Recent progress of laser driven particle acceleration at Peking University

Abstract

Recently, radiation pressure acceleration (RPA) has been proposed and extensively studied, which shows that circularly polarized (CP) laser pulses can accelerate mono-energetic ion bunches in a phase-stable-acceleration (PSA) way from ultrathin foils. It is found that self-organizing proton beam can be stably accelerated to GeV in the interaction of a CP laser with a planar target at {10}^{22} W/cm². A project called Compact LAser Plasma proton Accelerator (CLAPA) is approved by MOST in China recently. A prototype of laser driven proton accelerator (1 to 15 MeV/1 Hz) based on the PSA mechanism and plasma lens is going to be built at Peking University in the next five years. It will be upgraded to 200 MeV later for applications such as cancer therapy, plasma imaging and fast ignition for inertial confine fusion.

Graphical abstract

Keywords

phase-stable acceleration (PSA) / laser / ion acceleration / ignition

1 Phase-stable-acceleration

State-of-the-art lasers can deliver ultraintense, ultrashort laser pulses, with intensities exceeding {10}^{21} W/cm² and very high contrast ratios, in excess of {10}^{10} :1. These systems can avoid the formation of plasma by the prepulse, thus opening the way to laser-solid interactions with ultra-thin solid targets [1, 2]. Solid targets irradiated by a short pulse laser can be an efficient and flexible source of MeV protons as well as highly charged MeV ions. Such proton beams are already applied to produce high-energy density matter [3] or applied to radiograph transient processes [4], and they offer promising prospects for tumor therapy [5], isotope generation for positron emission tomography [6], and fast ignition of fusion cores [7].

In the intense-laser interaction with solid foils, usually there are three groups of accelerated ions. The first two occur at the front surface, moving backward and forward, respectively, and the third one is sheath acceleration (TNSA) that occurs at the rear surface [8–10]. As these output beams are accelerated only by electrostatic fields and have no longitudinal bunching in (x, p_x) plane, their distribution profiles used to be exponential nearly with 100\% energy spread. Although some techniques can be used to decrease the energy spread, however, they rely on relatively complicated target fabrication [11–13]. Recently, radiation pressure acceleration (RPA) has been proposed and extensively studied, which shows that ultra-intense laser pulses can accelerate mono-energetic ion bunches in a phase-stable-acceleration (PSA) way from ultrathin foils [14–25]. In these surface acceleration mechanisms, the linear polarized (LP) laser pulse is used and the J\times B heating [14] is efficient to generate the hot electrons. For a circularly polarized (CP) laser pulse with the electrical field E_L=E(x)[\sin ({\omega }_{L}t)z+\cos ({\omega }_{L}t)z], however, the ponderomotive force is f_p=\frac{m_e{c}^2}{2}\frac{\partial }{\partial x}a_L^{}{}_{}{}^2(x)x and its oscillating part vanishes. Here a_L(x)=eE/(m_e{\omega }_{L}c) is the normalized laser amplitude, and m_e, and {\omega }_L are the electron mass, laser frequency and charge, respectively. When a CP laser is normally incident on a thin foil, the electrons are pushed forward steadily by the ponderomotive force. There is a regime of proton acceleration in the interaction of a CP laser with a thin foil in a certain parameter range, where the proton beam is synchronously accelerated and bunched like in a conventional RF linac. The acceleration mechanism is thus named Phase Stable Acceleration (PSA). An analytic model is presented to show the acceleration and bunching processes during the laser interaction.

As the oscillating part of the ponderomotive force is zero for CP laser pulse and J\times B heating does not work, the interaction process is completely different from LP case. Figure 1 shows the electrical field profile and phase space projections for both circular and linear polarizations. In LP case, electrons are obvious heated by J\times B force and randomly distributed in the space. The charge separation field is many times smaller than in CP case [see Fig. 1(a)]. In contrast, the electrons are quickly pushed inward by the ponderomotive force of the CP laser pulse, so that they pile up in the front of laser pulse and make up of a compressed electron layer.

