A laboratory study of asymmetric magnetic reconnection in strongly driven plasmas

Abstract

Magnetic reconnection, the annihilation and rearrangement of magnetic fields in a plasma, is a universal phenomenon that frequently occurs when plasmas carrying oppositely directed field lines collide. In most natural circumstances, the collision is asymmetric (the two plasmas having different properties), but laboratory research to date has been limited to symmetric configurations. In addition, the regime of strongly driven magnetic reconnection, where the ram pressure of the plasma dominates the magnetic pressure, as in several astrophysical environments, has also received little experimental attention. Thus, we have designed the experiments to probe reconnection in asymmetric, strongly driven, laser-generated plasmas. Here we show that, in this strongly driven system, the rate of magnetic flux annihilation is dictated by the relative flow velocities of the opposing plasmas and is insensitive to initial asymmetries. In addition, out-of-plane magnetic fields that arise from asymmetries in the three-dimensional plasma geometry have minimal impact on the reconnection rate, due to the strong flows.

ARTICLE

Received 6 May 2014 | Accepted 2 Jan 2015 | Published 4 Feb 2015

M.J. Rosenberg1, C.K. Li1, W. Fox2, I. Igumenshchev3, F.H. Sguin1, R.P.J. Town4, J.A. Frenje1, C. Stoeckl3,V. Glebov3 & R.D. Petrasso1

Magnetic reconnection, the annihilation and rearrangement of magnetic elds in a plasma, is a universal phenomenon that frequently occurs when plasmas carrying oppositely directed eld lines collide. In most natural circumstances, the collision is asymmetric (the two plasmas having different properties), but laboratory research to date has been limited to symmetric congurations. In addition, the regime of strongly driven magnetic reconnection, where the ram pressure of the plasma dominates the magnetic pressure, as in several astrophysical environments, has also received little experimental attention. Thus, we have designed the experiments to probe reconnection in asymmetric, strongly driven, laser-generated plasmas. Here we show that, in this strongly driven system, the rate of magnetic ux annihilation is dictated by the relative ow velocities of the opposing plasmas and is insensitive to initial asymmetries. In addition, out-of-plane magnetic elds that arise from asymmetries in the three-dimensional plasma geometry have minimal impact on the reconnection rate, due to the strong ows.

DOI: 10.1038/ncomms7190

A laboratory study of asymmetric magnetic reconnection in strongly driven plasmas

1 Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. 2 Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA. 3 Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA. 4 Lawrence Livermore National Laboratory, Livermore, California 94550, USA. Correspondence and requests for materials should be addressed to M.J.R.(email: mailto:[email protected]

Web End [email protected] ).

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Magnetic reconnection1,2 is a pervasive phenomenon in the universe. In astrophysics, it is thought to be a key mechanism for energy release in the solar corona and in

solar ares, and it is important at the Earths dayside magnetopause (see Fig. 1a). In an earthbound context, it allows for fast reconguration of the conning magnetic eld and consequent energy loss in magnetized-fusion devices3. Reconnection most frequently occurs in these environments, and in fact universally in nature, in congurations where there is an asymmetry in the plasma density, temperature, magnetic eld strength, geometry and/or ow across the reconnection layer. In the magnetopause, for example, a strong solar wind drives reconnection across an asymmetric boundary, with differences of a factor of B0.3 in density and B7 in magnetic eld strength.

The plasma thermal b (ratio of thermal to magnetic pressure) is B0.1 at the high-eld, low-density magnetosphere and B1 at the low-eld, high-density magnetosheath and the plasma ram pressure bram (ratio of ram to magnetic pressure) is B50 on the solar-wind side, signifying a strongly driven reconnection46. Despite the prevalence of asymmetry in nature, it is only recently that studies have begun to explore its effects on reconnection, primarily in analytic theory7, in numerical simulations of collisional7,8 and collisionless plasmas912 and in some spacecraft measurements of the Earths magnetopause13,14.

Towards remedying the dearth of experimental investigations of asymmetric magnetic reconnection, here we describe the rst concerted, systematic laboratory effort to isolate and study the effects of asymmetry on magnetic reconnection, using strongly driven, colliding, laser-generated plasmas. We demonstrate that, in this strongly driven system, the rate of magnetic ux

annihilation in both symmetric and asymmetric experiments is dictated by the relative ow velocities of the colliding plasmas and, therefore, is insensitive to the initial asymmetries in the upstream plasma conditions or in the three-dimensional (3D) geometry of the colliding plasmas.

ResultsLaser-driven asymmetric magnetic reconnection experiments. The experiments were conducted at the OMEGA laser facility15. As shown in Fig. 1c, each experiment involved two 500-J beams of 351-nm laser light striking a 5-mm-thick CH foil for 1 ns and focused into 800-mm spots separated by 1.4 mm. The interaction of each laser beam with the foil produced an expanding, hemispherical plasma bubble with an azimuthal0.5 MG magnetic eld concentrated at its perimeter16, where the plasma b was around 10. Unlike previous investigations of reconnection in symmetric laser-produced plasma congurations1719, these experiments additionally introduced a delay (Dt) between the two beams incident on the foil. This enables the study of the interaction between plasma bubbles that are at different stages in their evolution, with differences in geometry, temperature, density, ram pressure (12 rV2, where r is the plasma density and V the bulk ow velocity) and magnetic ux. Only the relative timingno other propertywas varied between the two drive lasers, as the magnetic elds and plasma conditions produced by the interaction of a 500-J, 1-ns laser pulse with a 5-mm CH foil have been well characterized by proton radiography and Thomson scattering measurements in previous experiments20,21. The magnetic Reynolds number Rm (a measure of the strength of ow relative to magnetic diffusive processes) is of order 3,000, indicating that the magnetic eld was frozen into the owing plasma, as it is in most astrophysical contexts (where Rm 1).

