Physics of laser-driven plasma-based electron accelerators

E. Esarey, C. B. Schroeder, and W. P. Leemans

Rev. Mod. Phys. 81, 1229 – Published 27 August 2009

Abstract

Laser-driven plasma-based accelerators, which are capable of supporting fields in excess of $100 GV ∕ m$ , are reviewed. This includes the laser wakefield accelerator, the plasma beat wave accelerator, the self-modulated laser wakefield accelerator, plasma waves driven by multiple laser pulses, and highly nonlinear regimes. The properties of linear and nonlinear plasma waves are discussed, as well as electron acceleration in plasma waves. Methods for injecting and trapping plasma electrons in plasma waves are also discussed. Limits to the electron energy gain are summarized, including laser pulse diffraction, electron dephasing, laser pulse energy depletion, and beam loading limitations. The basic physics of laser pulse evolution in underdense plasmas is also reviewed. This includes the propagation, self-focusing, and guiding of laser pulses in uniform plasmas and with preformed density channels. Instabilities relevant to intense short-pulse laser-plasma interactions, such as Raman, self-modulation, and hose instabilities, are discussed. Experiments demonstrating key physics, such as the production of high-quality electron bunches at energies of $0.1 - 1 GeV$ , are summarized.

37 More

DOI:https://doi.org/10.1103/RevModPhys.81.1229

Authors & Affiliations

E. Esarey, C. B. Schroeder, and W. P. Leemans

Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 81, Iss. 3 — July - September 2009

