Laser-driven ion acceleration with hollow laser beamsC. Brabetz, S. Busold, T. Cowan, O. Deppert, D. Jahn, O. Kester, M. Roth, D. Schumacher, and V. Bagnoud Citation: Physics of Plasmas (1994-present) 22, 013105 (2015); doi: 10.1063/1.4905638 View online: http://dx.doi.org/10.1063/1.4905638 View Table of Contents: http://scitation.aip.org/content/aip/journal/pop/22/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Bidimensional Particle-In-Cell simulations for laser-driven proton acceleration using ultra-short, ultra-highcontrast laser Phys. Plasmas 21, 123104 (2014); 10.1063/1.4902125 The beat in laser-accelerated ion beams Phys. Plasmas 20, 103102 (2013); 10.1063/1.4824115 Effect of resistivity gradient on laser-driven electron transport and ion acceleration Phys. Plasmas 20, 093103 (2013); 10.1063/1.4820933 Energy scaling of monoenergetic electron beams generated by the laser-driven plasma based accelerator Phys. Plasmas 14, 023103 (2007); 10.1063/1.2434248 Demonstration of quasi-monoenergetic electron-beam generation in laser-driven plasma acceleration Appl. Phys. Lett. 86, 251501 (2005); 10.1063/1.1949289

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Laser-driven ion acceleration with hollow laser beams

C. Brabetz,1,2,a) S. Busold,2,3 T. Cowan,4,5 O. Deppert,6 D. Jahn,6 O. Kester,1,2 M. Roth,6

D. Schumacher,2 and V. Bagnoud2,3

1Goethe-Universit€at Frankfurt am Main, 60323 Frankfurt, Germany2GSI Helmholtzzentrum f€ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany3Helmholtz-Institut Jena, 07743 Jena, Germany4Helmholtz-Zentrum Dresden-Rossendorf, 01328 Dresden, Germany5Technische Universit€at Dresden, 01069 Dresden, Germany6Technische Universit€at Darmstadt, 64277 Darmstadt, Germany

(Received 27 August 2014; accepted 23 December 2014; published online 8 January 2015)

The laser-driven acceleration of protons from thin foils irradiated by hollow high-intensity laser

beams in the regime of target normal sheath acceleration (TNSA) is reported for the first time. The

use of hollow beams aims at reducing the initial emission solid angle of the TNSA source, due to a

flattening of the electron sheath at the target rear side. The experiments were conducted at the

PHELIX laser facility at the GSI Helmholtzzentrum f€ur Schwerionenforschung GmbH with laser

intensities in the range from 1018 W cm�2 to 1020 W cm�2. We observed an average reduction of

the half opening angle by ð3:0760:42Þ� or ð13:262:0Þ% when the targets have a thickness between

12 lm and 14 lm. In addition, the highest proton energies were achieved with the hollow laser

beam in comparison to the typical Gaussian focal spot. VC 2015 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4905638]

I. OVERVIEW

In the field of laser-driven ion acceleration, the cur-

rently most used and best understood mechanism is the tar-

get normal sheath acceleration (TNSA).1,2 In this scheme, a

high-intensity laser beam is focused onto a solid thin target

where it produces a plasma at the front surface and hot elec-

trons that travel through the target. On the rear side, the

electrons create a quasi-static electric field capable of field

ionization and acceleration of light particles, mostly pro-

tons, present in the contamination layer at the surface of the

target. The ions and electrons expand into the vacuum

behind the target as a quasineutral plasma cloud. Such parti-

cle beams, originating from the target rear side contamina-

tion layer, have outstanding properties like ultra-low

emittance3 and a pulse duration comparable to the laser

pulse duration. The properties of these beams like their

divergence and exponential energy spectrum can be directly

linked to the spatial distribution of the electron sheath; in

particular, spatial density gradients are influencing directly

the particle emission direction.4 The laser intensities typi-

cally used for such experiments range form 1018 W cm�2 to

1020 W cm�2 with laser pulse durations from a few tens of

fs up to some ps. The maximum proton energy Ep;max is

depending on the electron density ne and the hot-electron

temperature kBTe,5 which scales as the ponderomotive

potential with dimensionless electric field amplitude a0 as

kBTe / a0 /ffiffiffiffiffiffiffiffiffi

Ilaser

p. Only a weak scaling with the target

thickness or laser pulse duration was measured by Robson

et al.6 for a Gaussian beam.