Consequently, the magnetic elds were largely advected with the outward radial ow of the plasma bubbles, which expanded into each other and drove their oppositely directed magnetic elds to interact. The resultant magnetic eld conguration (Fig. 1b) has strong similarities to that of the magnetopause (Fig. 1a); a quantitative comparison of plasma conditions and reconnection-relevant parameters for the two contexts is presented in Tables 1 and 2.

The magnetic eld structures and the rates of magnetic reconnection in the experiments were studied using mono-energetic proton radiography22,23. The source of the imaging protons (labelled as the Backlighter in Fig. 1c) was fusion reactions of deuterium and helium-3 in an imploding, spherical glass capsule driven by 23 to 28 OMEGA lasers that deliver a total of 1112 kJ in a 1-ns pulse. The reactions produced an isotropic, B100-ps burst of monoenergetic 15-MeV protons that were divided into discrete beamlets by a 150-mm-period Ni mesh. The resultant proton radiographs allow measurements of the deections of individual proton beamlets due to magnetic elds around the laser-produced plasma bubbles, as shown in Fig. 2a, where individual images are organized according to both the duration of time since the plasma bubbles began to interact (tint)

and the difference in onset time between the two foil drive beams (Dt) in the experiment. The absolute time of proton emission from the backlighter was measured using the particle temporal diagnostic24.

Proton radiographs reveal B eld dynamics and reconnection. The most salient feature in the images of Fig. 2a is the deection of proton beamlets away from the centre of each bubble due to the azimuthal magnetic eld at each bubbles perimeter. In addition, there are distortions in the beamlet distributions in the

Magnetopause

Solar wind

Flow Flow

B field

[afii9845]1 [afii9845]2

B field

Foil drive beam

2328 backlighter drive beams

Mesh

CH foil

B field

Backlighter

Protons

CR-39

Foil drive beam (delayed t )

Figure 1 | Magnetic eld congurations and experimental set-up.(a) Magnetic elds at the magnetopause, where the solar wind drives asymmetric reconnection between the interplanetary magnetic eld and the Earths magnetosphere, bear similarities to (b) magnetic elds and ows in the asymmetric reconnection experiments. (c) In the experiments, the distance between the backlighter capsule and the CH foil was 1 cm, while the distance between the mesh and the foil was 0.2 cm. The distance between the backlighter and the CR-39 proton detector was 2728 cm,so the magnication was M 2728. The relative timing of laser onset of

the two foil drive beams was varied from Dt 0 to Dt 0.7 ns.

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Table 1 | Plasma parameters for experimental and magnetopause reconnection.

Location ne (cm 3) q (g cm 3) Te (eV) B (T) hZi Vow (lm ns 1) L

scale(lm)

Experiment (symmetric) 59 1019 1.62.8 10 4 700150 5020 3.5 45050 800200

Experiment (asymmetriclarge bubble) 816 1019 2.54.9 10 4 550150 5020 3.5 45050 1,200300

Experiment (asymmetricsmall bubble) 26 1019 0.61.8 10 4 900200 5020 3.5 45050 400100

Magnetopause (solar wind) 7 1 10 23 15 7 10 9 1 400 1016

Magnetopause (magnetosphere) 2 0.3 10 23 300 5 10 8 1 50 1014

Parameters include the electron density (n ), the mass density (r), the electron temperature (T ), the magnetic eld strength (B), the average ion charge (hZi), the ow velocity (V ) and the length

scale (L ), which can be roughly equated to the current sheet length (L). Experimental parameters are representative conditions just before the onset of reconnection (though conditions evolve signicantly throughout the experiment), while magnetopause conditions are based on refs 5,40 and their references and are representative of typical values and the degree of asymmetry between the solar wind and magnetosphere sides.

Table 2 | Derived reconnection-relevant parameters.

Location b bram VA (lm ns 1) Cs (lm ns 1) Rm S di (lm) dSP/di Experiment (symmetric) 8 22 100 250 3,000 600 40 0.9 Experiment (asymmetriclarge bubble) 11 38 70 220 3,000 500 30 1.9 Experiment (asymmetricsmall bubble) 6 13 130 280 2,000 600 50 0.3 Magnetopause (solar wind) 1 48 60 50 2 1014 3 1013 1011 0.02

Magnetopause (magnetosphere) 0.1 0.004 800 200 2 1013 3 1014 2 1011 3 10 5

Parameters characterizing the experimental and magnetopause environments based on the plasma conditions described in Table 1, including the ratio of thermal pressure to magnetic pressure (b), the ratio of ram pressure to magnetic pressure (b ), the Alfvn speed (V ), the sound speed (C ), the magnetic Reynolds number (R ), the Lundquist number (S), the ion inertial length (d ) and the ratio of

SweetParker current sheet width to ion inertial length (d /d ), a parameter describing the importance of two-uid or collisionless reconnection effects.

