Characteristics of laser-driven electron acceleration in vacuum

TLDR: In this article, a three-dimensional test particle simulation model that solves the relativistic Newton-Lorentz equations of motion in analytically specified laser fields is studied.

Abstract: The interaction of free electrons with intense laser beams in vacuum is studied using a three-dimensional test particle simulation model that solves the relativistic Newton–Lorentz equations of motion in analytically specified laser fields. Recently, a group of solutions was found for very intense laser fields that show interesting and unusual characteristics. In particular, it was found that an electron can be captured within the high-intensity laser region, rather than expelled from it, and the captured electron can be accelerated to GeV energies with acceleration gradients on the order of tens of GeV/cm. This phenomenon is termed the capture and acceleration scenario (CAS) and is studied in detail in this article. The accelerated GeV electron bunch is a macropulse, with duration equal to or less than that of the laser pulse, which is composed of many micropulses that are periodic at the laser frequency. The energy spectrum of the CAS electron bunch is presented. The dependence of the energy exchange in...

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Lawrence Berkeley National Laboratory
Lawrence Berkeley National Laboratory
Title
Characteristics of laser-driven electron acceleration in vacuum
Permalink
https://escholarship.org/uc/item/2d87p9f9
Authors
Wang, P.X.
Ho, Y.K.
Yuan, X.Q.
et al.
Publication Date
2001-11-01
Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California

Characteristics of laser-driven electron acceleration in vacuum
P. X. Wang, Y.K.Ho
a)
,X.Q.Yuan,andQ.Kong
Institute of Modern Physics, Fudan University, Shanghai 200433, China
A.M.Sessler, E. Esarey, and E. Moshkovich
Lawrence Berkeley National Laboratory, University of California, Berkeley CA 94720
Y.Nishida, N.Yugami, and H.Ito
Energy and Envirom. Science, Graduate School of Engin., Utsunomiya University, Japan
J.X.Wang, and S.Scheid
Institut f¨ur Theoretische Physikder, Justus-Liebig-Universit¨at, D-35392 Giessen, Ger-
many
ABSTRACT
The interaction of free electrons with intense laser beams in vacuum is studied using a
3D test particle simulation model that solves the relativistic Newton-Lorentz equations of
motion in analytically specified laser fields. Recently, a group of solutions was found for
very intense laser fields that show interesting and unusual characteristics. In particular, it
was found that an electron can be captured within the high-intensity laser region, rather
than expelled from it, and the captured electron can be accelerated to GeV energies with
acceleration gradients on the order of tens of GeV/cm. This phenomenon is termed the
capture and acceleration scenario (CAS) and is studied in detail in this paper. The maximum
net energy exchange by the CAS mechanism is found to be approximately proportional to
a
2
0
,intheregimewherea
0
 100, where a
0
= eE
0
/m
e
ωc is a dimensionless parameter
specifying the magnitude of the laser field. The accelerated GeV electron bunch is a macro-
pulse, with duration equal or less than that of the laser pulse, which is composed of many
micro-pulses that are periodic at the laser frequency. The energy spectrum of the CAS
1

electron bunch is presented. The dependence of the energy exchange in the CAS on various
parameters, e.g., a
2
0
(laser intensity), w
0
(laser radius at focus), τ (laser pulse duration), b
0
(the impact parameter), and θ
i
(the injection angle with respect to the laser propagation
direction), are explored in detail. A comparison with diverse theoretical models is also
presented, including a classical model based on phase velocities and a quantum model based
on nonlinear Compton scattering.
PACS number(s): 42.62.-b, 42.90.+m, 41.75.-i
a)
Author to whom correspondence should be addressed. Address correspondence to
Institute of Modern Physics, Fudan University, Shanghai 200433, China. FAX: +86-21-
65644415. Electronic address: hoyk@fudan.ac.cn
2

