Laser-driven generation of collimated ultra-relativistic positron beams

Abstract

We report on recent experimental results concerning the generation of
collimated (divergence of the order of a few mrad) ultra-relativistic
positron beams using a fully optical system. The positron beams are
generated exploiting a quantum-electrodynamic cascade initiated by the
propagation of a laser-accelerated, ultra-relativistic electron beam
through high-Z solid targets. As long as the target thickness is
comparable to or smaller than the radiation length of the material, the
divergence of the escaping positron beam is of the order of the inverse
of its Lorentz factor. For thicker solid targets the divergence is seen
to gradually increase, due to the increased number of fundamental steps
in the cascade, but it is still kept of the order of few tens of mrad,
depending on the spectral components in the beam. This high degree of
collimation will be fundamental for further injection into
plasma-wakefield afterburners.

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Laser-driven generation of collimated ultra-relativistic positron beams
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2013 Plasma Phys. Control. Fusion 55 124017
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IOP PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION
Plasma Phys. Control. Fusion 55 (2013) 124017 (6pp) doi:10.1088/0741-3335/55/12/124017
Laser-driven generation of collimated
ultra-relativistic positron beams
G Sarri1, W Schumaker2, A Di Piazza3, K Poder4, J M Cole4, M Vargas2,
D Doria1, S Kushel5, B Dromey1, G Grittani6, L Gizzi6, M E Dieckmann7,
A Green1, V Chvykov2, A Maksimchuk2, V Yanovsky2,ZHHe
2,
B X Hou2, J A Nees2, S Kar1, Z Najmudin4,AGRThomas2,CHKeitel3,
K Krushelnick2and M Zepf1,5
1School of Mathematics and Physics, The Queen’s University of Belfast, BT7 1NN, Belfast, UK
2Center for Ultrafast Optical Science, University of Michigan, Ann Arbor, MI 48109-2099, USA
3Max-Planck-Institut f¨
ur Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
4Imperial College of Science, Technology and Medicine, London SW7 2BZ, UK
5Helmholtz Institute Jena, Fr¨
obelstieg 3, 07743 Jena, Germany
6Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, 56124 Pisa, Italy
7Department of Science and Technology (ITN), Link¨
opings University, Campus Norrk¨
oping, SE-60174
Norrk¨
oping, Sweden
Received 3 July 2013, in final form 11 October 2013
Published 28 November 2013
Online at stacks.iop.org/PPCF/55/124017
Abstract
We report on recent experimental results concerning the generation of collimated (divergence
of the order of a few mrad) ultra-relativistic positron beams using a fully optical system. The
positron beams are generated exploiting a quantum-electrodynamic cascade initiated by the
propagation of a laser-accelerated, ultra-relativistic electron beam through high-Zsolid
targets. As long as the target thickness is comparable to or smaller than the radiation length of
the material, the divergence of the escaping positron beam is of the order of the inverse of its
Lorentz factor. For thicker solid targets the divergence is seen to gradually increase, due to the
increased number of fundamental steps in the cascade, but it is still kept of the order of few
tens of mrad, depending on the spectral components in the beam. This high degree of
collimation will be fundamental for further injection into plasma-wakefield afterburners.
(Some figures may appear in colour only in the online journal)
1. Introduction
The generation of ultra-relativistic and high-quality positron
beams in the laboratory is a field of research of paramount
importance due to its direct relevance to a wide range
of physical subjects, which include nuclear and particle
physics, laboratory astrophysics, and plasma physics. Due
to the obvious difficulties encountered in generating stable
antimatter, and in further accelerating it to ultra-relativistic
energies, this field of research has thus far been prerogative
of large-scale conventional accelerators, such as the recently
dismissed Large Electron–Positron Collider (LEP) [1], or the
Stanford Linear Accelerator (SLAC) [2]. Positron beams
with energy as high as 100 GeV have been obtained at
LEP, which contributed towards fundamental advancements
in nuclear and particle physics. In its basic configuration,
an electron beam was accelerated by a linear accelerator
(LINAC) up to 200MeV. This electron beam impacted onto
a tungsten target and generated a high-density population
of relatively low-energy positrons. After due storage,
these positrons were then accelerated up to approximately
100 GeV in a km scale synchrotron. However, such a
large size and subsequent high cost of these machines is
motivating the quest for alternative acceleration schemes;
in this context, plasma devices are appealing candidates
due to the extremely high accelerating fields that they
are able to support (of the order of 100 s of GV m−1,
compared to the typical MV m−1obtainable in conventional
accelerators). Laser–plasma accelerators have already
demonstrated the generation of electron beams with energy
per particle reaching [3], if not exceeding [4], 1 GeV and
energies per particles approaching 100 GeV are theoretically
0741-3335/13/124017+06$33.00 1© 2013 IOP Publishing Ltd Printed in the UK & the USA

Plasma Phys. Control. Fusion 55 (2013) 124017 G Sarri et al
predicted for the next class of high-power (10 PW) laser
systems [5]. Moreover, particle-driven plasma-wakefield
afterburners have been recently demonstrated to represent a
compact (meter-scale) and powerful device for further beam
acceleration [6].
