Brilliant XUV radiation from laser-illuminated near-critical plasmas

3.4 MB·

by  T. G. Blackburn

Brilliant XUV radiation from laser-illuminated near-critical plasmas
T. G. Blackburn,1,∗ A. A. Gonoskov,1,2,3 and M. Marklund1
1Department of Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
2Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod 603950, Russia
3Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod 603950, Russia
(Dated: January 26, 2017)
Bursts of extreme ultraviolet (XUV) radiation are generated by the nanoscale oscillations of
7 surfaceelectronsinplasmasilluminatedbyintense,linearly-polarised laserlight. Weshowthatthis
1 re-emission is especially efficient when the plasma electron density is between 1 and 10 times the
◦
0 relativistic critical density and the laser incidence angle is 60 . The resulting XUV flash, averaged
2 over the reflected pulse duration, has brilliance in excess of 1023 photons/s/mm2/mrad2 (0.1%
bandwidth)in the10–100 eV range, far abovethat of a third-generation synchrotron light source.
n
a
J
I. INTRODUCTION approximationaccurate within 5% is
5
2
n n λ
There has been extensive demonstration of radiation S = e 23 µm (1)
] sources in the extreme ultraviolet (XUV) to X-ray fre- a0ncr ≃ √I22
h
p quency range employing laser illumination of solid [1– where n is the electron number density in units
23
- 5] and gaseous targets [6–8]. High-frequency radiation of 1023 cm−3, I is the laser intensity in units of
m 22
naturally arises in these interactions due to the non- 1022 Wcm−2 and λ its wavelength in microns.
µm
s linear motion of electrons oscillating in the strong elec-
An overdense plasma, through which light cannot
a
tromagneticfields ofa relativisticallyintense laserpulse.
l propagate, is typically characterised by S & 1. In this
p ThegenerationefficiencyandspectralpropertiesofXUV
regime laser energy must be either reflected or absorbed
s. sources are of paramount importance for applications byelectronheatingandionmotion. Forhighly-overdense
c in diagnostic imaging [9, 10], the creation and study of
targets (S 1) electron heating is minimal and most of
i
s warm dense matter [11, 12] and for probing attosecond the laser e≫nergy is reflected. At moderate intensities,
y phenomena [13].
coherent wake emission leads to harmonic generation in
h
p Here we show that illuminating plasmas with elec- theultraviolet[3];athigherintensities,experimentshave
[ tron density between 1 and 10 times the relativistic demonstratedconversionefficiencies of0.01(10−5) to X-
critical density at 60◦ under realistic conditions cou- rayswithenergygreaterthan20eV(1keV)[17],or10−4
1
ples >3% of the laser energy to harmonics with en- in the tens of eV at a 3 [18].
v ergy ω > 10 eV. The brilliance of the reflected light, Harmonic generatio0n≃in the regime S 1 can be de-
68 1023 photonss−1mm−2mrad−2 at 0.1% bandwidth at scribed under the assumptionthat the ov≫erdensesurface
2 100 eV, is unprecedented in laser-solid interactions and acts as a relativistic oscillating mirror (ROM), perfectly
7 realisable at currently available high-intensity, short- reflectingtheincidentlightateveryinstantoftimewithin
0 pulse laser facilities. The physical origin of this radia- the wave cycle from a certain oscillating point [19, 20].
1. tionisnear-micronscaleoscillationoftheplasmasurface, The Doppler shift when this point moves back towards
0 which temporarily stores a large fraction of the laser en- the the observer at relativistic velocity leads to the in-
7 ergy in a longitudinal electric field; this compresses the creaseinfrequencyofthereflectedlight. Modelsbasedon
1 re-emissioninto an attosecond burst that has larger am- thisassumptionhavegiveninsightintopolarisationselec-
v: plitude than the incident light [14, 15]. tion rules [20, 21], the angular dependence of generation
i We use three dimensionlessparametersto characterise efficiency [22], and the power-law form of the intensity
X
the laser-plasma interaction: a = eE/(mcω), the nor- spectrum [23–27].