TNSA has been widely studied and is now used at many

facilities throughout the world, delivering ion energies up to

tens of MeV. Laser-accelerated ions are promising candi-

dates for several applications due to short-scale acceleration

length, high energy, and large particle numbers. Possible

applications are as an injector for conventional post-acceler-

ation,7,8 astrophysical phenomena,9 proton radiography,10 or

for medical ion treatment.11

Some TNSA properties, like the exponential energy

spectrum, make it difficult to inject the ions without energy

filtering and losses into conventional structures. The half

opening angle of the outgoing ion beam is energy-dependent

and reaches up to 30� for low ion energies, which can be too

large due to geometrical acceptance of following elements.

Several different approaches for reducing the divergence are

known, e.g., target shaping or with external plasma cells.12

But other publications show that the ion beam shape can also

be influenced by the laser focal spot shape.4

In this paper, we show that one can reduce the initial

divergence of laser-accelerated ions by use of engineered

laser beam shapes. This is done with a spiral phase element

(SPE)13 inserted early in the laser amplifier to produce a hol-

low, doughnut-like laser focus profile at the target surface.14

The experimental data are supported by particle-in-cell (PIC)

simulations. The experiments were done on the petawatt-

class laser facility PHELIX15 (petawatt high energy laser for

heavy ion experiments) located at GSI Helmholtzzentrum

f€ur Schwerionenforschung GmbH, Germany. Basic laser pa-

rameters for this experiment were FWHM laser pulse dura-

tion sL¼ 650 fs, laser beam energy EL¼ 70 J, and a contrast

level of about 10�7.

II. SIMULATION

In preparation for the experiments two-dimensional

particle-in-cell simulations were performed with thea)Electronic mail: c.brabetz@gsi.de

1070-664X/2015/22(1)/013105/6/$30.00 VC 2015 AIP Publishing LLC22, 013105-1

PHYSICS OF PLASMAS 22, 013105 (2015)

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EPOCH-2D16 simulation code to study the interplay

between laser focus geometry and target thickness.

Depicted in Figure 1 are the accelerating electric Ex fields

in target normal direction. By varying the target thickness

in the simulation, an optimum was found to be in the range

of 14 lm–18 lm for the parameters available at PHELIX.

Optimum target thickness in this context means that the

accelerating electric field becomes flat (Figure 1(c), 15 lm

target) compared to the electric field of a Gaussian focal

spot (Figure 1(a), 5 lm target). Figure 1(b) illustrates the

electric TNSA field of a hollow laser beam onto a 5 lm tar-

get, which resembles the characteristic shape of the imping-

ing laser beam. Indeed, when the target is too thin in

comparison to the intensity distribution function, the hollow

feature is imprinted directly onto the electron sheath, while

thick targets wash the effect out. The simulated laser inten-

sity is I0 ¼ 1019 W cm�2 with a Gaussian shaped temporal

pulse duration of sL¼ 650 fs and perfect contrast. In the

experiment, the energy is almost kept constant while the

intensity distribution is changed from Gaussian to

doughtnut-like. This means the intensity is not held con-

stant and reduced for the later, which according to scaling

laws should reduce the maximum achievable ion energy.

The intensity is only a quarter of the Gaussian one if the

beam energy is held constant as indicated in Figure 2.

Therefore, a hollow laser beam focus together with a well

chosen target thickness (deduced from the PIC simulations)

would lead to a flat electron sheath. This in turn creates a

less divergent ion beam, although a lower maximum ion

energy has to be expected.