On the other hand, laser-driven high-energy positron
beams are much harder to generate. Researchers from
the Lawrence Livermore National Laboratory (LLNL)
demonstrated the possibility of generating a population of
relativistic positrons by focusing a kJ-class laser on a mm-thick
gold target [7]. Despite the intrinsic interest of these results,
a major drawback is represented by the broad divergence of
these beams (cone aperture of θLLNL 20◦), which prevents
from efficient storage and further acceleration. Arguably, the
easiest way to generate a significant population of positrons
is to exploit the electromagnetic cascade initiated by an
ultra-relativistic electron beam propagating though a solid
target. This is the physical phenomenon exploited also in
the positron generation stage in conventional accelerators,
such as LEP [1]. It is intuitive that the resulting positron
beam would present a divergence whose lower limit is given
by the divergence of the primary electron beam. In the
LLNL experiment, the impact of the laser pulse onto the gold
target generated, inside it, a broadly divergent electron beam
(θe−20◦), as expected for this sort of generation mechanism.
Hence, the subsequently generated positrons preserved the
same degree of divergence. An alternative solution is obtained
if the electron generation and the electromagnetic shower
producing the positrons are separated into two different stages.
This idea was first brought forward by Gahn and collaborators
[8]. In that work, the electrons were first generated during
the interaction of a low-intensity laser pulse with a gaseous
target; the generated electron beam subsequently triggered
an electromagnetic shower during propagation through a
high-Zsolid target. However, the low intensity of the laser
available at the time, together with a non-optimized electron
generation in the gas, did not allow for a better degree of
collimation; a divergence of the order of 20◦wasinfact
reported.
Since this proof-of-principle experiment, laser-driven
electron acceleration has dramatically improved; collimated
(θLWFA 1–2 mrad 0.06◦) and high-energy (ELW FA GeV)
electron beams can now be generated when a high-intensity
laser pulse propagates through a gaseous target, exploiting
a physical mechanism known as laser wakefield acceleration
(LWFA) [9]. In this article, we show that, combining the recent
improvements in laser-wakefield electron acceleration with the
proof-of-principle idea introduced by Gahn and collaborators,
collimated ultra-relativistic positron beams (divergence of the
order of a few mrad and energy of the order of hundreds of
MeV) can be generated in a relatively small-scale laser-driven
setup. We envisage that these positron beams would be of
interest for a wide range of practical applications. First of
all, such a low divergence obtained is indeed encouraging
towards the further acceleration of these beams with plasma
afterburners (an idea first experimentally tested by Blumenfeld
and collaborators [6]). Moreover, the high density obtained
makes laboratory-based studies of astrophysically relevant
electron–positron-ion plasma phenomena finally accessible.
A thorough characterization of this physical scenario is
indeed necessary in order to advance our understanding of
astrophysical jets, which have been observed to be ejected
by some of the most powerful or compact objects in the
known Universe, such as black holes, pulsars, and quasars
[10]. Finally, these results promote the idea of the near-term
construction of GeV laser-driven electron–positron colliders.
These machines would finally provide a relatively cheap
platform for experimental studies of nuclear and particle
physics, making this branch of experimental physics finally
widely accessible on a University level.
