguns capable of achieving the plasma-jet parameters with regard to mass, density, and velocity [7], [10] and (2) coaxial Fig.1. Illustration ofthePLX-αexperimental setup,whichwillultimately haveatleast36andupto60(asshown)coaxialplasmagunsmountedaround gunswith much lower currentdensity that used ablative mass a2.74-m-diametervacuum chamber. Shownareplasmagunswithintegrated injection [31]. The new PLX-α guns essentially combine the capacitor banks and a spherically imploding plasma liner compressing a plasma-jet performance and gaseous injection of the railguns magnetized plasma target. The PLX-α project is focused on developing the plasmalinerandisnotaddressing theplasmatarget. with the coaxial electrode geometry of the coaxial guns. Figure 2 shows a full-assembly drawing of the new PLX- α coaxial gun and its integrated pulsed-power module. We II. PLX-αCOAXIAL PLASMAGUNS chose to mount the capacitors that drive the main gun- New contoured-gap coaxial plasma guns were designed electrode discharge onto the back of each gun both to min- and fabricated for the PLX-α project. The rationale for the imize inductance and to eliminate the complexity and cost contoured-gap coaxial-gun concept with pre-ionized mass of requiring many parallel transmission lines. Details of the injection for launching high-mass, high-density jets to > electrodes (on the right side of the figure, hidden from view) 50 km/s was previously laid out in a series of seminal are proprietary information of HyperJet Fusion Corporation. works [29]–[31]. The design of the new PLX-α coaxial guns The contours on both the outer and inner electrode surfaces was governed by the need to achieve particular plasma-jet were designed based on a series of MACH2 [32] simulations performance parameters to meet requirements of the PLX-α that led to the desired, calculated plasma-jet parameters. The project (see Sec. II-A), while establishing a basis for a gun primary function of the contours is to eliminate the “blowby designthatcouldbefurtherdevelopedandscaleduptobecome instability”[30],whichmustbeavoidedinorderto accelerate fusion relevant. high-mass jets. The guns each have a fast gas valve (GV) mounted at the rearendofthe innerelectrodeto minimizegastraveldistance A. Plasma-jet requirements fromtheGVtothebreech(i.e.,thecoaxialgapattherearend Plasma-jet requirements were determined largely based on the desire to build the lowest-cost experiment that would allow studies of plasma-liner formation and convergence in reactor-relevant physics limits inferred from the parameter regimesstudiedin[3].Theselimitsare:(1)plasma-jetmerging occurs in the collisional limit, i.e., the jet interpenetration depth is small compared to the jet radius, (2) the plasma equation-of-state(EOS)hassufficientionizationandexcitation states to provide a significant energy sink (including strong radiative losses) compared to the thermal energy of the jet, and (3) the plasma flow is strongly supersonic, i.e., the sonic Mach number M ≡V /C &10, where V is the directed jet s jet jet speed and C the jet internal sound speed. Requirements s (1)and(3)leadtominimumallowablejetdensityandvelocity, respectively. Requirements (2) and (3) necessitate the use of heavier species such as Ar, Kr, or Xe, though we use lighter elements as well for establishing a scaling database. Table I Fig.2. Illustration ofthePLX-αcoaxial gunwithintegrated pulsed-power summarizes the required and achieved plasma-jet parameters components. SeealsoFig.7. SUBMITTEDTOIEEETRANS.PLASMASCI. 4 of the gun) and also twenty tungsten “ignitor pins” (i.e., pre- peak electron density n at that position (2.2×1016 cm−3) is e ionizers,orPI)distributeduniformlyintheazimuthaldirection estimatedbydividingthepeakline-integratedelectrondensity aroundthe breech.The GVs are typically pressurizedat up to hn ℓi≈3.3×1017 cm−2 by the diameter, and integration of e 20 psig (for the three- and six-gun experiments described in the interferometer signal over the FWHM gives the FWHM Sec. III) using any gas or mixture available in a compressed- jet mass (0.8 mg). The peak n at the gun exit would be e gas bottle (Ar has been our primary working gas, but we also muchhigher(priorto anyspreadingof the jet). Table I shows use H , He, N , Ne, Kr, and Xe on PLX). Details of the GV theaveragedparametersandstandarddeviationsachievedover 2 2 andPIdesignsareproprietaryinformationofHyperJetFusion fifteen shots with the following settings: V = −4.7 kV gun Corporation. (center gun electrode charged negatively), V = 8.4 kV, GV The gun firing sequence is as follows. All the capacitor V =28 kV, t =−600 µs, and 10-psig-Ar GV pressure. PI GV banks are first charged to the desired voltages (see Secs. II-C As seen in Table I, the averagedjet performanceis close to and III-A for typical values). The GV is triggered first at t≈ the requirements but a little shy for jet mass and length. An −600µs(forAr)tofill thegunbreechwithneutralgas.Then upgraded GV (rev. 10), now being tested at HyperV, allows the PI system is fired att≈−20 µs to ionize the gasfill, and much higher gas-fill pressure (> 50 psig), which is expected finally the main gun bank is triggered (defined to be t = 0) to help satisfy both the jet mass and length requirements in to accelerate the ionized plasma out of the coaxial gun. Gun future experiments. The new GV is also intended to improve performance can be tuned by varying the GV fill pressure, jet-to-jet balance as discussed in Sec. III-B4. capacitor-bank voltages, and GV and PI trigger times. III. PLX-αTHREE-AND SIX-GUN EXPERIMENTS C. Plasma-jet characterization ThefirstphaseofthePLX-αproject,inadditiontocoaxial- gun development and testing at HyperV Technologies, also Experimentalstudiesofsingle-plasma-jetperformancewere includes six-gun experiments at LANL (Fig. 4) in order performed at HyperV Technologies in order to optimize jet to: (1) successfully operate six guns simultaneously as a performance, and to make progress toward meeting the re- demonstration of technical readiness to perform experiments quirements given in Table I. Jet reproducibility was assessed using 36–60 guns for spherical plasma-liner formation, and and the bank voltage and trigger times optimized over a 368- (2) assess the effects of discrete jet merging on plasma-liner shotcampaignfiringa single coaxialgunusingargon.During formation that could cause significant degradationsfrom one- this campaign, the gun fired correctly at the triggered time dimensional (1D) imploding-plasma-liner performance [3], with better than 97.5% reliability. [34]. These jet-merging effects include M-degradation due Figure 3 shows representative photodiode and interferome- trydatafromtransverseviewsatvariousdistancesdownstream from the exit of the gun. These measurements were used to infer jet velocity, length, peak density, and mass as follows. The time delay between the photodiode signals gives the jet velocity(53km/s).Thefull-width,half-maximum(FWHM)of theinterferometersignal,alongwith thevelocity,givesthejet length(7.8cm).Assumingajetdiameterof15cmattheview- ing position (33.6 cm downstream of the exit of the gun), the Fig.3. Interferometer(cm−2)andphotodiode(arb.)signalsvs.time(HyperV Fig.4. Photograph(takenJan.31,2017)ofthePLXfacility atLANLwith shot 201704251255) for transverse views across the plasma jet at various sixPLX-αcoaxialgunsmountedinahexagonalpatternona2.74-mspherical distances (as indicated inthe legend) from theexit ofthe gun.TheHyperV vacuum chamber. The large port in the middle of the hexagon provides the interferometerisaquadrature,heterodynesystemusinga623-nmHeNelaser launchpositionsofsevenchordsofafiber-coupled,visibleinterferometer[see modulatedat110MHz[33],andthephotodiodearrayissimilartothesystem alsoFig.6(a)].Thecartatthelowerleftholdsthecapacitorbanksthatpower described inSec.III-A. theGVandPIsystemsforallsixguns. SUBMITTEDTOIEEETRANS.PLASMASCI. 