Ions acceleration by Peta-watt class laser pulses and pellet compression in a fast ignition scenario
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Ions acceleration by Peta-watt class laser pulses and pellet
compression in a fast ignition scenario
C. Benedetti ∗ , P. Londrillo† , T. V. Liseykina∗∗ , A. Macchi‡ , A. Sgattoni ∗ and G.
Turchetti∗
∗
Dipartimento di Fisica Università di Bologna, INFN sezione di Bologna
†
Dipartimento di Astronomia, Università di Bologna, INAF sezione di Bologna, INFN sezione di Bologna
∗∗
Institute for Computational Technologies, SD-RAS, Novosibirsk, Russia, Max-Planck-Institute for Nuclear
Physics, Heidelberg, Germany
‡
polyLAB, CNR-INFM, Pisa, Italy
Abstract. Ions drivers based on standard acceleration techniques have faced up to now several difficulties. We consider here
a conceptual alternative to more standard schemes, such as HIDIF, which are still beyond the present state of the art of particle
accelerators, even though the requirements on the total beam energy are lowered by fast ignition scenarios. The new generation
of petawatt class lasers open new possibilities: acceleration of electrons or protons for the fast ignition and eventually light
or heavy ions acceleration for compression. The pulses of chirped pulse amplification (CPA) lasers allow ions acceleration
with very high efficiency at reachable intensities (I ∼ 1021 W/cm2 ), if circularly polarized light is used since we enter in the
radiation pressure acceleration (RPA) regime. We analyze the possibility of accelerating carbon ion bunches by interaction of
a circularly polarized pulses with an ultra-thin target. The advantage would be compactness and modularity, due to identical
accelerating units. The laser efficiency required to have an acceptable net gain in the inertial fusion process is still far from
the presently achievable values both for CPA short pulses and for long pulses used for direct illumination. Conversely the
energy conversion efficiency from the laser pulse to the ion bunch is high and grows with the intensity. As a consequence
the energy loss is not the major concern. For a preliminary investigation of the ions bunch production we have used the PIC
code ALaDyn developed to analyze the results of the INFN-CNR PLASMONX experiment at Frascati National Laboratories
(Rome, Italy) where the 0.3 PW laser FLAME will accelerate electrons and protons. We present the results of some 1D
simulations and parametric scan concerning the acceleration of carbon ions that we suppose to be fully ionized. Circularly
polarized laser pulses of 50 J and 50-100 fs duration, illuminating a 100 µ m 2 area of a 20 nm thick carbon target, produce
2 · 1011 monoenergetic ions of 0.5 GeV with 30% efficiency. Fully 3D simulations show a non dramatic degradation of the
beam properties. In order to reach regimes interesting for the inertial fusion, 1-2 KJ lasers with pulse duration in the 100-500
fs range should be considered with an illuminated surface of few hundreds squared microns, which would insure ∼ 10 12 ions
per shot to be produced. The efficiencies would range from 30% to 70% so that the energy of ions would vary from 0.3 to
1.5 KJ. With a few hundreds of such lasers a total energy of ∼ 0.2 ÷ 0.6 MJ, required in the fast ignition scenario, would be
reached. By tailoring the space distribution of the beams and their time sequence an adiabatic compression may be reached
avoiding the issues related to the charge neutralization in the final focus.