Interation time (tint) Interation time (tint)

0.1 ns

0.4 ns 0.7 ns 0.1 ns

Symmetric (t < 0.5 ns)

Asymmetric (t < 0.5 ns)

1.0 ns

0.4 ns 0.7 ns 1.0 ns

|BxdI|

(MG m)

200 150 100 50 0

0 ns 0.3 ns

Symmetric (t < 0.5 ns)

Laser onset differential (t)

3.6 mm

Laser onset differential (t)

0 ns 0.3 ns 0.7 ns

[p10]per1

0.7 ns

Asymmetric (t < 0.5 ns)

150 [p10]per1

[p10]int

[p10]per2

|BxdI| (MGm)

100

50

00 1 2 3 4

Lineout position z (mm)

Figure 2 | Proton radiography data. (a) 15-MeV-proton images and (b) inferred path-integrated magnetic eld strength maps at different interaction times tint (since the beginning of bubble interaction) and for differing amounts of bubble asymmetry as parameterized by the laser onset differential Dt(the difference in onset times of the two bubble-generating beams) Each image covers a eld of view (at the foil) of 3.6 mm by 3.6 mm. (c) A sample lineout of R B dl

, is integrated along the z direction (yellow arrow) to measure the magnetic ux F R R B dl

dz, with limits of integration bracketing

each region of interest indicated by the vertical lines.

image regions corresponding to the interaction of the two bubbles, where there are bubble deformation and reconnection of magnetic elds. In all cases, the proton-path-integrated magnetic eld strength can be determined from the magnitude of the beamlet deections x relative to where they would have been in the image plane in the absence of elds: R B dl

xmpvp=qA,

where mp (vp) is the proton mass (velocity), q is the proton charge and A is the foil-detector distance18. Resulting maps of path-integrated magnetic eld are shown in Fig. 2b. At the later times, most of the eld maps show annihilation of magnetic ux and the deformation of magnetic eld structures in the reconnection region.

The magnetic ux annihilated in the reconnection region was calculated as DFann (Fper1 Fper2) Fint, where Fper1 and

Fper2 were the uxes at the perimeters of the individual plasma bubbles and Fint was the ux measured in the interaction region, where reconnection occurred. The ux in each case was measured as a line-integral of the path-integrated magnetic eld strength over the region of interest (see Fig. 2c) as F R R B dl

dz,

where dz is the differential length along the lineout direction, perpendicular to the magnetic elds.

The bubble expansion speed Vb, as estimated based on the radius of the outer extent of magnetic eld structure around an individual bubble, is a relatively constant 45050 mm ns 1 over

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the duration of the experiment. This ow velocity is much larger than the nominal Alfvn speed VA0 B=

m0r

p , the speed at which ions can rearrange the magnetic eld structure, which is

B100 mm ns 1 at the perimeters of the expanding plasma bubbles just before their collision. Consequently, and in contrast to many previous experiments25, magnetic reconnection was strongly driven, with the plasma bubbles driven together faster than the natural velocity at which the magnetic elds can adjust.

The measured annihilated ux is compared with the ux advected into the reconnection region based on the constant ow velocity Vb in Fig. 3. This ow-based magnetic ux scales as 2Vbtint R B dl

, where Vb is the measured radial expansion

velocity; tint is the duration of time since the bubbles began to collide, and R B dl

is the measured path-integrated magnetic

eld strength through the perimeter of the smaller bubble. (The larger bubble carries some magnetic elds at a greater height away from the foil than in the smaller bubble, so that some of the magnetic elds of the larger bubble are unopposed by the smaller bubble in the collision process. Thus, the path-integrated eld strength that can be annihilated is limited to that contained in the smaller bubble.) In both symmetric and asymmetric cases, the rate of reconnection was nearly equivalent to the ow-based rate, as the ux annihilated DFann is 2Vbtint R B dl

. In contrast,

this measured rate of ux annihilation is much faster than that based on the nominal Alfvn speed, as DFannB10DFAlf, where

DFAlf VA0tint R B dl

is the amount of ux advected into the

reconnection region based on a relative inow at the Alfvn speed, and the nominal Alfvn speed VA0 B100 mm ns 1 is based on plasma conditions just before collision in the symmetric experiments (see Table 2). This result indicates that the rate of reconnection is much faster than that based on initial, undriven, upstream conditions, demonstrating that ux pileup resulting from the strongly driven collision is likely required to amplify the local magnetic eld strength and Alfvn speed to permit reconnection at the ow-based rate. In future experiments, precise, local measurements of the plasma density and magnetic eld strength will be obtained to compare local parameters, rather than initial parameters, to the measured rate of magnetic ux annihilation. Such measurements will help evaluate, based on experimentally determined plasma parameters, scaling relations

for the reconnection rate under asymmetric conditions, as will be further discussed below in the context of equation (1). Notably, reconnection in the asymmetric experiments was only 2030% slower than in the symmetric experiments, an essentially insignicant difference. It can, therefore, be concluded that the reconnection rate was governed primarily by the relative velocities of incoming and opposing plasmas, independent of the plasma asymmetry.

Reconnection-relevant plasma parameters. Calculation of the plasma parameters in the experiments shows that the magnetic reconnection was strongly driven and that two-uid effects (decoupled ions and electrons) were important. To estimate the key plasma parameters, we used measurements and simulated quantities from other recent, similar experiments to characterize plasma conditions immediately before collision in a typical, symmetric experiment. These conditions represent the initial conditions in the reconnection region. Though these conditions evolve throughout the experiment, with the density and magnetic eld strength likely enhanced early in the collision process, they represent a solid baseline for establishing the regime of these experiments. These parameters are summarized in Tables 1 and 2. Thomson scattering measurements of local plasma conditions indicated an electron temperature Te 0.70.15 keV and an ion

temperature of Ti 0.30.1 keV at the plasma bubble perimeter

just before collision in a typical symmetric experiment, at a height of 450 mm away from the foil21. The variation in temperature along the collision plane was of order 50% within 250 mm of this height21. The electron density, as predicted by LASNEX

radiation-hydrodynamics simulations26,27 of individual laser-produced plasma bubbles, was neB59 1019 cm 3 within the

magnetic eld region just before interaction, varying by an additional factor of 2 along the collision plane and increasing by a factor of B10 towards the centre of the plasma bubbles. On the basis of quasi-neutrality in this fully ionized CH plasma, with an average charge of hZi 3.5, the ion density was niB1.5