0
r
a malised amplitude of an electromagnetic wave with elec- We consider here plasmas with electron density S <
tric field strength E and angular frequency ω; θ, the an- 10 (but above the threshold for relativistic self-induced
gle between the laser wavevector and the target normal; transparency),wherethe reflectionprocessisnotinstan-
and S, the ratio of the electron number density n to taneous. Instead energy is first accumulated in a charge
e
that of the relativistic critical density a n [16]. Here separation field when the laser radiation pressure dis-
0 cr
n = ǫ mω2/e2 is the non-relativistic critical density, placeselectronsfromtheplasma-vacuumboundary. This
cr 0
and e, m are the electron charge and mass, c the speed energy is then re-emitted when the electrons propagate
of light, with ǫ the vacuum permittivity. A convenient backtowardstheboundary. Duetotherelativisticnature
0
of the motion, the displaced electrons are compressed
into a thin layer. The relativistic electron spring (RES)
modelofGonoskovet al.[14]successfullydescribesthese
interactions by assuming that emission from the sepa-
∗ [email protected]
rated ions and electrons compensates the incident radia-
2
tionwithin the plasma bulk, while allowingenergyaccu-
mulation in the separation region.
Emission of a thin layer has been studied in the con-
text of creating reflected and transmitted attosecond
pulses [28, 29] and in thin-foil interactions [30, 31]. Such
a layer forms automatically in the RES regime leading
to the emission of attosecond [32] bursts with amplitude
severaltimesthatoftheincidentlight[14,15,33],aswell
as bright incoherent beams [34].
If the reflected amplitude exceeds the incident ampli-
tude byafactorf 1forS <10,andwiththeassump-
≫
tion that the plasma is perfectly reflective,an amplitude
increaseoff impliesthatthetemporalwidthofthepulse
isreducedbyafactorf2 andsocharacteristicharmonics
are produced of order n f2. It is therefore advanta-
≃
geous to access the RES regime of plasma dynamics to
ensure efficient generation of high harmonics.
There has been considerable work devoted to optimis-
ing XUV generation [35], including PIC simulation of
few-cyclelasers[29,36],developmentofanalytics[14,22]
andexperiment. Ithasbeenshown,forexample,thatthe
denting of the plasma surface by the laserlight pressure,
which would otherwise increase the divergence of the
highharmonics,maybecompensatedbytailoringthein-
put laser pulse [37]. Simulations have also demonstrated
FIG. 1. a) The interaction geometry under consideration is
the advantages of multiple reflection geometries [38] and
a p-polarised laser pulse incident on a semi-infinite plasma
specially-designed waveforms for the incident light [39].
slab with initial electron density n0 = Sa0ncr at an angle to
Herewefocus onthe basicpropertiesofthe laser-plasma
the target normal of θ. b) The electron density ne/n0 in the
interaction with a view to optimising the XUV yield.
boosted frame (see text) as a function of axial displacement
The paper is laid out as follows: first, we show in de- z′ andtimet′ whenlaserlightwithpeakamplitudea0 =60.4
tailthe advantagesofthe RESmechanismby comparing isincidentat60◦ ontoplasmawith(i)S =1and(ii)S =20.
the illuminationofanear-criticalandahighly-overdense c) In the lab frame, the amplitude of the reflected light ar
plasma in section II. Then in section III we use 1D relativetotheinitialamplitudea0 for(i,blue)S =1and(ii,
particle-in-cell (PIC) simulations to find the laser-target yellow-dashed)S =20. d)Thereflectivityperunitfrequency
configuration that maximises XUV generation. Having Rω of the plasma, i.e. Fourier spectra of the pulses shown in
c).