III. SETUP

To create the hollow beam we insert a SPE in the laser

beam path to apply a helical phase to the laser beam. This is

done at an early stage in the laser amplification chain,

namely, at the input of the pre-amplifier, where one has not

to worry about damage threshold or B-integral. It makes the

SPE also small and easily exchangeable. The SPE was

designed with two main ideas in mind: first it should gener-

ate a self-similar mode that will stay invariant with propaga-

tion, keep its shape at focus, and minimize dangerous

hot-spots in the intermediate field. Second, it should opti-

mize the energy extraction in the main amplifier and for that

have a near field fluence distribution as close to a top-hat as

possible. The SPE mostly mimics the phase of a Laguerre-

Gaussian mode exhibiting a singularity on axis. An

additional amplitude mask takes care of the amplitude distri-

bution of the field (it creates a near top-hat distribution) and

ensures a good energy fill-factor. That allows to maintain a

maximum energy extraction of the amplification stages. See

Figure 3 for two example on-shot focus images in the

PHELIX sensor behind the main-amplifier section.

Illustrated in (a) is the hollow focus while in (b) for compari-

son the Gaussian focus is shown. Laser aberrations lead to

the modulation of the intensity on the ring seen in (a). The

alignment and quality of the laser before an upcoming high

energy shot is checked with sensors throughout the laser

chain. If necessary it can be adjusted with adaptive optics

systems.

The targets used in the experiment were flat gold foils.

For the target and laser alignment a side- and focus-view

diagnostic were used. During the alignment procedure, the

beam was brought to target chamber center and its focus was

optimized using 5 degrees of freedom (2 for a centering mir-

ror, 3 for the F#10 90 degree off-axis parabola). After that

the target was moved into place using a side viewing system

with an accuracy better than 10 lm, which is an order of

magnitude better than the Rayleigh range of the beam. As

proton beam diagnostics, we used radio-chromatic-films

(RCF) in stack configuration to allow for a high spatial and

energy resolution of the proton beam acquisition.17 The short

pulse laser beam arrives under 10� to the target normal as it

is diagrammed in Figure 4.

FIG. 1. 2D particle-in cell simulations for the accelerating electric field within the TNSA mechanism. The three simulation snapshots are taken at the same

time step (1050 fs) and same simulated laser intensity of I0 ¼ 1019 W cm�2, pulse duration of sL¼ 650 fs, and a perfect contrast. (a) For comparison the electric

field of a Gaussian focal spot on a 5 lm thick target. (b) On the same target thickness, a simulation with a hollow focal spot. (c) The same hollow focal spot is

impinging on a 15 lm thick target.

−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1

Radius (a.u.)

Nor

mal

ized

inte

nsity

Gaussian beamLaguerre beam

FIG. 2. Transverse focus intensity profiles of a Gaussian (solid line) and a

hollow (dashed line) laser beam of the same energy (two-dimensional).

013105-2 Brabetz et al. Phys. Plasmas 22, 013105 (2015)

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IV. EXPERIMENTS

To cover a large parameter range, we studied foil thick-

nesses from 3 lm to 20 lm in the experiments. Beside vary-

ing the target thickness, the beam shape was also varied:

from Gaussian for reference to the Laguerre-Gaussian-like

mode LG01. For reproducible measurements, the target foil

was always aligned to the best focal position. The energy of

the shots was varied within the 12 cm round subaperture of

the PHELIX beam, delivering 50 J–80 J of laser energy on

the target (for the Gaussian and the ring shaped beam). The

laser pulse duration was always held constant at sL¼ 650 fs.

We also had the opportunity to apply the new ultrafast opti-

cal parametric amplifier of PHELIX to conduct some experi-

ments with ultra-high temporal contrast.18 With this method

a temporal contrast level better than 10�10 is reached beside

the normal contrast level of PHELIX of about 10�7. This

was done to study the influence of the pre-plasma on the ion

acceleration.