2.5 1019 cm 3. In addition, the initial magnetic eld strength

at the perimeter of each bubble, within a B100 mm-thick ribbon of magnetic elds, was B 0.30.5 MG, as predicted by

LASNEX

and conrmed by experimental data20. These numbers imply that the ratio of thermal pressure to magnetic pressure was b (nekTe nikTi)/(B2/2m0) 515, while the ratio of ram

pressure to magnetic pressure was bram 12 rV2b B2=2m0

15 30. It is noted again that the reconnection was strongly

driven, by virtue of bram 1, or, equivalently, Vb VA0, as

previously discussed.

The signicance of two-uid reconnection effects in the experiments is assessed by comparing the length scale for electronion decoupling to the width of the reconnection region. The ion inertial length, the distance over which electrons and ions decouple in a plasma, was di c/opi 3050 mm, where opi is the

frequency of ion oscillations in a plasma. On the basis of the radiographs, the length L of the boundary layer current sheet was 800200 mm, while the Lundquist number, the ratio of diffusive to Alfvn timescales, was S m0LVA0/ZB450750, where Z is the

plasma resistivity. As a result, the current sheet width in the experiments, as predicted by SweetParker reconnection theory28,29, was dSP L= S

p 25 45 mm and therefore

dSP/diB0.9. The ion gyroradius ri in the experiment was approximately equal to the ion inertial length of 3050 mm. On length scales shorter than di or ri, the ions are demagnetized, while the electrons remain tightly bound to the magnetic eld lines and electron ow carries magnetic ux into the annihilation region. The conditions in the experiments, with dSP/dit1, were

far different from those required for a single-uid reconnection

150

100

Symmetric (t < 0.5 ns) Asymmetric (t > 0.5 ns)

[p10] ann(MG m mm)

50

Alfvn

0 0 20 40 60 80 100 2Vbtint|Bxdl| (MG m mm)

Figure 3 | Measured annihilated ux. The thin, dotted line denotes the annihilated ux based on the ow velocity, while the thick, dashed line indicates the annihilated ux based on a nominal Alfvnic reconnection rate

DFVA0tint R B dl

. Error bars principally denote uncertainty in the boundaries of the magnetic ux regions and the magnitude of proton beamlet deections.

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model, which requires that dSP=di 1. All of these parameters

evolved with time throughout these highly dynamic experiments, but, on the whole, collisionless or two-uid effects were important in the reconnection process just as they are in magnetopause reconnection (where electron densities of B10 cm 3 and magnetic eld strengths of B10 nT imply dSP/diB10 3).

Simulations aid and conrm interpretation of measured data. To help interpret the physics in these experiments, two-dimensional (2D) numerical simulations were performed. First, the azimuthally symmetric 2D structure and evolution of each individual bubble was simulated with 2D DRACO30 and LASNEX31

radiation-hydrodynamics codes. At the point in time when the individual bubbles were about to collide, the conditions in both bubbles (radial proles of density, temperature, magnetic eld strength and ow velocity) on a plane parallel to the foil and 200 mm away from the foil surface were recorded. This height was chosen because it represents the height at which the plasma bubbles initially make contact with each other in the symmetric experiments. The proles of hydrodynamic quantitiesdensity, temperature and ow velocitywere obtained from DRACO

simulations, while magnetic eld proles were qualitatively based on those generated by LASNEX simulations.

The DRACO simulations use inverse bremsstrahlung absorption of laser energy and local, ux-limited32 Spitzer electron heat transport with a ux limiter of f 0.06. Previous laser-foil

experiments at a low laser intensity t2 1014 W cm 2, relevant

to the present experiments, have demonstrated good agreement with DRACO-simulated hydrodynamics33. LASNEX simulations use local, ux-limited Spitzer heat ux, with a ux limiter of f 0.1.

Though non-local effects were not included in either DRACO or

LASNEX, agreement of these models with experimental results under relevant or near-identical experimental conditions21 suggests that this is not a major limitation. The magnetic eld model in LASNEX includes the rTe rne source term and

convection due to plasma ows and heat-ux (Nernst) effects. These LASNEX simulations did not include RighiLeduc heat-ux effects, though it has been found that the inclusion of those terms does not signicantly modify the hemispherical shape and magnitude of the magnetic eld structure. LASNEX simulations

identical to those used here have been found to reproduce the path-integrated magnetic eld strength in single laser-produced plasma bubbles under conditions identical to the present experiments, producing agreement between proton radiography measurements and synthetic radiographs based on LASNEX-

simulated magnetic elds20. (To date, DRACO-simulated path-integrated magnetic elds have not been veried in comparison to experimental results as have the LASNEX-simulated path-integrated magnetic elds and so LASNEX-simulated magnetic elds are used.) Electron and ion temperature measurements of individual laser-produced plasma bubbles under identical conditions have also been captured by these LASNEX simulations21. Thus, though the out-of-plane eld structure has not been directly veried experimentally, these LASNEX simulations are believed to reasonably capture the generation and evolution of magnetic eld structure produced in a single laser-foil interaction under these experimental conditions.

