Energetic proton beams are very useful for radiography, cancer therapy, and high-energy physics. The world's largest and highest-energy conventional particle accelerator, the Large Hadron Collider, is designed to collide opposing particle beams of protons at an energy of 7TeV per particle. It lies in a tunnel 27 kilometers in circumference, as much as 175 meters beneath the Franco-Swiss border near Geneva, Switzerland. In contrast, the scale of a laser-driven proton accelerator could be much smaller and the cost correspondingly lower.
The simplest method to accelerate protons with a laser pulse is ‘target-normal sheath acceleration’ (TNSA). In its basic form, a laser pulse illuminates a ∼1μm-thick gold target. The target electrons, ionized and heated greatly by the laser pulse, move to the far side of the target, and form an intense charge separation field. This field in turn accelerates protons inside the target to high energy, and the efficiency of the acceleration is dependent on the number and temperature of the hot electrons. A double layer target is a refinement of the idea, where the target is made up of a vertical gold slab backed by a ‘proton patch’ that is made of plastics that contain many hydrogen atoms. This has the advantage of producing a monoenergetic proton beam. However, with a simple double layer (DL) target, much of the laser energy is lost by reflection of the laser pulse. To address this, we have developed a complex double layer (CDL) target design,1 (see Figure 1), which can obtain more than three times the proton energy for the same laser and target parameters compared with the simple DL. As a result, the 180MeV protons required for proton therapy can be achieved with existing lasers. With our CDL, the energy spread is also halved, which is another requirement for medical applications. It enables the deposit of proton energy within a small volume so that healthy cells are not destroyed.
Sketch of a laser pulse interacting with our complex, slice-enhanced, DL target. From left to right, the sketch shows the laser pulse (A, red trapezoid with wavy line), the horizontal gold slice (B, orange), the gold vertical slab (C, yellow), and the thin proton patch (D, purple). Electrons and ions are represented by circles with negative (cyan) and positive (red) signs, respectively. The short black arrows indicate the directions of the electrons and ions, and the long red arrows (E) indicate the direction of the target normal sheath field.1
In our setup, we shine the laser pulse onto the front edge of a horizontal gold slice, placed normal to a simple vertical gold slab and proton patch (see Figure 1). This sets up an inhomogeneous oscillating electromagnetic field at the surface of the slice, known as the ponderomotive force. This, in turn, pulls electrons out of the slice and accelerates them forward along its surface. These electrons are not only energetic, but also highly collimated, so that they can easily propagate through the adjoining DL to form a stronger, longer-living, and more localized ‘sheath field’—the electric field in the thin layer containing more electrons than ions—behind the target. More importantly, with our CDL target, almost no light is reflected by the horizontal slice that supplies the energetic electrons, so that more laser energy is transferred to the hot electrons and eventually to the protons.
Figure 2. Ion phase space (x, vx)at different instants. x: length. vx: velocity in the x-direction. mi: ion mass. a0: normalized laser amplitude. n0: background plasma density.
Hot electrons are necessary for the TNSA, and therefore, linearly polarized laser pulses are often used. However, for a circularly polarized (CP) laser pulse, the absence of the oscillating longitudinal laser field reduces the heating greatly. There is only a steady component of the ponderomotive, i.e., the light pressure dominates the interaction. The light pressure pushes the electrons, which are low in mass, inwards, while the high-atomic-number (e.g., gold) ions, having more mass, are left behind. This leads to an electron-ion double-layer structure at the front (laser-facing) surface of the target gold slab. When the target is initially cold, the structure appears as a moving quasi-steady positive electrostatic field at the front of the target. Cold ions in such a field are totally reflected and thus accelerated by the field. The steady-state ion acceleration can be maintained over a relatively long time. The accelerated ion velocity (in the non-relativistic limit) is 2vp, where .
My colleagues and I realized that after all the local ions are accelerated, a second acceleration process by the same electrostatic field will begin subsequently, if the laser pulse is long enough.2 The almost monoenergetic ion beam produced by the first acceleration process is excited to a higher energy. We call this technique radiation pressure acceleration (RPA). Under suitable conditions, the pulsed accelerating process can be further repeated and very-high-energy ion beams can be obtained (see Figure 2).
Ion phase space (x, vx
) at t = 60T from one-dimensional particle-in-cell simulation.3
T: laser period. c: speed of light. λ: wavelength.
For a thick foil, a long time is needed for all the target ions to be accelerated by a quasi-steady laser piston. However, for a thin target, this is greatly reduced, and the target ions can be repeatedly accelerated many times within a short period. Furthermore, if we irradiate the thin target with an ultra-intense CP laser pulse, the ions experience more acceleration cycles (see Figure 3).3,4 We have obtained a quasi-monoenergetic GeV proton beam with conversion efficiency of more than 50%.
