Magnetic Reconnection and Plasma Dynamics in Two-Beam Laser-Solid Interactions
P.M. Nilson,1L. Willingale,1M.C. Kaluza,1,*C. Kamperidis,1S. Minardi,2M.S. Wei,1,†P. Fernandes,1M. Notley,3
S. Bandyopadhyay,3M. Sherlock,3R.J. Kingham,1M. Tatarakis,2Z. Najmudin,1W. Rozmus,4R.G. Evans,3
M.G. Haines,1A.E. Dangor,1and K. Krushelnick1
1Department of Physics, Imperial College, London SW7 2AZ, United Kingdom
2Technological Educational Institute of Crete, Chania, Crete, Greece
3Central Laser Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon., United Kingdom
4Department of Physics, University of Alberta Edmonton, Alberta, Canada
(Received 22 May 2006; published 19 December 2006)
We present measurements of a magnetic reconnection in a plasma created by two laser beams (1 ns
pulse duration, 1 ? 1015Wcm?2) focused in close proximity on a planar solid target. Simultaneous
optical probing and proton grid deflectometry reveal two high velocity, collimated outflowing jets and
0.7—1.3 MG magnetic fields at the focal spot edges. Thomson scattering measurements from the
reconnection layer are consistent with high electron temperatures in this region.
DOI: 10.1103/PhysRevLett.97.255001PACS numbers: 52.38.Fz, 52.30.?q, 52.35.Vd, 52.50.Jm
Plans for achieving ignition by inertial confinement on
the National Ignition Facility and the Laser Me ´gajoule will
use a hohlraum-generated, temporally shaped radiation
drive to implode a deuterium-tritium pellet. The thermal
radiation drive is generated by focusing multiple laser
beams in close proximity to each other on the inner surface
of a high-Z hohlraum cavity .
A detailed knowledge of the hohlraum plasma evolution
is required for improving hohlraum design and for bench-
marking multidimensional radiation hydrodynamic codes.
Magnetic fields are often important for electron energy
transport  in such experiments but, until recently, have
largely been ignored and have proven difficult to imple-
ment into existing codes. Experimental benchmarking data
is required, and consequently there is much interest in
spatially resolved measurements of the evolution of hot
(>1 keV) and dense (ne> 1019cm?3) plasmas. Schemes
investigated include laser-exploded foils [3,4] and the con-
vergent flows from conical  and cylindrical targets .
In this Letter, we present measurements of the plasmas
created by closely focusing two heater beams on a planar
foil target. The two plasmas typically collide and stagnate,
yet for laser spot separations of greater than about seven
focal spot diameters, the sudden appearance of two very
distinct, highly collimated jets can be observed. The azi-
muthal rTe? rne magnetic fields that are generated
around each laser spot  have also been observed using
proton deflectometry. These measurements reveal plasma
dynamics and a magnetic field distribution in accordance
with a reconnection geometry.
During reconnection, two counterstreaming plasmas
meet, and the local diffuson of a magnetic field within a
neutral current sheet allows field lines to break and recon-
nect . Some fraction of the magnetic energy is converted
into thermal energy as the system relaxes to a lower energy
state and reorganizes its field line topology [9,10]. Several
theories have identified the important role of field-aligned
outflowing jets in energy conservation. However, many
details of the acceleration and heating mechanisms remain
unknown.In our experiment, Thomson scattering measure-
ments in the reconnection layer reveal high electron tem-
peratures of 1.7 keV. Such high electron temperatures are
in contrast to the high ion temperatures that are more
consistent with a hydrodynamically stagnating plasma in
the absence of magnetic fields [11,12]. The experimentally
observed plasma flows and magnetic field convection, high
electron temperatures, and jet formation are consistent
with a magnetic reconnection.
The experiment used the Vulcan laser at the Rutherford
Appleton Laboratory, UK. The experiment is shown in
Fig. 1. Two heater beams, with wavelength ? ?
1:054 ?m, irradiated either an aluminum or gold target
foil. A 1 ns duration square pulsewas used with an average
energy of 200 J per heater beam. The targets were 3 mm ?
5 mm foils of 20–100 ?m thickness. Each beam was
focused using f=10 optics to a focal spot diameter of
30–50 ?m FWHM, giving an incident laser intensity of
1 ? 1015Wcm?2. The two heater beams were aligned
with varying on-target separations.
FIG. 1 (color online).
The target geometry and field configu-
PRL 97, 255001 (2006)
22 DECEMBER 2006
© 2006 The American Physical Society
The target plasma was diagnosed with multiple diagnos-
tics. Firstly,a 10pspulse duration,263nm probebeam was
passed transverse to the target surface at various times.
