September, 2012

Plasma Science and Fusion Center Massachusetts Institute of Technology

Cambridge MA 02139 USA This work was supported by the U.S. Department of Energy, Grant No. DE-FG52-09NA29553, NLUF, Grant No. DE-NA0000877, LLE, Grant No. 414-090-G, and LLNL, Grant No. B580243. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted. Submitted for publication to Physical Review E.

PSFC/JA-12-29

Characterization of single and colliding laser-produced plasma bubbles using Thomson scattering

and proton radiography

Rosenberg, M. J., Ross, J. S.*, Li, C. K., Town. R. P. J.*, Seguin, F. H., Frenje, J. A., Froula, D. H.**, Petrasso, R. D.

* Lawrence Livermore National Laboratory, Livermore, CA ** Laboratory for Laser Energetics, University of Rochester, Rochester, NY

Characterization of single and colliding laser-produced plasma bubbles using Thomsonscattering and proton radiography

M. J. Rosenberg,1, ∗ J. S. Ross,2 C. K. Li,1 R. P. J. Town,2 F.

H. Seguin,1 J. A. Frenje,1 D. H. Froula,3 and R. D. Petrasso1

1Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA2Lawrence Livermore National Laboratory, Livermore, CA 94550, USA

3Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14623, USA(Dated: September 17, 2012)

Time-resolved measurements of electron and ion temperature using Thomson scattering havebeen combined with proton radiography data for comprehensive characterization of individual laser-produced plasma bubbles or the interaction of bubble pairs, where reconnection of azimuthal mag-netic fields occurs. Measurements of ion and electron temperatures agree with lasnex simulationsof single plasma bubbles, which include the physics of magnetic fields. There is negligible differencein temperatures between a single plasma bubble and the interaction region of bubble pairs, thoughthe ion temperature may be slightly higher due to the collision of expanding plasmas. These resultsare consistent with reconnection in a β∼8 plasma, where the release of magnetic energy (<5% ofelectron thermal energy) does not appreciably affect the hydrodynamics.

PACS numbers: 52.50.Jm, 52.35.Vd, 52.38.Fz, 52.70.Kz

I. INTRODUCTION

Characterization of laser-produced plasmas is impor-tant in a variety of experiments relevant to both inertialconfinement fusion and basic plasma physics, where mea-surements of the temperature and magnetic field evolu-tion are critical to understanding the plasma dynamics[1–4]. Such plasmas are especially relevant in indirect-drive inertial confinement fusion, where multiple lasersirradiate the inside of a cylindrical hohlraum [5]. Pre-viously, Thomson scattering [6] has been used to diag-nose the temperature evolution of laser-produced plas-mas, both in indirect-drive hohlraums [7] and in planarlaser-foil experiments [8, 9].

One particular scientific application of laser-foil inter-actions is the study of self-generated azimuthal magneticfields around laser-produced expanding, hemisphericalplasma bubbles [10, 11] and their reconnection. Mag-netic reconnection [12] has been explored traditionally inthe context of astrophysical plasmas [13, 14] or in thelaboratory with plasmas at low density (∼1014 cm−3)and low plasma β, the ratio of thermal energy densityto magnetic energy density (∼0.01-0.1) [15, 16]. Re-cent experiments have assessed the evolution and re-connnection of magnetic fields in the high-energy-densityregime [17, 18], through the interaction of multiple laser-produced plasma bubbles [9, 19–23]. Several of theseexperiments have utilized the proton radiography tech-nique [24] to probe these laser-produced plasma bubbles,producing quantitative data on the strength of laser-generated magnetic fields [9, 19–22]. Though some mea-surements of electron and ion temperature have beenmade in these experiments [9], a comprehensive, time-

∗ mrosenbe@mit.edu

resolved set of measurements has yet to be published.In this study, Thomson-scattering measurements have

been used to characterize the temperature evolutionat different times and locations in the laser-producedplasma bubbles and in the interaction region of bubblepairs. The data offers a comprehensive, time-resolved setof measurements of local electron and ion temperaturesin single and interacting laser-produced plasma bubbles,in conjunction with proton radiography data used to infermagnetic fields. Measurements of electron and ion tem-peratures in the reconnection region of laser-generatedmagnetic fields provide unique information on the tem-perature evolution in a high-β reconnection event. Byjuxtaposing temperature data in the reconnection regionto comparable data in the single bubble experiment, itis possible to infer the role of magnetic reconnection andthe hydrodynamic collision of the two bubbles in shapingthe thermal properties of the plasma.