However, the proton energy scales with t1/3 or x1/3, where t and x are the acceleration time and distance, respectively. As a result, when the velocity of the accelerated proton becomes comparable with the speed of light, it requires a relatively long accelerating distance. In addition, with a long interaction time, many undesirable effects, such as multidimensional instabilities, appear. If we consider the target thickness (l∝a/n, where l is the target thickness, n is target density, and a is laser amplitude), the proton energy scales with a instead of l. This makes it rather difficult to produce protons of tens of GeV by RPA, even with an ultra-intense high-contrast laser pulse.
To obtain protons of ∼102GeV or even TeV, it is necessary to seek other acceleration approaches which can run stably in a much longer time or distance, like the ‘bubble regime.’ We know that electrons can be well accelerated over a long time by the rear-negative wake field in a laser-driven bubble. When a short intense laser pulse propagates in an underdense plasma, a bubble-like wake is formed just behind the laser pulse. There are only background ions inside the bubble while all the electrons are expelled out of the bubble by the ponderomotive force of the laser pulse. We have verified that protons can be similarly accelerated to high energies over a long time by the front positive wake field in the electron-bubble structure, as long as they are trapped in the acceleration field.5
Energy spectrum of protons from the simulation.6
To enhance the quality of the trapped protons, we have proposed a sequential-radiation-pressure and bubble-acceleration-regime proton acceleration scheme to generate high-quality monoenergetic protons.6 It shows that protons in a microtarget (located in an underdense plasma of high charge-to-mass ratio) can be accelerated firstly by the radiation pressure of a short circularly polarized laser pulse and then easily trapped and accelerated stably in the front of the bubble for a relatively long distance. 2D simulations show that a quasi-monoenergetic proton beam with 38GeV peak energy can be obtained by a short 2:14×1023W/cm2 laser pulse (see Figure 4).
We have also found that the proton energy can be increased dramatically by using a transverse super-Gaussian laser pulse instead of more usual transverse Gaussian pulses. With a 2:14×1023W/cm2 laser pulse in tritium plasma of density 1:5×1020/cm3, we have obtained 76GeV high-quality quasi-monoenergetic protons. This method shows promise for the generation of TeV protons.7
In conclusion, for different energy regimes, different acceleration methods can be used. For 100–1000MeV protons used for cancer therapy, advanced TNSA is a good choice because of its stability and low requirement for pulse quality. For GeV protons used for radiography of large samples, one may use RPA for its high efficiency in this regime. For 100–1000GeV protons used for high energy physics, the laser-driven bubble method may provide a high-acceleration gradient for a long length. We are now working to improve the bubble-acceleration method in order to accelerate protons to an energy higher than 7TeV, which is the highest energy obtained with a conventional accelerator.
This work is supported by the 973 Program (2011CB808104), the National Natural Science Foundation of China (10834008, 60921004, and 61008010), Shanghai Natural Science Foundation (10ZR1433800), and the Program of Shanghai Subject Chief Scientist (09XD1404300).
Shanghai Institute of Optics and Fine Mechanics
Baifei Shen is a full professor, and he received his PhD degree in optics in 1994. He visited the Max Planck Institute for Quantum Optics (Germany) and Ruhr University (Germany) as a Humboldt scholar and also, separately, visited the Argonne National Laboratory (USA) and the High Energy Accelerator Research Organization (Japan). He works on laser accelerator research.
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2. X. M. Zhang, Multistaged acceleration of ions by circularly polarized laser pulse: monoenergetic ion beam generation, Phys. Plasmas 14, no. 7, pp. 073101, 2007.
3. X. M. Zhang, Efficient GeV ion generation by ultraintense circularly polarized laser pulse, Phys. Plasmas 14, no. 12, pp. 123108, 2007.
4. B. F. Shen, Z. Z. Xu, Transparency of an overdense plasma layer, Phys. Rev. E 64, no. 5, pp. 056406, 2001.
5. B. F. Shen, Bubble regime for ion acceleration in a laser-driven plasma, Phys. Rev. E 76, no. 5, pp. 055402, 2007.
6. B. F. Shen, High-quality monoenergetic proton generation by sequential radiation pressure and bubble acceleration, Phys. Rev. ST AB 12, no. 12, pp. 121301, 2009.
7. X. M. Zhang, Ultrahigh energy proton generation in sequential radiation pressure and bubble regime, Phys. Plasmas 17, no. 12, pp. 123102, 2010.