INTRODUCTION from 3 ÷ 4 MJ to ∼ 0.2 ÷ 0.6 MJ according to the es-
timates presented in the HiPER design study [3]. In the
The heavy ions drivers based on classical acceleration meanwhile R&D on high intensity linacs was carried out
devices have been investigated in the US and UE by for ADS and nuclear wastes transmutation projects such
the following different approaches based respectively on as TRASCO [4]. The initial design concerned a 70 mA
induction linacs and RF linacs plus storage rings. The superconducting linac for protons with a final energy of
HIDIF design [1, 2], presented ten years ago, was based 1.6 GeV. The injector and the first section of the linac
on a linacs cascade up to the main linac and a set of have actually been built. The number of particles stored
rings for bunch compression and storage. With a total in the linac is ∼ 5·1011 for a transit time of 1 µ s. The cor-
number of 2.5 · 1015 particles at 10 GeV the energy de- responding energy of the outcoming protons is 0.13 KJ
posited on the target is 3 ÷ 4 MJ. (two scenarios with so that with 1500 discharges the required 0.2 MJ would
Bi+ ions depositing 3 and 4.5 MJ respectively were ac- be obtained. The bunching of the beam and the injection
tually considered in the HIDIF design report). The fast into the rings for storage and compression remain serious
ignition reduces the energy to be deposited on the target challenges even though some problems concerning col-lective instabilities and electron clouds effects have been the picoseconds laser pulse of 70 KJ required to produce
solved for the R&D of SIS 100 and 300 at GSI [5]. The the hot spot is about 60, the actual gain would be 1. The
fast ignition scenario would require only 2 storage rings same problem exists in the present HiPER design. As a
and a single ion species. The extraction schemes based consequence the real breakthrough towards a power plant
on the unstable resonances 1/3 or 1/4 would introduce where the net gain factor should be at least 10, consists
further improvements [6]. However a dedicated and ex- in increasing the laser efficiency by one order of magni-
pensive research program would be needed to overcome tude. Possibly the diode pumped long pulse lasers will
the present stage of conceptual design. remain the main avenue to achieve the compression pro-
We propose here an alternative approach based on the ac- vided that a sufficiently high efficiency is reached. The
celeration of ions driven by super-intense and short laser pathway we propose may be explored by simulations and
pulses interacting with a very thin solid target. If the in- in the near future by experiments with the petawatt lasers.
teraction is dominated by the radiation pressure of the
laser pulse, the thin target may be accelerated as a whole
resulting in a very dense, highly collimated and monoen- THE TNSA AND RPA REGIMES
ergetic bunch of ions (neutralized by accompanying elec-
trons). As it is the bulk of the target that is accelerated, The ion acceleration process based on the interaction
the scheme is particularly suitable for the acceleration of of an intense laser pulse (> 1018 W/cm2 ) with a thin
ions heavier than protons. Early numerical simulations solid target (0.1 ÷ 10 µ m) has been widely investi-
for linearly polarized laser pulses show the onset of ra- gated during recent years. Theoretically two accelera-
diation pressure dominance at intensities close to 1023 tion regimes can be identified: the TNSA (Target Normal
W/cm2 [8]. Later theoretical work has shown the advan- Sheath Acceleration)[11] and the RPA (Radiation Pres-
tages of using circularly polarized pulses at normal inci- sure Acceleration)[9, 10, 12, 13, 14]. Up to now, in nearly
dence [9, 10]. This allows in principle to approach GeV all the experiments the acceleration process has been sat-
energies already with laser pulse having an intensity of isfactorily explained according to the first regime. Exper-
few times 1020 W/cm2 and picoseconds duration, which iments to prove the feasibility of the RPA are planned in a
are presently feasible. As an example, from a carbon tar- next future. In the TNSA regime the laser first accelerates
get having 1023 atoms per cm3 a bunch of 1012 ions the electrons of the target. Then the hot electrons create a
can be accelerated if the thickness and the (uniformly) sheath around the target setting up a strong space charge
illuminated area are respectively 0.1 µ m and 100 µ m2 field due to charge separation which accelerates the cold
or 0.02 µ m and 500 µ m2 . Much theoretical and com- ions. The ion maximum energy is dominated by the tem-
putational work remains to be done, e.g. to identify the perature and the density of the hot electrons and hence
optimal parameters to accelerate ions at GeV energies scales as (I λ 2 )1/2 , λ being the wavelength of the laser.
with realistic solid density and to address the issue of Concerning the properties of the accelerated ion beam in
target stability during the acceleration stage. The radia- both simulations and experiments the energy spectrum is
tion pressure acceleration regime with circularly polar- found to be quasi-thermal (very high momentum spread)
ized pulses has yet to be demonstrated experimentally. with a cut off at a maximum energy [15]. The angular
Open technical issues may include the need of laser pre- distribution of the ions is quite broad: the average diver-
pulse suppression for thin target acceleration and the fea- gence is in the range 10o ÷ 20o with the high energy ions
sibility of normal incidence and circular polarization for having smaller divergence.