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic of LPAs: (a) LWFA, (b) PBWA, (c) self-modulated (SM) LWFA, and (d) resonant laser pulse train. Shown are the excited plasma wave potentials (solid lines) and right-moving laser intensity envelopes (dashed lines).Reuse & Permissions
Figure 2
(Color) Plasma density perturbation excited by Gaussian laser pulse with $a_{0} = 1.5$ , $k_{0} ∕ k_{p} = 20$ , $k_{p} L_{rms} = 1$ , and $k_{p} r_{0} = 8$ . Laser pulse is traveling to the left.Reuse & Permissions
Figure 3
Time-averaged plasma density perturbation $n ∕ n_{0} - 1$ (dotted curve), plasma wave electric field $E_{z} ∕ E_{0}$ (solid curve), and plasma temperature $T ∕ T_{0}$ (dashed curve) excited by a Gaussian laser pulse with normalized intensity $a = 2$ and rms length $k_{p} L_{rms} = 1$ (centered at $k_{p} ξ = 0$ ).Reuse & Permissions
Figure 4
Maximum plasma wave electric field amplitude $E_{WB} / E_{0}$ [Eq. (28)] vs initial temperature $β_{th}^{2}$ with $γ_{p} = 10$ and $γ_{⊥} = 1$ . The dotted curve is the ultrarelativistic result $β_{p} = 1$ and the dashed line is the cold limit.Reuse & Permissions
Figure 5
Single particle orbits in phase space $(\tilde{p}, k_{p} ξ)$ for an electron in a small amplitude sinusoidal plasma wave with a normalized potential given by $ϕ = ϕ_{0} \cos ψ$ , with $γ_{p} = 10$ and $ϕ_{0} = 0.1$ . Solid curve is separatrix. Dashed curve is the cold fluid orbit. Excitation of the plasma wave by a laser pulse with a half-sine envelope of length $λ_{p} ∕ 2$ (head at $k_{p} ζ = 0$ ) is assumed.Reuse & Permissions
Figure 6
Phase-space separatrix $γ_{s} (ψ)$ plotted for several values of the plasma wave amplitude $E_{\max} ∕ E_{0} = 0.18$ , 0.47, 1.5, 3.2, and 5.8, with $γ_{p} = 20$ . The value $E_{\max} ∕ E_{0} = 0.18$ corresponds to the innermost curve and $E_{\max} ∕ E_{0} = 5.8$ corresponds to the outermost curve. From 61.Reuse & Permissions
Figure 7
Schematic of laser pulse frequency upshifting by a plasma wave with $v_{p} ≃ v_{g} ≃ c$ (pulse moving to the right). Positive frequency shifts require the laser pulse $a$ to be centered about regions of the plasma wave $(δ n = n - n_{0})$ with a decreasing density.Reuse & Permissions
Figure 8
Time-averaged density variation $δ n ∕ n_{0}$ (dashed curve) and axial electric field $E_{z} ∕ E_{0}$ (solid curve) in an LWFA driven by a Gaussian laser pulse (pulse is moving to the right, centered at $k_{p} ζ = 0$ with rms intensity length $L_{rms} = k_{p}^{- 1}$ ) for (a) $a_{0} = 0.5$ and (b) $a_{0} = 2.0$ .Reuse & Permissions
Figure 9
Amplitude of axial electric field $E_{z}$ [normalized to the maximum amplitude of a flat-top pulse $E_{N} = (a_{0}^{2} ∕ 2) ∕ {(1 + a_{0}^{2} ∕ 2)}^{1 ∕ 2}$ ] plotted as a function of laser pulse length $k_{p} L_{rms}$ for the LWFA examples shown in Fig. 8: $a_{0} = 0.5$ (solid curve) and $a_{0} = 2.0$ (dashed curve). The laser pulse envelope is $a = a_{0} \exp (- ζ^{2} ∕ 4 L_{rms}^{2})$ .Reuse & Permissions
Figure 10
Examples of PBWA consisting of four beat pulses with $a_{0} = 1.2$ in a plasma of density $n_{0} = 10^{16} {cm}^{- 3}$ (293): (a) without optimization $Δ ω = ω_{p}$ , showing the effects of detuning, and (b) with optimization $Δ ω < ω_{p}$ . Normalized intensity profile $a^{2}$ (solid curve), wake potential $ϕ$ (dotted curve), and axial field $E_{z} ∕ E_{0}$ (dashed curve) vs $t - z ∕ c$ . Pulses are linearly polarized (moving to the left).Reuse & Permissions
Figure 11
Maximum electric field amplitude $E_{z} ∕ E_{0}$ vs $a_{T}^{2} = m a_{0}^{2}$ for $m = 1$ , 3, 5, 10, and 100 optimized square laser pulses with $a_{0} = 1$ .Reuse & Permissions
Figure 12