Probe beam light refracted by the target plasma was reim-
aged and divided into two diagnostic channels with a mag-
nification of 13 and a resolution of 5 ?m. Shadowgraphy
was used to monitor the global plasma dynamics, while the
plasma electron density was measured using a modified
Nomarski interferometer. A combination of reflective and
bandpass (?? ? 10 nm) interference filters was used to
reduce the detectable self-emission from the target.
Shadowgrams of aluminum interactions are shown in
Figs. 2(a) and 2(b). For laser spot separations of around
200 ?m in Fig. 2(a), a quasihomogenous plasma is ob-
served at t ? t0? 2:0 ns, where the heater beams turn on
at t0. The darker areas correspond to regions which are
opaque to the probe light and also regions where there are
large density gradients. Figure 2(b) demonstrates the sur-
prising result that upon separating the laser spots to around
400 ?m, a very prominent, high velocity flow of plasma is
5 ? 107cms?1away from the target surface. This image
was taken at t ? t0? 1:5 ns.
Similar dynamics are observed in gold interactions, as
shown in Figs. 2(c) and 2(d), with laser spot separations of
around 400 ?m. Figure 2(c) is an interferogram of the
midplane taken at t ? t0? 0:4 ns, showing the first low
density interaction between the laser ablated plasmas fol-
lowinga finite transit time from each laser spot.Figure2(d)
is a shadowgram taken at t ? t0? 2:5 ns and shows the
subsequent jet formation. A simultaneous interferogram is
shown in Fig. 2(e). The central plasma feature is not a
stagnation column butthe transverse projection oftwohigh
velocity jets. Localized fringe shifts identify the two highly
collimated jets. They exhibit great symmetry and extend
over 400 ?m from the target surface and have an electron
density of around 6 ? 1019cm?3. Radiation losses in the
gold target has produced more collimated flows in com-
parison to the aluminum target. Further evidence for the
early formation of the two jets comes from viewing the
interaction at 90?such that both jets are clearly seen
separated [Fig. 2(f)].
The sudden appearance of two distinct jets from the
midplane is an important observation and an unexpected
result if only hydrodynamics were considered. Once the
plasma generated from one laser spot has reached the mid-
plane, its dynamics are influenced by the presence of the
plasma generated by the other laser spot. Here there will be
a conversion of streaming ion kinetic energy into ion
thermal energy where the two flows stagnate and thermal-
ize. Increasing the laser spot separation not only alters the
collisionality ofthe interaction at the midplane, butalsothe
competition between the thermal plasma pressure nekBTe
and the magnetic pressure B2=2?0in this region. The
thermal plasma pressure will reduce here as the laser spot
separation increases. The plasma dynamics at the midplane
will become increasingly sensitive to the azimuthal rTe?
rneself-generated magnetic fields that are convected into
this region through the lowering of the plasma-? (i.e., the
ratio of thermal and magnetic pressures).
To further study the magnetostatic and electrostatic field
effects, face-on proton grid deflectometry  was per-
formed. The protons were derived from a 20 ?m thick
gold foil located 2 mm behind the main target. A high-
intensity, 1 ps pulse duration beam, with an energy of
100 J, was focused onto the gold foil using an f=3:5 off-
1019Wcm?2was achieved with a focal spot of 8–10 ?m
FWHM, containing 30–40 per cent of the energy.
Typical deflectometry data are shown in Fig. 3 for
aluminum target interactions. By t0? 100 ps, protons
have been radially deflected away from each of the focal
spots by the azimuthal magnetic fields. Proton density
perturbations in the focal regions are caused by the local-
ized electric and magnetic fields associated with fine-scale
filamentary structures at the target surface. A region of
FIG. 2 (color online).
of aluminum targets (a, b) and gold targets (c–f). The probe
beam geometry is shown (lower right).
Transverse 263 nm probe beam images
PRL 97, 255001 (2006)
22 DECEMBER 2006
proton accumulation is observed between the two focal
spots, consistent with the azimuthal magnetic fields de-
flecting protons into the region of magnetic field null.
By t0? 500 ps, the magnetic fields generated in the
plasma have expanded across the target surface at around
107cms?1and started to interact with each other and form
a reconnection geometry (as shown schematically in
Fig. 1). At later times, the thin interaction region of around
100 ?m thickness develops instabilities, characteristic of
the azimuthal magnetic fields, counterstreaming flows, and
velocity shear present. It is clear that the plasma is magne-
tized and the presence of the magnetic field is greatly
affecting the plasma dynamics.