Analytic ts to separate magnetic eld proles simulated by

LASNEX and hydrodynamic proles simulated by DRACO were then used in concert as initial conditions for further simulation through the bubble interaction phase using the 2D, planar particle-in-cell (PIC) code PSC in a manner previously applied to other experiments involving reconnection in laser-driven plasmas34,35. Though not perfectly self-consistent, the parameters used to initiate the PIC simulations appropriately capture the

strongly driven and high-b regime of the experiments and the physics relevant to the reconnection process. The use of a PIC code, rather than a hydrodynamic code, is necessary during the interaction phase to capture the physics of two-uid reconnection. The PIC simulations include the effect of collisions through the use of a Monte Carlo collision operator35, though collisions do not signicantly contribute to the reconnection dynamics. The PIC simulations do not account for continued laser-generation of plasma or of magnetic elds, which articially stunts the evolution of the small bubble in the asymmetric simulation. These PIC simulations represent a 2D treatment of a fully 3D structure of the hemispherical plasma bubbles and, as such, they do not allow for out-of-plane advection of plasma or elds. This consequently forces a strong collision of magnetic elds. However, the PIC simulations initiated from hydrodynamic codes appropriately capture the physical regime and illuminate key processes dictating the plasma collision and reconnection as they occur in both symmetric and asymmetric experiments.

In basic agreement with the data, the PIC simulations show (Fig. 4) the emergence of a reconnection layer in the interaction region, the annihilation of magnetic elds and the deformation of the plasma bubbles due to their hydrodynamic collision. The simulated reconnection rates, expressed in Fig. 4c in terms of the reconnection-related out-of-plane electric eld (Ey), are nearly indistinguishable in the symmetric and asymmetric simulations. This result is consistent with experimental observations. Magnetic eld amplication due to ux pileup up to a factor of 4 is observed in the simulations as a consequence of the strongly driven interaction, as in previous modelling studies of related experiments35. The simulations show a comparable degree of ux

40 40

Symmetric Asymmetric

Asymmetric

B (Binit)

5 4 3 2 1 0 80

z(d i0)

E y/(B init V A,init)

0 0

40 40

80

15

5

0 0 2 3 4 Time (ns)

1

0

80

80

0

x (di0)

x (di0)

10 Symm.

Figure 4 | 2D PIC simulation results. Simulated magnetic eld strength in a plane parallel to the foil at the time of peak reconnection rate for the cases of (a) symmetric and (b) asymmetric interacting plasma bubbles. Spatial units are in terms of a nominal ion skin depth di0 11 mm and the

magnetic eld strength is in terms of the peak initial magnetic eld strength Binit 0.5 MG. The simulated reconnection electric elds (c), normalized to

initial magnetic eld strength and Alfvn speed, are approximately equal in symmetric and asymmetric simulations, consistent with experimental results. The electric eld is expressed in terms of Binit and the nominal

Alfvn speed VA,init 31 mm ns 1 B1/3VA0 in the simulation (based on Binit

and the peak simulated density ne,init 6.8 1020 cm 3), with these scale

values used for normalization (see Table 3). The asymmetric simulation shows a delay in the onset of reconnection, because in this case it takes longer for sufcient pressure to build up on the small-bubble side to push back and drive reconnection. This effect is likely exaggerated in the simulation due to the lack of modelling of the continued laser drive, which in reality increases the pressure on the small-bubble side.

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Table 3 | Scale parameters for PIC simulations.

ne,init (cm 3) Binit (T) VA,init (lm ns 1) di0 (lm) Cs0 (lm ns 1)

6.8 1020 50 31 11 250

Fundamental scale parameters in the simulations include the maximum initial electron density (n ) and the maximimum initial magnetic eld strength (B ), while derived parameters include the Alfvn speed (V ), ion inertial length (d ) and sound speed (C ).

pileup in both symmetric and asymmetric cases, though pileup occurs inversely to the density or ram pressure asymmetry and slightly more weakly overall in the asymmetric simulation. This ux pileup likely explains the fast reconnection rates inferred from the measured magnetic ux data in symmetric and asymmetric experiments. This result indicates, in a manner consistent with prior symmetric simulations34 and the experimental result discussed above, that the reconnection rate in a strongly driven system is dependent more on the characteristics and strength of the drive mechanismas determined by the ow velocitythan on ambient plasma conditions and asymmetries.

The reconnection electric elds are predominantly attributable to the Hall JHall B electromotive force and the electron pressure

tensor in the current sheet, and they are driven at the periphery of the reconnection region by ion-driven magnetic eld advection Vi B. Similar magnitudes of the Vi B term in the symmetric

and asymmetric cases arise from the ram pressure around the current sheet, which is approximately equal in the symmetric and asymmetric simulations despite the large asymmetry between the two sides of the current sheet in the asymmetric case. This result suggests that the bulk plasma ows drive electrons to rearrange themselves in a way that produces a strong reconnection electric eld and a rapid reconnection, and that this process is largely insensitive to asymmetries.