shown that this is a plasma with S 1 illuminated by
◦ ≃
laser light at an angle of θ = 60 , much as RES the-
ory predicts, we turn to 2D PIC simulation results in
section IV. We present our results for the angular and n0/cosθ and streaming velocity csinθ perpendicular to
brilliancepropertiesofthe XUVpulseandshowthatthe the target normal. Therefore the problem is reduced to
1D and 2D results are broadly consistent. We conclude one with a single spatial dimension [40].
by discussing the prospects of our work in section V. TodemonstratetheadvantagesoftheRESmechanism,
we compare the results of 1D3V particle-in-cell (PIC)
simulations using the spectral code elmis [41] of plasma
II. THE RELATIVISTIC ELECTRON SPRING with S = 1 and S = 20. The former is within the RES
MECHANISM regime; the latter in the ROM regime. In both cases
the laser has lab-frame profile a sinφcos2(φ/24) with
0
Theinteractiongeometryunderconsiderationisshown a0 =60.4 and wavelength λ=1µm; this corresponds to
in fig. 1a: we have a laser pulse with normalised am- apeakintensityof5 1021Wcm−2 andfullwidthathalf
×
plitude a and angular frequency ω incident on a cold maximum (FWHM) of 15 fs. In the boosted frame, the
0 ′ ′
plasma withelectrondensity Sa n atanangle θ to the laser has phase φ = ωcosθ(t z /c) and is p-polarised
0 cr ′ −
target normal. We will assume that the ions are suffi- (along x). The plasma is initialised with density pro-
′
ciently massive that they do not move. For the moment file ne,0 = Sa0ncrH(z )/cosθ, where H is the Heaviside
we work in the frame boosted by csinθ in the direction step function, velocity vx′,0/c= sinθ and temperature
−
parallelto the plasma surface. Neglecting the transverse 100 eV. It is represented by 200 (macro-)electrons and
′
intensityvariationofafocussedlaserpulse,inthisframe ions (Z/A=0.05) per cell of size ∆z =λ/(1800cosθ).
the laser may be treated as a plane wave with ampli- Figure 1b shows the electron density as a function of
′ ′
tude a cosθ normally incident on a plasma with density axial displacement z and time t. The oscillations arise
0
3
becausethelaserradiationpressurepusheselectronsinto
the plasma, gathering them into a thin region of high
′
charge density at z . The uncompensated ion current in
e
′ ′
theregion0<z <z setsupelectrostaticandmagneto-
e
static fields, the former exerting a force on the electron
density spike that balances and then exceeds the radi-
ation pressure. The fact that this force is proportional
′
to the displacementz , assumingthe downstreamregion
e
is entirely cleared of electrons, is the origin of the name
‘relativistic electron spring’ [14].
During the phase of the motion when the electrons
′
return towards z = 0, they acquire kinetic energy from
theplasmafields,reachinghighγ. Whentheirtransverse
velocity changes sign, at which moment in the lab frame
they propagate towards the observer along the specular
direction,alarge-amplitudeburstofradiationisemitted.
This is shown in fig. 1c: for S = 20, the waveform ac-
quiresanon-sinusoidalshapebuttheamplitudedoesnot
exceeed a , whereas for S = 1 for the waveform is char-
0
acterised by sharp transitions between positive and neg-
ative field and amplitude increase f = max(a /a ) 3.
r 0
≃
The consequence of this is seen in the Fourier analysis
of the reflected intensity R shown in fig. 1d: the high-
ω
harmonic intensity is an order of magnitude larger for
S =1 across the spectral range ω >10 eV. FIG. 2. The increase in the peak amplitude (a,c) and the
percentageoflaserenergyconvertedtoXUVwithω>10eV
Thisisbroadlyconsistentwiththeoreticalpredictions: (b,d) when plasma with electron density ne = Sa0ncr is il-
luminated by laser light with peak intensity I0 at an angle θ
RES theory predicts a frequency spectrum that decays
to the target normal. In (a,b) S is fixed at S = 1 and the
quasi-exponentially with harmonic order [14], in con-
intensityandangleofincidencearevaried;in(c,d),theangle
trast to the power-law decay ∂I/∂ω ω−m expected ◦
of incidence is fixed at θ=65 and theintensity and density
∝
in the ROM regime. Baeva et al. [23] predict a universal varied. IntensitiesanddensitiesforwhichS =1areindicated
m = 8/3, but a range 5/3 < m < 7/3 is seen in PIC with dashed lines.
