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In order to generate high quality ion beams through the stable radiation pressure acceleration (RPA) of the near critical density (NCD) target, we propose a new type of target where an ultra-thin high density (HD) layer is attached to the front surface of an NCD target, which has a preferable self-supporting property in the RPA experiments than the ultra-thin foil target. It is found that in one-dimensional particle-in-cell (PIC) simulation, by the block of the HD layer in the new target, there emerges the hole-boring process rather than propagation in the NCD layer when the intense laser pulse impinges on this target. As a result, a typical RPA structure that the compressed electron layer overlaps the ion layer as a whole is formed and a high quality ion beam is obtained, e.g., a circularly polarized laser pulse with normalized amplitude
High quality ion beams acceleration through the laser-plasma interaction has been widely studied for the past few decades because of its many significant applications, such as low-cost tabletop accelerators,[1] hadron therapy of oncological diseases,[2] and inertial confinement fusion.[3–5] A number of acceleration mechanisms have been proposed, for instance, electrostatic shock acceleration,[6–9] target normal sheath acceleration,[10–12] magnetic vortex acceleration,[13–16] and radiation pressure acceleration (RPA),[17–35] etc. Among all these mechanisms, the RPA that by using the circularly polarized laser, in which the generation of the hot electron is effectively suppressed and the steady radiation pressure is dominated,[17,22,33,36] is regarded as the highly promising scheme due to the high energy conversion efficiency and the production of the high-quality fast ions.[17,23,34] In the RPA, the acceleration process contains two stages, the hole-boring (HB) stage and the light-sail (LS) stage. In the HB stage, the light pressure of the laser pulse compresses and deforms the front surface of the target, which allows the laser pulse to penetrate deeply into the target.[29,33] In the LS stage, the compressed electron layer overlaps the ion layer and they form a quasi-electric-neutral plasma mirror, which detaches from the target and is boosted as a whole by the light pressure of the laser pulse.[31,33]
In the RPA experiment, the ultra-thin foil target is conventionally used due to their high density,[33] which can block the intense laser pulse and generate a strong charge separation field. Therefore, the ions in the target could have enough time to respond to the field and catch up with the fast moving electron layer. Eventually, the RPA structure that the electron layer overlaps the ion layer as a whole can be formed and the ions in this structure are able to be accelerated to a high energy in the LS stage.[23] However, the thickness range of the ultra-thin target is usually from tens of nanometres to micrometre,[31] which leads to a terrible self-supporting property in reality. Hence, such a vulnerable target should increase the difficulty of the experiment operation. An ideal solution is to reduce the density and increase the thickness of the target. Therefore, the near-critical density (NCD) target, whose density is usually from
Recently, the NCD target has drawn wide interests and a series of investigations about the interactions of the laser pulse with the NCD target have been presented.[16,36–40] For example: making the NCD layer as a laser shaping instrument to obtain a steep-front laser pulse,[36] realizing the electron acceleration by using two consecutive laser pulses interacting with an NCD target[37] or through the direct laser acceleration[38] and the relativistic resonant phase locking[39] in the NCD region, and generating the high-quality ion beams by the laser wake field acceleration[40] or the magnetic vortex acceleration[16] in the NCD region. However, there is little detailed research about the RPA of the NCD target until now. In this paper, we investigate the monoenergetic ion beam acceleration through the RPA of the NCD target by proposing a new type of target that a high density (HD) layer is attached to the front surface of the NCD target.
The organization of this paper is as follows. In Section
In the RPA, the energy of the accelerated ions in different RPA stages is related to the intensity of the laser pulse with different scales. In the HB stage, the ion energy is[28]
In the LS stage, the ion energy is[17]
For realizing the RPA of the NCD target, a new type of target is proposed and the schematic of the new target is shown in Fig.
Since the proton has the highest charge-to-mass ratio among all ions, which means the highest acceleration efficiency in the RPA,[33] we choose the pure hydrogen as the target material of the NCD layer. In addition, two other difficulties of the RPA are the loss of the electrons and the development of instability in the acceleration, which would lead to the transparency of the electron layer and broaden the energy spread of the accelerated ions.[32] In order to realize a more efficient stable RPA of the proton, a lower charge-to-mass ratio target material should be used in the HD layer, which works as a “buffer” of instability[30] and also can supply the abundant electrons to the front electron layer to maintain the quasi-electric-neutral RPA structure, which is known as the leaky light-sail regime.[31] The difference is, in previous researches about the mixed multi-species foil target,[30–32] there is a time lag for the initial mixed ions layer evolved into the layered ions layers, i.e., light ion layer in the front and heavy ion layer in the back, in the acceleration process. Therefore, it would take a while for the heavy ions to come into play. However, in our scheme, we have set that the heavy and light ions are separated initially, and placed in the HD layer and the NCD layer respectively. There are two reasons for this specific structure of the new target. On the one hand, there is no time lag for the separation of the heavy and light ion layers due to our target structure, and the stable RPA ion structure, layered ions layers, could be formed earlier than the common mixed multi-species foil target. On the other hand, the Coulomb repulsion from the heavy ions to the light ions, which has a contribution to the acceleration of the light ions,[25,32] would start to work while the laser penetrates the HD layer. The light ions under the ultra strong accelerating field can be accelerated very efficiently at the beginning of the interaction, just like being shot by a “slingshot”. Therefore, we use the carbon ion in the HD layer. By this new scheme, it is expected that the stable RPA of the NCD layer can be realized and a high energy proton beam with low energy spread can be generated.
