Two surface plasmon decay of plasma oscillations

0.37 MB·English

by  Thomas Kluge

Two surface plasmon decay of plasma oscillations
∗
T. Kluge, J. Metzkes, K. Zeil, and M. Bussmann
Helmholtz-Zentrum Dresden-Rossendorf, Germany
U. Schramm and T.E. Cowan
Helmholtz-Zentrum Dresden-Rossendorf, Germany and
TU Dresden, Germany
5 (Dated: March 23, 2015)
1
The interaction of ultra-intense lasers with solid foils can be used to accelerate ions to high
0
energies well exceeding 60 MeV [1]. The non-linear relativistic motion of electrons in the intense
2
laserradiationleadstotheiraccelerationandlatertotheaccelerationofions. Ionscanbeaccelerated

r from the front surface, thefoil interior region, and thefoil rear surface (TNSA, most widely used),
a
or thefoil may be accelerated as a whole if sufficiently thin (RPA).
M
Here, we focus on the most widely used mechanism for laser ion-acceleration of TNSA. Starting
from perfectly flat foils we show by simulations how electron filamentation at or inside the solid
0
leadstospatialmodulationsintheions. Theexactdynamicsdependverysensitivelyonthechosen
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initial parameters which has a tremendous effect on electron dynamics. In the case of step-like

densitygradientswefindevidencethatsuggests atwo-surface-plasmon decayofplasmaoscillations
]
h triggering a Raileigh-Taylor-like instability.
p
-
m
In laser ion acceleration, an ultra intense laser inter- ier ions remain almost at rest during the relevant time
s actswithasolidandquicklyionizesitssurface. Thelaser scales of electron motion. Of course this is not strictly
a
light creates an immense pressure on the surface, pro- correctsince otherwise no RTI instability could develop.
l
p duces large and fast electron currents into the solid and Fig. 1(a) shows exemplary part of the electron density
.
s excites plasma waves. In such a scenario many instabili- distribution of simulation A t = 18π = 9T0 after the
c
ties develop which can disrupt the surface and break up laser maximum has reached the foil front surface, and
i
s the electron currents. Fig. 1(b) shows the corresponding ion density distribu-
y
It has been shown previously that instabilities in ultra- tion. Inthis simulationthe electronspushedintothe foil
h
p thin solid foils can imprint onto the spatial structure of at2ω0bythelaserLorentzforcearepronetoatransverse
[ ionsintheregimeofrelativisticallyinducedtransparency Weibel-likeinstability[9]. The2ω0electronslabsbecome

targetnormalsheathacceleration(RIT TNSA[2])orra- filamented transversely and create energetic channels al-
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diation pressure acceleration (RPA [3]) [4] – mostly at- most normalto the foil surface which are surroundedby
v
1 tributed to the Rayleigh-Taylorinstability (RTI) [5]. In- strong quasi-static magnetic fields. This happens during
1 stabilities behindthe foils canalsodevelopduringthe ps the first few plasma wavelengths λ ≡2πω−1 =2πn−1/2
p p e,0
3 timescalesoftheplasmaexpansionofTNSA[6]. Herewe ascanbe seeninFig.2a. The ionaccelerationatthe foil
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show that instabilities developing in solid foils can also rear surface then follows this structure(cp. Fig, 1a,b).
0
. be of significance for the laser absorption and ion accel- It is this that is different to the mechanism described
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erationforthickerfoilswherenoRIToccurs. Wepresent in [6]: the rear surface ion’s acceleration itself is struc-
0
results from particle-in-cell (PIC) simulations using the tured transversely from the beginning since the driving
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1 code ipicls2d [7] and refer the reader to our Ref. [8] energetic electrons reach the rear surface filamented al-
: for experimental evidence. We use dimensionless units readyincontrasttotherelativelyslowWeibelinstability
v
i with c = e = me = ω0 = 1 and measure distances in witnessed in [6] during the ion acceleration. Of course
X x-direction(the laserdirection)relativeto the initialfoil both can happen concurrently.
r frontsurfacepositionandtimesrelativetothetimewhen
a
the laser intensity maximum reaches x = 0. In most of We now study the case of step-like density gradientat
our analysis we will focus on two simulations, compar- thefrontsurface(simulationB).Incomparisontosimula-
ing the cases of a flat foil with exponential preformed tionA,wherethebulkelectronsremaineddistributedal-
plasmaonthesurface(simulationA)andwithout(simu- mosthomogeneouslytransverselyatthesurfaceandonly
lationB),the fullsimulationparametersaregiveninthe energeticelectronsbecamefilamentedinsidethefoil,here
caption of Fig. 1. thefoilsurfacealreadyshowstransversestructurebothin
electrondensity (Fig.2b,c)andenergydensity (Fig.2a),
One main finding is that instabilities which are prone withthelatternotincreasingduringpassagethroughthe
to evolve in all of our simulations imprint on the ion foilcontrarilyto simulationA.The reasonforthis lies in
density distribution behind the foil slab even for the mi- thedensityrippleswhichgiverisetofilamentedinjection
cron thick foils used. The instabilities we discuss in this of electrons, similar to the mechanism described in [10].
paperaredevelopingintheelectronsfirstsincetheheav- We therefore conclude that in simulation B another fila-
2
1
0.03
0.5
0 0
2λ
0
(a) (b) (c)
FIG.1. (a)Partoftheelectronenergydensitydistributionatt=18π =9T0 afterthelaser,normalizedto2/3ofitsmaximum
and (b) ion density distribution of simulation A, and (c) electron energy distribution of simulation B. Simulation parameters:
only the plane defined by the laser propagation direction (x-axis) and the electric field polarization (y-axis) is simulated,
assuming invariance of the system in z-direction; simulation box 10λ0 ×10λ0, 192 cells per λ0 and laser period T0; laser is
modeledbyatransverselyplanewavewithshortgaussianrisewith1sigma-widthof2λ0/cfollowedbyaflattop,wavelengthλ0,
peak intensity I0[W/cm2]=1.38×1020/(λ0[µm])2 corresponding to a normalized field strength a0 =[2I0/(ncmec3)]1/2 =10
where nc = meǫ0ω02e2 is the critical electron density for the laser with angular frequency ω0; laser is aligned normal to the
target foil surface; flat target foils modeled by a fully preionized plasma slab of 2λ0 thickness: ions with charge-to-mass ratio
Q/M =1/2 and neutralizing electrons with density ne,0 =100nc; front of the foils is modeled by an exponentially increasing
preplasma with scale length L, (a) and (b) L=2π/10=0.1λ0 (simulation A) and (c) L=0 (simulation B).
0.5λ
0
(b) (c)
(a)
FIG. 2. (a) Transverse electron energy density contrast when co-moving with one of the 2ω0 electron slabs after it is injected
intothesolidforsimulationA(blackline)andsimulationB(gray/redline). (b,c)Electrondensitysnapshotatt=18π =9T0
for (b) simulation A and (c) simulation B.
mentation mechanism must be present. Density ripples with the characteristic1ω0 longitudinal oscillationis ob-
usuallyarecreatedbyRTIandthedensitydistributionin servedinoursimulationonlyatlatertimes growingonly
Fig.2cshowsapatternconsistentwiththelinearstageof slowly, which we attribute to larger k . However, con-
S
RTI.Yet,typicallytheaveragedistanceλS betweenden- sidering not the 2ω0 oscillation as a driving source but
−1
sity maxima (wave number k = λ ) should be given the plasma oscillations excited by the disturbances we
S S
by the smallest transverse scale that could seed the in- find good numerical agreement. Fig. 3 shows a compar-
stability, since the growth rate Γ ∼= (gk )−1/2 (g is the ison of kPIC for a number of simulations we performed
S S
acceleration of the surface) is largest for the largest kS. with different parameters (varying ne,0 and a0) with the
Hence we are looking for a mechanism that can seed a analytical value k . The agreement is generally rather
S
transverse density fluctuation which is then prone to a good. Also, we find oscillations at ω /2 in the spectrum
p
RTI growth [11, 12]. Such a mechanism was described of surface oscillations, Fig. 3(b). Here we defined a den-
e.g. in [13, 14] where a generationof 2D electronsurface sity level and recorded the position in x-direction (laser
oscillations (2DESOs) by a parametric decay of 2ω0 os- direction) where the rising density reaches that value.
cillations of the foil surface in the laser field was found. We then computed the temporal Fourier transform of
There from initially purely longitudinal driving oscilla- this position averaged over the positions along the y-
tions of the surface (for the 2ω0 oscillations the driver direction at the density ripple maxima, neglecting the
frequency is ωD = 2ω0), oscillations in a standing wave regions in between. The result would be a strong signal
along the surface are generated via excitation of upward around the laser harmonics (overlying all other signals)
anddownwardmovingandinterferingsurfacewaveswith which however are expected to be transversely flat here.
ω = ω /2 and k given by [Eqn. (6) in [15]]. For our Thereforewetooktheoscillationatthe”‘innersurface”’.
S D S
∼
simulation conditions this would correspond to k = 1, By this we mean the oscillation of the falling density
S
much smaller than the value extracted from the PIC slope behind the region of laser pressure steepened elec-
∼
simulation kSPIC = 7.7. This decay of 2ω0 oscillations trondensity,whichcanscreenthe lowerlaserharmonics.
3
((a) kS(calculated) (c)
FIG. 3. (a) kPIC versus calculated k from [Eqn. (6) in [15]] not including thermal effects. (b) and (c) Temporal Fourier
S S
transform of surface oscillations for (b) simulation B and (c) a simulation with same parameters as B but ne,0 = 300 and
a0 =30 (details see text). Thetime over which theoscillations were evaluated is indicted in thelegend.
the foil. The exact mechanism and scale of spatial mod-
ulationsinthe beamofhotelectronsandionssensitively
depends on the initial parameters. For the pursuit of
higher ion energies at higher laser intensities, e.g. avail-
1λ able at (future) Petawatt laser systems, a deeper under-
standing and further characterizationof laser and target
parameter dependent plasma instabilities will be essen-
FIG. 4. Energy density distribution for simulations with pa-
tial.
rameters as simulation B but with initial surface roughness.
Thelargestspatialfrequencyisindicatedbytheblackbar,the The work has been partially supported by EC FP7
smallestistwicethissize. Theamplitudeofthesurfacerough- LASERLAB-EUROPE/CHARPAC (contract 284464)
ness is 0.1λ0. Color scale is the same as in Fig. 1. Largest and by the German Federal Ministry of Education and
surface ripple growth occurs when the spatial frequency k
S Research (BMBF) under contract number 03Z1O511.
is seeded, with a characteristic mushroom shape (non-linear
RTI) growing at the front (central panel). Here, kPIC =7.6,
S
k =7.3.
S
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