simulation [26]; in any case, weakening of the power-law
decay to m 1.62 has been observed in thin-foil exper-
iments wher≃e XUV emission may attributed to electron III. OPTIMAL DENSITY AND ANGLE OF
nanobunches [28]. INCIDENCE
However, in these results the two processes are par- We now discuss how the plasma density and angle of
tially mixed due to the effect of the laser temporal pro- incidence can be chosen to maximise the increase in re-
file. The effective S varies across the pulse: the leading flected amplitude and the yield of high harmonics. Pre-
edge encountering a clean, sharp transition to S > 1, vious work considering single-wavelength light indicates
whereas the trailing edge encounters a surface with fi- that an optimum exists for plasma with S 0.5 and
nite densitygradient. Thisiswhythe differencebetween θ 62◦ [14]. To check this, we have perfor≃med a pa-
≃
RES and ROM shown in fig. 1c is clearest in the lead- rameterscaninlaserintensity I , plasmadensity n and
0 e
ing edge of the reflected pulse (towards negative φ). For angle of incidence θ with 1D PIC simulation. The laser
the case S = 20, a pre-plasma of lower density is pulled pulse shape andother simulationparametersare asused
out into vacuum as the surface breaks up under the ac- in fig. 1. The covered range is 5 1020Wcm−2 I
0
tionofthe intensepulse; the trailingedgeofthe incident 1022Wcm−2, 1/4 S 4, and 0◦×<θ <80◦. ≤ ≤
≤ ≤
light reflects from this lower density region, leading to The figures of merit we use to characterise the inter-
the RES-like features seen towards positive φ in fig. 1c. actionarethe 4th orderaverageamplitude andthe XUV
reflectivity. We define the nth order average amplitude
A full analysis of the effect of pre-plasma and its rela- an / an R andV/R andV, where the integralis cal-
h ri h ii≡ r i
tion to the laser pulse length is beyond the scope of this culated over the entire spatial domain of the pulse, for
work; it suffices here to indicate that where we refer to incident and reflected waveforms a and even integer
i,r
the optimal S of a clean plasma interaction, our results n. Setting n = 2 would be equivalent to calculating
willapplytolaserpulsesreflectingfromlongscale-length the reflectivity of the plasma, so 0 (cid:10)a2(cid:11)/(cid:10)a2(cid:11) 1
≤ r i ≤
pre-plasma before highly overdense targets. for all I , n and θ. By setting n = 4 instead, we en-
0 e
4
hance the contribution of large-amplitude components S . 0.25, it occurs that the nanobunch velocity merely
to the integral and therefore acquire a measure of the grazes the βx′ = 0 axis, and the reflected waveform is
amplitude increase. The XUV conversion efficiency R unipolar rather than bipolar, with longer duration. This
is calculated by transforming the backward-propagating reduces the XUV reflectivity even though the amplitude
electricandmagneticfieldstothelabframeandperform- is still increased across the range 0.25 S <2.
≤
ingFourieranalysistodeterminethereflectivityperunit We may conclude that for a laser pulse with realistic
frequency Rω (∂Ur/∂ω)/Ui, where Ui,r is the energy temporal profile, irradiating plasma with 0.5 S <2 at
of the incomin≡g and outgoing pulses respectively. Then 50◦ θ 70◦ leads to conversionof 30% of t≤he incident
≤ ≤
R ≡ RωminRωdω for some minimal energy ωmin, which energy to harmonics with energy ω > 10eV, with an
we set to 10 eV. For the waveforms shown in fig. 1c, associated increase in the peak intensity. Furthermore,
where I = 5 1021Wcm−2 and θ = 60◦, we have the agreementbetweenthe 1D theory of Gonoskovet al.
