Post-acceleration of protons in helical coil (HC) targets driven by intense, ultrashort laser pulses can enhance ion energy. This scheme realizes the post-focusing and acceleration of protons, which has attracted widespread attention. Due to the challenges in maintaining synchronous acceleration, however, the current reported experimental energy gain is generally low and still cannot meet the requirements for medical applications. The research challenge lies in how to ensure stable post-acceleration of protons in HC.

This work elaborated that the electric field mismatch caused by the current dispersion effect is the main factor limiting the synchronous acceleration of protons for the first time. Based on the research findings, it proposes a two-stage structure combining drift sections and HCsto regulate current dispersion, reshape electromagnetic waves, and achieve synchronous cascaded acceleration of protons. With optimized parameters, the energy gain of protons is increased by 4 times. Over 100 MeV protons can be obtained using a petawatt laser which is promising for the application of particle physics, radiation therapy, and materials science.

Figure 1. (a): Structure of two-stage solenoid acceleration; (b): Proton energy gain under PW laser.

A thorough analysis of the underlying physical principles of EMF evolutions and beam dynamics in HC, and the enhanced approaches and effects of two-stage HC were published in High Power Laser Science and Engineering, vol. 11, Issue 4 (Zhipeng Liu, Zhusong Mei, Defeng Kong, Zhuo Pan, Shirui Xu, Ying Gao, Yinren Shou, Pengjie Wang, Zhengxuan Cao, Yulan Liang, Ziyang Peng, Jiarui Zhao, Shiyou Chen, Tan Song, Xun Chen, Tianqi Xu, Xueqing Yan, Wenjun Ma. Synchronous post-acceleration of laser-driven protons in helical coil targets by controlling the current dispersion[J]. High Power Laser Science and Engineering, 2023, 11(4): 04000e51).

Figure 2. (a): The structure of a single-stage HC and a two-stage HC. Two sections of HC are connected by a straight wire. (b) and (c): Spatial-temporal distribution of the longitudinal electric field in single-stage and two-stage HC. The green dash lines mark the extreme points of electric fields. (d): The E_x distribution and the position of protons within single-stage (top layer) and two-stage (bottom layer).

The laser-driven electromagnetic wave (EMW) has a short pulse width (several ps) and a wide spectrum (GHz-THz), which is highly susceptible to dispersion effects due to the inductance of the HC. After current dispersion, the accelerating field of the EMW lags behind that of the proton beam. Protons that were accelerated to a few ps ago will soon lose acceleration or get deceleration. In the simulation, the energy gain of the single-stage HC is only 10 MeV at PW laser.

The paper proposed a scheme that connects the two sections of HCs with a drift section, where the propagation speed of the EMW is much faster than that of the proton beam. This allows for the control of the acceleration phase. After passing through the drift section, the protons can be matched again with the acceleration phase. The cut-off energy of protons is enhanced to 100 MeV, and the energy gain is four times that of single-stage HC. This scheme is both concise and innovative, making it highly feasible for experimentation and valuable for further applications.

The two-stage HC provides stable and continuous post-acceleration of protons, achieving significant energy gain without the need for additional laser injection. In the future, more studies will further explore the multi-dimensional optimization of experimental parameters, and prepare to use the two-stage HC to achieve high-energy collimated proton beams with hundred MeV using petawatt-class lasers.