I. INTRODUCTION
Recent advances in laser technology have yielded light intensities as high as Iλ
2
=10
20
W/cm
2
· µm
2
,whereI and λ are the laser intensity and wavelength in units of W/cm
2
and
µm, respectively. Consequently, there have emerged many new frontier research areas in both
applied and fundamental physics [1]. Among these, the development of laser-driven electron
acceleration mechanisms is a fast advancing area of scientific research [2]. Compared with
the 20 MV/m acceleration gradient provided by contemporary linear accelerators, the 10
7
MV/m electric field gradients of the laser field have made laser acceleration a very promis-
ing candidate for the development of compact high-energy accelerators. But laser acceler-
ation has several technological difficulties. For instance, most of the reported acceleration
mechanisms have involved plasma [3], [4]. To avoid the problems inherent in laser-plasma
interaction such as plasma instabilities, the far-field laser acceleration of free electrons in
vacuum has received new attention. In this research area, there is a long-standing question
of whether or not an electron can get a net energy gain, assuming an unlimited interaction
length, from a laser beam in free space. According to the Lawson-Woodward Theorem, the
electron can get no net energy gain through the entire interaction [5], [6], [7], [8], [9]. But
this conclusion is only confined to low intensity laser fields, i.e., energy gains that are lin-
early proportional to the laser field. Malka et al. [10] reported the observation of electrons
accelerated to MeV energy in vacuum by intense lasers with a
0
=3,wherea
0
≡ eE
0
/m
e
ωc
is a dimensionless parameter specifying the magnitude of the laser field, −e and m
e
are the
electron charge and mass, respectively, c the speed of light in vacuum, and ω the angular
frequency of the electromagnetic wave. In terms of the peak laser intensity and wavelength,
a
0
=0.85 × 10
−9
λ[µm](I[W/cm
2
])
1/2
. Earlier, electrons accelerated to a fraction of eV [11]
or a few keV [12] at low intensity and 100 KeV [13] at higher intensity had been observed.
To give a more exact answer to the above question, we devised a model to study the
interaction of electrons with a laser field based upon a 3D computer simulation code to solve
the relativistic Newton-Lorentz equations of motion [14]. The results show that a large net
3

energy gain is possible [14]. In this model, electrons were injected at a specified angle into
a continuous laser beam. For a
0
 0.1, there is no noticeable energy transfer between the
electron and the laser beam. As a
0
increases from 0.1 to more than 10, the electron begins to
obtain more and more net energy, which is of several MeV magnitude when a
0
nears 10. The
most surprising and meaningful result is that as a
0
approaches or exceeds 100 (a
0
 100),
the electron can be captured and violently accelerated to GeV energy by either continuous
or sufficiently long-pulsed laser beams with acceleration gradients on the order of tens of
GeV/cm. We refer to electron acceleration in this regime as the capture and acceleration
scenario (CAS).
The main purpose of this paper is to study the characteristics of electron scattering by
intense pulsed laser beams and to determine the dependence of the net energy exchange on
various parameters such as the laser intensity. Special attention has been paid to exploring
the physics of the CAS, such as determining the conditions under which a capture trajectory
emerges, and finding the scaling of the maximum energy gain of the accelerated electrons
with respect to laser intensity. The numerical results are compared to various theoretical
models. Some of these results have been recently and breifly presented in Ref. [15], and in this
paper these results, as well as additional aspects of CAS, are studied in detail. This study
has significance in determining parameters for experimentally testing laser-driven electron
acceleration in vacuum.
Theoretical models based upon classical physics that we consider are the ponderomotive
potential model (PPM) and a phase velocity synchronization model. The PPM is a classical
description in which the time-averaged electron motion is modeled by assuming that the
electron moves in an effective ponderomotive potential, which is obtained by averaging the
Newton-Lorentz equations of motion over the fast quiver oscillation of the electron in the
laser field [3], [16], [17], [18], [19], [20], [21]. Such quivering motion is argued [11] to be
analogous to a kind of stimulated scattering process. At low laser field intensities (a
0
 0.1)
PPM stands well in describing the electron averaged motion in the electromagnetic field
[22]. In this paper we will extend the PPM to the high laser intensity region and compare
4

Frequently asked questions

Q1. What have the authors contributed in "Characteristics of laser-driven electron acceleration in vacuum" ?