0
that: (cid:10)a4(cid:11)/(cid:10)a4×(cid:11) = 2.1 and R = 0.24 for S = 1; and [14]andsimulationforarealisticpulseshapeisexcellent.
r i
(cid:10)a4(cid:11)/(cid:10)a4(cid:11)=1.0 and R=0.030 for S =20.
r i
Let us first consider the situation where S is fixed to
be 1 and the intensity and angle of incidence are varied, IV. PROPERTIES OF THE XUV PULSE
shown in figs. 2a and 2b. Here the electron density n is
e
implicitly increasedwith intensity asrequiredbyeq.(1). Inthisspirit,wehavecarriedoutaparameterscaninS
There is a broad maximum in (cid:10)a4r(cid:11)/(cid:10)a4i(cid:11) between 45◦ andθ withthe2D3VPICcodeepoch[42]. Forallsimu-
◦
and 75 , over which interval the peak intensity of the lations,the laseris focussedto aspotwithwaist4µmat
reflected pulse is increased by almost a factor of 10. As- the plasma surface and peak intensity 5 1021Wcm−2
sociated with this is a strong increase in the conversion (a = 60.4). Its temporal profile and w×avelength are
0
efficiency to >10 eV light: there is little XUV emission the same as in the 1D simulations: sin2 with FWHM
for θ .20◦ but more than 20% of the pulse is converted 15fs and λ = 1µm respectively. The simulation do-
for 55◦ & θ . 75◦. Furthermore, neither the amplitude main,[0,16] [ 3,24]λinthexandy-directions,contains
increase nor conversion efficiency demonstrate a strong electron-ion×pl−asma (Z/A = 0.05) in the region y 0.
dependence on intensity, which is consistent with the S- The resolution varies between 200 and 500 cells pe≤r λ,
scaling of plasma dynamics proposed by Gordienko and andthenumberofparticlespercellbetween24and48for
◦
Pukhov [16]. The optimal angle θ 60 is consistent each species. The laser is injected from the left bound-
≃
with that proposed in Gonoskov et al. [14]. ary at an angle θ to the target normal; to reduce the
◦
Fixing the angle of incidence at 65 , we explore length of plasma, and so the number of computational
intensity-density space in figs. 2c and 2d. These re- particles, required to model the interaction, the simu-
sults are also consistent with the S-scaling: provided lation domain moves along x with velocity csinθ. The
the density is matched to the intensity as specified by amplitude and harmonic content of the reflected light is
eq. (1), the amplitude increase and XUV reflectivity are analysed once the pulse has moved a perpendicular dis-
constant at the 10% level even though the intensity in- tance of 12µm from the plasma surface. The explored
creases by a factor of 40. Figure 2d shows that there is range is 0.5 S <15 and 30◦ θ 70◦.
≤ ≤ ≤
broadmaximumin the XUV reflectivity forplasma with In moving from one to two spatial dimensions we en-
0.5.S .2. Thisthresholdisconsistentwiththeoretical countertwonewphysicaleffectsthataltertheXUVgen-
expectations Gonoskov et al. [14]. The fact that S =0.5 eration process. The first is that the conservation of
isathresholdratherthanamaximumisaneffectoflaser transverse kinetic momentum, which applies exactly in
temporal envelope: if the density is set so that S = 0.5 1D,islifted,leadingtoincreasedelectronheatingandre-
isachievedatthepulsecentre,thereissufficientelectron ductionoftheplasmareflectivity. Secondly,thevariation
heatingthatthesharpsurfacebreaksupundertheaction in laser intensity across the plasma surface (or, equiva-
of the pulse foot. lently,thevariationintheeffectiveS)leadstoaspatially
Figure 2c shows that the increase in the reflected am- varyingdisplacementoftheelectron-ionboundaryandto
plitude is maximised for slightly lower S than the XUV wavefront curvature of the reflected light. Both of these
reflectivity,whichisnotconsistentwithoursimpleexpec- effects are more pronounced for plasma of lower S.
