Ion acceleration by superintense laser-plasma interaction

Andrea Macchi, Marco Borghesi, and Matteo Passoni

Rev. Mod. Phys. 85, 751 – Published 10 May 2013

Abstract

Ion acceleration driven by superintense laser pulses is attracting an impressive and steadily increasing effort. Motivations can be found in the applicative potential and in the perspective to investigate novel regimes as available laser intensities will be increasing. Experiments have demonstrated, over a wide range of laser and target parameters, the generation of multi-MeV proton and ion beams with unique properties such as ultrashort duration, high brilliance, and low emittance. An overview is given of the state of the art of ion acceleration by laser pulses as well as an outlook on its future development and perspectives. The main features observed in the experiments, the observed scaling with laser and plasma parameters, and the main models used both to interpret experimental data and to suggest new research directions are described.

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Received 21 October 2011

DOI:https://doi.org/10.1103/RevModPhys.85.751

Authors & Affiliations

Andrea Macchi^*

Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (CNR/INO), U.O.S. “Adriano Gozzini,” Pisa, Italy, and Department of Physics “Enrico Fermi,” University of Pisa, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy

Marco Borghesi^†

Centre for Plasma Physics, The Queen’s University of Belfast, BT7 1NN Belfast, United Kingdom and Institute of Physics of the ASCR, ELI-Beamlines Project, Na Slovance 2, 18221 Prague, Czech Republic

Matteo Passoni^‡

Dipartimento di Energia, Politecnico di Milano, Via Ponzio 34/3, I-20133 Milan, Italy

^*http://www.df.unipi.it/~macchi andrea.macchi@ino.it
^†m.borghesi@qub.ac.uk
^‡matteo.passoni@polimi.it

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Vol. 85, Iss. 2 — April - June 2013