The dominant electric field is in the target normal direc-
tion^E ? E^ z; therefore, the protons are deflected by the
^ v ?^B force. The proton flux has a range of energies and
experiences the magnetic field over some characteristic
length LBdepending on the probing time after t0.For LB?
100 ?m at t ? 100 ps, an apparent grid deflection on the
film of 500 ?m (for protons of 13.5 MeV) indicates a
magnetic field of around 1.3 MG. Such conditions and
the range of imaged grid deflections around the laser focal
spot edges indicate magnetic fields in the range 0.7–
1.3 MG at t ? t0? 100 ps.
Thomson scattering (TS) was used to measure the elec-
tron temperature in the aluminum interactions. Fig. 4(a)
shows the two locations where TS light was collected on
different shots using a 10 J, 263 nm probe beam of 1 ns
(square) pulse duration. The probe beam was aligned par-
allel to the target surface and focused to 50 ?m using f=10
optics. The length of the cylindrical scattering volume was
approximately 70 ?m. Scattered light was collected at
? ? 90?and reimaged with a magnification of 1.5 onto a
100 ?m spectrometer slit. The signal was spectrally dis-
persed using a 3600 lines=mm grating and a 1 m spec-
trometer coupled to a streak camera. The time-resolved TS
spectrawere measured with a temporal resolution of100ps
and a wavelength resolution of 0.05 nm.
Figure 4(b) shows a TS spectrum from scattering vol-
ume 1. For t0? 1:0 ns < t < t0? 2:0 ns, two ion acoustic
features are observed. Their separation reduces in time,
indicating a decreasing electron temperature from hydro-
dynamic expansion. Figs. 4(c) and 4(d) show the spectra at
t ? t0? 1:5 ns and t ? t0? 2:25 ns with theoretical fits
that have been obtained from standard collisionless theory
of the dynamical form factor . The electron and ion
velocity distribution functions are Maxwellians, the elec-
tron density is ne? 5 ? 1019cm?3, and the fits include
experimental broadening due to the wavelength resolution
of 0.05 nm. The separation between the two ion acoustic
resonances in Figs. 4(c) and 4(d) are consistent with elec-
tron temperatures of 800 eVand 700 eV, respectively. The
slight asymmetry in the ion acoustic peaks in Fig. 4(d) is
FIG. 3 (color).
target interactions taken 100 ps, 500 ps, and 800 ps after the
heater beams arrive at the target surface. Each image is shown
for protons with an energy of EP? 13:5 MeV.
Proton grid deflectometry images of aluminum
FIG. 4 (color).
from scattering volumes 1 (b, c, d) and 2 (e, f). The spectra are
compared with standard theoretical fits  (c, d). A spectrum
from the reconnection region is shown in (e) and compared in (f)
to the spectrum predicted using the ion distribution function
(IDF) shown in (g) (blue curve). This IDF is calculated using a
hybrid kinetic ion and fluid electron code . See text for
The scattering geometry (a) and the TS spectra
PRL 97, 255001 (2006)
PHYSICAL REVIEW LETTERS
22 DECEMBER 2006
modeled by an electron drift velocity of 3:0 ? 107cms?1. Download full-text
Such a drift of the bulk electrons may occur in response to
the heat flux carried by fast particles.
Figure 4(e) showsa TSspectrum from scattering volume
2. Electrons are not directly heated by the laser beams in
this region. A large increase in the ion acoustic peak sepa-
ration for t > t0? 1:0 ns is observed. For an equilibrium
plasma, a straightforward fit of the experimental scattering
spectrum at t ? t0? 1:2 ns in Fig. 4(f) would result in an
electron temperature of 9 keV. X-ray pinhole imaging
confirmed the presence of plasma heating at the midplane;
however, such temperatures are unphysically high, particu-
larly since the plasma in volume 2 has to expand into this
region from the laser heated coronas (volume 1) where the
temperature was measured at 700–800 eV.
To understand the plasma conditions in volume 2, we
have performed 2D simulations using a hybrid code 
with kinetic ions and fluid electrons. The measured plasma
parameters from volume 1 provided boundary conditions
within two laser spots. Transverse plasma expansion re-
sults in two counterstreaming ion populations as described
by the calculated ion distribution functions (IDFs) in
Fig. 4(g). The green curve is the spatially integrated IDF
as a function of the velocity along the line joining the two
laser spots, while the blue curve is a function of the
velocity along the TS diagnostic viewing angle. We have
included such an IDF (blue curve), i.e., the sum of two
shifted Maxwellians, in the calculation of the TS spectrum
at t ? t0? 1:2 ns, as shown in Fig. 4(f). Avery good fit to
the experimental data has been obtained for an electron
Te? 1:7 keV
1020cm?3) and the ion flow velocity
107cms?1which is on the order of the sound velocity.