This paper is organized as follows: Section II describesthe experiments and measurement techniques; Section IIIcontrasts experimental and modeled results; Section IVdiscusses the findings; and Section V presents concludingremarks.

II. EXPERIMENTS

Laser-foil experiments were conducted at the OMEGAlaser facility [25]. In each experiment, a 5-µm CH foilwas irradiated by one or two 351 nm (3ω) beams in a 1-ns pulse with 500 J/beam and SG4 phase plates, produc-ing an 800 µm spot size with a 4th-order supergaussianprofile [26]. For the dual-beam reconnection experiments,laser spots were separated by 1.2-1.4 mm. In separate ex-periments, monoenergetic proton radiography data [27]and 4ω Thomson scattering data [28] were obtained forthe single or pair of laser-foil interactions. These experi-

2

ments provide complementary information on the evolu-tion of magnetic fields and ion and electron temperaturesboth in laser-produced plasma bubbles and in the mag-netic reconnection of bubble pairs.

46929

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z

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z

r

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optics

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pro

be b

eam

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k4ω

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ka

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FIG. 1. Experimental setup for the Thomson-scattering ex-periments (a). In these experiments, the Thomson-scatteringprobe beam was incident at a 79◦ angle relative to the foilnormal (z-axis), nearly parallel to the foil surface, while thedetector was at 37◦ to the normal, such that the scatteringangle was 63◦ and the scattering vector 21◦ to the foil normal.Locations probed are shown for (b) single bubble experimentsand (c) reconnection experiments.

The setup for the Thomson-scattering experiments isshown in Figure 1. The Thomson-scattering techniqueutilizes a frequency-quadrupled (263.5 nm) probe beamand a streaked detector system for time-resolved mea-surements of the scattered light spectrum, from whichelectron and ion temperature histories are inferred forthe laser-produced plasma [28]. On different shots, theprobe beam was focused onto three different locations ineach of the (b) single bubble and (c) interacting bubblegeometry. The Thomson-scattering volume can be de-scribed as a cylinder approximately 60 µm in diameterand ∼75 µm in length, providing a local measurement ofthe plasma conditions [28].

From the spectrum of light scattered by ion-acousticfluctuations the electron and ion temperature can be de-termined [6]. To first order, the electron temperatureis proportional to the square of the wavelength shift ofthe probe beam; the spectral shape of ion-acoustic fea-

tures is sensitive also to the ion temperature [7]. Theelectron density can also be inferred from the absolutemagnitude of the scattered light spectrum, but densitymeasurements were not obtained in this study.

(a)

Backlighter

Backlighter

drive beams

Mesh grid

CH foil CR-39

Protons

Interaction beam

(b)

Backlighter

Backlighter

drive beams

CR-39

Protons

Interaction beam

Interaction beam

FIG. 2. Proton radiography setup for (a) the single bub-ble experiments and (b) the reconnection experiments. Thedistance between the backlighter and the CH foil is 15 mm,while the distance between the mesh grid and the foil is 2mm. These experiments, the first using this configuration,were originally reported by Li et al. [19, 20].

The proton radiography setup is shown in Figure 2for both (a) the single laser-foil experiments and (b)the dual laser-foil (reconnection) experiments. A D3He-filled, thin-glass-shell backlighter was illuminated by 20OMEGA beams, delivering 8.5 kJ in a 1-ns pulse andproducing monoenergetic 3- and 15-MeV protons fromrespective DD and D3He fusion reactions. These back-lighter protons were divided by a mesh grid into discretebeamlets before sampling the laser-produced CH plasma.The proton beamlets were then deflected by magneticfields surrounding the plasma plasma bubbles and theirpositions were recorded using the solid-state nucleartrack detector CR-39. Given the known proton energy asmeasured by proton spectrometers [29], the measured de-flection of each beamlet was used to infer quantitativelythe path-integrated magnetic field strength through theplasma. The absolute timing of the proton arrival atthe plasma was determined by the proton temporal di-agnostic (PTD) [30], which measures the time of protonemission from the backlighter. These experiments weredescribed originally by Li et al. for single laser-producedplasma bubbles [19] and for the interaction of multiplebubbles [20]. Though the Thomson-scattering measure-

3

ments and the proton radiography data were obtainedon different shots, the experiments used comparable laserand target parameters.