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Images

Figure 1
Artist’s view of a typical experiment on proton emission from laser-irradiated solid targets.Reuse & Permissions
Figure 2
Proton energy spectrum from the rear side of a $100 μ m$ solid target irradiated by a 423 J, 0.5 ps pulse at normal incidence, corresponding to an intensity of $3 \times 10^{20} W {cm}^{- 2}$ . The integrated energy of protons indicates a conversion efficiency of $≃ 10 %$ for protons above 10 MeV. From 396.Reuse & Permissions
Figure 3
Example of the profile of energy deposition of protons and C ions in water, compared to those of electrons, x and $γ$ rays, and neutrons. Protons and C ion profiles are characterized by the Bragg peak at the end of the path. The quantity plotted is the relative dose, i.e., the energy absorbed per unit mass. From 9.Reuse & Permissions
Figure 4
Maximum proton energy from laser-irradiated solid targets as a function of the laser irradiance and for three ranges of pulse durations, reporting experiments up to 2008. Two trend lines are overlaid, the shallower one corresponding to a $\sim I^{1 / 2}$ dependence, and the steeper one to a scaling proportional to $I$ . From 39.Reuse & Permissions
Figure 5
Numerical solution of the electrostatic “plasma sheet” model based on Eq. (10) plus the exchange of initial position for crossing plasma sheets (see text for details). The trajectories of a limited number of sheets (1 over 20) in the ( $x, t$ ) plane are shown. The driver field has the profile of an evanescent wave with peak amplitude $0.5 m_{e} ω c / e$ in vacuum and a ${sin }^{2} (π t / 2 τ)$ rising front with $τ = 5 T$ where $T = 2 π / ω$ . A density $n_{e} / n_{c} = (ω_{p} / ω)^{2} = 5$ is assumed.Reuse & Permissions
Figure 6
Hot electron temperature as a function of irradiance from experiments of sub-ps laser-solid interaction. See Table 5.2 in 151 for details on experimental parameters, diagnostic methods, and references. The lines give scaling laws derived from different models [FKL: 127; W: 437; GB: 154; B: 47]. From 151.Reuse & Permissions
Figure 7
Cartoon showing some of the possible acceleration mechanisms in the interaction with a thick solid target, including TNSA at the rear side (see Sec. 2c1), hole boring RPA at the front side (see Sec. 2c2), and backward acceleration in the plasma blowoff [see, e.g., 76]. Also shown are the hot electron flow leading to sheath formation and expansion at the rear side and the associated return current.Reuse & Permissions
Figure 8
Results from multiparametric 2D simulations for a double layer target (115; 114). The maximum energy of protons accelerated from the rear layer is shown as a function of laser pulse energy $E_{L}$ and for different values of the intensity $I$ , pulse length $L_{p}$ , and focal spot diameter $D$ . The target density and thickness are $n_{e} = 100 n_{c}$ and $ℓ = λ$ , respectively. From 114.Reuse & Permissions
Figure 9
A typical RCF stack obtained in an experiment with the TARANIS laser at Queen’s University, Belfast. Higher numbers correspond to higher energy protons with layer 1 corresponding to $\sim 1 MeV$ and layer 9 to $\sim 12 MeV$ . From 105.Reuse & Permissions
Figure 10
Left: Schematic of a Thomson parabola (courtesy of S. ter-Avetisyan). Right: A typical example of ion traces obtained with the Thomson parabola.Reuse & Permissions
Figure 11
Proton emission from a wedge target effectively having two rear surfaces. Two separate spots are produced on the detector, showing that most of the protons originate from the rear side of the target. From 396.Reuse & Permissions
Figure 12
Effect of impurity removal on carbon ion spectra. (a) and (b) show C ions traces (from CR-39 track detectors) and spectra from Al foils coated with a C layer on the rear side, in the presence of hydrocarbon contaminants on the surface. In (c) and (d), the contaminants had been previously removed by resistive heating. From 182.Reuse & Permissions
Figure 13
Proton probing of the expanding sheath at the rear surface of a laser-irradiated target. (a) Setup for the experiment. A proton beam is used as a transverse probe of the sheath. (b)–(g) Temporal series of images produced by the deflection of probe protons in the fields, in a time-of-flight arrangement. The probing times are relative to the peak of the interaction. (h) A deflectometry image where a mesh is placed between the probe and the sheath plasma for a quantitative measure of proton deflections. From 356.Reuse & Permissions
Figure 14
Top: Modulations in the proton distribution, for different energies, on a RCF detector from a target with microgrooves imprinted on the rear side. The target is a $18 μ m$ thick Al foil irradiated at $10^{19} W {cm}^{- 2}$ . Bottom: The effect of electron removal by magnetic fields, showing that the proton beam emittance is not significantly affected. The images are for 6.5 MeV protons and the target thickness is $40 μ m$ . From 80.Reuse & Permissions
Figure 15