tation that the two should be maximised together. The Infigs.3ato3cweshowsnapshotsofthe amplitudeof
◦
originofthis is a changein the characterof the reflected the reflected light for incidence angle 60 and S of 0.5,
waveformwhen moving to lower density. The number of 4 and 8. For the lowest density, we see that the wave-
attosecondbursts is set by the number of times the elec- fronts of the leading edge are almost flat, corresponding
tron nanobunch’s transverse velocity βx′ (in the boosted to reflection in the specular direction. The lineout along
frame) changes sign. In the optimal regime, this occurs this vectorshowsthe sharpspikes thatarecharacteristic
once per laser period, leading to a concentration of the of the RES mechanism. Towards the peak of the pulse,
reflected energy in a single emission event. As the ve- where the amplitude reaches near twice its initial value,
locity changes sign, so too does the sign of the reflected the wavefrontsare become curved due to ponderomotive
amplitude, leading to the sharptransitions between pos- denting of the plasma surface. Behind this, however,the
itive and negative field shown in fig. 1c. However, if RES spikes are lost as the laser reflects from that non-
5
FIG.3. (a-c)(upper)Colourmapsand(lower)lineoutsalong
thespeculardirectionoftheamplitudeoflightreflectedfrom
aplasmawithS =a)0.5,b)4andc)8illuminatedbyalaser
pulse with peak intensity 5×1021Wcm−2 at an incidence
angleθ=60◦. d)Thepercentageoflaserenergyconvertedto FIG.4. (a–c) Rω,Ω,thereflectivityperunitphotonenergy ω
per unit solid angle cosθ, for plasma with S = a) 0.5, b) 4,
radiation with 10eV <ω <50eV and e) comparing a (blue,
◦ and c) 10 illuminated by a laser pulse with peak intensity
solid) lineout of that conversion efficiency along θ = 60 to 5×1021Wcm−2, wavelength 1µm and waist 4µm, showing
(yellow, dashed) that predicted by 1D simulations, scaled by
slices through colour maps ii) at the (blue, solid) 10th and
0.5.
(yellow,dashed)20thharmonics. (d)ThebrillianceforS =4.
uniform plasma surface.
TheseeffectsaremitigatedbymovingtohigherS. For ics become more distinct, with smaller divergence, as S
S = 4, fig. 3b shows that the wavefronts are near flat increases. Slices at the 10th and 20th harmonics show
across the entire pulse. While the amplitude is only in- that for S = 4 and 10 the reflected energy is concen-
creasedto1.2 itsinitialvalue,RES-likefeaturescanbe trated within a window ∆(cosθ) 0.05, corresponding
× ◦ ◦ ≃
seenacrossthewholeofthereflectedwaveform. Similarly toahalf-angleof3 at60 . Forcomparison,theincident
tofig. 2c, fig.3cshowsthatatS =8,the leadingedgeof laser pulse with waist w0 = 4µm and wavelength 1µm
◦
thepulseacquiresthenon-linearreshapingcharacteristic has half-angle divergence θlaser = λ/(πw0) 5 . One
≃
of the ROM mechanism. might expect that the wavelengthdependence in this re-
The consequence of increased electron heating and lationleadstodecreasingdivergencewithincreasinghar-
non-uniformity of the plasma surface is to shift the op- monicorder. Howeverfig.4showsthatthe divergenceof
timum for XUV generation from S = 1 to S 4. Nev- the 20th harmonic is near,not half, that ofthe 10th, and
ertheless, the XUV reflectivity shown in fig. 3≃d still has therefore the dominant effect is the overalldivergence of
the broad peak between 50◦ and 70◦ we expect based the laser pulse.