In order to discuss the PSA regime easily, a simple model can be derived to elucidate the bunch formation for laser plasma interaction [21, 28]. A linear profile of both in the electron depletion region (E_{x1}=E_{0}x/d for ) and in the compressed electron layer (E_{x2}=E_0[1-(x-d)/l_s] for ) can be seen in Fig. 2. The parameter E₀, n_{p0} and l_s are related by the equations E_0=4\pi end and n_{p0}{l}_s=nd\approx n_{0}d. As the E_{x1} increases with x, the protons starting at initial positions are debunched (longitudinally defocused) and their density will decrease in the electron depletion region. On the contrary, because the E_{x2} decreases with x, the protons inside the compression layer () can be bunched by the electrostatic field E_{x2}. The equilibrium between the electrostatic and the ponderomotive forces on electrons is only transitorily lost and the electrons rearrange themselves quickly to provide a new equilibrium if the laser pulse is not over. So the light pressure exerted on the electrons (1+\eta )I_L/c is assumed to be balanced by the electrostatic pressure E_{0}e{n}_{p0}{l}_s/2. Here η is the reflecting efficiency.

As the purely hydrodynamic description is not adequate to describe the interaction between the protons and electrons, dynamic equations are derived based on this model [28]. We introduce \xi =(x_i-x_r) with , where x_r=d+l_s/2 represents the position for the reference particle. The force acting on a test ion is given by F_i=q_i{E}_0[1-(x_i-d)/l_s]. Thus, the motion equation for the proton is \frac{{\mathrm{d}}^2{x}_i}{\mathrm{d}{t}^2}=\frac{q_i{E}_0}{m_i{\gamma }^3}[1-(x_i-d)/l_s], γ is the relativistic factor for reference particle. The phase motion (\xi ,t) can be written as

\begin{array}{}\text{(1)}& \begin{array}{cc}\ddot{\xi }=-{\Omega }^2\xi ,\hfill & {\Omega }^2={\displaystyle \frac{q_i{E}_0}{m_i{l}_s{\gamma }^3}}\hfill \end{array}\end{array}

For the reference ion γ varies slowly and E₀ is assumed to be quasi-constant the longitudinal phase motion (\xi ,t) is a harmonic oscillation. We can obtain

\begin{array}{}\text{(2)}& \xi ={\xi }_0\sin (\Omega t)\end{array}

\begin{array}{}\text{(3)}& \dot{\xi }=-{\xi }_0\Omega \cos (\Omega t)\end{array}

If we take the laser amplitude a_L=5, n_0/n_c=10, and \gamma =1 for protons at the beginning, the period of the first longitudinal oscillation is about 8T_L, which was consistent with the simulation results as shown in Fig. 5. If the final energy of reference particle W_r=300 MeV, then energy spread \mathrm{\Delta }W/W_r={\xi }_0\Omega /W_r will be less than 4\%.

2 PIC simulation

In order to examine the present model and dynamics process, we carried out one-dimensional (1D) simulations by a fully relativistic PIC simulation code (KLAP) [21, 31] and 100 particles per cell per species, with cell sizes of {\lambda }_L/100. In PIC simulations a laser pulse with a_L=5 and duration 100T_L is incident on a purely hydrogen plasma (cold, step boundary, overdense plasma slab with n_0/n_c=\omega _p^{}{}_{}{}^2/\omega _L^{}{}_{}{}^2=10 and D=0.2{\lambda }_L) where n_c=m_e\omega _L^{}{}_{}{}^2/(4\pi e^2) is the critical density, {\omega }_p is the plasma frequency. In simulations the target boundary is located at x=10{\lambda }_L and the laser impinges on it at t=10T_L, {\lambda }_L and T_L are the laser wavelength and period. The a_L is the laser field amplitude given in units of the dimensionless parameter, and m_e, {\omega }_L and e are the electron mass, laser frequency and charge, respectively.

The snapshots of the electrostatic field profile in Fig. 2(a) shows that the depletion region expands with time and the proton density in this region decreases, so that the slope of the field in the depletion region reduces gradually. In the compressed electron layer, it is found that the width of the compression layer remains to be equal to the skin depth (l_s\approx {\lambda }_L/20). Therefore the charge separation field in this layer nearly keeps the same steep linear profile, even though the maximum separation field is decreased slightly. It means the protons in the compressed electron layer can be synchronously accelerated and bunched by the charge separation field, so that the phase oscillations appear in the proton phase space (see Fig. 3), which is quite similar with the radio frequency accelerator.