The interaction of free electrons with intense laser beams in vacuum is studied using a 3D test particle simulation model that solves the relativistic Newton-Lorentz equations of motion in analytically specified laser fields. This phenomenon is termed the capture and acceleration scenario ( CAS ) and is studied in detail in this paper. 

Q2. Why do the CAS electrons have a limited spread in space?

Due to the features of high outgoing energies and small angle spread, the outgoing CAS electrons compose a high-energy bunch with a limited spread in space. 

Q3. What is the prominent feature of Fig. 3(c)?

The most prominent feature of Fig. 3(c) is that the phase experienced by the CAS electron varies extremely slowly even in the early acceleration stage. 

Q4. What is the effect of the CAS electrons on the laser field?

the electron can be trapped in the acceleration phase for long times to gain considerable energy from the laser field. 

Q5. Why is the CAS regime beyond current technology?

Because the required laser intensity is very high, experimental research on NLCS in the regime of CAS is beyond current technology. 

Q6. What is the simplest way to calculate the electron orbits?

Assuming that the laser field is a one-dimensional (1D) plane wave of the form a = a(z − ct), the electron orbits can be calculated exactly [27], [28], [29]. 

Q7. How can the electrons be accelerated in 3D?

In 3D, this can occur by transverse scattering of the electrons, as discussed in Refs. [10], [21], or by the pulse diffracting, as is discussed in the following. 

Q8. What is the energy-momentum configuration of the laser?

The authors use a four-dimensional energy-momentum configuration to specify the electron state (γ, Px, Py, Pz), where the Lorentz factor γ, the momentum P are normalized in the units of mec 2 and mec, respectively. 

Q9. What is the phase velocity of the wave along the trajectory?

The phase velocity of the wave along a particle trajectory can be calculated by theequation∂ϕ/∂t+ (Vϕ)J (∇ϕ)J = 0, (28)where (Vϕ)J is the phase velocity of the wave along the trajectory and (∇ϕ)J is the gradient of the phase along the trajectory. 

Q10. What is the phase slippage velocity of an electron in a vacuum electromagnetic plane wave?

As the authors know, the phase slippage velocity of an electron (relative the laser field phase fronts) in a vacuum electromagnetic plane wave can be approximately estimated by c/(2γ2 q ), where γq = (1 − v2q/c2)1/2 and vq is the electron velocity along the wave propagation direction. 

Q11. What is the upper limit to the energy gain in the CAS?

These simple estimates imply that the upper limit to the energy gain ∆Emax in the CAS is proportional to a 2 0, and that the relevant acceleration gradient can reach tens of GeV/cm. 

Q12. How many electrons can be accelerated to GeV?

From Fig. 2(b), it can be seen that about 20% of electrons can be accelerated to GeV which display typical CAS trajectories [14], if the electrons are uniformly distributed in all phase φ0 ∈ [0, 2π]. 

Q13. What is the scaling law for the electrons from the laser field in vacuum?

To explore the scaling law for the net energy gain of the electrons from the laser field in vacuum, the authors use Em = mec 2γfm to represent the outgoing electrons’ maximum energy as φ0 and ∆td vary over the whole range of interest. 

Q14. What is the difference between the CAS and the electron inelastic scattering?

For the CAS, the electrons can be captured into the intense field region rather than expelled from it and the captured electrons can be accelerated to GeV energies with acceleration gradients of tens of GeV/cm. 

Q15. What is the wave phase velocity for the IS trajectory?

From Fig.7(c) the authors can see the wave phase velocity (solid line) for the IS trajectory is much faster than the electron dynamic velocity (dotted line).