super-intense pulses. Producing 1012 collimated bunches The RPA regime is in principle a more efficient way to
of protons or ions with energies above 1 GeV is a tough accelerate ions using lasers if compared to “standard“
challenge, but the recent progress on lasers is encourag- TNSA. The basic features of the mechanism can be stud-
ing. Typically a bunch with negligible transverse veloc- ied by means of a simple model where we consider the
ity distribution at 1.25 GeV would carry an energy of 0.2 interaction of a plane wave (the laser) with a moving mir-
KJ and one thousand of such beams would allow a uni- ror (the over-dense target). The momentum equation for
form energy deposition on the target. The repetition rate the mirror that moves under the effect of the radiation
from 1 to 5 Hz is reached by the imminent generation pressure is easily written: denoting by v ≡ cβ the velocity
of petawatt lasers. The efficiency of conversion of the of the mirror, the (normalized) momentum for the mirror
laser energy into the beam energy is high, above 50%, is given by u = √ β 2 ≡ β γ
and increases with the energy. The real bottleneck is the 1−β
efficiency of the laser itself. Assuming 65% efficiency √
du 1 u2 + 1 − u
for acceleration and 2% for the laser pulse generation a = √ , (1)
dt τ u2 + 1 + u
0.2 KJ bunch has a cost of 15 MJ, which is roughly the
fusion energy release. In this case even though the gain where τ −1 = 2I/µ c2, I is the (constant) intensity of the
given by the ratio between the ions beams energy and incident radiation and µ is the areal mass of the mirror.Assuming that u(0) = 0, the integration of equation (1) 3.0 30
gives 20_nm
ion peak energy [GeV]
ion peak energy [GeV]
2 3
2.0 20
u + (u2 + 1)3/2 − 1 = t/τ .
u+ (2)
3
1.0 10
So for t/τ 1 we have u(t) ' t/τ and asymptotically,
50_nm
1/3 100_nm
when t → ∞, we have u(t) ' 43tτ . The solution (2) as- 0.0
0.0 1.0 2.0
0
0 250 500 750 1000
sumes a constant intensity I illuminating the target. Deal- I [1021W/cm2] Elaser[J]
ing with finite length laser pulses with a variable inten-
sity profile I = I(x − ct), equation (1) must be integrated FIGURE 1. Left: ion peak energy as a function of the laser
intensity. The circles correspond to PIC simulations, the black
together with the one describing the displacement of the curve to the analytical result obtained from the boosted mirror
mirror model. For an illuminated surface σ = 100 µ m2 , a pulse du-
dx cu
= cβ = √ . (3) ration τ = 100 fs and an intensity I = 1021 W/cm2 we have
dt 1 + u2 E laser = 100 J and the figure can be read as a function of
the laser energy. Right: theoretical ion peak energy as a func-
An analytic solution for u(t) is no longer available but a tion of the laser energy for three different target thickness
numerical solution can be easily worked out. Let’s con- d = 20, 50, 100 nm.
sider now the radiation reflected by the moving mirror in
the laboratory frame. The relation between the frequency
of the radiation before (ω ) and after (ω 0 ) the reflection is intensities it is possible to observe RPA provided a cir-
given by s cularly polarized (CP) laser pulse is utilized instead of a
ω0 1−β linearly polarized (LP) pulse. Using a CP pulse at nor-
= . (4) mal incidence on the target the longitudinal component
ω 1+β
of the Lorentz force oscillating at twice of the frequency
In the relativistic limit β → 1 we have that ω 0 → 0, of the laser vanishes (for a plane wave) or is relatively
as a consequence the energy of the incoming photon small (for a finite laser spot size). Removing this com-
is completely absorbed by the mirror. This regime en- ponent we highly reduce the electron heating and the
sures asymptotically the maximum efficiency (ideally resulting constant ponderomotive expulsion can sustain
∼ 100%) in transferring the laser energy to the target. quasi-statically the charge displacement. A 1D model of
This simple model assumes that the laser momentum is the RPA regime with CP laser pulses for thick targets
directly coupled to the ions but this is not the case in (> 1µ m) has been proposed by Macchi et al. in [9]. In
the laser-target interaction because the laser first interacts this paper we will deal with thin targets (10 ÷ 100 nm at
with the electron plasma. If the electrons heat forming a realistic densities) where the model of the laser-boosted
sheath around the target then an efficient coupling laser- mirror presented above can give a reliable description of
ion is no longer possible and we observe the classical the process. Concerning the scaling law for the kinetic
TNSA. To observe the RPA we need that electrons co- energy (Ki ) of the ions as a function of the laser pulse en-
herently displace (without heating too much) leading to ergy (EL ) the numerical integration of equations (1) and
the formation of a space charge field dominated by a sin- (3) suggests that KI ∝ ELα where α = 2 at low pulse en-
gle positive spike, this field can then accelerate the ions ergy and α = 1 at high energy.