These two resonances are the result offour ‘‘beamlike’’ ion
modes in the plasma caused by interpenetrating flows 
that will be present post-reconnection.
Such electron temperatures are surprisingly high since
there is no direct laser heating in this region. If the mid-
plane interaction consisted of a standard collision, it would
be ion heating that dominated the interaction [11,12]. The
electrons gain energy subsequently through electron-ion
equilibration. However, the time scale over which this
occurs is many nanoseconds. We measure high electron
temperatures that cannot be reconciled to electron-ion
equilibration alone or compressional heating (this is not
an efficient plasma compression geometry). This therefore
indicates another energy source. Such a source would need
to supply energy to the electrons at a sufficiently high rate
that it was not simply radiated away. The only source
available with sufficient free energy that could be provided
at such a rate is the conversion of magnetic energy into
plasma thermal energy through a reconnection mechanism.
The present interaction can be compared to the Sweet-
Parker (SP) model of magnetic reconnection [17,19]. For
aluminum plasmas, the Alfve ´n velocity vA? 1:35 ?
107cms?1, the Alfve ´n transit time ?A? LH=vA? 7:4 ?
10?10s,and the resistive diffusiontime scale ?R? ?0L2
ne? 2:5 ?
ui? 2:0 ?
??? 2:2 ? 10?8s,
800 eV, and B?1MG. Here, the perpendicular Spitzer re-
sistivity ?perp? 2?kis used because the current flows per-
pendicular to the field. The SP reconnection rate is given
by ??R?A?1=2? 4 ns. However, such estimates are subject
to significant uncertainty. LHcould be tens of microns in
the reconnection region and reduce the calculated recon-
nection rate to around 0.5 ns. The SP model has also been
shown not to be universally applicable, such as in solar
flares , for example, where the predicted reconnection
rate is orders of magnitude too slow. Further study is re-
quired to confirm the validity of the SP model in this case.
In summary, we have studied a magnetic reconnection
geometry created in a laser-produced plasma. The mag-
netic fields, plasma flows, field convection, jet formation,
and high electron temperatures (for relatively large laser
spot separations, in which the magnetic pressure will be-
come increasingly important at the midplane) are consis-
tent with a magnetic reconnection rather than a standard
hydrodynamic collision in the absence of magnetic fields.
Such interaction geometries may help in elucidating the
microphysics and heating mechanisms during magnetic
The authors acknowledge the assistance of the CLF staff
and the support of the UK Engineering and Physical Sci-
ences Research Council and AWE plc, Aldermaston, UK.
LH? 100 ?m,
*Present address: Institute for Optics and Quantum
†Present address: Center for Energy Research, University
of CA, USA.
 J.D. Lindl et al., Phys. Plasmas 11, 339 (2004).
 P. Nicolai et al., Phys. Plasmas 7, 4250 (2000).
 R.L. Berger et al., Phys. Fluids B 3, 3 (1991).
 P.W. Rambo et al., Phys. Plasmas 1, 4050 (1994).
 D.R. Farley et al., Phys. Rev. Lett. 83, 1982 (1999).
 S.H. Glenzer et al., Phys. Rev. Lett. 79, 1277 (1997).
 J.A. Stamper et al., Phys. Rev. Lett. 40, 1177 (1978).
 D. Biskamp, Phys. Rep. 237, 179 (1994).
 T.D. Phan et al., Nature (London) 439, 175 (2006).
 H. Ji et al., Phys. Rev. Lett. 80, 3256 (1998).
 O. Rancu et al., Phys. Rev. Lett. 75, 3854 (1995).
 C. Chenais-Popovics et al. Phys. Plasmas 4, 190 (1997).
 A.J. Mackinnon, Rev. Sci. Instrum. 75, 3531 (2004).
 J. Sheffield, Plasma Scattering of Electromagnetic
Radiation (Academic, New York, 1975).
 M. Sherlock et al., Phys. Plasmas 11, 1609 (2004).
 L.V.Powersand R.L.Berger,Phys.Fluids 31, 3109 (1988).
 P.A. Sweet, in Electromagnetic Phenomena in Cosmical
Physics, edited by B. Lehnert (Cambridge University
Press, New York, 1958) p. 123.
 E.N. Parker, J. Geophys. Res. 62, 509 (1957).
(Princeton University Press, Princeton, NJ, 2004).
 M.G. Kivelson and C.T. Russell, Introduction to Space
England, 1995), and references therein.
PRL 97, 255001 (2006)
PHYSICAL REVIEW LETTERS
22 DECEMBER 2006