Beg, F.N.

Casey, D.T.

Frenje, J.

Li, C.K.

Manuel, M.J.

Petrasso, R.D.

Rinderknecht, H.G.

Seguin, F.H.

Sinenian, N.

Zylstra, A.B.

DSpace@MIT

                        March, 2012  Plasma Science and Fusion Center Massachusetts Institute of Technology Cambridge  MA  02139  USA             The work de- scribed here was done as part of the first author’s PhD thesis and supported in part by NLUF/DOE (Grant No. DE-FG03-03SF22691), FSC/DOE (Grant No. DE- FC02-04ER54789), LLE (No. 412160-001G), LLNL (No. B504974), and GA under DOE (DE-AC52-06NA27279). Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.  PSFC/JA-12-3   Mapping Return Currents  in Laser-generated Z-pinch Plasmas  M. J.-E. Manuel, N. Sinenian, F. H. S ́eguin, C. K. Li,  J. Frenje, H. G. Rinderknecht, D. T. Casey, A. B. Zylstra, and R. D. Petrasso  Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA   F. N. Beg  Department of Mechanical and Aerospace Engineering, UC, San Diego, CAM. J.-E. Manuel - APL - Mapping Stalk FieldsMapping Return Currents in Laser-generated Z-pinch PlasmasM. J.-E. Manuel, N. Sinenian, F. H. Se´guin, C. K. Li, J. Frenje, H. G. Rinderknecht, D. T. Casey, A. B. Zylstra,R. D. PetrassoPlasma Science and Fusion Center, MIT, Cambridge, MAF. N. BegDepartment of Mechanical and Aerospace Engineering, UC, San Diego, CA(Dated: 27 March 2012)Dynamic return currents and electromagnetic field structure in laser-generated Z-pinch plasmas have beenmeasured using proton deflectometry. Experiments were modeled to accurately interpret deflections observedin proton radiographs. Current flow is shown to begin on axis and migrate outwards with the expandingcoronal plasma. Magnetic field strengths of ∼1 T are generated by currents that increase from ∼2 kA to∼7 kA over the course of the laser pulse. Proton deflectometry is demonstrated to be a practical alternativeto other magnetic field diagnostics for these types of plasmas.PACS numbers: 52.70.-m, 52.50.Jm, 52.59.QyKeywords: proton radiography, return current, Z-pinchThere has been significant effort made to measurespatial distributions of current and magnetic fields inZ-pinch plasmas1–3. Conventional techniques, namelyFaraday rotation and B-dot probes, have limitations aswire Z-pinch plasmas have very high density in the coreand significant density and temperature gradients in thecoronal plasma. Proton deflectometry can provide infor-mation about current strength as well as magnetic fieldtopology in these plasmas.In this letter, the first spatially resolved measurementsof dynamic currents in Z-pinch plasmas have been madeusing monoenergetic proton deflectometry. Plasma is cre-ated by large return currents4 driven through the sup-porting stalk structure of laser-irradiated targets. Thestalk ablates due to ohmic heating and a Z-pinch plasmaforms with an azimuthal, self-generated magnetic field.The laser interaction with the target produces a positivepotential5 on the target assembly, resulting in a radialelectric field on the stalk. The strength and location ofthese electromagnetic fields has been determined usingmonoenergetic proton deflectometry.Experiments were performed at the OMEGA6 laser fa-cility using the configuration shown in Figure 1a. A thin-glass capsule filled with equimolar D3He gas was drivenby 20 beams to produce fusion protons. This implosiongenerates monoenergetic DD and D3He fusion protons ina quasi-isotropic manner as demonstrated7–10 in manyexperiments. The fusion burn region has an approx-imately Gaussian radial profile with a FWHM of ∼45µm7 and a burn duration of ∼150 ps. Only DD protonswere used in these experiments and a sample spectrum isshown in Figure 1b. An upshift in energy is observed dueto the positive potential11,12 on the backlighter capsuleduring proton production. A detailed schematic of thetarget assembly is shown in Figure 1c with typical dimen-sions and materials listed. The resultant Z-pinch plasmawas radiographed on a CR-39 plastic nuclear track de-tector. Proton fluence and relative energy images weregenerated from processed13,14 