The article is organized as follows: section 2will briefly
describe the physics underlying the quantum-electrodynamic
cascade initiated by an ultra-relativistic electron beam in a
high-Zsolid. Section 3will discuss the experimental evidence
of ultra-relativistic positron beams with a few mrad divergence
if solid targets with a thickness comparable to or smaller than
the radiation length of the material is used. Section 4will
instead show that the positron divergence increases if thicker
solid targets are used, but that it will still remain of the order
of 10–20 mrad (1◦). Finally, a conclusive paragraph will be
provided by section 5.
2. QED electromagnetic showers: a simple model
The production of cascade showers during the passage of
high-energy particles through matter have been investigated
for a long time and we refer here to the classic textbook [11].
We limit to quantum-electrodynamic cascades involving only
electrons, positrons and photons at energies much larger than
the electron rest energy m(units where ¯h=c=1 are
employed in this section). In particular, we assume that
the cascade is initiated by a pencil-like beam of electrons
propagating perpendicularly to the target. At ultra-relativistic
energies, the cascade can be assumed to propagate essentially
along the initial direction of propagation of the electron
beam [11]. Thus, the electron/positron distribution functions
f∓(E, d ) and the photon distribution function fγ(E, d ) depend
only on the energy Eand on the thickness dof the target.
At ultra-relativistic energies, one can in first approximation
neglect electron and positron energy losses as resulting from
Compton scattering with the electrons of the fixed atoms and
from the ionization of the fixed atoms at the passage of the
cascade. In this case, the only processes to be included in
the kinetic equations describing the evolution of the cascade
are the emission of photons by electrons and positrons via
bremsstrahlung [12] and the creation of an electron–positron
pair by a photon [13], both processes occurring in the field
of a heavy atom. It is useful to rescale the target thickness
din terms of the radiation length of the material. For an
order of magnitude estimate of Lrad, we can assume here to be
in the total-screening regime which, for an electron with energy
εemitting a photon with energy ω, occurs if the parameter
S≡αZ1/3ε(ε −ω)/(ωm) is much larger than unity (here,
α≈1/137 is the fine structure constant, mis the rest mass
of the electron and a Thomas-Fermi model of the atom is
assumed [13]). In this regime, and by including Coulomb
2

Plasma Phys. Control. Fusion 55 (2013) 124017 G Sarri et al
corrections, the radiation length is approximately given by
[13]: Lrad ≈1/[4α(Zα)2nλ2
CL0], where nis the number of
atoms per unit volume, λC=1/m =3.9×10−11 cm is the
Compton wavelength, and L0=log(183Z−1/3)−f (Zα),
with f(x) =∞
=1x2/(2+x2). The radiation lengths of
Pb and Ta are thus, respectively: Lrad (Pb)=5.6 mm and
Lrad(Ta )=4.1 mm. By setting δas the target thickness din
units of the radiation length Lrad, i.e. δ=d/Lrad , the kinetic
equations can be approximately written as [11]
∂f±
∂δ =−1
0
dvψrad(v) f±(E , δ) −1
1−vf±E
1−v,δ

+1
0
dv
vψpair(v )fγE
v,δ
,(1)
∂fγ
∂δ =1
0
dv
vψrad(v ) f−E
v,δ
+f+E
v,δ

−µ0fγ(E, δ), (2)
where the functions
ψrad(v) =1
v1+(1−v)2−(1−v) 2
3−2b,(3)
ψpair(v ) =v2+(1−v)2+v(1−v) 2
3−2b,(4)
µ0=7
9−b
3,(5)
with b=1/18 log(183/Z1/3), are related to the cross section
of bremsstrahlung and pair photo-production in the field of
a heavy atom with charge number Z(see [11] for details).
The electron and the positron distribution enter symmetrically
in the above equations. As an example, figure 1depicts the
calculated number of ultra-relativistic electrons and positrons
(E>120 MeV) generated once an electron beam with a
flat spectrum ranging from 120 MeV to 1 GeV (total number
of electrons: 2.7×109) propagates through a Pb target of
different δ. As we can see, a maximum in positron number
(Np2.5×108) is obtained for δ≈2. Increasing the
target thickness above this value, induces a net decrease in
positron yield. This can be intuitively understood by noting
that, for such thick targets, there is a higher probability
that any generated positron within the target might undergo
an energy loss during the propagation through the rest of
the solid.