Laser pulse train consisting of four optimized sine-shaped laser pulses with $a_{0} = 1.2$ and $n_{0} = 10^{16} {cm}^{- 3}$ . Normalized intensity profile $a^{2}$ (solid curve), wake potential $ϕ$ (dotted curve), and axial field $E_{z} ∕ E_{0}$ (dashed curve) are plotted vs the comoving variable $t - z ∕ c$ (293). Pulses are linearly polarized (moving to the left).Reuse & Permissions
Figure 13
Ambient plasma density $n_{p} ∕ n_{0}$ (solid curve) and spot size $r_{s} ∕ λ_{p}$ (dashed curve) vs normalized propagation distance $c τ ∕ Z_{R}$ for a self-modulated LWFA with $n_{0} = 2.8 \times 10^{18} {cm}^{- 3}$ . Laser is initially converging such that the minimum spot size in vacuum is reached at $c τ = 3 Z_{R}$ . From 144 Reuse & Permissions
Figure 14
Standard LWFA (dashed curve) with $n_{0} = 1.4 \times 10^{17} {cm}^{- 3}$ and the self-modulated LWFA (solid curve) with $n_{0} = 2.8 \times 10^{18} {cm}^{- 3}$ : (a) Peak accelerating field and (b) peak energy of the injected particles vs propagation distance $c τ$ . From 144.Reuse & Permissions
Figure 15
Normalized laser intensity ${∣ a ∣}^{2}$ for the self-modulated LWFA case at (a) $c τ = 2 Z_{R}$ and (b) $c τ = 3.2 Z_{R}$ . Laser pulse is moving to the right. From 144 Reuse & Permissions
Figure 16
Self-modulated LWFA case. (a) Axial electric field $E_{z}$ and (b) normalized plasma electron density $n ∕ n_{0}$ vs $ζ$ at $c τ = 3.2 Z_{R}$ . From 144.Reuse & Permissions
Figure 17
(Color) Electron density wake from an electron beam with energy $0.5 GeV$ , peak density $n_{b} = 5 n_{0}$ , and rms beam sizes $k_{p} σ_{x} = k_{p} σ_{y} = k_{p} σ_{z} = 1 ∕ \sqrt{2}$ (Gaussian profiles). The electron beam is moving toward the right with its center located at $k_{p} z = 62.5$ in a plasma of density $n_{0} = 5 \times 10^{17} {cm}^{- 3}$ . Numerical parameters: four particles per cell and cell size (in all directions) of $0.7 μ m$ .Reuse & Permissions
Figure 18
(Color) Electron density wake driven by a laser pulse with $a_{0} = 0.3$ , rms length $68 μ m$ (Gaussian longitudinal profile), and spot size $r_{0} = 10 μ m$ (Gaussian transverse profile). The laser is moving toward the right (peak located at $k_{p} z = 7$ ) in a plasma density $n_{0} = 1.2 \times 10^{16} {cm}^{- 3}$ $(λ_{p} = 300 μ m)$ . Numerical parameters: four particles per cell, transverse resolution $d x = d y = 0.33 μ m$ , and longitudinal resolution $d z = 3.125 μ m$ .Reuse & Permissions
Figure 19
(Color) Electron density wake at $ω_{p} t = 27.7$ driven by a laser pulse with an initial envelope given by $a = a_{0} \exp (- z^{2} ∕ 2 L^{2}) \exp (- x^{2} ∕ r_{0}^{2})$ with $a_{0} = 5$ , $L = 4.2 μ m$ , $r_{0} = 9 μ m$ , and $λ = 0.8 μ m$ . The laser is propagating to the right in a plasma of density $n_{0} = 7 \times 10^{18} {cm}^{- 3}$ . Numerical parameters: longitudinal cell size $d z = 0.03 μ m$ , transverse cell size $d x = d y = 0.7 μ m$ , and four particles per cell.Reuse & Permissions
Figure 20
(Color) Wakefields driven by a laser pulse with $a = 0.5$ in the blow-out regime. (a) Longitudinal electric field and (b) transverse electric field, normalized to $E_{0}$ , as a function of $k_{p} z$ and $k_{p} x$ , for the parameters of Fig. 19 at $ω_{p} t = 27.7$ .Reuse & Permissions
Figure 21
Lineouts of (a) longitudinal electric field on axis (b) and transverse electric field at $k_{p} z = 13$ for the parameters of Fig. 19 at $ω_{p} t = 27.7$ .Reuse & Permissions
Figure 22
Initial electron momentum ${\tilde{p}}_{t}$ required to be trapped by a plasma wave with field amplitude $E_{peak} ∕ E_{0}$ and phase velocity $γ_{p} = 5$ (dotted curve), $γ_{p} = 10$ (solid curve), $γ_{p} = 20$ (dashed curve), and $β_{p} = 1$ (dash-dotted curve), assuming an initial plasma temperature $β_{th} = 10^{- 2}$ .Reuse & Permissions