5 to shock heating and seeding of non-uniformities that could exacerbate deceleration-phase instabilities at the liner/target interface (in future, integrated liner-on-target experiments). The instabilities could lead to liner/target mix and reduce the overall effectiveness of plasma liners as a compression driver of magnetized plasma targets to fusion conditions. A. Experimental and diagnostic setups Figure 4 shows the six-gun configuration, i.e., a hexagonal arrangement with 24 ◦ between adjacent guns. We can fire all six guns simultaneously or any arbitrary subset of them. We often fired two or three guns for better diagnostic access to andinterpretationofplasma-shockevolutionbetweenadjacent merging jets. TableIIsummarizesthespecificationsofthecapacitorbanks driving the six plasma guns. Each gun has an integrated ca- pacitorbank(-5kV,575µF,7.2kJ)drivingthemainelectrode discharge. A separate capacitor bank (12 kV, 96 µF, 6.9 kJ) drives all six GVs of the six guns, and yet another separate capacitorbank(30kV,12µF,5.4kJ)drivesallsixPIsystems. Afinalcapacitorbank(-30kV,6µF,2.7kJ)drivesthemaster- trigger(MT)systemforallsixguns.TypicaloperationonPLX has utilized -4.5 kV, 8.5 kV, 24 kV, and -28 kV for the gun- electrode, GV, PI, and MT banks, respectively. Allbanksareswitchedbyhigh-voltage,high-currentspark- gap switches custom made by HyperV Technologies. Each 575-µFbankdrivingthegunelectrodesconsistsofsixseparate sub-banks driven by six separate spark-gap switches. These switches (6 per gun, and 36 total for 6 guns) are triggered by the MT bank. The switches are pressurized to various static pressures with either Ar or Ar/N (90%/10%) mixture 2 (gun switches) or N (GV, PI, and MT switches); the switch 2 gasesarepurgedfor15–30saftereachexperimentalshot.All switchesaretriggeredbyopticallycoupledsignalsthatlargely eliminatenoise-inducedmisfires. Figure5 showssampleelec- trical currents from the gun, GV, and PI banks for a three- gun experiment. Note the large imbalance for one of the GV currents; this is consistent with observed jet-to-jet imbalance leadingtoongoingimprovementsintheGVdesignandpower delivery, as discussed in Sec. III-B4. Fig. 5. Electrical-current waveforms, measured by Rogowski coils, for Diagnostics for the six-gun experimentsare summarized in (a) gun electrodes, (b) GVs, and (c) PIs for a representative three-gun Table III. The twelve-chord,fiber-coupled,visible interferom- experiment(shot1062;chargevoltages:5kVforthegunelectrodes,10kVfor theGVs,and-24kVforthePIs).Thesewaveformswereabsolutelycalibrated eter (using a 320-mW, 651-nm solid-state laser and upgraded tounits ofkA byequating the time-integrated value ofeach signal with the known,storedchargeintheirrespective capacitor banks. TABLEII CAPACITOR-BANKSPECIFICATIONSFORTHESIX-GUNPLX-α EXPERIMENTSATLANL. from a previous eight-chord system [35], [36]) and broad- band visible survey spectrometer have both been described in Banks Capacitor Totalbank Ratedbank detail elsewhere [7], [13]. The survey-spectrometer detector (#/bank) capacitance (µF) voltage (kV) (0.160 nm/pixel resolution at 510 nm) is now upgraded to Gun NWL13339 575 -5 electrodes (18) pergun a PI-MAX2 intensified charge-coupled-device(CCD) camera Gas Maxwell32567 96 12 (1024× 256 pixels, 16-bit dynamic range, typical exposure valve (GV) (4) for6guns of 1–2 µs), and the collection optic has also been upgraded Pre- Maxwell32814 12 30 suchthatthediameteroftheviewingchordatthepositionsof ionizers (PI) (2) for6guns interestwithintheplasmaisabout1cm.Theirsetups(initially, Master Maxwell32814 6 -30 using only seven of the twelve interferometer chords) are trigger(MT) (1) for6guns shown in Fig. 6(a). The high-resolutionspectrometeris a 4-m SUBMITTEDTOIEEETRANS.PLASMASCI. 6 TABLEIII SUMMARYOFDIAGNOSTICSFORTHESIX-JETEXPERIMENTS. Diagnostic Measurement Parameter(s) inferred 12-chord phaseshift line-integrated electron interferometer (timeresolved) densityhneℓi survey visiblelinespectra chord-averaged spectrometer (timegated) ne,Te,Z high-resolution visiblelinespectra line-integrated spectrometer (timegated) Ti andDopplershift photodiode visible light Vjet and array (timeresolved) axial profile CCDcamera visibleimage Vjet and (singleframe) (timegated) globalplasmaappearance CCDcamera visibleimagesequence sameasabove (12frames) (timegated) andplasmaevolution McPherson 2062DP, with 2400 mm−1 grating (1.52 pm/pixel at480.6nm),coupledtoaStanfordComputerOptics4QuikE intensified-CCD camera (752 × 482 pixels, 10-bit dynamic range, typical exposure of 1 µs); plasma light is collected at a chamberwindowwith two 2-in.,100-mmachromaticlenses [Fig. 6(b)] and transported to the spectrometer with a bifur- cated80×100-µm-corefiberbundle(sothattwoviewscanbe recordedsimultaneously).Thediameterofthe viewingchords atthepositionsofinterestareabout1.5cm.Forthephotodiode arrays,twochannelsoflightarecollectedthrough1-mm,5/16- in.-deeppinholesneartheendofeachgunnozzle(Fig.7),and transported through optical fibers (SH-4001) to a photodiode- array board that digitizes the signals at 100 MHz with 14- bit dynamic range. The light level received at the photodiode Fig.6. (a)Projected view ofinterferometer chords 1–7withrespect tothe locationofthesixgunsasviewedfrombehindtheguns.Thechordsgostraight board can be attenuated by physically adjusting the distance across the chamber maintaining parallel separation, whereas the guns point betweenagapineachfiber.Thesingle-frameintensified-CCD towardtargetchambercenter(TCC).Thesurvey-spectrometercollectionoptic camera is a DiCam Pro ICCD (1280×1024 pixels with 12- is moved around to overlap with any of the seven interferometer chords. In theprojectedplane(asdepicted),thearcformedbytheinterferometerchords bit dynamic range), positioned as shown in Fig. 6(b), and the is5.7cmfromTCC.However,wherechords3and5actuallyintersectthejet- 12-frameintensified-CCDcamerais an InvisibleVision UHSi propagation axes is14.7cmfromTCC.(b)CCD-camera (singleframe)and 12/24 (1000×860 pixels with 12-bit dynamic range). Doppler-spectroscopyviewingpositions(side-onviewofthejetspropagating towardTCC).ThetwoDoppler-spectroscopychordscanbeseparatelymoved around to the various radii shown along the “primary-shock” line or the B. Initial diagnostic results “secondary-shock” line. In this subsection, we present initial, sample results from key diagnostics from a series of three- and six-gun experi- were both also observed and studied in 3D hydrodynamic ments;allshotsreportedhereusedargon.Thesewereourfirst simulations [25]. full experimental campaigns, and thus jet performance was not yet optimized.Furthermore,we operatedwell below peak 2) Photodiode arrays: These provide measurements of powers/energiesof our capacitor banks, as we were exploring V jet . Light is collected as shown in Fig. 7; a view dump parameter space and did not wish to push the limits of our eliminatespickupofstraylightandreflections.Figure9shows systems yet. sample photodiodeand the inferredV jet values. The latter are 1) CCD-camera images: Figure 8 shows time series of determined by dividing the distance (2 cm) by the time shift intensified-CCDcameraimages(fromthesingle-frameDiCam that maximizes the correlation between the two normalized Pro)fromthree-andsix-gunexperiments,showingtheforma- photodiode signals from each gun. For the dataset presented tionof“primary”shocks(duetomergingofadjacentjets)and in Sec. III-B, V jet is generally in the range 30–45 km/s. presumed “secondary” shocks (due to subsequent merging of 3) Doppler spectroscopy: This provides ion-temperature theinitialmerged,shockedplasmas).Detailedpriordiagnostic T measurements at the shock region between two merging i studies [14], [15] of plasma jets with similar densities and plasma jets as depicted in Fig. 6(b). Figure 10(a) shows an velocities showed, through quantitative diagnostic measure- example of the data from the CCD detector. Figures 10(b) ments and analyses, that what we are calling primary shocks and 10(c) show the data, instrumental-broadeningprofile, and isconsistentwithcollisionalobliqueshocksformingalongthe the best fit to the data of a Gaussian convolved with the merge plane of adjacent jets. Primary and secondary shocks instrumental profile, for the secondary-shock and primary- SUBMITTEDTOIEEETRANS.PLASMASCI. 7 the simulation). From the synthetic data, it can be seen that chords 1 and 5 are predicted to have the highest values of hn ℓi, consistent with those chords intersecting the position e of primary shocks [see Fig. 6(a)]. Similarly, chords 3 and 7 are predicted to have the lowest values of hn ℓi, consistent e with those chords intersecting the position of jets. Two key, initial conclusions are drawn from the compari- son between experimental and synthetic interferometry data: (1) very good agreement of the order-of-magnitude of hn ℓi e gives us confidence in our knowledge of the jet parameters and leading-order accuracy of the simulations; and (2) poor agreement in the variation of hn ℓi vs. chord number is e indicative of insufficient balance (in mass and/or velocity) among jets, and thus the symmetry seen in the synthetic data (e.g., between chords 1/5, 3/7, etc.) is not reproduced in the Fig.7. Photograph showingthetwophotodiode views thatprovide precise measurementsoftheplasma-jetvelocityjustbeyondtheendofthegunnozzle. experiment. The lack of symmetry over a wide range of time The photodiode mounting structures and view dump are made from Noryl, isalsoapparentinFig.11(a).Numericalsimulationsofsix-jet chosenforitselectrical-insulation andlow-outgassing properties. experiments that incorporate unbalanced jet velocities and/or trigger times are aiding our interpretation of these data (see Sec. IV-A for further discussion). In order to improve the jet- shock views, respectively. For the cases shown in Fig. 10, to-jet balance, we plan to upgrade our GVs and have also T =6.0±0.13and4.3±0.11eVatt=42µsandR=20cm i addedtheabilitytofinetune(throughvariableresistancesand along the secondary and primary shock lines, respectively. inductances)theelectricalcharacteristicofeachofthesixGV Based on this time and viewing position, T = 6.0 eV is i transmissionlines.The newGVs(rev.10)willprovidehigher likely indicative of T of the secondary-shock plasma. We i precision and repeatability in the amount of mass injected. have also observed up to T ∼ 30 eV (for argon) at the i Varyingtheresistance/inductanceoftheGVtransmissionlines time (t ≈ 25 µs) and spatial position (R ≈ 50–60 cm) has already allowed us to tune the jet injected mass and of the primary shock, but T cools quickly (over ∼ 10 µs) i velocity,asobservedintheriseinchamberpressureaftereach by equilibrating with electrons (full results on ion shock shot, photodiode signals, and camera images. heating/dynamics for different gas species will be reported 5) Survey spectroscopy: By comparing survey- elsewhere). As discussed below in the survey-spectroscopy spectroscopy data with non-local-thermodynamic-equilibrium section, T remains much colder throughout the primary and e (non-LTE) PrismSPECT [38] spectral calculations that utilize secondary shock-formationprocess. n values consistent with interferometry data, we are able to e Measurement of ion heating as an essential property of place bounds on T and Z¯ of the observed plasma volume; e collisional plasma shocks [37] is an interesting study in its this methodology was previously described in detail [13] and own right, which we are pursuing as part of a separate applied in multiple experimental configurations [13]–[16], project on the experimental study of plasma shocks. Here, [39]. Figure 12(a) shows an example of spectra from several our interest in shock ion heating is to provide constraining viewing chords, showing that there is little variation over data in order to properly assess its role in degrading the these chords. The chords intersect the jet-propagation axes jet/liner M ∼ C s −1 ∼ (T e +T i ) −1/2. Because T e does not at approximately 14.7 cm. Figure 12(b) shows an example increase much throughout the jet-merging process [15], [16] of a comparison between data and spectral calculations, (also see survey-spectroscopy results below) due to strong showing good agreement for a calculation that assumes thermal and radiative loss rates, ion heating dominatesthe M n = 1015 cm−3 and T = 1.6 eV (for which Z¯ = 0.99). e e degradation.The latter would lead to stronger liner spreading On the other hand, for calculations assuming T ≤ 1.5 eV e andis predictedto seriouslydegradethe ability of the liner to or T ≥ 1.9 eV, the agreement between the spectral data e compressamagnetizedtargetplasmatoreactor-relevantfusion and PrismSPECT calculations becomes dramatically worse, conditions[34].Ongoingresearchusingtwo-temperature(2T) implying that 1.5 < T < 1.9 over a large spatial area and e hydrodynamic simulations (see Sec. IV-A) is investigating time range for the merging plasma jets. the role of ion shock heating on plasma-liner formation, convergence,and performance. IV. NUMERICAL MODELING 4) Multi-chord interferometry: Multi-chord interferometry Inthissection,weprovideabriefoverviewofthemodeling is used to measure hn ℓi and to assess its variation across the e research in support of the PLX-α project. However, detailed spatial arc of the interferometer chords shown in Fig. 6(a). modeling results will be reported elsewhere. Figure 11(a) shows an example of hn ℓi for each of the e seven chords vs. time. Figure 11(b) shows a comparison A. Plasma-liner formation and convergence between hn ℓi (t = 36 µs, averaged over shots 1019–1032) e and synthetic data from a 3D hydrodynamic simulation of Weusetwo3Dhydrodynamiccodestosimulatejetmerging the six-gun experiment (see Sec. IV-A for a description of (two, three, and six guns) and spherical (4π) plasma-liner SUBMITTEDTOIEEETRANS.PLASMASCI. 8 Fig. 8. Intensified-CCD camera images (10-ns exposure, logarithm ofintensity, false color, cropped to1280×850 pixels each) showing the evolution of (a)–(d)3-gun(shots1064,1066,1061,1069)and(e)–(h)6-gunexperiments(shots1007,1038,1041,1043).Aslabelledinthe3-gunimagesequence,primary shocks(b)formalongthemergeplaneofadjacent jets,and(presumed)secondaryshocks(d)formduetosubsequentmergingoftheprimary-shockplasmas. SUBMITTEDTOIEEETRANS.PLASMASCI. 9 Fig.9. (a)Samplephotodiodesignals vs.timefromthreeguns.Foreachgun,photodiodeviewingchordsarespaced2cmapartandorientedtransverseto thedirection ofjetpropagation (seeFig.7).(b)InferredVjet foranensembleofshotsattwogunchargevoltages (4and5kV). formation and convergence(18–600 guns). The former are in The4π simulations(withuptoN =600jets)havefocused supportofourongoingexperiments(studyingshockdynamics onstudiesoflineruniformityandram-pressure(ρv2)evolution between mergingjets and/or forming a section of a liner with as the liner forms and converges radially toward stagnation. six jets). The latter are to guide our preparation for planned For N ≤ 60, the simulations directly inform planned PLX-α 4π experiments over the next two years. experiments,whichaimtoform4π implodinglinerswith36– 60 jets and ∼ 100–150 kJ of total liner kinetic energy, and The two 3D codes being used are SPFMax [40], a predict peak ρv2 ∼ 50 kbar. For N > 60, the simulations smoothed-particle-hydrodynamic code, and FronTier [41], a are assessing the jet and uniformity requirements to achieve hydrodynamiccodewithfronttracking.AspartofthePLX-α fusion-relevantconditions, requiring total liner kinetic energy project, we have performed significant benchmarking of the of &30 MJ and peak ρv2 &150 Mbar [3], [34]. codes against jet-merging experimental results, and we have added physics capabilities to the codes, including Braginskii thermal transport and viscosity [42], optically thin radiation B. Plasma-liner compression of a magnetized target loss, advanced equation-of-state (EOS) table lookup (using A separate modeling task is studying plasma-liner com- custom-generated non-LTE PROPACEOS tables [43] from pression of a magnetized target in 1D and 2D, using the Prism Computational Sciences), and 2T (i.e., separate T i and multi-fluid magnetohydrodynamic (MHD) code USim [45]. T e evolution) modeling. A major purpose of this task is to identify and optimize SPFMaxandFronTierhavebeenusedtosimulatethree-and PJMIF configurations with energy gain, guided by the results six-jet merging to guide diagnostics setup, generate synthetic of [3], [34]. New physicscapabilitieshavealso beenaddedto data [see Fig. 11(b)] for comparisons to the diagnostic data, USim as part of the PLX-α project, including optically thin andaideourunderstandingofthecomparisons.Forgenerating radiation loss, non-LTE tabular EOS table lookup (also using the synthetic data in Fig. 11(b), we ran SPFMax using the PROPACEOS tables [43]), Braginskii viscosity [42], and α- six-gun setup of Fig. 6(a) with the following initial argon- particle energy deposition based on the model implemented jet parameters: velocity of 35.8 km/s, T = T = 2.5 eV, in [34]. A second important purpose of this task is to assess i e ion density n = 3.17 × 1016 cm−3, diameter of 8.5 cm, and understand the degradation of energy gain in going from i length of 10 cm, and leading edge of the jets at R=130 cm. 1D to 2D, and to examine the further degradation of energy The simulation included non-LTE argon EOS, single-group gain when nonuniformities (based on the work described in opacity, 2T, and ion and electron thermal conduction. To Sec. IV-A) are imposed on the liner/target interface, which help understand the disagreement between the experimen- exacerbate Rayleigh-Taylor instabilities at the stagnating in- tal and synthetic interferometry seen in Fig. 11(b), we ran terface. Indeed, one specific objective of this task is to set six-jet FronTier simulations that included random variations requirements on the liner uniformity for PJMIF to remain among jet velocities (up to 10%) and/or trigger times (up viable as a fusion-energy concept. to 1 µs); these results show that the symmetry of primary- and secondary-shockformationis indeed drastically degraded V. SUMMARY AND PLANS compared to the case with identical jet velocities/timings We have described an experiment to form and character- (further motivating our ongoing efforts to improve the jet-to- ize a section of a spherically imploding plasma liner, as a jet balance). We also plan to use VISRAD [44] to generate development step toward PJMIF [1], [2]. This work is the synthetic spectral data to compare with spectroscopy data. first phase of the ARPA-E-sponsored PLX-α project, which SUBMITTEDTOIEEETRANS.PLASMASCI. 10 Fig. 11. (a) Line-integrated electron density hneℓi vs. time (shot 1008) frommulti-chordinterferometry[basedonthesetupofFig.6(a)].“Regionof interest” refers to the approximate time duration whenjets merge toform a liner section. (b) Data points are hneℓi (t = 36 µs, averaged over shots 1019–1032) vs. chord number; error bars are the standard deviation over theshotrange. Thebars aresynthetic data from3DSPFMaxhydrodynamic simulations ofthesix-gunexperiments (seeSec.IV-A). Fig. 10. (a) High-resolution-spectroscopy data (shot 1083, 1-µs exposure) showing two views of a singly ionized argon spectral line, corresponding tothe R=20-cm positions showninFig. 6(b). Thevertical and horizontal axesrepresenttheheightofthespectrometerslitandwavelength,respectively. (b)Verticallyintegratedsignal(arb.)vs.wavelength(centeredat480.602nm) for the secondary-shock-line view (Ti = 6.0±0.13 eV) and (c) primary- shock-line view (Ti =4.3±0.11eV),from(a).TheerrorquotedforTi is thecurve-fitting errorassumingPoissonweighting ofthespectral data. aims to culminate with the formation and study of a spheri- Fig.12. (a)Visiblesurveyspectra(t=38µs,2-µsexposure)vs.wavelength cally imploding plasma liner (as a standoff MIF compression forviews corresponding tointerferometer chords2–6[seeFig.6(a)]forsix- driver)formedby merging36–60supersonic plasma jets. The gun argon experiments. (b) Comparison of survey-spectrometer data (t = latter are launched by newly developed coaxial plasma guns 1 3 0 2 1 µ 5 s, cm 2- − µs 3 e a x n p d os T u e re = )a 1 n . d 6 a e P V r . ismSPECTspectralcalculationassumingne= fabricatedbyHyperVTechnologiesCorp.(nowownedbynew fusion startup HyperJet Fusion Corporation). ThispaperreportskeyearlyresultsfromthePLX-αproject: survey spectroscopy, hi-resolution spectroscopy, and multi- (1) design and operation of the new HyperV coaxial plasma chord interferometry),and (4) diagnostic results showing that guns and characterization of plasma-jet parameters, (2) com- the key potentially deleterious physics issues associated with pletion of the PLX facility/diagnostic upgrades for six-gun jet merging(e.g., ion shock heating leading to Mach-number- experiments,(3)successfuloperationofuptosixplasmaguns degradation and the seeding of nonuniformities that may andkeydiagnostics(photodiodearrays,fastimagingcameras, exacerbate deceleration-phase instabilities of the liner/target SUBMITTEDTOIEEETRANS.PLASMASCI. 