as a “single object” and in case of a thin (few nanome-
tres) target the entire foil can be accelerated. This accel-
eration scheme implies also that the energy spectrum of NUMERICAL RESULTS AND HIF
the accelerated ions is monoenergetic. The fundamental
condition that needs to be fulfilled in order to enable the
PERSPECTIVES
RPA mechanism is that the electron displacement creat-
We present here the results of a parametric scan in the
ing the space charge field is sustained by the ponderomo-
target thickness and pulse duration, performed with the
tive force (i.e. by the radiation pressure of the laser) in a
PIC code ALaDyn [16], for three different values of the
quasi-static way so they are in quasi-equilibrium.
laser pulse energy E=10, 50, 1000 J. The first two val-
Esirkepov et al. showed [8] that for a linearly polarized
ues correspond to CPA lasers commercially available,
laser pulse the dominance of the RPA over TNSA is pos-
the last one is relevant for HIF but is beyond the present
sible at high laser intensities: the transition from TNSA
state of the art. Anyhow the experiments with thin tar-
towards RPA begins at I > 1021 W/cm2 and for I > 1023
gets at lower energies will allow to draw a possible path-
W/cm2 we have the so called “laser piston” regime. How-
way for HIF with laser produced ion bunches. In figure
ever it has been noted [9, 10] that even at lower laser
1 (left panel) we present the ion energy and efficiency105
1000J
100 We consider here a typical 1 KJ pulse pulse with
10 4 1000J τ = 250 fs whose power is 4 PW. If it illuminates a
50fs
75
150 ÷ 200 µ m2 target of 30 ÷ 35 nm thickness the num-
peak energy [MeV]
ber of accelerated ions is ∼ 4 · 1011 , supposing they are
100fs
103
efficiency [%]
50J 150fs
50J 50fs
200fs 100fs
80% of the total (in a cubic micron there are 1011 car-
50
2 10J 150fs
10 200fs
101
25 bon ions). The ions energy then ranges between 650 and
800 J in accordance with the efficiency estimates. There-
10J
10 0
0 10 20 30 40
0
0 10 20 30 40 fore we obtain a 700 J beam with a 1 KJ laser: with
300 lasers, we reach 210 KJ which is the minimum en-
thickness [nm] thickness [nm]
ergy budget required in a fast ignition scenario. Possi-
FIGURE 2. Left: ion peak energy as a function of the target
thickness for three different laser energies E=10,50,1000 J. The bly one should increase this number to take into account
dots of different colours correspond to 1D PIC simulations with the neglected 3D effects. However we believe this is a
pulse duration τ = 50, 100, 150, 200 fs. The black curve is the possibility that should be explored. Its main advantage
comparison with the mirror analytic results. Right: the same is modularity, with respect to conventional accelerators.
for the efficiency η defined as the ratio between the ions total Indeed experiments with a single laser are needed to find
energy and the laser pulse energy η = E ions /E laser . the optimal conditions of efficiency and energy for the
selected ion type. Working with many very short ion
100 bunches has another advantage for the final focus. In-
deed a very simple computation shows that 25 beams can
80 be focused on a 4 × 4 mm target from the distance of 1
20_nm
m assuming a small directional uncertainty. Considering
the beams as point-like bunches of N ions one has sim-
efficiency [%]
60
50_nm
ply to integrate the equations of motion for the Hamil-
tonian H = ∑i p2i /2M + q2 ∑i< j ri−1 j where M = NA m p
40
100_nm
20 and Q = NZe are the bunch mass and charge. Letting L
is the length unit we choose comparable with the target
0
0 250 500 750 1000
size after the scaling r0 = r/L, t 0 = ct/L and p0 = p/Mc
Elaser[J] we obtain
FIGURE 3. Efficiency as a function of the energy for three H p0 2i 1
different target thickness D = 20, 50, 100 nm obtained theoret-
H0 = 2
= ∑ +ξ ∑ 0 , (5)
Mc i 2 i< j ri j
ically from the boosted mirror model.