First the comparison of ring and Gaussian focal spot

geometries and their effect on the maximum proton

energy in the TNSA regime are studied. This is illustrated in

Figure 5, where the maximum proton energy at the cut-off is

plotted against the calculated laser intensity. The laser inten-

sity is inferred from the measured focal spot size and the

on-shot measured laser energy. The focal spot size is meas-

ured at the FWHM for the Gaussian and the ring, while for

the latter the inner dark area is factored in. This is realized

by applying a mask at FWHM threshold level and measure

the area (count the pixel) that are above this limit. For the

two displayed focus images in Figure 3, this method yields

Aring¼ 5223 pixel for the ring and AGaus¼ 2299 pixel for the

Gaussian one. A particular care has been taken to minimize

the impact of on-shot aberrations. An adaptive optics loop

has been used and the beam wavefront is also recorded dur-

ing the shot to ensure that no large distortion happens to the

beam (see Figure 3 for on-shot focus images). Changing the

focal spot geometry from a Gaussian shaped to the smallest

ring focal spot with the SPE, the focus radius doubled and

therefore the intensity drops to a quarter if the energy of the

laser beam is kept constant (Figure 2). The variation in inten-

sity is induced by different energies delivered from the

PHELIX laser system. The maximum proton energy is meas-

ured with RCF stacks. A typical energy detection gap

between the last RCF films is about 2 MeV, and therefore, an

energy error of þ2 MeV is assumed for all shots.

It is observed that the data points with a Gaussian focal

spot (blue triangles) fit very well to a power scaling Ep;max

¼ a� Iblaser with b ¼ 0:73 6 0:04. The same power scaling

FIG. 3. Comparison of the on-shot

focal spots measured after the main-

amplifier, normalized to the intensity

of the Gaussian spot (b). (a) The hol-

low focus and (b) the Gaussian focus.

In (a), the effect of the remaining laser

aberrations is seen and modulate the

intensity by a factor of 2 on the ring.

FIG. 4. Sketch of the used experiment

setup.

1018

1019

1020

10

20

30

40

50

Laser intensity (W cm−2)

Max

imum

pro

ton

ener

gy (

MeV

)

Gaussian focal spotfit GaussianRing focal spotfit ring

FIG. 5. The different focal spot geometries and their effect on the maximum

proton energy in the TNSA regime. With applied phase mask (LG01, green

circles) for laser beam shaping, a stronger coupling to the laser intensity can

be observed in comparison to the shots with the Gaussian focal spot (blue

triangles). The fit yield for the ring b ¼ 1:3260:08 and b ¼ 0:7360:04 for

the Gaussian case of the power scaling.

013105-3 Brabetz et al. Phys. Plasmas 22, 013105 (2015)

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is assumed for shots with the SPE (green circles). As illus-

trated in the figure with a steeper gradient a stronger cou-

pling to the laser intensity Ilaser is found in comparison to

the Gaussian focal spot, which result in an exponent

b ¼ 1:32 6 0:08 for the ring. Also notable is that the highest

proton energies were reached with the phase mask exceeding

35.8 MeV (the detection limit of the used RCF configura-

tion). One possible explanation for this unexpected feature is

that the ring focal spot also shapes the front-plasma surface.

Due to the ponderomotive force the electron density in the

central dark area increase. This pile up can lead to increased

energy transfer from the laser to accelerating electrons inside

the plasma. This assumption is supported by measuring the

hot (up to 7 MeV) electrons of a Gaussian and a ring laser

shot. In both cases, the hot electron temperature was nearly

the same, while one would expect a reduced temperature for

the later with reduced laser intensity. We measured an elec-

tron temperature kBTe ¼ ð3:3360:12ÞMeV for the Gaussian

beam and ð3:2860:22ÞMeV for the hollow beam.

