Physics of chromatic focusing, post-acceleration and bunching of laser-driven proton beams in helical coil targets

Abstract

To increase the fluence and the maximum energy of laser driven ion beams in view of potential applications such as isochoric heating of dense material or isotope production, it has been proposed to attach a helical coil normally to the rear side of the irradiated target. By driving the target discharge current pulse through the coil, this scheme allows to focus, post-accelerate and select in energy a part of the ion beam. The previously published results are extended to higher laser pulse energies and longer coils. This leads to an increased number of guided protons and the generation of several proton bunches. Large scale particle-in-cell simulations with realistic boundary conditions reproduce well the experimental results. A detailed analysis of the numerical simulations and an analytical model demonstrate the crucial role of the discharge current pulse dispersion in the proton bunch trapping and focusing.

Synchronous post-acceleration of laser-driven protons in helical coil targets by controlling the current dispersion

“…Due to the alternative acceleration and deceleration, the final energy gain is relatively low. The highest energy gain for the most energetic protons, in our case, is 19%, which is comparable to the reported experimental results [ 21 , 27 , 28 , 34 ] .

Figure 4 (a) Snapshots of proton distributions in phase space ( x , p x ) and the longitudinal electric field at 60, 240 and 360 ps, in a single-stage HC. (b) Longitudinal electric field (red curve) in the coordinate frame of the traveling highest-energy protons, and the evolution of the cut-off energy (blue curve) in a single-stage HC, where the three groups of green circles mark the three statuses in (a).

…”

“…The phase velocity and group velocity of the EMP are equal and independent of frequency, and the HC is considered a dispersionless medium. Bardon et al [34] used finite-difference time-domain (FDTD) codes [37,38] to simulate the current propagation through the HC, which is a suitable approach to simulate the EMF at full-scale (nanosecond and centimeter scales). However, their simulations lacked particle dynamics analysis to reveal the effect of velocity dispersion on post-acceleration.…”

“…As shown in Figure 6(b), the pulse duration of the current in the second stage is greater than that in the first stage due to the current dispersion. The evolution of the dispersion current will become more stable as the pulse duration expands, as demonstrated by Bardon et al [ 34 ] . Therefore, the acceleration of the protons in the second stage can be more stable.…”

“…When such a broadband current propagates along an HC, the dispersion affected by coupled inductances and capacitances is nonnegligible. Bardon et al [ 34 ] found that in the simulation, the velocity dispersion of the current leads to progressive modification of HCPA, which may be one of the most important reasons for the termination of acceleration in a long HC. Since previous experiments and simulations did not consider current dispersion, an in-depth investigation of its effect on long-time synchronization between the post-acceleration field and protons is important.…”

Dual stage approach to laser-driven helical coil proton acceleration

“…The HC accelerators [3,4,13,14] consist of a helix of wire perpendicular to the rear surface of a typical flat foil (FF) target. Irradiating the foil generates simultaneously a proton beam at its rear surface and a positively charged unipolar electromagnetic (EM) pulse, tens of ps in duration, which flows along the helix wire at v EM ≃ 0.98c [3,[15][16][17].…”