In this part, the 1D PIC simulations are performed to verify our new scheme. For the new scheme (HD-NCD target), the length of the simulation box is 111 μm, and the grid resolution is 0.01 μm. A circularly polarized laser pulse with a Gaussian envelope
Firstly, figure
Secondly, the evolution of the phase space distributions of the proton is shown in Fig.
It should be noticed that, in previous researches about the RPA,[19,20,22] in which the ultra-thin solid target is used, the accelerating field in the HB stage is generated by the charge separation of the ultra-thin solid target itself. When the intense laser pulse enters the foil target, the strong ponderomotive force pushes the electron forward and leaves the electron depletion layer behind. In the electron depletion layer, the protons under the linearly increased electrostatic field are accelerated and form the higher velocity flat-top in the phase space distribution. In the compressed electron layer, the protons under the linearly decreased electrostatic field are rapidly reflected to double electrostatic field velocity and form the lower velocity flat-top in the phase space distribution. Therefore, at the end of the HB stage, there appears the double flat-top structure in the phase space distribution of the proton.[22] However, in our scheme, the ultra high accelerating field in the HB stage is mainly generated by the charge separation in the HD layer of the target. When this strong electrostatic field along with the laser pulse enter the NCD layer, the proton in the NCD layer would be directly reflected by this fast moving electrostatic field and involved in the linearly decreased accelerating field, which leads to the single lower velocity flat-top in the phase space distribution of the proton. Therefore, in our scheme, the double-flat-top structure did not show up in the phase space distribution of the proton, as seen in Figs.
Finally, the energy spectra of the proton in the 1D simulations are presented in Fig.
In the 1D PIC simulations, we have confirmed that a high quality proton beam can be generated through the stable RPA of the NCD target by the new scheme. In this part, the two-dimensional PIC simulations are performed to prove this new scheme. For the new scheme (HD-NCD target), the size of simulation box is 111 μm × 32 μm, which is composed of 11100 × 3200 cells along the x and y directions. The normalized amplitude of circularly polarized laser pulse
In the 2D case, figure
However, for the HD-NCD target, the intense laser pulse is effectively blocked by the HD layer and the penetrating velocity slows down sufficiently. Therefore, the protons can catch up with the electron layer, and a clear proton layer can be noticed distinctly, as shown from Figs.
The evolution of the phase space distributions of the proton is presented in Fig.
The energy spectra and energy angular distributions of the proton in the 2D simulations are presented in Fig.
In conclusion, for the sake of generating high quality ion beams through the stable RPA of the NCD target, we put forward a new type of target that an ultrathin HD layer is attached to the front surface of an NCD target. In the 1D PIC simulations, it is found that, when an intense laser pulse impinges on an NCD layer directly, the laser will propagate in the NCD layer due to the relativistic self-induced transparency. Therefore, the typical RPA structure cannot be formed and the protons are unable to be accelerated effectively. However, in the new scheme, by the block of the HD layer, the laser penetrating velocity is reduced effectively, and the proton can catch up with the fast-moving electron layer by the strong charge separation field. There emerges the HB process rather than the propagation in the NCD layer. As a result, a typical RPA structure that the compressed electron layer overlaps the proton layer as a whole can be formed. Eventually, the protons can be effectively accelerated to high energy in this RPA structure. By the use of carbon ions in the ultra-thin HD layer, a more efficient stable RPA is realized and a monoenergetic proton beam is obtained finally. Through this new scheme, a 1.2-GeV proton beam with an energy spread of only 5% is generated by using a circularly polarized laser pulse with the normalized laser amplitude a = 120. In the 2D PIC simulations, the accelerating characteristics of the proton are similar to those of the 1D simulations. Therefore, this new scheme is also applicative in a high dimensional situation. By varying the amplitude of the laser pulse, the thickness and the initial electron density of the HD layer, it yields essentially similar results, which shows that our new scheme is robust. However, it should be noticed that, some other simulation parameters, including the parameters of the NCD layer, are not taken into account. The detailed simulation results on these parameter effects will be shown in our following paper. Compared with the traditional ultra-thin foil target, the most important meaning of the new scheme is that the thickness of the target in the new scheme is relatively larger, which means a preferable self-supporting property in reality. Therefore, this new type of target is an ideal substitution to the ultra-thin foil target in practical RPA experiments. Through this new scheme, a high quality ion beam can be obtained through the stable RPA of the NCD layer, which has many significant applications, i.e., tabletop accelerator, tumor therapy and inertial confinement fusion.
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