Electric field profile in a sheath with two electron temperatures. The field is normalized to $T_{h} / e λ_{Dh}$ and is shown for cold-to-hot electron temperature ratio $b = T_{c} / T_{h} = 0.01$ and for different values of the pressure ratio $a b = p_{0 c} / p_{0 h} = 1$ (dotted line), $a b = 10$ (dashed line), and $a b = 100$ (solid line). The $x$ coordinate is normalized to the cold electron Debye length $λ_{D c}$ corresponding to $a b = 10$ . From 320.Reuse & Permissions
Figure 16
Sketch of the density and velocity profiles from the self-similar solution for isothermal plasma expansion; Eq. (22). The front of charge separation at $x = x_{f} (t)$ and the rarefaction front at $x = - c_{s} t$ are also indicated. The electric field is uniform in the $- c_{s} t < x < x_{f} (t)$ region.Reuse & Permissions
Figure 17
Velocity spectrum of heavy ions ( $H$ ) and light ions ( $L$ ) at two different times from the numerical simulation of the expansion of a two-species plasma using a Boltzmann-Vlasov-Poisson model. Black dashed lines are analytical profiles based on self-similar solutions. The spectrum of light ions shows a peak typical of a multispecies expansion. From 423.Reuse & Permissions
Figure 18
Electric field profiles at different times from the numerical simulation of the collisionless expansion of a slab of warm plasma. Thick and dashed lines show results from a PIC code (28) and a hydrodynamics code (284), respectively. Both simulations assume a $40 μ m$ thick proton plasma slab with initial density $n_{0} = 3 \times 10^{19} {cm}^{- 3}$ and electron temperature $T_{e 0} = 500 keV$ . The inset shows the detail of the field distributions at early times, with the field in the PIC simulation extending over a finite distance. From 356.Reuse & Permissions
Figure 19
Experimental scaling of proton energy cutoff with laser power and pulse duration. Squares are data from experiments performed with the DRACO laser at FZD (Dresden), showing a linear scaling with power in the short-pulse (30 fs) regime. Other points are data from other laboratories; see 467 for references and details. The fitting lines correspond to the static model by 379 with different colors (labels) corresponding to different values of the pulse duration $τ_{1}$ as given in the legend. From 467.Reuse & Permissions
Figure 20
Maximum detectable proton energy as a function of target thickness for high-contrast (HC) and low-contrast (LC) conditions. Data are shown for both backward (BWD) and forward (FWD) directed ions, respectively, showing the symmetrical behavior of TNSA for HC and ultrathin targets. The LC results show the existence of an “optimal” thickness determined by the laser prepulse causing early target disruption, similar to 199. The laser pulse had 65 fs duration, $(0.5 - 1) \times 10^{19} W {cm}^{- 2}$ intensity, 45° incidence, and $P$ polarization. From 66.Reuse & Permissions
Figure 21
Experimentally observed (a) cutoff proton energies and (b) conversion efficiency (for $> 1.5 MeV$ protons) for $2 μ m$ thick Au targets as a function of surface area, evidencing the effect of electron refluxing. The laser pulse had 400 fs duration, $2 \times 10^{19} W {cm}^{- 2}$ intensity, 45° incidence, and $P$ polarization. From 49.Reuse & Permissions
Figure 22
Ion spectra from preheated Pd substrate targets from which hydrogen contaminants have been removed (181). Black curve: spectrum of $C^{5 +}$ ions. Blue curve: spectrum of the dominant substrate charge state ${Pd}^{22 +}$ . Green and red curves: simulated $C^{5 +}$ and ${Pd}^{21 +}$ spectra. Gray curve: spectrum of dominant $C^{4 +}$ ions from a heated W target. Magenta curve: $C^{5 +}$ signal from a cold Pd target. In the cases of black and blue curves, an ultrathin layer of graphite is present on the target surface, and a quasimonoenergetic spectrum appears. In the last two cases (gray and magenta curves) the targets have a thick layer of carbon contaminants and do not form a monolayer source, resulting in exponential-like spectra. From 181.Reuse & Permissions
Figure 23
(a)–(c)Schematic of laser-driven electrostatic lens. (d), (e) RCF stack beam profiles for protons of 9 and 7.5 MeV, respectively, showing that the 7.5 MeV protons are focused by the fields inside the cylinder and form a black spot on the RCF. (f): Proton spectra. Green line: spectrum obtained under same triggering conditions as in (e). Black line: typical exponential spectrum obtained when cylinder is not triggered. From 424.Reuse & Permissions
Figure 24
Hole boring acceleration by a ${CO}_{2}$ laser pulse in a gas jet. The left frame shows ion spectra for various values of the intensity $I_{15}$ (in units of $10^{15} W {cm}^{- 2}$ ) and the electron density $n = n_{e} / n_{c}$ : (a) $I_{15} = 6.4$ , $n = 6.1$ ; (b) $I_{15} = 5.5$ , $n = 6.1$ ; (c) $I_{15} = 5.9$ , $n = 7.6$ ; (d) $I_{15} = 5.7$ , $n = 8.0$ . The right frame shows the observed scaling of ion energies with the ratio $4 I / n c$ . From 313.Reuse & Permissions
Figure 25
