Transmission and homogenization of laser-driven proton beams with broadband spectra

Over the past few decades, laser accelerators made continuous progress. Thanks to the ultra-high electric field gradient (100 GV/m) generated by the interaction of laser and plasma, protons can be accelerated to MeV energy at a micron scale, being expected to be a new generation of widely used compact accelerators. The laser-driven proton beam has the characteristics of μm-level size (point source), ampere-level peak current, broadband energy spectrum, and large divergence angle. Irradiation applications need a uniform dose distribution, requiring the transformation from a point source to a large area of uniformly distributed particles. Increase of utilization efficiency requires that beams with energy spread as large as possible can be transmitted, while the chromatic aberrations pose a challenge to the homogenization of the beams, including the homogenization of the beams with the same energy and different initial divergence angles, and the homogenization of the beams with different energies. The weak focusing of the constant gradient magnetic field can focus in the horizontal and vertical directions at the same time, and analyze the energy in the horizontal direction. The integration of focusing and energy analysis can achieve achromatic transmission, or significantly reduce the influence of chromatic aberrations. This paper studies the transmission characteristics of proton beams in weak-focusing magnetic fields. The homogenized transformation for protons with the same energy in the horizontal direction from a point to a large area by point-to-parallel imaging is demonstrated. Point-to-parallel imaging is not a necessary condition for homogenization; transformation without point-to-parallel imaging in the vertical direction also obtains good homogeneity. The conditions for positional achromaticity in the horizontal direction are explored, and the transmission and homogenization of proton beams with 20% energy spread can be achieved with appropriate design. In positional achromatic transmission, the chromatic aberrations still have influence, causing the proton beam with large energy spread to deviate from the center of the beamline in the horizontal direction. In order to reduce the influence of chromatic aberrations, a special steering magnet is designed after the weak-focusing magnet to correct the divergence angle in the horizontal direction. The relationship between the correction amount of divergence angle and the position in the horizontal direction is obtained through parameter scanning, which can be well fitted by a 4 order polynomial. After correcting the divergence angle, the proton beam with large energy spread returns to the center of the beamline at the beamline exit. With a slit and energy spectrum shaping, proton beams with 80% energy spread can be obtained for irradiation with better uniformity. When the deflection radius is designed to be 0.65 m, the weak-focusing beamline can transmit proton beams with 1–20 MeV energy, 80% energy spread, and an initial divergence angle of ±50 mrad. After changing the magnetic field direction, electron beams with 1–200 MeV energy, 40% energy spread can be transmitted. The transmission and homogenization of the proton beam with 80% energy spread greatly improves the utilization efficiency. Higher energy particle beams can be delivered using superconducting or pulsed magnet technology. The study found that the influence of chromatic aberrations is much larger in the beam transmission with a quadrupole triplet lens (strong focusing), and as energy cannot be accurately analyzed, it is difficult to improve. In comparison, the weak-focusing magnetic fields have significant advantages for beam homogenization.