CR-39 samples.0.0 0.2 0.4 0.6 0.8 0 1 2 3 4 5 Yield/MeV Energy [MeV] DD (b) ×109 L~35 mm OD~145 µm L~8 mm  OD~145 µm L~13 mm  OD~82 µm L~1 mm  OD~17 µm (c) FoV S1 (Boron) S2 (Boron) S3 (SiC) S4 (SiC) DD Protons 1.39 cm CR-39 21 cm θ I (a) ϕ FIG. 1. (a) Experimental geometry. The stalk symmetryaxis makes an angle θ≈39.4◦ with the imaging axis which isnecessary for net deflections due to B fields. Residual positivecharge on the target creates a potential φ that drives a currentI up the stalk. (b) Sample fusion proton spectrum. (c) Anexpanded view of the stalk assembly holding the target (notto scale). Approximate lengths (L) and outer diameters (OD)are listed for the Boron (B) and Silicon-Carbide (SiC) fibercomponents. The approximate field of view is indicated bythe dashed circle.The experimental geometry was modeled using theGeant415,16 framework to accurately interpret proton ra-diographs. Two sample synthetic radiographs are illus-trated in Figure 2a. The first case is a simple 140 µmdiameter boron stalk with no fields. The stalk stopsand scatters DD protons as demonstrated by the white‘shadow’ in the <N> image. The second Geant4 simula-tion example presented in Figure 2a has implemented ax-isymmetric E and B fields. A constant current I and lin-ear charge density λ are distributed uniformly within sep-arate cylindrical annuli around the cold stalk. This modelapproximates a situation where the current preferentiallyflows in the expanding hot plasma, due to lower resistiv-ity, and the positive potential manifests as a charge im-M. J.-E. Manuel - APL - Mapping Stalk Fields 2(a) Fluence  [µm-1] Energy [MeV] High 0 ≤3.0 ≥3.5 I  = 7 kA       λ = 1.3 µC/m  I  = 0 kA λ = 0 µC/m ~3.7 mm 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.6 1.2 1.8 Normalized Fluence Radius [mm] (b) RB RE halo shadow valley WB WE FIG. 2. (a) Synthetic proton radiographs. E and B fieldsare defined by a linear charge density λ and current I, re-spectively. (b) Fluence lineouts, indicated by arrows, of thesecond case in a). The mean radii of distributed λ (RE) andI (RB) are shown and the widths (WE and WB) of the cylin-drical annuli indicated by dotted lines. Qualitative lineoutfeatures are labeled.balance. A total of six parameters characterize simulatedB and E fields: the current I and charge density λ; themean radii of each annulus, RB and RE ; the correspond-ing widths, WB and WE . Assuming an axisymmetricstructure, E fields are directed radially outward and Bfields are azimuthal around the stalk and vary only asa function of radius. These independently defined pa-rameters determine the appearance of resultant protonradiographs in a specified geometry.In Figure 2b two fluence lineouts are shown from differ-ent positions along the stalk axis (indicated by arrows).In this simulation I=7 kA, λ=1.3 µC/m and spatial pa-rameters were set as follows: RB=675 µm, RE=250 µm,WB=350 µm, and WE=100 µm. An asymmetry is ob-served due to the differing optical characteristics at loca-tions along the stalk. However, in many cases the qual-itative features labeled in Figure 2b may be intuitivelyexplained by the parameters defined in the simulation.Because the angle (θ) is not 90◦, focusing optics varyalong the stalk. Furthermore, to observe a net deflec-tion due to azimuthal B fields the angle θ must be <90◦.With the current directed away from the target, resultantB fields act to focus protons towards the stalk generatingthe halo, whereas the positive potential generates electricfields which deflect protons away from the stalk and pro-duce the valley. The precise development of the halo andvalley, however, is a result of the combined forces of bothB and E fields. For this reason, the relative positionsand magnitudes of these forces−as defined by the six in-put parameters−determine the characteristic features ofproton radiographs in a truly coupled manner.Target stalks were imaged at four different times rela-tive to the onset of the laser drive as indicated (•) in Fig-ure 3a. Both fluence <N> and energy <E> images