III. RESULTS

Images of both individual and interacting plasma bub-bles, using 15-MeV protons, are shown in Figure 3.These images, which have been published previously, re-veal the evolution and reconnection of magnetic fieldsaround laser-produced plasma bubbles [19, 20]. The pub-lished images are used here to illustrate the location ofThomson-scattering regions in the nearly identical ex-periments conducted in this work. In the single bubbleimages (Figure 3a), Thomson scattering regions are lo-cated either at the center of the bubble (red star, r=0,z=450 and 1000 µm) or towards the bubble edge (greentriangle, r=600 µm, z=450 µm). The approximate bub-ble size (yellow circle) is shown to illustrate the locationof the bubble perimeter relative to the outer Thomson-scattering region. Note that the bubble edge is not thelocation of beamlet pileup, since that feature is the re-sult of proton deflection and does not represent the ac-tual radius of the bubble. The sample times indicatedfor the proton radiography images were obtained usingPTD. Since the bubble has expanded beyond a radiusof 600 µm by t=0.9 ns, the Thomson-scattering data atr=600 µm obtained for t>0.9 ns are well within the bub-ble perimeter.

Thomson-scattering measurements in the reconnectionexperiments (Figure 3b) were all made in the center ofthe reconnection region, at the midpoint between thebubble centers (red star, at z=250, 450, and 700 µm).As shown in the first reconnection image, the interactionof the two plasma bubbles has already begun at t=0.67ns. Thomson scattering measurements of the interactingplasma bubbles were made from t∼0.8-3.1 ns, so the dataare obtained when the bubbles are interacting and theirmagnetic fields reconnecting.

Streaked Thomson-scattering spectra are shown in Fig-ure 4, for each of the experimental geometries depictedin Figure 1. These images show the time evolution ofscattered light spectra and reflect changes in the plasmaconditions at the particular locations in the experiments.Wavelength shifts in both features reflect changes in theplasma flow, while changes in the inter-line spacing indi-cate evolution of the electron temperature [6]. Lineoutsare taken to produce spectra at different times through-out the experiment from which the time history of elec-tron and ion temperatures is inferred.

The times chosen for spectral analysis in shot 46931are shown at the bottom right of Figure 4. Each lineoutintegrates over 120 ps to reduce the statistical noise in thespectrum. The relative timing of the spectral snapshotswithin a particular shot is known to ±50 ps, while the ab-solute uncertainty in the timing is ±100 ps. The resultingspectra and their fits are shown in Figure 5. The fitted

spectra are convolutions of the Thomson scattering formfactor and the estimated instrumental response function,represented by a Gaussian of full-width at half maximum0.055 nm. Additional broadening of the measured spec-tral features not accounted for by the fits may be due tospatial gradients of electron and ion temperatures acrossthe finite Thomson scattering volume. Uncertainties inthe inferred electron and ion temperatures are based onthe quality of fit.

Measurements of the time-dependent electron and iontemperatures at three locations in the single bubbleplasma are shown on the left side of Figure 6 andcompared to temperatures predicted by two-dimensional(2D) lasnex [31] hydrodynamics simulations at the ap-propriate location. The lasnex simulations used in thisstudy include the physics of magnetic fields and theirgeneration from nonparallel gradients in electron tem-perature and electron density [32, 33]. The simulationsinclude flux-limited electron diffusion and the Braginskiicross-field transport terms, which may modify hydrody-namic profiles [34]. The inclusion of magnetic fields haslittle effect (<10%) on lasnex predictions of electronand ion temperatures over the time when Thomson scat-tering measurements were obtained.