Due to the ultra-relativistic nature of the particles involved,
the divergence of the electrons and positrons escaping the
target is expected to be inversely proportional to their Lorentz
factor. If the target thickness is less or equal to the radiation
length of the material, the average cone angle is given by
θ2
e+≈1/γ 2
e+[13]. For thicker targets instead, a multiple
step cascade is likely to occur, and the average cone angle can
be estimated as [14]
θ2
e+≈19.2 MeV/c
p√δ, (6)
with pbeing the momentum of the particle. Again, the inverse
proportionality with the particle Lorentz factor is preserved
even though the divergence increases with the square root of
the target thickness.
Figure 1. Calculated number of ultra-relativistic (E>120 MeV)
positrons (a) and electrons (b) escaping a Pb target of different
thicknesses δonce an electron beam with a flat spectrum ranging
from 120 MeV to 1GeV (total number of electrons: 2.7×109)
propagates through it.
3. Positron beam divergence if δ1
In this section, we will discuss in detail the divergence of
the positron beams obtained in an experimental campaign
carried out at the HERCULES laser [15], hosted by the
Centre for Ultrafast Optical Science at the University of
Michigan, US. A detailed description of the experiment,
together with the energy spectrum and density of the positron
beams obtained can be found in [16]; however, we will
repeat part of it here, for the sake of clarity. A sketch of
the experimental setup is depicted in figure 2(a). A laser
beam with energy EL=0.8 J and duration τL=30 fs was
focused (peak intensity of IL≈6×1018 Wcm
−2) onto the
edge of a 3 mm wide supersonic He gas-jet, doped with 2.5%
of N2. Once fully ionized, the electron density inside the
gas-jet was 9 ×1018 cm−3. This interaction delivered, via
ionization injection [17], a reproducible electron beam with a
divergence with a full-width half-maximum of 1.4mrad and
a broad spectrum extending to approximately 200 MeV (see
figure 2(b)). The laser-accelerated electron beam interacted
with mm-size high-Zsolid targets of different materials (Cu,
Sn, Ta, Pb) and thicknesses (from 1.4 to 6.4mm). However,
we will concentrate here only on the results obtained using
2.8 mm and 4.1 mm of Ta. A magnetic spectrometer was
used to separate the electrons and positrons which were then
recorded on a LANEX screen and an Image Plate, respectively.
3

Plasma Phys. Control. Fusion 55 (2013) 124017 G Sarri et al
Figure 2. (a) Sketch of the experimental setup adopted at the HERCULES laser. (b) Typical electron signal on the LANEX screen if no
solid target is inserted in the electron beam path. The full-width total maximum of the electron beam divergence is 2.5 mrad, corresponding
to a full-width half-maximum of 1.4 mrad. Details of the resulting electron spectrum and charge can be found in [16]. (c) Typical positron
signal on the Image Plate if 4.1 mm of Ta are inserted in the electron beam path. The corresponding positron spectrum can be found in [16].
The beam presents a divergence of the order of 3–4mrad, depending on the spectral component of the beam. Figures 1(b) and (c) are
adapted from [16].
Figure 3. Divergence of the positron beam escaping from 4.1 mm of Ta as a function of the positron energy. Empty green circles depict the
measured divergence in mrad (θe+), solid blue circles and red crosses indicate the measured and simulated product θe+γe+, respectively.
2.8 mm of Ta provided similar results.
The magnetically dispersed axis provides the spectrum of the
beams (see [16]), whereas the orthogonal axis provides a
direct measure of the beam divergence. A spectrally resolved
measurement of the beam divergence can thus be obtained in
a single shot and it is depicted in figure 3for 4.1 mm of Ta
(2.8 mm of Ta provided similar results). As we can see, a
divergence of the order of 3–4mrad is obtained, with higher
energy positrons being expelled in a narrower cone than the
lower energy ones. This must be expected, since a multi-step
cascade is unlikely for this range of target thicknesses and,
therefore, the average positron beam divergence scales as
θ+
e≈1/γ +
e(see full blue circles in figure 3), being γ+
e
the Lorentz factor of the escaping positrons. It is worth
noticing here that this measured positron divergence is two
orders of magnitude smaller than that obtained in [7] with a
much more energetic laser (1 kJ compared to 0.8 J used in our
experiment). It is remarkable also that such a relatively cheap
device (a 1 J laser system like the one used in this experiment is
now commercially available) can generate collimated positron
beams with a density that is only two orders of magnitude
smaller than the one obtained in the 2.4 mile long linear
accelerator in SLAC (compare n+
e≈2×1014 cm−3reported
in [16] with n+
e≈5×1016 cm−3reported in [2]).