weregenerated from DD-proton radiographs and are shownfor each sampled time in Figure 3b. In fluence images,darker pixels indicate higher fluence and in energy im-ages, darker pixels indicate lower energy. Because elec-(b) Shot: 51246  1.9 ns 51244  1.1 ns 51247  2.4 ns 51250  3.4 ns <N> <E> 0 0.5 1 1.5 2 2.5 3 3.5 Time [ns] I=1×1014 W/cm2 I=4×1014 W/cm2 (a) FIG. 3. (a) The picketed laser pulse used on 35 µm thick CHshells. Proton arrival times are shown by points lying on thetime axis. (b) Proton fluence radiographs <N> taken at fourtimes relative to the laser drive where darker pixels designatehigher fluence. The corresponding mean energy images <E>are also shown where darker pixels indicate lower energy.trons are leaving the target, a residual positive chargeis left on the target and stalk with a return current di-rected as illustrated in Figure 1a. During the pulse, pos-itive charge accumulates and the position and strengthof the return current evolves. In some cases, the S3(SiC) segment of the stalk is not visible, so discussionis limited to the S2 (B) segment in the top of the im-ages (chamber-side). Similar features are observed at thebottom (target-side) of the stalk, though the diameter,material, and optical characteristics are different.Proton fluence images reveal dynamic E and B fieldstructure over the duration of the laser pulse. The firstimage in Figure 3b at 1.1 ns shows no sign of the stalkshadow, but a fluence enhancement is observed in itsplace. This is caused by the return current flowing nearthe stalk surface, focusing protons to where the shadowwould have been. By 1.9 ns, the valley and the halohave become well formed. At 2.4 ns, the stalk shadowhas become clearly visible and all of the current flowsin the coronal plasma. After the laser pulse has turnedoff, a strong positive charge and return current are stillprevalent. In the last two radiographs, some instabilitiesare observed jetting out from the stalk; these stochasticfeatures are not modeled.An iterative procedure was implemented to infer thelocation and strength of return currents and residual pos-itive charge. The amplitude of features observed in flu-ence images is directly related to the magnitudes of thecurrent (I) and charge density (λ) through complex elec-tromagnetic optics, though the location and shape arestrongly coupled to all parameters. Therefore, a uniquesolution may be found by achieving reasonable agreementbetween experimental and synthetic radiographs in theM. J.-E. Manuel - APL - Mapping Stalk Fields 30 250 500 750 1000 1250 1.0 1.5 2.0 2.5 3.0 3.5 Location [µm] RB RE (a) 0 2 4 6 8 1.0 1.5 2.0 2.5 3.0 3.5 Current (I) [kA] Charge (λ) [µC/m] Time [ns] I λ (c) 0 20 40 60 80 0 2 4 6 8 1.0 1.5 2.0 2.5 3.0 3.5 Emax [MV/m] Bmax [T] Time [ns] (d) 0.01 0.1 1 10 0.0 0.5 1.0 1.5 2.0 1.0 1.5 2.0 2.5 3.0 3.5 Resistance [Ω/m] Inductance [µH/m] (b) FIG. 4. (a) Location and width of cylindrical annuli for cur-rents and net charge plotted versus time. (b) Estimated in-ductance and resistance per unit length. (c) Inferred current Iand charge density λ. (d) Corresponding peak field strengths.specified geometry.Uncertainties in measurements are estimated based onthe sensitivity of synthetic data to variations in inputparameters and the variation of experimental data dueto different analysis parameters (i.e. lineout width andlocation). Non-axisymmetric behavior observed in ex-perimental data also contributes some uncertainty to theinferred measurement, but those areas are not used incomparisons with synthetic radiographs. Taking thesesources of error into consideration, constant error barsare conservatively estimated to be ±0.5 kA and ±0.3µC/m for the current and charge density respectively.Uncertainties in spatial parameters RB/E and WB/E arenot shown in plots, but are estimated to be ±50 µm.Measurements of current dynamics are illustrated inFigure 4a. The current annuli, characterized by RB andWB , were used to calculated the inductance and resis-tance per unit length, and are shown in Figure 4b as afunction of time. To