on 1D theory and simulation, and fig. 3e shows that for Thedistributionofenergyinωandcosθisbroaderand
S > 4, the 2D reflectivity is within a factor of two that noisier for S = 0.5 than it is for S = 4,10. The broad-
predicted by 1D simulations. Even though we expect ening is caused by ponderomotive denting of the plasma
losses to electron heating to become larger when irra- surface, which increases the curvature of the reflected
diating near-critical plasmas, this is outweighed by the wavefronts as shown in fig. 3a. Break-up of the plasma
XUV reflectivity increase attributable to the storage of surface and ejection of hot electrons then leads to the
energy in plasma fields during non-linear motion of the emissionofhigh-frequencyradiationawayfromthespec-
plasma surface. ularaxis. We note thatdespite these losses,the peak re-
Furthermore,theemissionoftheseharmonicsisclosely flectedintensityinthiscaseisfourtimesitsinitialvalue.
collimated along the specular direction, with angular di- For the initial conditions under consideration here, this
vergencecomparableto that of the incoming laserpulse. corresponds achieving over two cycles a reflected inten-
We show in fig. 4 colour maps of R , the reflectivity sity of 2 1022Wcm−2, equal to the current record[43].
ω,Ω
×
per unit frequency ω and solid angle cosθ. The harmon- It has been proposed that curved plasma surfaces may
6
beusedtofocushighharmonicstoextremeintensity,ex- oscillatingradiationpressure ofthe laser. We havejusti-
ploiting the reduction in the diffraction limit [44]; such fied the theoretical prediction of the optimal parameters
◦
effects would stand in addition to the intensity increase S = 1, θ = 60 with high-resolution 1D PIC simulation,
arising from the RES mechanism. and shownwith 2D simulations that for the near-critical
Finally,weusethespectralreflectivityfromsimulation plasmasrequiredtoprobethisregime,increasedelectron
to estimate the brilliance, which is a measure of pho- heating is not sufficient to overcome the intrinsic advan-
ton phase-space density. Assuming a fiducial distance in tageoftheRESprocess. ThiscangeneratereflectedEM
the z-direction (perpendicular to the simulation plane) radiation with peak intensity four times higher than the
of 1µm, a duration equal to the laser pulse FWHM of incidentintensityeveninplanargeometry,aswellashigh
◦
15 fs, anda half-angle divergenceof3 , we show in fig. 4 harmonicscollimatedatthedegree-level. Theconversion
thatthebrillianceisoforder1023photons/s/mm2/mrad2 efficiencyof>3%leadstobrilliancesinthe10sofeVun-
(0.1%bandwidth)atω =100eV,fortheoptimalparam- precedented in laser-solidinteractions.
◦
eters of S =4, θ =60 . This is five orders of magnitude
largerthanthatachievedinthird-generationsynchrotron
light sources [45]. ACKNOWLEDGMENTS
The authors acknowledge support from the Knut and
V. CONCLUSIONS
Alice Wallenberg Foundation (T.B., A.G., M.M.), the
Swedish Research Council (grants 2012-5644 and 2013-
We have explored how the relativistic electron spring 4248, M.M.), the Russian Science Foundation (project
mechanismleadstobrightburstsofXUVradiationwhen no. 16-12-10486, A.G.) and the Russian Foundation for
plasma with electron density n satisfying 1 < S = Basic Research (project no. 15-37-21015, A.G.). Sim-
e
n /(a n ) < 10 is illuminated by intense laser light ulations were performed on resources provided by the
e 0 cr
(a 1). The physical origin of this enhanced emis- Swedish National Infrastructure for Computing (SNIC)
0
≫
sion is the storage of energy in plasma electromagnetic at the High Performance Computing Centre North
fieldswhentheelectron-ionboundaryisdisplacedbythe (HPC2N).
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