The overall electron temperature behavior agrees withLASNEX simulations. The electron temperature at eachlocation decreases after the laser turns off around t∼1ns, with the magnitude and time-scale of decay gener-ally matching those predicted by lasnex over the period1<t<2 ns. Beyond t∼2 ns, the measured electron tem-peratures level off around 300 eV, while the simulatedelectron temperatures continue to decrease. This discrep-ancy may be caused by slight heating of the plasma bythe probe beam at late times, which is not accounted forin the lasnex simulations. At t∼1.5 ns, the measuredelectron temperatures appear slightly lower than lasnexpredictions. Such a discrepancy would be consistent withthe previous observation of magnetic fields around a sin-gle plasma bubble decaying faster than predicted [19].That result could be explained by the measured electrontemperature being lower than the simulated temperature,which would produce a faster diffusion of magnetic fields.

The ion temperature measurements also agree withlasnex simulations. In some experiments, the early-time ion temperatures are higher than predicted, thoughthere is a large uncertainty in those measurements dueto relatively poor fits to the measured spectrum. As theion temperature is inferred from the ratio of trough topeak amplitude in the scattered light spectrum, its uncer-tainty is especially sensitive to the looseness of fit causedby temperature gradients across the Thomson scatteringvolume. In all three single-bubble experiments at t>1.5ns, the timing of the ion temperature evolution matchesLASNEX predictions, consistent with what was observedfor the electron temperatures.

Thomson scattering measurements of electron and iontemperatures in the reconnection region of the collidingplasma bubbles are shown on the right side of Figure

4

0.3 ns 3.0 ns2.4 ns1.8 ns1.5 ns1.2 ns0.9 ns0.6 ns

0.67 ns 1.42 ns

(a)

(b)

FIG. 3. 15-MeV-proton radiography images of (a) single laser-produced plasma bubbles and (b) interacting plasma bubblesundergoing magnetic reconnection. The approximate bubble size is indicated in the single bubble images (yellow circle), andthe location of Thomson scattering regions are shown at r=0 (red star, for both z=450 µm and z=1000 µm) and at r=600µm (green triangle, for z=450 µm) for t>0.9 ns. In the interacting bubbles experiments, the Thomson scattering regions arelocated in the reconnection layer at r=600 µm (red star, for z=250 µm, z=450 µm, and z=700 µm). These images were firstpublished by Li et al. [19, 20].

6. At each height in the reconnection layer, the electrontemperature decreases after the laser has turned off. Atz=450 µm and z=700 µm, the ion temperature decreasesmonotonically, while at z=250 µm, there is a slight in-crease in the ion temperature for 1<t<1.7 ns before itdecreases. Since the interacting plasmas bubbles are in-herently three-dimensional, 2D lasnex simulations arenot applicable for these experiments.

IV. DISCUSSION

The single bubble electron and ion temperature dataare well-modeled by lasnex and depict the convectionand cooling of the laser-produced plasma bubble in theperiod after laser shutoff, as the bubble is allowed to ex-pand into the ambient vacuum. Measured electron andion temperatures at fixed points in the experimental ge-ometry level off at late times, as hotter plasma near thebubble center is convected through the Thomson scatter-ing regions. At all three locations in the single plasmabubble, the measured electron temperature at t>2 ns isgreater than lasnex predictions, possibly due to con-tinued heating of the plasma by the Thomson scatteringprobe beam. It should be noted that the late-time com-parison of experimental data to lasnex simulations iscomplicated also by the emergence of instabilities, whichbreaks the 2D bubble symmetry after the laser turns offaround t∼1.2 ns [19].

Having measurements of the conditions in both singleand interacting plasma bubbles allows assessment of theeffect of the plasma collision and magnetic reconnection

on the energetics of the system. A comparison of time-dependent electron and ion temperatures measured at (r=600 µm, z=450 µm) in the single bubble case versusthe interacting bubbles case is shown in Figure 7. Asshown in Figure 7a, there is a negligible difference in theelectron temperature history between the single bubbleand reconnection cases during the time when magneticreconnection is occurring between the two bubbles. Thus,the magnetic field energy released during reconnectiondoes not noticeably raise the electron temperature. Thisresult is in contrast to the findings of Nilson et al. [9],where an increase in the electron temperature to 1.7 keVwas inferred from Thomson scattering measurements inthe reconnection region of laser-produced plasma bub-bles. The minimal impact of magnetic reconnection onthe electron temperature of the plasma is expected forreconnection at high plasma β, where the magnetic pres-sure is small in comparison to the hydrodynamic pressureof the plasma.