The snapshots of phase-space distributions of electrons and ions at t=200T_L are plotted in Figs. 4(a) and (b). It shows that a bunched proton beam with a very high density is formed in the phase space (x,p_x), because protons inside the compressed electron layer always execute periodical oscillations as described by Eq. (3). The protons in the electron depletion region (between x=0 and 100) are debunched and form a long tail in the phase space, however, its density is two-orders lower than in the compressed electron layer. As a result, the debunched protons seem to have disappeared in the proton spatial distribution and the proton energy spectrum, which are shown in Figs. 4(c) and (d), respectively. Figure 4(c) implies that both particles have the same density profiles and a quasi-neutral beam is therefore obtained. In this case, the space charge fields are weak and the proton beam can propagate over a long distance without explosion, which is advantageous to transport the high current ion beams in applications. The energetic proton beam has a low FWHM energy spread () and high peak current as shown in Fig. 4(d). The energy spread is completely in agreement with our earlier estimation based upon Eq. (3). Note that the proton bunch has an ultrashort length about the skin depth l_s or about 250 attoseconds in time ({\lambda }_L=800 nm). The number of accelerated protons in the bunch is about n_0{l}_s\theta, where θ is the focused beam spot area. This gives about quasi-monoenergetic protons for a focused beam diameter of 40\mu \mathrm{m} in the present simulation.

In 1D simulations it is found that the proton energy depends on the product of target density and thickness. The proton energy and the energy spread are plotted versus the electron area density in Fig. 5(a). It shows that the energy spread can be optimized near the condition a_L\propto (n_0/n_c)D/{\lambda }_L. Figure 5(b) suggests that the proton energy increases almost linearly with the laser pulse duration at first, Later it turns to be saturated because the protons become relativistic.

For appropriate parameters, CP pulses may accelerate foils as a whole with most of the transferred energy carried by ions. The basic dynamics are well described by a 1D PSA model. Acceleration terminates due to multi-dimensional effects such as transverse expansion of the accelerated ion bunch and transverse instabilities. In particular, instabilities grow in the wings of the indented foil, where light is obliquely incident and strong electron heating sets in. Eventually, this part of the foil is diluted and becomes transparent to the driving laser light. The central new observation in the present paper is that this process of foil dispersion may stop before reaching the centre of the focal spot and that a relatively stable ion clump forms near the laser axis which is efficiently accelerated. The dense clump is about 1–2 laser wavelengths in diameter. The stabilization is related to the driving laser pulse that has passed the dispersed foil in the transparent wing region and starts to encompass the opaque clump, keeping it together (see Fig. 6).

Figure 7 highlights the central results concerning clump evolution. The total number of protons, compris-ed within a {\lambda }_L/2 distance from the laser axis and shown in Fig. 7(a), drops after time t=26 from an initial value of 2.5\times {10}^{10} due to transverse expansion, but this trend is interrupted at about t=35, when the foil becomes transparent in the wing region and the new regime of quasi-stable acceleration sets in. In the present 2D-PIC simulation, about 1.7\times {10}^{10} protons (1 nano-Coulomb) are trapped in the central clump and are accelerated to an ion energy of approximately 1 GeV. The ion energy spectra exhibit sharp peaks, as it is seen in Fig. 7(b).

Maximum proton energy versus laser intensity is plotted in Fig. 8. The black squares represent results from the 2D-PIC simulations described below. They follow an effective scaling of I^{0.8}.

3 Proof of principle experiment

There were successful experimental demonstration on ion acceleration from ultrathin diamond like carbon foils (DLC) irradiated by ultrahigh contrast laser pulses of energy 0.7 J focused to peak intensities of 5\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2 [29]. A reduction in electron heating is observed when thelaser polarization is changed from linear to circular, leading to a pronounced peak in the fully ionized carbon spectrum at the optimum foil thickness of 5.3 nm as shown in Fig. 8. 2D particle-in-cell simulations reveal that those C⁶⁺ ions are for the first time dominantly accelerated in a phase-stable way by the laser radiation pressure.