estimate resistivity, the Spitzer form(η ∝ T−3/2e ) was assumed for a coronal Boron plasmawith Te∼1 keV. It is important to note the low effec-tive resistivity per unit length of the plasma ∼0.1 Ω/m,as compared to the room temperature measurements of∼108 Ω/m for the Boron fiber. From these calculations,an estimated time constant (τ∼L/R) was found to in-crease from ∼0.2 µs to ∼20 µs. This variability is domi-nated by the changing resistance of the current carryingplasma. Moreover, these time scales are much longerthan any relevant plasma time scales (∼ns), indicatingthat the current will remain well after the ∼3 ns laserpulse. Although, as the plasma expands and cools, theresistance will increase and the effective decay time de-crease, though this does not occur during the sampledtime.Measurements of I and λ are shown in Figure 4c.Charge accumulation increases in time eventually flatten-ing out around ∼1.3 µC/m at 1.9 ns. Furthermore, theresultant return current increases from ∼2 kA to ∼7 kAat 2.4 ns and slightly decays a few hundred ps after thelaser turns off. The current begins near the stalk surfaceand then preferentially flows outward with the expand-ing coronal plasma due to the reduced resistivity. Peakmagnetic field magnitudes were found to decrease sharplyfrom ∼4 T to ∼1 T and remained approximately constantthroughout the sampled times.In summary, the first measurements of the dynamic lo-cation of current flow in laser-generated Z-pinch plasmashave been made. The feasibility of using proton deflec-tometry to map electric and magnetic field evolution in a‘single wire’-style Z-pinch configuration has been demon-strated. The skewed angle of the stalk allowed protonsto be sensitive to both self-generated electric and mag-netic fields. For currents of a few kA, ∼3 MeV protonsprovided a reasonable amount of deflection without leav-ing the field of view. If larger currents were present,higher energy protons would be needed to properly mapthe field evolution. The model discussed provided an ab-solute measure of current and charge accumulation whilecapturing the important effects on proton deflections. Inthese experiments, return currents were measured andfound to increase from ∼2 kA to ∼7 kA during a pick-eted laser pulse. Observations made herein motivate fur-ther investigation of dynamic current flow measurementsin larger machines, such as the Z-Accelerator. Further-more, short-pulse proton radiography with Z-Beamletcould provide high temporal and spatial resolution of fieldstructure in advanced pinch configurations at Z.ACKNOWLEDGMENTSThe authors would like to express their gratitude tothe engineering staff at LLE for their support. The workdescribed here was done as part of the first author’sPhD thesis and supported in part by NLUF/DOE (GrantNo. DE-FG03-03SF22691), FSC/DOE (Grant No. DE-FC02-04ER54789), LLE (No. 412160-001G), LLNL (No.B504974), and GA under DOE (DE-AC52-06NA27279).1F. N. Beg, et al. Plas. Phys. Cont. Fus., 39 (1997).2S. N. Bland, et al. Rev. Sci. Instrum., 77, 10E315 (2006).3V. V. Ivanov, et al. Phys. Rev. Lett., 97, 125001 (2006). PRL.4R. F. Benjamin, et al. Physical Review Letters, 42, 890 (1979).5J. S. Pearlman et al. Applied Physics Letters, 31, 414 (1977).6T. R. Boehly, et al. Optics Communications, 133, 495 (1997).7C. K. Li, et al. Phys Rev Lett, 97, 135003 (2006).8J. R. Rygg, et al. Science, 319, 1223 (2008).9C. K. Li, et al. Science, 327, 1231 (2010).10F. H. Seguin, et al. Physics of Plasmas, 19 (2012).11D. G. Hicks, et al. Physics of Plasmas, 7, 5106 (2000).12F. H. Se´guin, et al. Rev Sci Inst, 74, 975 (2003).13M. J. Manuel. Rev. Sci. Instrum., 82, 095110 (2011).14N. Sinenian, et al. Rev. of Sci. Instrum., 82, 7 (2011).15S. Agostinelli, et al. Nuc Inst Meth A, 506, 250 (2003).16J. Allison, et al. IEEE Trans Nuc Sci, 53, 270 (2006).

Mapping Return Currents in Laser-generated Z-pinch Plasmas

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Mapping Return Currents in Laser-generated Z-pinch Plasmas

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