The ion temperature histories (Figure 7b) are nearlyidentical given the large uncertainties at early times,though the appearance of a slightly higher Ti in the col-liding bubbles case at t∼1.3 ns is suggestive of a hydrody-namic collision of plasmas, independent of magnetic re-connection [35]. The ion-ion mean free path under theseconditions is approximately 1 µm, so the plasma is colli-sional and some kinetic energy from the colliding plasmasis expected to be transferred to ion thermal energy.

These data can also be used to more precisely identifythe plasma β for these laser-produced plasmas, definedas

5

FIG. 4. Streaked Thomson scattering spectra from single bubble experiments (top) and interacting bubble experiments (bot-tom), at the locations depicted in Figure 1. The yellow lines at the bottom right indicate the times that were chosen for spectralanalysis for shot 46931. For improved statistics, the spectra were integrated over 120 ps at each lineout, as indicated by thewidth of the lines. The resulting lineouts are shown in Figure 5.

263.2 263.4 263.6 263.8 264

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FIG. 5. Measured spectra (blue) and their fits (black) obtained from six lineouts of the streaked image on shot 46931 shown inFigure 4. Changes in the interline spacing and the ratio of trough to peak amplitude depict evolution of the electron and iontemperatures at (r=600 µm, z=250 µm) in the interaction region of the colliding plasmas. Additional broadening of measuredspectral features in comparison to their fits may be due to spatial gradients in electron and ion temperature across the Thomsonscattering volume.

β =nikTi + nekTe

B2/2µ0, (1)

where ni (ne) and Ti (Te) are the ion (electron) densityand temperature, and B is the magnetic field strength.

lasnex simulations give an approximate electron den-sity, while Thomson scattering and proton radiogra-phy data give the temperatures and the magnetic fieldstrength, respectively. Since each of the measurementsis performed locally and at different times, care must betaken to ensure that appropriate values are used. For ex-ample, proton radiography data provide snapshots of the

6

0 0.5 1 1.5 2 2.5 3 3.50

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r

FIG. 6. Simultaneous, time-dependent Thomson scattering measurements of electron temperatures (filled markers) and iontemperatures (open markers) at different positions in the single bubble (left) and interacting bubbles (right). Single bubble dataare compared to lasnex predictions of electron temperature (solid lines) and ion temperatures (dashed lines). Comparisonsbetween measured electron and ion temperatures demonstrate differences in electron-ion thermal equilibration at differentlocations and times in these experiments, as discussed in Section IV.

magnetic-field strength at the expanding bubble perime-ter where the magnetic fields are concentrated, whileThomson scattering data are taken at fixed locations (e.g.r=600 µm).

At t=0.91 ns in the single bubble experiment, the bub-ble perimeter is located at r=700 µm, just outside theThomson scattering region at r=600 µm. At t=1.20 ns,the earliest Thomson scattering measurement at that lo-cation gives Te=0.65 keV and Ti=0.26 keV at (r=600 µm,z=450 µm). These temperatures, and the ∼0.5 MG mag-netic field inferred from the proton radiography data areapproximately representative of the plasma conditionsat the bubble perimeter at t=0.9-1.2 ns and r=600-700µm. Along with the lasnex-predicted electron densityof 7×1019 cm−3, these parameters are used to estimateβ∼8. Therefore, the magnetic energy density is approxi-mately one eighth of the total thermal energy density atthe bubble perimeter.

Similarly, the expansion velocity of the plasma bub-ble can be used to infer the ratio of plasma thermal en-ergy to kinetic energy of the expanding plasma bubble.For a bubble expansion velocity of V∼500 µm/ns, asinferred from proton radiography data [19] and consis-tent with the Doppler shifts in the Thomson-scatteringspectra, there is approximately 3 times as much energycontained in the kinetic energy of the expanding bubble( 12nimiV

2) as there is contained in the thermal energy(nikTi + nekTe), and about 25 times as much energy asin the magnetic fields (B2/2µ0). These results reinforcethe picture of plasma bubble interaction where the dy-namics is dominated by hydrodynamic processes, eventhough energy is released by the reconnection of largemagnetic fields. At the high densities present in theseexperiments, the maximum energy released by the dis-sipation of 0.5 MG magnetic fields sets an upper boundon the increase in electron temperature of ∼80 eV. The

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Ti[k

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Colliding Bubbles

(b)