Remarkably, under a wide range of conditions reconnection occurs at the rate implied by the dynamics of the plasma bubble collision, with the local electron behaviour dictated by the strong collision process. The reconnection rate (reconnection electric eld) produced in the simulations is also consistent with an analytic theory of asymmetric reconnection7 based on a hybrid Alfvn speed and magnetic eld strengthinferred from the local density and magnetic eld strength on each side of the current sheetand the current sheet aspect ratio (opening angle of the reconnection outow), as

Ey VA;

hybrid 2B1B2

aspect ratio of 0.25, the analytic model predicts EyB1.4 107

V m 1, which compares favourably to the simulated EyB1.6 107 V m 1. Near the peak reconnection rate in the

asymmetric simulation, based on simulated densities of2.0 10 4 g cm 3 (ne 6.4 1019 cm 3; large bubble) and

1.6 10 4 g cm 3 (ne 5.2 1019 cm 3; small bubble), mag

netic eld strengths of 1.0 and 1.7 MG and an aspect ratio of 0.29, the analytic model predicts EyB1.0 107 V m 1, close to the

simulated EyB0.8 107 V m 1 at that time. Although agreement

with this steady-state model can only be considered suggestive, rather than explanatory, for this strongly driven system, based on the consistency between the equation (1) theory7 and the PIC simulations, and between the PIC simulations and the measured data, the experimental results provide a rough conrmation of the theory. As was mentioned earlier, a goal of future experiments is to obtain experimental measurements of r1, r2, B1 and B2 in the reconnection region, to make a direct evaluation of the scaling relation of equation (1) under these strongly driven and dynamic conditions.

The picture provided by the experimental results, PIC simulations and equation (1) theory7 suggests that under such strong external drive, the plasma conditions evolve to permit reconnection at the ow-based rate, regardless of the initial magnetic eld, density or ram pressure asymmetry. The concept of driven reconnection has been described in previous computational work36, including the assertion that the strength of driving ows or the self-consistent out-of-plane electric eld can determine the rate of reconnection through modication of local plasma conditions. The results presented here provide strong experimental evidence of this phenomenon in a regime characterized by strong plasma ows and likely ux pileup, with the remarkable observation that magnetic ux is annihilated at nearly exactly the rate dictated by the ow velocities. This property is found to apply generally, for both symmetric and asymmetric conditions across the current sheet.

Though recent theoretical work37 has found that under certain conditions in high-b plasmas, heat ows (rather than Alfvnic ows or, in the case of the present experiments, plasma uid ows) dictate the reconnection rate, the parameters of these experiments are such that heat-ux effects are small compared to the dominant uid ow. Heat-ux effects are dominant for a ratio of b=ocetei 1, where the Hall parameter ocetei is the product

of the electron cyclotron frequecy and the electronion collision time. In a computational study37 at b/(ocetei)B6006,000, heat-ux effects were dominant, but for the smaller values of b present in these experiments, b/(ocetei)B0.11 and heat-ux effects are subdominant. The large value of the Hall parameter in these experiments, with oceteiB2040, also indicates that heat conduction perpendicular to the magnetic eld is strongly suppressed. This has been conrmed as well in the PIC modelling, which indicates that the ow-related advection of magnetic elds is much greater than the heat-ux (Nernst) magnetic advection.

3D geometry effects have little impact on reconnection rate. Though the 3D structure of the plasma bubble collisions is a notable feature of these experiments, in this particular geometry it

dL ; 1

where B1 (B2) is the magnetic eld strength and r1 (r2) is the plasma density on the large (small) bubble side of the current sheet, and d/L is the current sheet aspect ratio. The hybrid Alfvn speed VA,hybrid is dened7 as

V2A;hybrid

B1B2B1 B2 m0r1B2 r2B1

: 2

Agreement between the simulated reconnection rates and the predictions of this theory is illustrated based on instantaneous, local conditions around the time of peak reconnection rate. The PIC simulations show that the dynamically evolving asymmetry in the reconnection layer departs signicantly from initial asymmetries: primarily, the initial asymmetry is one of plasma density, but as the system evolves and pressure balance is established around the layer the magnetic eld asymmetry becomes dominant. At the peak reconnection rate in the symmetric simulation, based on the simulated density of2.4 10 4 g cm 3 (ne 7.7 1019 cm 3 for this fully ionized

CH plasma), magnetic eld strength of 1.7 MG, and current sheet

B1 B2

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B (MG)

0.9

z x

y

0.3 0.3 Magnetic fields

0.9

z

y

0.1

Tilt, Shear

Hall

Z(cm)

0

Reconn. plane

Current sheet

0.1

0.1

0

0.1 0.2

y (cm)

Vxe/Cs0

5

Reconnection rate

Tilt

Flat

4

2

2

4

0

z

E y(arb. units)

x

00 1

0.5Time (arb. units)

Figure 5 | Out-of-plane magnetic elds due to 3D effects. (a) LASNEX

simulation of magnetic elds around asymmetric plasma bubbles just before their collision shows (b) how magnetic elds at the reconnection plane are produced, including the quadrupolar Hall magnetic elds (black) and out-of-plane elds due to the tilted reconnection plane and out-of-plane velocity shear across the current sheet (grey). 2D PIC simulations initiated with out-of-plane (Tilt) elds show (c) modied electron ows but (d) a reconnection rate identical to those without external out-of-plane elds (Flat).

was found that changes to the magnetic eld structures due to a tilt in the reconnection plane and out-of-plane velocity shear have negligible impact on the reconnection rate in this strongly driven case. Figure 5 illustrates two asymmetric plasma bubbles and their magnetic elds just before the collision. Because the bubbles collide in such a way that the reconnection plane (y0 0) is not

parallel to the foil (y 0), the azimuthal magnetic elds have a

component out of the reconnection plane, forming a bipolar eld structure antisymmetric about x0 0 with a magnitude

Btilty

0 B0 sin y, where y is the tilt angle between the foil and the

reconnection plane and B0B0.5 MG is the magnitude of the azimuthal magnetic eld at the perimeter of each bubble. With yB25, Btilty

0

0:3 B0.