Figure 23
Fraction of trapped electrons $f_{trap}$ [Eq. (67)] vs the initial temperature of a Gaussian plasma electron distribution $β_{th}^{2} = k_{B} T_{0} ∕ m c^{2}$ for three different nonlinear plasma wave amplitudes driven by a laser with $k_{p} L_{rms} = 1$ and $a_{0} = 3.65$ $({\hat{E}}_{m} ≃ 1.75)$ , $a_{0} = 4.15$ $({\hat{E}}_{m} ≃ 2)$ , and $a_{0} = 4.75$ $({\hat{E}}_{m} ≃ 2.25)$ , with $γ_{p} = 10$ .Reuse & Permissions
Figure 24
Profiles of the pump laser pulse $a_{0}$ , the wake $ϕ$ (dashed curve), and the forward $a_{1}$ injection pulse, all of which are stationary in the $ψ = k_{p} (z - v_{p} t)$ frame and the backward injection pulse $a_{2}$ , which moves to the left at $≃ 2 c$ .Reuse & Permissions
Figure 25
Longitudinal phase space showing beat wave separatrices (solid curve), an untrapped plasma wave orbit (dashed, lower curve), a trapped plasma wave orbit (dotted curve), and a trapped and focused plasma wave orbit (dash-dotted, upper curve).Reuse & Permissions
Figure 26
Electron distribution in longitudinal $(u_{z}, ψ)$ phase space (a) before injection pulse collision $(ω_{p} Δ t = 0)$ , (b) during collision $(ω_{p} Δ t = 3)$ , (c) just after collision $(ω_{p} Δ t = 14)$ , and (d) at $ω_{p} Δ t = 114$ ( $38 MeV$ electron bunch with $1 fs$ duration, 0.2% energy spread, and $0.9 mm mrad$ normalized transverse emittance). The separatrix between trapped and untrapped wake orbits (solid line) is shown. From 243.Reuse & Permissions
Figure 27
Laser spot size $r_{s}$ vs normalized propagation distance $c τ ∕ Z_{R}$ for (a) vacuum diffraction, (b) $L = λ_{p} ∕ 4$ , and (c) $L = λ_{p}$ , with parameters $P = P_{c}$ , $a_{0} = 0.9$ , and $λ_{p} = 0.03 cm$ . (d) Guiding of $L = λ_{p}$ pulse in a preformed parabolic plasma density channel with $Δ n = 1 ∕ π r_{e} r_{s}^{2}$ . From 262.Reuse & Permissions
Figure 28
Laser spot size $r_{s}$ vs propagation distance $c τ$ for (a) a channel-guided LWFA, (b) vacuum diffraction, and (c) the self-modulated LWFA shown in Figs. 14, 15, 16. From 71.Reuse & Permissions
Figure 29
Plasma electron density $n ∕ n_{0}$ at $c τ = 20 Z_{R}$ for a channel-guided LWFA. Initial density profile is parabolic with a depth $Δ n = Δ n_{c} = 1 ∕ π r_{e} r_{0}^{2}$ . From 71.Reuse & Permissions
Figure 30
Axial electric field $E_{z}$ on axis at $c τ = 20 Z_{R}$ for channel-guided LWFA shown in Fig. 29. From 71.Reuse & Permissions
Figure 31
Laser spot size vs propagation distance $z = c τ$ in vacuum (dashed curve) and in a plasma channel (solid curve) located at $0.5 < z < 1.5 cm$ for a low-power $P ⪡ P_{c}$ mismatched pulse. From 56.Reuse & Permissions
Figure 32
Schematic of an channel-guided LPA experimental setup. Plasma channel formation uses the ignitor and heater laser pulses. The main drive pulse propagates down the plasma channel, driving a wakefield and self-trapping electrons. Density profiles are measured using a frequency-doubled probe beam. An integrating current transformer (ICT) is used to measure the charge per bunch of the electron beam. A dipole magnet permits electron beam energy distribution measurements. Additional detectors are used to monitor laser pulses, plasma, and secondary radiation (e.g., terahertz radiation, $γ$ rays, and neutrons).Reuse & Permissions
Figure 33
(Color) Mode images of laser propagation with $4 TW$ $(P ≃ 2 P_{c})$ peak power. The guided output mode after $2.4 mm$ $(> 10 Z_{R})$ of propagation (b) is indistinguishable from the input mode (a). The effect of the channel can be seen by comparison to vacuum propagation over the same distance where the output mode is diffracted (c). The output mode with gas jet on but without the guide displays enhanced diffraction (d). