Abstract
Keywords
1. Introduction
In this decade, active research has been carried out on the laser plasma acceleration concept[
We organize the remainder of this paper as follows. Section
2. Overview of laser plasma electron acceleration
Laser-driven plasma-based accelerators have evolved from a groundbreaking concept by Tajima and Dawson[
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In fact, there has been significant experimental progress in laser wakefield acceleration of electron beams since the incipient experiments on laser wakefield accelerators successfully demonstrated ultrahigh gradient acceleration of the order of , using chirped pulse amplification lasers with 10-TW class peak power and 1 ps pulse duration[
For many practical applications of electron beams, quality, stability and controllability of the beam performance such as energy, energy spread, emittance and charge are indispensable in addition to compact and robust features of accelerators. In this context, breakthrough experiments[
Although self-injection is a robust method relying on self-focusing, self-compression of the laser pulse and expansion of the bubble[
For laser plasma acceleration reaching GeV-level energies, it is essential to propagate intense laser pulses over a centimeter-scale distance in underdense plasma. For this purpose, a preformed plasma density channel with a parabolic radial distribution[
3. Energy scaling of laser wakefield acceleration in the relativistic regime
3.1. Propagation of relativistic laser pulses in plasma
The wave equation for the normalized vector potential describing the evolution of a laser pulse with laser wavelength and duration (full width at half maximum, FWHM) in a plasma channel can be written as[
Under the matched condition that no phase shift of the laser pulse occurs, the group velocity is written as , where a correction factor for the group velocity is defined as[
3.2. Laser plasma acceleration in the quasi-linear regime
In the linear laser wakefield with the accelerating field , the equations of the longitudinal motion of an electron with the normalized velocity and electron energy are given by[
Setting the initial electron phase at , the maximum energy gain is given by
3.3. Laser plasma acceleration in the bubble regime
Previous laser plasma acceleration experiments that successfully demonstrated the production of quasi-monoenergetic electron beams with narrow energy spread have been elucidated in terms of self-injection and an acceleration mechanism in the bubble regime[
In self-guided laser wakefield acceleration, where a driving laser pulse propagates by means of self-channeling, the equations of longitudinal motion of an electron are approximately written as[
Ref. | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
(%) | (mm) | (TW) | (fs) | (GeV) | (%) | |||||
[ | 5.7 | 0 | 8.7 | 182 | 35 | 19 | 55 | 3.9 | 0.8 | 12 |
[ | 3 | 0 | 8 | 65 | 6.6 | 15 | 60 | 2.8 | 0.72 | 14 |
[ | 1.3 | 0 | 13 | 110 | 4.9 | 15 | 60 | 3.8 | 1.45 | 100 |
[ | 5.7 2.5 | 0 | 1 3 | 45 | 3.8 | 16 | 40 | 2.3 | 0.8 | 25 |
[ | 3 | 0 | 3 5 | 40 | 4.1 | 15 | 60 | 2.3 | 0.46 | 5 |
[ | 0.48 | 0 | 67 | 625 | 18 | 50 | 160 | 3 | 2 | 10 |
[ | 2.1 | 0 | 4 | 212 | 15 | 21 | 60 | 3.7 | 0.35 | 25 |
[ | 1.3 | 0 | 10 | 212 | 8 | 21 | 60 | 3.7 | 0.87 | 30 |
[ | 2 0.8 | 0 | 4 10 | 212 | 5.8 | 21 | 60 | 3.7 | 3 | 30 |
[ | 4.3 | 5 | 33 | 40 | 5.8 | 25 | 37 | 1.4 | 1 | 5.9 |
[ | 3.5 | 5 | 33 | 12 | 1.4 | 25 | 80 | 0.75 | 0.5 | 13 |
[ | 8.4 | 5 | 15 | 18 | 5.1 | 23 | 42 | 0.84 | 0.5 | 2.5 |
[ | 1.9 | 5 | 40 | 24 | 1.55 | 17 | 27 | 1.7 | 0.56 | 2.8 |
[ | 1.8 | 5 | 30 | 32 | 1.96 | 22 | 80 | 1.4 | 0.52 | 5 |
[ | 3.1 | 5 | 40 | 130 | 13.7 | 21 | 55 | 3 | 1.8 | 50 |
Table 1. Parameters of experiments on GeV-class laser wakefield acceleration.
For a driving laser pulse propagating in a plasma channel, the equations of electron motion are given by setting in Equations (
The matched power corresponding to the matched spot size is calculated as
3.4. Beam loading effects
In laser wakefield acceleration, an accelerated electron beam induces its own wakefield and cancels the laser-driven wakefield. Assuming the beam loading efficiency defined by the fraction of the plasma wave energy absorbed by particles of the bunch with the rms radius , the beam-loaded field is given by , where is the accelerating field without beam loading, given by for the bubble regime . Thus, the loaded charge is calculated as[
3.5. Comparison with experimental results on GeV-class electron beams
Table
For self-guided laser wakefield acceleration, the multi-GeV acceleration results reported in Refs. [
In Ref. [
4. Design of 10-GeV-level laser plasma accelerators
At present, the most near-term prospects for 10-GeV-level laser plasma acceleration are confidently given by the scaling and methods described in the previous section. Here, we consider design examples of laser plasma accelerators capable of delivering 10-GeV electron beams with bunch charges of 160 pC ( electrons per bunch) for three cases: a self-guided laser plasma accelerator in the bubble regime with , a channel-guided laser plasma accelerator in the bubble regime with and a channel-guided laser plasma accelerator in the quasi-linear regime with . For all three cases, we present design parameters for the laser and plasma for a driving laser wavelength of 800 nm. Table
Case | A | B | C | D | Ref. [ |
---|---|---|---|---|---|
(GeV) | 10 | 10 | 10 | 40 | 38 |
1.9 | 2.7 | 1.1 | 0.28 | 0.22 | |
0 | 5 | 5 | 0 | ||
0.38 | 0.42 | 0.87 | 4.7 | 5 | |
800 | 800 | 800 | 800 | 800 | |
3 | 2 | 1.5 | 2 | 2 | |
1.35 | 1.13 | 1.06 | 1.19 | ||
2.3 | 2.9 | 3.6 | 3.2 | ||
29 | 29 | 57 | 103 | 100 | |
128 | 95 | 127 | 238 | 160 | |
238 | 114 | 250 | 1483 | 1400 | |
1.5 | 1.1 | 0.91 | 1.3 | 1.04 | |
30 | 11 | 32 | 353 | 220 | |
160 | 160 | 160 | 300 | 300 | |
C | 0.596 | 0.945 | 0.989 | 1.05 | |
0.77 | 0.68 | 0.67 | 0.79 |
Table 2. Design parameters for 10-GeV-level laser plasma accelerators in comparison with the results of the 3D PIC simulation[16]. Case A stands for the self-guided case in the bubble regime, designed by the formulas given in Section
4.1. Self-guided laser plasma accelerator in the bubble regime
For a given energy gain , the operating plasma density is determined from Equation (
4.2. Channel-guided laser plasma accelerator in the bubble regime
The operating plasma density is determined by
The matched spot radius becomes
4.3. Channel-guided laser plasma accelerator in the quasi-linear regime
For a given , the pulse duration is given by
5. Conclusion
We have provided an overview of recent progress in laser plasma accelerators from the perspective of experiments on the production of GeV-level electron beams, and scaling formulas to describe energy gain for a self-guided laser plasma accelerator in the bubble regime (), a channel-guided laser plasma accelerator in the bubble regime () and a channel-guided laser plasma accelerator in the quasi-linear regime (). Although most previous experiments have been focused on electron injection into the plasma bubble and the production of high-quality electron beams with small energy spread and emittance, employing a millimeter-scale gas jet, recent experimental results beyond 1-GeV acceleration allow us to test the scaling formulas in depth, which are necessary for the design of the operating parameters of laser plasma accelerators to satisfy requirements such as energy gain and beam charge. Taking account of the group velocity correction factor in the propagation of laser pulses with relativistic intensity, characterized by , through plasma channels, including initially uniform plasma with and a preformed plasma channel with , provides the correct accelerator length equal to the dephasing length as well as the proper operating plasma density. Meanwhile, we found that the accelerating field reduction factor due to beam loading can be properly evaluated by applying the resultant scaling formulas to recent experimental results for multi-GeV laser plasma accelerators[
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