Illustrated in Figure 6 is the dependency of the scaled

maximum proton energy Ep;max=Iblaser on the target thickness,

which was varied between 3 lm and 20 lm. The lower blue

triangles are shots with the Gaussian focal spot where no

clear dependency on the target thickness is observed. The

green circles represent shots with the SPE and normal

PHELIX contrast level. A relation between the maximum

proton energy and the target thickness is observed. The

measured optimum target thickness range is from 12 lm to

14 lm. This can be explained with the conducted PIC

simulations (see Figures 1(b) and 1(c)). If the target thick-

ness is too thin, the rear-side electron sheath exhibits the

same hollow feature as the impinging laser. Therefore, in the

center, the electric field is lower and more protons are accel-

erated to only lower energies. Going towards the optimum

target thickness, i.e., the electron sheath resembles the

desired flat sheath, the maximum accelerating electric field is

applied over the whole focal area. We have the maximum

proton energy. For even thicker targets the electrons scatter

to a larger region on the rear side and therefore lower the

maximum electric field, which leads also to lower proton

energies.

In addition, experiments with the best temporal contrast

level available, i.e., better than 10�10, were conducted, and

the results are illustrated in the same figure (red triangles for

the Gaussian focal spot and red circles for shots with hollow

beam). Again, no clear dependency on the target thickness is

observed in the case of a Gaussian focal spot: no visible dif-

ference could be observed for experimental data collected

with both temporal levels. The trend of the red circles (SPE)

indicates that there is also an optimum target thickness in the

same range, as it was observed with the normal contrast

level. However, more data would be necessary to confirm

this trend and fully measure the suspected optimum.

The measurements of the envelope half opening angle

of shots on targets with the optimum target thicknesses are

plotted in Figure 7. If the accelerating electron sheath

approaches the desired flat shape a more directed proton

beam is expected. That means that fewer protons should be

scattered into the border region of the outgoing proton beam

from the laser-driven ion acceleration. Analyzing the proton

beam size in each RCF layer of an experiment at a fixed pro-

ton intensity should reveal a smaller proton imprint area as it

is illustrated. The threshold for the proton beam boundary

was set to a fixed value of 2000 protons per pixel (one pixel

is approximately 25 lm� 25 lm). This limit was chosen to

distinguish clearly from the occurring background (mostly

electron) signal. Each of the plotted data points represents an

RCF layer in a shot and is scaled to the corresponding maxi-

mum proton energy for comparison. In total, 15 shots are0 5 10 15 20 25

0.2

0.4

0.6

0.8

1

Target thickness (µm)

Nor

mal

ized

max

imum

pro

ton

ener

gy /

(lase

r in

tens

ity)b

Ring focal spotRing, best contrast

0 5 10 15 20 250.2

0.4

0.6

0.8

1

Target thickness (µm)

Nor

mal

ized

max

imum

pro

ton

ener

gy /

(lase

r in

tens

ity)b

Gaussian focal spotGaussian, best contrast

(a)

(b)

FIG. 6. Scaling of the maximum proton energy with different target thick-

nesses. The blue triangles represent shots with a normal Gaussian focal spot.

The green circles represent shots with the SPE and normal PHELIX contrast

level. In red circles and triangles drawn are the shots with the best PHELIX

laser contrast level, i.e., 10�10.

0.2 0.3 0.4 0.5 0.6 0.7 0.85

10

15

20

25

30

35

enve

lope

hal

f ope

ning

ang

le (

°)

Normalized maximum proton energy

Gaussian focal spotRing focal spotfit Gaussianfit ring

FIG. 7. The comparison of different focal spot geometries with normalized

measured proton energies and their effect on the envelope half opening

angle. Observed is, we achieve a smaller envelop half opening angle with an

applied phase mask, given by the two average lines (blue triangles for a

Gaussian focal spot, green circles for a ring focal spot). The last layer is

always omitted because of the weak proton beam signal therein.