(a) Energy per nucleon vs time from the analytical solution [Eq. (32)] of the LS model with $R = 1$ . The dashed line gives the asymptotic $\sim t^{1 / 3}$ behavior. (b) Scaling of the energy per nucleon as a function of the dimensionless pulse fluence $a_{0}^{2} τ$ (where $τ$ is the pulse duration in units of the laser period) and of the surface density $ζ$ [Eq. (5)] for $ζ = 1$ (black line), 3.16 (green line), 10 (blue line), 31.6,(orange line) and 100 (red line). The values on the upper horizontal axis give the fluence in $J {cm}^{- 2}$ corresponding to $a_{0}^{2} τ$ for $λ = 0.8 μ m$ .Reuse & Permissions
Figure 26
Three-dimensional simulations of thin-foil acceleration in the radiation pressure dominant regime (see text for parameters). Top: Snapshots at $t = 40 T$ of ion density isosurface and Poynting vector in the $y = 0$ plane. Bottom: The maximum ion kinetic energy vs time and the ion phase-space projection ( $x, p_{x}$ ) at $t = 80 T$ . The solid line corresponds to the analytical calculation according to the LS model. From 112.Reuse & Permissions
Figure 27
(a) Three typical narrow-band spectra for $Z / A = 1 / 2$ impurity ions observed from thin ( $0.1 μ m$ ) metallic targets [for parameters of shots 1–3, see the explanation in (b)]. (b) Peak energies for both ions with $Z / A = 1 / 2$ (filled squares) and protons with $Z / A = 1$ (empty squares) for seven shots with different polarization parameters [see, e.g., Eq. (11)]: $ϵ = 0$ (LP), 0.47 (EP), and 0.88 (CP). The peak energy is plotted as a function of the parameter $a_{0}^{2} τ_{p} / χ$ , which corresponds to $(m_{p} / 2 m_{e}) Ω τ_{p}$ in our notations. The parameter set [ $a_{0}$ , target material, thickness ( $μ m$ ), polarization] for the data points 17 is [15.5, Cu, 0.1, LP], [10, Cu, 0.05, CP], [13.8, Cu, 0.1, EP], [7.5, Al, 0.1, LP], [6.9, Al, 0.1, EP], [13.6, Al, 0.5, CP], and [14.1, Al, 0.8, LP], respectively. The circle is the data point from 185. The solid line is the LS scaling (35). From 204.Reuse & Permissions
Figure 28
Proton spectra from ${CO}_{2}$ laser interaction with a hydrogen gas jet. (a) Different spectra for a smooth (long) pulse (lower line) and a pulse train of 3 ps spikes (upper line); in the latter case, a peak appears in the spectrum. (b) Narrow spectra obtained in different shots. See text for parameters. From 172.Reuse & Permissions
Figure 29
Spectra of $C^{6 +}$ ions from laser interaction with ultrathin targets in the regime of relativistic transparency as a function of target thickness and laser polarization. From 184.Reuse & Permissions
Figure 30
Sketch of magnetic field sustained acceleration of ions, showing the topology of the magnetic and electric fields and the flows of escaping and returning electron currents. From 56.Reuse & Permissions
Figure 31
Proton probing of magnetic fields. (a), (c) Probing deflectogram of a laser-irradiated foil (ns pulse, $10^{15} W {cm}^{- 2}$ on a $6 μ m$ Al foil) obtained with a 5.5 MeV proton beam facing the foil, entering from the nonirradiated side in (a) and from the opposite, laser-irradiated side in (c). The inversion of the deflection pattern reveals the effect of a toroidal $B$ field [the asymmetrical pattern in (c) is due to a nonideal intensity distribution in the focus]. (b), (d) Particle tracing simulations for the conditions of (a) and (c) assuming a suitably parametrized $B$ field. From 65.Reuse & Permissions
Figure 32
The left shows the proton imaging setup with increased dynamical range in the time domain (338, 339). By placing a wire target at an angle with respect to the probe beam it is possible to resolve the propagation at a velocity close to $c$ of a field front along the laser-irradiated wire, as shown in the right (top: experimental images, bottom: particle tracing simulations). From 338.Reuse & Permissions
Figure 33
Heating of solid targets by protons. (a) Experimental setup for flat and focusing target geometries. Each target consists of a flat or hemispherical $10 μ m$ thick Al foil irradiated by the laser, and a flat $10 μ m$ thick Al foil to be heated by the protons. (b) Corresponding streak camera images showing space- and time-resolved thermal emission at 570 nm from the rear side of the proton-heated foil. Proton focusing by the hemispherical foil leads to a stronger, more localized heating. From 321.Reuse & Permissions
Figure 34
Setup for x-ray probing of a solid Al target heated by protons: (a) top view of the experiment, (b) schematic of the x-ray spectrometer; (c), (d) snapshots of temperature and density profiles of the heated $1.6 μ m$ thick Al foil as given by self-consistent simulations, demonstrating isochoric heating up to 15 eV temperatures. From 266.Reuse & Permissions
Figure 35
Concept of proton-driven fast ignition in the TNSA-based, cone guided scheme. Typical parameters required for the ion beam and optimization issues are also indicated. From 208.Reuse & Permissions
Figure 36
Top: Overview of an experimental setup for integrated dosimetry and cell irradiation system by laser-accelerated protons. Bottom: Fluorescence microscopy view of SKX tumor cell nuclei irradiated with such system, showing that the number of DNA double-strand breaks (bright spots, yellow-pink in the color version) increases with the delivered dose. From 223.Reuse & Permissions

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