For realistic laboratory-based astrophysical studies, it is
though necessary to obtain higher positron densities whilst
preserving their narrow divergence. In order to do so, two
different approaches can be adopted: either the energy and
number of the primary electrons can be increased, or a thicker
target can be used (see section 2, in which it is predicted that the
maximum positron yield is obtained for a target thickness of the
order of twice the radiation length). An experiment was then
carried out at the Astra-Gemini laser [18], which can provide
laser pulses with much higher energy (up to 15 J, compared to
0.8 J) and thus electron beams with higher charge and energy.
The main results of this campaign will be discussed in the next
section of the article.
4. Positron beam divergence if δ>1
As mentioned at the end of the previous section, a
straightforward way to increase the density and maximum
4

Plasma Phys. Control. Fusion 55 (2013) 124017 G Sarri et al
Figure 4. Sketch of the experimental setup adopted at the Gemini laser. The magnet is drawn tilted by 90◦, for the illustration purposes. The
setup closely resembles the one adopted in HERCULES (see figure 2) with the only differences that a higher energy laser pulse (EL15 J)
and a longer and less dense gas-jet (20 mm, ne2×1018 cm−3) were used.
energy of the positron beam is to increase the overall charge
and energy of the primary electron beam. This can be
easily achieved if more energetic laser pulses are used.
Another experimental campaign was thus carried out at the
Astra-Gemini laser [18], hosted by the Central Laser Facility
at the Rutherford Appleton Laboratory, UK. This system can
ensure laser pulses with a duration of 40 fs and an energy of the
order of 15 J (i.e. more than fifteen times higher than that used
in HERCULES, see previous section). Indeed, experimental
results obtained using the Astra-Gemini laser have recently
demonstrated the possibility of generating ultra-relativistic
electron beams with maximum energy of the order of the GeV
and overall charge of the order of hundreds of pC (associated
number of electrons of the order of 109–1010)[19]. The setup
adopted in this experimental campaign was thus essentially
identical to the one shown in figure 2, with the only difference
that a higher energy laser pulse and a lower density gas-jet
were used (see figure 4). In order to ensure a stable and
high-charge electron beam, the gas-jet pressure was chosen so
that it was higher than threshold for ionization injection [17]. A
20 mm long gas-jet (97% He, 3% N2) with a backing pressure
of 45 bar (corresponding, once fully ionized, to an electron
density of the order of 5 ×1018 cm−3) was thus used. This
allowed generating a higher energy electron beam (see figure 5
for a typical electron spectrum as arising from the laser–gas
interaction). The maximum energy of the electron beam was
consistently of the order of 600 MeV and the charge carried
by electrons with energy exceeding 160 MeV was of the order
of 300 pC, with a shot-to-shot fluctuation within 10%. The
divergence angle of the laser-accelerated electrons was in this
case slightly higher than the one discussed in the previous
section, having a full-width half-maximum of 2 mrad. In this
experiment we again tried different materials (Ta, Pb, Mo, Sn)
of different thicknesses (from a few mm up to a few cm).
However, for the sake of this article, we will discuss here
only the targets that ensured the highest positron yield, i.e.
Pb. For this material, we studied the electron beam interaction
with targets with a thickness of 0.5, 1, 2 and 4 cm which
roughly correspond to 1, 2, 4 and 8 radiations lengths. Also
in this case, positron beams with a monotonically decreasing
spectrum were obtained, similarly to those reported in [16],
yet with a higher number and maximum energy. A detailed
Figure 5. Typical electron spectrum as arising from the laser–gas
interaction in the Astra-Gemini experiment. The maximum energy
of the electron beam was consistently of the order of 600 MeV and
the charge carried by electrons with energy exceeding 160MeV was
of the order of 300 pC with a shot-to-shot fluctuation of the order
of 10%.
discussion of the positron spectra obtained in this experiment
will be reported elsewhere [20], and we will focus here our
attention only on the beam divergence, main focus of this
article.