where
as a function of the energy of the laser pulse or its in- q2 NZ 2 e2 1 NZ 2 me r cl
ξ= 2
= = , (6)
tensity which is the same if we keep fixed the uniformly Mc L A m p c2 L A mp L
illuminated surface σ and the pulse duration τ . The main 2
features are an initial quadratic growth of the ions en- and me c2 = 2.8 · 10−15 m is the classical electron radius.
e
ergy with the laser energy (or intensity). The efficiency For carbon ions and L = 1 mm we have ξ = 4.2 · 10−3.
(figure 1 right panel) grows with the energy and reaches Such a low value in the dimensionless Hamiltonian ex-
100% asymptotically. Both the peak energy and the ef- plains why the space charge repulsion does not cause dra-
ficiency increase as the target thickness decreases (see matic effects in the final focus if the number of bunches
figure 1 and 2 for comparison with 1D PIC simulations). low enough (≤ 20). Having a sequence of 30 multiple
However there is very likely a thickness limit (growing shots by 10 lasers each one, one might have an adiabatic
with energy) below which 3D instabilities might break deposition in a few nanoseconds, choosing 100 ps as the
the scaling law. It is not an easy task to say which is the time interval between two multiple shots.
ideal thickness for HIF ion beams. Since the skin depth
for C6+ is 7-8 nm a value ranging between 3 and 6 skin
depths might be reasonable. Taking into account that the MULTI-DIMENSIONAL EFFECTS
results of the analytical model are close to the PIC sim-
ulations, see figure 2, we can estimate from figure 3 that Presently available computing power makes it possible
the efficiency is between 65% and 85% for a thickness to simulate RPA of thin targets with realistic solid den-
between 20 ÷ 50 nm. As a consequence, assuming that sity and proper numerical resolution only in 1D. Real-
the ions energy is in the 10 GeV range, we expect an ef- istic 3D simulations are possible only for feasible model
ficiency of 65÷75%. problems with relatively low densities. Nevertheless suchsimulations are useful to address (at least qualitatively) to produce ion beams for tumors therapy (hadrother-
the most important issues that are not included in 1D ge- apy). As a consequence there might be a common re-
ometry. Here we summarize the most important results search area which, jointly with the modularity of this ap-
of a 3D simulation campaign which have been reported proach, renders funding more affordable. A large number
elsewhere [10]. Besides the realism of the geometry, it of questions are waiting to be explored first of all sys-
is noticeable that 3D simulations also include the con- tematic 3D simulations and validation with experiments
straint of angular momentum conservation, which is of at presently available laser energies. The compression
relevance because a circularly polarized wave carries a phase with this type of beams, in a fast ignition scenario,
non-vanishing angular momentum. A relevant degree of should also be addressed in order to assess the laser pa-
angular momentum absorption by the plasma has been rameters. If more accurate virtual experiments confirm
found in 3D simulations, creating an azimuthal ion cur- that this approach is possible, a dedicated experimental
rent and revealing that non-adiabatic processes (violating campaign might be undertaken.
the conservation of “photon number” that would imply
no angular momentum absorption at all) are at play dur-
ing RPA (so that the thin target can not be considered ACKNOWLEDGEMENTS
an ideal perfect mirror) [10]. As found in 1D parametric
studies, an optimal target thickness for RPA exists, as too This work has been supported by the INFN grants
thick targets can not be accelerated as a whole, but too HALODYST and BBAR for beam dynamics and PLAS-
thin targets are transparent to the laser pulse (relativisti- MONX for laser acceleration.
cally induced transparency is expected to contribute sig-
nificantly at the intensities or relevance). In 3D, when
using a pulse with a Gaussian intensity profile the lat- REFERENCES
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CONCLUSIONS
We have presented a possible scenario for HIF where
the ions are accelerated by PW lasers in the RPA
regime which allows to obtain very high efficiencies
on very thin targets. Even though KJ lasers with sub-
picosecond pulses obtained with the CPA techniques are
not presently available, they might be in a near future.
Lasers with 100 ÷ 200 J energies are being consideredYou can also read