In addition, LASNEX simulations indicate that a rapid upward expansion of the small bubble (Vy,smallB500 mm ns 1), in contrast to the weaker upward expansion of the large bubble at the interaction point (Vy,largeB200 mm ns 1), creates a

DVy0B270 mm ns 1 out-of-plane velocity shear across the current sheet, leading to the generation of additional out-of-plane magnetic elds38. For DVy0B270 mm ns 1, Bz0B0.4B0, and the velocity shear gradient spread out over B400 mm, Bsheary

0 0:2 B0 in the same bipolar orientation as that caused by

the reconnection plane tilt. Both of these effects are estimated to produce out-of-plane magnetic elds comparable to two-uid or Hall reconnection out-of-plane magnetic elds (typically0.10.5B0 (ref. 35)) that arise consistently with electron currents, indicating that these additional out-of-plane elds might have been expected to impact the reconnection process.

However, based on the data, with reconnection occurring at a similar rate in symmetric and asymmetric experiments, it is

inferred that these out-of-plane magnetic elds and their interference with Hall magnetic elds and electron currents have minimal net effect on the reconnection rate. The imposed out-of-plane magnetic elds enhance the electron inow on the small-bubble side and stymie electron inow on the large-bubble side due to the JHall Btilt force in the -z0-direction. 2D PIC

simulations with additional out-of-plane tilt magnetic elds were conducted to assess this effect and have conrmed this result (Fig. 5c), demonstrating enhanced electron ow on the upper side of the current sheet, reduced electron ow on the lower side, but no net change in the reconnection rate (Fig. 5d). (In contrast, PIC simulations with a quadrupolar out-of-plane magnetic eld, opposed to the quadrupolar Hall magnetic elds in each quadrant, show a reconnection rate that is reduced by a factor of B3.) These tilt simulations indicate that typical electron ow speeds related to the Hall current are approximately half of the bulk ow velocity VeB0.5Vb. It is hypothesized that the minimal impact of the modication of electron ows on the reconnection rate is due to the reconnection process being strongly externally driven, as the small net fractional change in electron velocity DVe,nett0.1Ve from the increase in Ve on one side and decrease

on the other side is negligible in comparison with the large inow speeds (DVe;net Vb). Interestingly, these results bear on

collisionless guide-eld reconnection in strongly driven systems, where small perturbations in the local physics due to out-of-plane elds may be overwhelmed by the strong drive mechanism, in contrast to tenuous, low-b, quasi-steady plasmas39.

DiscussionStrongly driven asymmetric magnetic reconnection has been systematically studied in the laboratory using colliding bB10 laser-produced plasmas. The super-Alfvnic annihilation of magnetic elds is observed to occur at nearly the same, ow-based rate in asymmetric and symmetric experiments. In support of these experiments, 2D PIC simulations indicate that near-equal reconnection electric elds, consistent with local electron physics at the current sheet, is supported and generated by bulk plasma ows into the reconnection region that are nearly equal, on average, in symmetric and asymmetric cases. Out-of-plane magnetic elds, due to the asymmetry in geometry and velocity shear, are predicted to modify electron ow in this two-uid reconnection event, but are inferred to have minimal impact on the reconnection rate in this experiment. This result is due to the fact that the net change in inow is small compared to the rapid inow velocity in this strongly driven system. Strongly driven, two-uid asymmetric magnetic reconnection such as studied in these experiments occurs in many astrophysics and space physics environments, most notably at the Earths dayside magnetopause. The results of these experiments suggest that the rate of reconnection at the magnetopause may be dictated by the strength of the solar wind, which determines the local plasma conditions immediately around the current sheet, and is insensitive to the strongly asymmetric initial plasma conditions far upstream of the reconnection site. Future experiments with different drive conditions may explore a more extensive parameter space of asymmetries in magnetic eld strength, density, and drive and directly assess, using locally measured quantities, the predicted reconnection rate scalings.

Methods

Target and detector information. The target foil was 1:1 C:H parylene, with a density of 1.11 g cm 3. The capsule imploded to produce backlighter protons was a SiO2 shell with a 420-mm diameter and a 2-mm-thick wall, lled with 18 atm of equimolar deuterium (D)/helium-3 (3He) gas. The Ni mesh was 60 mm thick. 15-MeV backlighter protons are recorded at 100% efciency as individual tracks deposited in the solid-state nuclear track detector CR-39, ltered by 7.5 mm Ta, B1,500 mm CR-39 and 200 mm Al.

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Data processing. The CR-39 is etched at 80 C for 23 h in a 6-N solution of NaOH, which reveals the tracks with diameters on the order of B10 mm. An automated microscope scans and records information about the protons tracks, including their location on the piece of CR-39. Custom software is used to determine track properties and to transform that information into an image of proton uence incident on the CR-39. The number of proton tracks per area is plotted in Fig. 2a, with the mesh placed between the backlighter source and the experiment producing a grid pattern in proton uence consisting of an arrayof individual proton beamlets. A semi-automated Matlab routine identies the centroid of proton beamlet locations and the orientation and spacing of the unperturbed grid, based primarily on the beamlet points far from the centre that have not been deected. Connecting beamlets to their original grid point, a map of proton beamlet deection is constructed. The magnitude of the magnetic eld strength integrated along the path of the backlighter proton beamlet is inferred from the magnitude of the beamlet deection.

Modelling parameters. The 2D (azimuthally symmetric) DRACO simulations, from which the hydrodynamic proles of density, temperature and ow velocity were obtained and subsequently fed into the PIC simulations, used a non-uniform Eulerian moving grid, with the highest resolution of 0.25 mm in the direction perpendicular to the foil and 1 mm in the direction parallel to the foil. The time step in the DRACO simulations was around 3 10 14 s (0.03 ps).