FIG. 7. Comparison of time-dependent (a) electron tem-perature and (b) ion temperature for single plasma bubbles(blue) and colliding plasma bubbles (red) after the bubblecollision around t∼0.7 ns. There is a negligible differencein temperatures between the single bubble and colliding-bubbles case, though the ion temperature around t=1.3 nsis ∼50% higher in the colliding-bubble case (barely withinuncertainty). These results are consistent with the hydrody-namic collision of plasma bubbles at β�1.

actual energy released is estimated to be lower [20], cor-responding to an electron temperature increase of only∼20 eV. Each of these estimates is negligible comparedto the measured electron temperature of 650 eV.

The simultaneous, time-resolved measurements of elec-tron and ion temperatures shown in Figure 6 hint at theprocess of thermal equilibration between species at differ-ent locations in the expanding plasma bubble. It shouldbe emphasized that these time-dependent measurementsare not tracking a parcel of plasma, but rather samplingdifferent locations in the bubble geometry as they passthrough the fixed Thomson scattering region (e.g. atr=600 µm, z=450 µm).

In the single bubble case, at each of (r=0, z=450 µm),(r=0, z=1000 µm), and (r=600 µm, z=450 µm), the elec-tron temperature is greater than the ion temperature att∼1.2 ns by a factor of ∼1.5-2.5, due to the preferentialabsorption of laser light by the electrons. As the centralregion of the plasma bubble expands through the Thom-son scattering regions, the electrons and ions move closerto equilibrium, such that by t∼1.8 ns, the temperaturesare within 25% of each other. The difference betweenelectron and ion temperatures in the colliding bubblesexperiments is not substantially different from the singlebubble case, and temperatures approach each other grad-

ually for t>1 ns. In both sets of experiments, the electronand ion temperatures never quite equilibrate. This resultmay be due to the absorption of energy from the Thom-son scattering probe beam, which preferentially heats theelectrons.

For a CH plasma at ne∼1020 cm−3 and Te∼650 eV,conditions near the bubble perimeter (r=600 µm, z=450µm) at early times, the electron-ion equilibration timeis τeq∼4 ns. As this timescale is longer than the dura-tion of the experiment, it is unlikely that the perime-ter plasma experiences significant thermal equilibration.The appearance of equilibration is more likely a conse-quence of the convection of plasma from denser regionsat the center of the bubble, where an electron density of∼5×1020 cm−3 is predicted at early times. The equili-bration time under those conditions is closer to τeq∼1 ns,so some thermal equilibration likely has occurred by thetime that plasma passes through the Thomson scatteringregion.

V. CONCLUSIONS

Time-resolved electron and ion temperature data havebeen presented for single and colliding plasma bubblesgenerated by laser-foil interactions. These data have beencombined with magnetic field data to produce a compre-hensive picture of the thermal and magnetic evolutionof both individual plasma bubbles and the magnetic re-connection of interacting bubble pairs. The single-bubbleelectron and ion temperature data are in good agreementwith lasnex simulations.

Comparison of the temperature data between the sin-gle bubble and the interacting bubbles elucidates the im-pact of magnetic reconnection and hydrodynamic colli-sion on the thermal properties of the plasma. The tem-perature data reveal a negligible difference between thesingle bubble and the reconnection case, though the iontemperature may be slightly higher at early times in thebubble collision. These results are consistent with the hy-drodynamic collision of plasma bubbles at β�1, wheremagnetic reconnection does not appreciably alter the dy-namics and the estimated increase in electron tempera-ture due to the release of magnetic energy is <5% of thetotal. A comparison of the energy sources in the systemcorroborates this picture: the kinetic energy density ofthe expanding bubble is ∼3 times its thermal energy den-sity and ∼25 times its magnetic energy density. Thesedata will help guide future studies of magnetic recon-nection and basic plasma physics using laser-foil interac-tions.

ACKNOWLEDGMENTS

The authors would like to thank the OMEGA oper-ations crew for their assistance in carrying out theseexperiments. This work is presented in partial ful-

8

fulliment of the first author’s PhD thesis and is sup-ported in part by US DoE (Grant No. DE-FG52-

09NA29553), NLUF (DE-NA0000877), LLE (No.414-090-G), and LLNL (No.B580243).

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