11 interface in future target-compression experiments) can now [9] F. D. Witherspoon, S. Brockington, A. Case, S. J. Messer, L. Wu, bestudiedin a seriousmanner;thesestudiesareongoing,and R.Elton,S.C.Hsu,J.T.Cassibry,andM.A.Gilmore,“Development of MiniRailguns for the Plasma Liner Experiment,” Bull. Amer. Phys. further details and conclusions will be reported elsewhere. Soc.,vol.56,p.311,2011. Ongoing three- and six-jet experiments are providing com- [10] S. Brockington, A. Case, S. Messer, L. Wu, and F. D. Witherspoon, prehensivedatasetsonionshockheatingforseveralplasma-jet “TheHyperV 8000 µg,50 km/splasma railgun forPLX,”Bull. Amer. Phys.Soc.,vol.57,p.134,2012. species (H, He, N, Ne, Ar, Kr, Xe) and two different jet- [11] A. Case, S. Messer, S. Brockington, L. Wu, F. D. Witherspoon, and merging angles. Upon installation of improved gas valves, R. Elton, “Merging of high speed argon plasma jets,” Phys. Plasmas, which are expected to improve the jet-to-jet balance, we vol.20,no.1,2013. [12] S. Messer, A. Case, L. Wu, S. Brockington, and F. D. Witherspoon, will then focus on obtaining more interferometry data to “Nonlinear compressions in merging plasma jets,” Phys. Plasmas, better assess the uniformity of the liner section formed by vol.20,no.3,2013. merging six jets [i.e., the setup shown in Fig. 6(a)]. Finally, [13] S.C.Hsu,E.C.Merritt,A.L.Moser,T.J.Awe,S.J.E.Brockington, J. S. Davis, C. S. Adams, A. Case, J. T. Cassibry, J. P. Dunn, M. A. we are incorporating a number of engineering improvements Gilmore,A.G.Lynn,S.J.Messer,andF.D.Witherspoon,“Experimen- to the coaxial plasma guns to maximize both the assem- tal characterization of railgun-driven supersonic plasma jets motivated bly/operationalefficiencyandquality/quantityofexperimental byhighenergydensityphysicsapplications,”Phys.Plasmas,vol.19,p. 123514,2012. data for planned experiments with 36–60 guns to form 4π [14] E. C. Merritt, A. L. Moser, S. C. Hsu, J. Loverich, and M. Gilmore, sphericallyimplodingplasmaliners(overthe nexttwo years). “Experimental characterization of the stagnation layer between two These experimentswillprovidecriticaldata on the magnitude obliquelymergingsupersonicplasmajets,”Phys.Rev.Lett.,vol.111,p. 085003,2013. and evolution of liner nonuniformityand ram pressure during [15] E. C. Merritt, A. L. Moser, S. C. Hsu, C. S. Adams, J. P. Dunn, radial convergence, to allow continued technical assessment A. Miguel Holgado, and M. A. Gilmore, “Experimental evidence for and development of the PJMIF concept. collisionalshockformationviatwoobliquelymergingsupersonicplasma jets,”Phys.Plasmas,vol.21,p.055703,2014. [16] A. L. Moser and S. C. Hsu, “Experimental characterization of a ACKNOWLEDGMENTS transition fromcollisionless tocollisional interaction between head-on- merging supersonic plasma jets,” Phys. Plasmas, vol. 22, p. 055707, The authors thank R. Aragonez, R. Martinez (dec.), 2015. J. Vaughan,and M. Lunafor valuabletechnicalcontributions, [17] J.LoverichandA.Hakim,“Two-dimensionalmodelingofidealmerging plasmajets,”J.FusionEnergy,vol.29,p.532,2010. and Dr. G. Wurden for loaning numerous items of diagnostic [18] J. T. Cassibry, R. J. Cortez, S. C. Hsu, and F. D. Witherspoon, hardware.SectionIIIofthispapersummarizestheinvitedtalk “Estimatesofconfinementtimeandenergygainforplasmalinerdriven byS.HsuandpostersbyS.LangendorfandK.Yatesthatwere magnetoinertial fusion using an analytic self-similar converging shock model,”Phys.Plasmas,vol.16,p.112707,2009. presented at the International Conference on Plasma Science [19] R. Samulyak, P. Parks, and L. Wu, “Spherically symmetric simulation (ICOPS) in Atlantic City, NJ, May 22–25, 2017. This work ofplasmalinerdriven magnetoinertial fusion,”Phys.Plasmas,vol.17, was supported by the Advanced Research Projects Agency– p.092702,2010. [20] T.J.Awe,C.S.Adams,J.S.Davis,D.S.Hanna,S.C.Hsu,andJ.T. Energy (ARPA-E) of the U.S. Department of Energy (DOE). 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