013105-4 Brabetz et al. Phys. Plasmas 22, 013105 (2015)

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displayed: 10 for the hollow laser beam and 5 for the

Gaussian one. The scaling by the reached maximum proton

energy is necessary because the opening angle is energy-

dependent. The size of the proton signal in a RCF can be

converted to an opening angle with the measured distance of

the RCF stack to the laser-matter interaction. They are fitted

with a polynomial of type hðEp=Ep;maxÞ ¼ a2 � ðEp=Ep;maxÞ2þ a1 � ðEp=Ep;maxÞ þ a0. It is observed in Figure 7 to

achieve a smaller envelope divergence with an applied phase

mask, given by green circled data points (the parameters are

a2 ¼ �22:86; a1 ¼ �0:18; a0 ¼ 27:76). The blue triangles

represent the data that were recorded with the Gaussian focal

spot (which parameters are a2 ¼ �25:07; a1 ¼ 0:33; a0

¼ 31:25). In average, the reduction is ð3:0760:42Þ�, which

corresponds to ð13:2 6 2:0Þ% for target thicknesses from

12 lm to 14 lm.

Despite the effect of aberrations on the laser focal spot,

the influence on the electron sheath is driven by the symme-

try. The flattening of the sheath is dependent on the size of

the hollow feature and proper target thickness, as it was dem-

onstrated with the PIC simulations. Therefore, we see a sym-

metric reduction in the divergence of the outgoing proton

beam despite the not-homogeneous but still symmetric laser

focal spot (see example proton profiles in the Appendix).

V. CONCLUSION

In the frame of these experiments laser-driven proton

acceleration was studied within the target normal sheath

acceleration regime with an emphasis on varying the trans-

versal laser focus profile to manipulate the generated proton

beam via the electron sheath. The goal of these experiments

was to change the initial conditions of the emitted ion beam

from the TNSA source. The accelerated proton beam exhib-

its a large divergence angle. To reduce this energy-

dependent (up to 60�) opening angle the demonstrated

method shapes the rear side electron sheath using specially

shaped laser beams. This can be done using helical phase

plates. The result is a hollow focal spot on the target with an

intensity minimum in the center. Main diagnostic for the

generated protons within the conducted experiments were

the radiochromic films.

We experimentally showed that one can create and use

shaped beams at a petawatt-scale laser facility. This was the

first time that laser-driven ion acceleration with a hollow

laser beam was experimentally demonstrated. The experi-

mental data concerning the envelope divergence are in agree-

ment with the simulations predicting a flat electron sheath.

Improvements on the laser-driven ion acceleration with

shaped laser beams were demonstrated and compared to

laser-driven ion acceleration with Gaussian focal spots. The

initial proton beam parameter, the envelope half opening

angle, was reduced by ð3:0760:42Þ� or in other words

ð13:262:0Þ%. The scaling of the maximum proton energy

Ep;max with a different power of Ilaser was experimentally

verified for experiments with a hollow laser focus. It

appeared that the highest proton energies were achieved with

the hollow laser beam exceeding 35.8 MeV. Also, the de-

pendency of the proton energy as well as the opening angle

on the target thickness with the hollow beam was demon-

strated within the target thickness range of 5 lm–20 lm.

With further improvements to the laser beam quality

(more homogeneous shape of the laser focal spot), the effect

on the protons will increase. Then, the application of this

method for envelope divergence reduction will have an influ-

ence on conventional structural elements next in line or

downstream experiments. Less particles are lost, e.g., due to

the acceptance of the used ion optics so the capture effi-

ciency increases. Or in the connected experiments a higher

proton flux is achieved.

ACKNOWLEDGMENTS

The authors want to thank the PHELIX laser team for

their excellent work. Financial support was granted by

HIC4FAIR.

APPENDIX: EXAMPLE RCF PROFILES

In Figure 8 are two examples for recorded RCF shown,

which correspond to a proton energy of 11.0 MeV and

22.1 MeV, respectively. Displayed are two shots: the upper

one for the Gaussian focal spot and the lower one with the

SPE. Both are with similar parameters concerning the target

and laser energy.

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