The LASNEX simulations, from which the approximate magnetic eld proles were obtained and subsequently fed into the PIC simulations, used a 2D, azimuthally symmetric slab geometry composed of arbitrarily shape quadrilaterals. The hydrodynamics was Lagrangian, but in the event of severe grid distortions, the grid was remapped to a more regular shape. These simulations were initiated with a 5-mm thick, 2,000-mm radius foil in a 5,000-mm by 2,000-mm low-density gas background. The gas is used in the simulations for numerical reasons, to give the foil something to expand and rezone into, with a density chosen so that it does not alter the dynamics of the foil. The gas on the laser side had 120 210 zones that

decreased in size in the direction perpendicular to the foil as the zones got closer to the foil. The back side of the foil had 60 210 zones which were also decreased in

size closer to the foil. The foil itself had very thin zones in the direction perpendicular to the surface, 0.01 mm on the front and back surfaces, which increased in size up to about 0.3 mm towards the middle of the foil; the radial zone size was 6 mm. In the Lagrangian framework, the zone size evolved with the simulation, so that by 1 ns into the simulation, the smallest zone in the direction perpendicular to the foil was around 1.5 mm wide. The time step was not xed, and was dynamically determined based on a number of physical processes. Typically, the time step ranged from 0.01 to 1.0 ps during the simulation.

The PSC PIC simulations were run as initial value problems, starting with analytic ts to proles of hydrodynamic quantities such as density, temperature and ow velocity from DRACO simulations and proles of magnetic eld based on

LASNEX simulations. The initial electric elds were based on V B advection and

the initial plasma current was t to self-consistently match the magnetic eld prole. The scaling of magnitudes was done to match key dimesionless parameters in the PIC simulation, including: the characteristic electron density (ne,init), close to

the peak initial density; the characteristic electron temperature (Te,init); the peak

ow speed (Vinit); the peak magnetic eld (Binit); and length scales associated with proles of these quantities. The simulations use heavy electrons (electron mass is only 1/100 of the ion mass) and a fairly low speed of light (a factor of 510 greater than the characteristic electron thermal speed). These non-physical characteristics force choices to be made in scaling the physical units from DRACO and LASNEX to

dimensionless quantities as used in running the PIC simulation. The dimensionless magnetic eld magnitude in the PIC simulation is scaled to match the plasma thermal b, while the ow speed magnitude is scaled to match the ow Mach number (V/Cs0). The collisionality or resistivity is tuned to match the Lundquist number (S), which is equivalent to matching the ratio of the characteristic electronion collision rate to electron cyclotron frequency (nei,init/oce,init 0.25),

where oce,init is based on the characteristic magnetic eld strength Binit. The overall PIC modelling procedure is similar to that described by Fox et al.35 The global ion skin depth (di0) is the key unit of length and is based on the characteristic density.

The simulation size for the symmetric simulations was 320 160 di0 and for the

asymmetric simulations was 320 320 di0. This difference in size is attributed to a

subtle difference in boundary conditions. For both cases, the boundary conditions are double periodic. In the symmetric case, this is equivalent to an innite chain of plasma bubbles. In the asymmetric case, it is equivalent to an innite chain of plasma bubble pairs (large and small). The simulation grid was 10,000 5,000 for

the symmetric simulations and 6,400 6,400 for the asymmetric simulations.

Approximately 4.5 109 particles were used, with 400 particles per cell at the

characteristic density ne,init. The time steps, expressed in units of the characteristic

plasma frequency ope,init (based on the characteristic density ne,init) are dt 0.17/o

pe,init for the symmetric simulations and ne,init) are dt 0.27/o

pe,init

for the asymmetric simulations.

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Acknowledgements

We thank the OMEGA operations and target fabrication crews for their assistance in carrying out these experiments and J. Schaeffer, R. Frankel and E. Doeg for their help in processing of CR-39 data used in this work. We also thank Paul Cassak, Stephen Bradshaw and James Drake for discussions on asymmetric reconnection. The PIC simulations were conducted on the Titan supercomputer through the INCITE programme at the Oak Ridge Leadership Computing Facility, supported by the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This work was performed in partial fulllment of the rst authors PhD thesis and supported in part by the U.S. DoE (Grant No. DE-FG03-09NA29553, No. DE-SC0007168), LLE (No.414090-G), NLUF (No.DE-NA0000877), FSC (No.415023-G) and LLNL (No.B580243).

Author contributions

M.J.R. designed and executed the experiments, analysed the data, developed the discussion and wrote the manuscript; C.K.L. conceptualized the experiment, initially developed the measurement technique and contributed to the discussion and interpretation of experimental results; W.F. performed the PIC simulations and contributed to the discussion and interpretation of results; I.I. performed detailed radiation-hydrodynamics simulations; F.H.S. initially developed the measurement technique and assisted in interpretation of experimental data; R.P.J.T. performed initial radiation-hydrodynamics simulations; J.A.F. assisted with complementary measurements and scrutiny of experimental results; C.S. and V.G. analysed the complementary data; R.D.P. helped develop the measurement technique initially and was involved in technical discussions.

Additional information

Competing nancial interests: The authors declare no competing nancial interests.

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How to cite this article: Rosenberg, M. J. et al. A laboratory study of asymmetric magnetic reconnection in strongly driven plasmas. Nat. Commun. 6:6190doi: 10.1038/ncomms7190 (2015).

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