4 Laser plasma lens

In principle higher proton energy (for example, GeV) can be realized by using a higher laser intensity, however, in order to accelerate ions to a relativistic velocity, hole-boring effects and transverse instabilities should be restrained, which normally require extremely high laser intensity (>{10}^{21}\mathrm{W}/{\mathrm{cm}}^2), sharp rising front, and high temporal laser contrast (>{10}^{10}), which are very challenging for state of art laser technology. We propose a plasma lens to make high intensity, high contrast laser pulses with a steep front (see Fig. 10). When an intense, short Gaussian laser pulse pass through nearly critical dense plasma, the laser pulse will be compressed and focused into a channel due to self-focusing and self-modulation. If it is used as a plasma lens, three pulse shaping effects are realized synchronously: i) pulse focusing that results in laser intensity enhancement; ii) laser profile steepening; iii) absorption of non- relativistic prepulse. The transmission efficiency of the lens can be as high as 60\% and it will be useful for many applications such as generation of high-energy ions and electrons.

5 Self-matching resonance acceleration

In the critical dense plasma there is a novel self-matching resonance acceleration (SMRA) regime for generating dense relativistic electron beams by using ultraintense circularly-polarized laser pulses in near-critical density plasmas [32]. Under these conditions, the self-generated quasistatic magnetic fields (both azimuthal and axial) play an important role. When the self-generated quasistatic axial magnetic field is strong enough to pinch and trap thermal relativistic electrons, an overdense electron bunch is trapped and formed in the center of the laser channel as shown in Fig. 11.

In combination of the self-generated magnetic fields (both in axial and azimuthal direction) and the laser pulse, relativistic electrons can experience two processes: in the trapping process, the electron betatron frequencies and phases are adjusted automatically to match the resonance conditions; in the resonance process, the matched electrons are accelerated continuously along the laser propagation direction. All resonance electrons show similar dynamic behavior, which can be explained by the SMRA model, in which a collimated relativistic electron beam with overcritical density, helical structure, and plateau profile energy spectrum, can be generated. This experiment might be very promising for MeV hard photon (X/\gamma ray) production or ion acceleration.

The energy spectrum of electrons for the LP laser case shows a thermal-like distribution due to lack of the axial magnetic field, while the angular distribution of electron energy for the LP laser case shows a larger divergence angle and a lower energy peak.

6 Target fabrication

In order to realize Phase Stable Acceleration of ions, it is necessary to have free-standing nanometer-thickness target [29]. By using the filtered cathodic vacuum arc system, we have successfully manufactured free standing, diamond-like-carbon (DLC) films. The foil thickness can be accurately controlled by the arc counts as Fig. 12 shows. The thickness of films has been characterized by atomic force microscope. Figure 13 is a 5 nm DLC foil coated on Si substrate.

7 Proton acceleration from two layer targets

A novel efficient and stable mechanism has been designed to generate 200 MeV proton bunch by irradiating a two-layer targets (near-critical density layer+solid density layer with heavy ions and protons) with a p-polarized Gaussian pulse at intensity of {10}^{20}\mathrm{W}/{\mathrm{cm}}^2 (see Fig. 14). The laser intensity is enhanced by the laser self-focusing effect in the near-critical density layer. Meanwhile the electrons are efficiently accelerated in the laser propagation direction by the direct laser acceleration. It is further found that when the self-generated quasistatic axial magnetic field is strong enough to pinch and trap the thermal relativistic electrons, an overdense electron bunch can appear in the center of the plasma channel produced by the laser pulse. In the case of CP laser pulse a collimated relativistic electron beam with overcritical density and helical structure is generated [32]. A stronger sheath field is hence built up at the rear side of the solid density layer by the combination interaction of the shaped laser pulse and the energetic electrons, leading to more efficient and stable proton acceleration. Compared to a single-layer solid target, Fig. 15 implies the proton peak energy is increased by a factor of three and the energy spread is remarkably decreased from the two-layer target [33–35].

8 CLAPA project at Peking University

A project called Compact LAser Plasma proton Accelerator (CLAPA) is approved by MOST in China recently. A prototype of laser driven proton accelerator (1\sim 15 MeV/1 Hz) based on the PSA mechanism and plasma lens will be built at Peking University in the upcoming five years (see Fig. 16). It will be upgraded to hundreds of MeV proton later for the applications such as cancer therapy, plasma imaging and fast ignition for inertial confine fusion.

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