The divergence of the positron beam for these target
thicknesses is plotted, as a function of the positron energy,
in figure 6(a). It must be noted that the acceptance angle
of the spectrometer was of the order of 8 mrad. It was thus
impossible to directly measure any divergence larger than
this value; therefore, the experimental points are limited to
this range (empty squares, solid circles, and empty circles
in figure 6(a)) whereas the solid lines arise from matching
FLUKA simulations [21]. These simulations were performed
assuming an initial electron beam with a spectral shape as
the one depicted in figure 5impacting onto a Pb target of
the required thickness. 106electrons were simulated, and
every single simulation point is the result of an average over
five identical runs, in order to minimize any stochastic error
arising from the random seed generator of the code. The output
of the simulation was then cross-checked by comparing the
simulated and experimentally measured positron and electron
spectrum at the exit of the solid target [20]. The good
agreement between these two quantities indicated a good
reliability on the simulated positron divergence. As we can
see, the divergence effectively increase as the target thickness
5

Plasma Phys. Control. Fusion 55 (2013) 124017 G Sarri et al
Figure 6. (a) Spectrally resolved divergence of the positron beam
for different target thicknesses. Lines depict the divergence as
obtained by matching FLUKA simulations, whereas the solid
circles, empty squares, and empty circles depict the experimentally
measured values for target thicknesses of δ=1, δ=2, and δ=4,
respectively. (b) Product θe+γe+for different target thicknesses. For
each target thickness, the product remains approximately constant,
clear indication of the inverse proportionality between the
divergence angle and the Lorentz factor of the particles.
is increased, but it is still of the order of 10–20 mrad for
δ4. In order to check the inverse proportionality with
the particle Lorentz factor, the product θ+
eγ+
eis plotted, as
a function of the particle energy, in figure 6(b). As we can
see this inverse proportionality is well respected for all target
thicknesses, and the divergence is also roughly proportional
to √δ, in good agreement with equation (6). It is worth
noticing that targets thicker than twice the radiation length do
neither provide an increase in positron yield (see discussion in
section 2) nor in maximum energy. Moreover, they induce,
due to a higher order cascade and increased probability of
scattering, a significantly wider divergence. It is thus clear
that the optimum properties of the positron beam (density,
maximum energy, and divergence) can be achieved only for
δ≈2. For this case, we obtain: θe+γe+≈3–4 rad. This value
allows us to estimate the normalized emittance of the beam.
In a first approximation, this can be expressed, at the exit of
the solid target, as ζe+≈θe+γe+De+, being De+the beam source
size. This latter value is, according to FLUKA simulations,
of the order of 100 µm for δ=2. The normalized emittance
can then be estimated as: ζe+≈100πmm mrad. This value is
comparable to that obtained in LEP (ζLEP =60πmm mrad) [1]
and could be further improved if primary electrons with a
narrower divergence could be used.
5. Conclusions
We have reported on an experimental study of the divergence
of laser-driven ultra-relativistic positron beams. For optimum
experimental parameters, a beam divergence of a few
mrad is obtained, resulting in a positron beam normalized
emittance that is comparable to that achieved in large
conventional accelerators such as LEP. Such a relatively
low divergence suggests the possibility of implementing
plasma afterburners for further acceleration of the positrons,
towards the construction of a small-scale, plasma-based
high-energy positron beam-line. This would be beneficial
not only for fundamental nuclear and particle physics
studies but also for laboratory-scale studies of astrophysical
plasmas.
Acknowledgments
The authors are grateful for all the support received by the staff
of the Central Laser Facility. The authors also acknowledge
the funding schemes NSF CAREER (Grant No 1054164) and
NSF/DNDO (Grant No F021166). GS wishes to acknowledge
the support from the Leverhulme Trust (Grant No ECF-2011-
383). ADP is grateful to AI Milstein and to AB Voitkiv for
stimulating discussions.
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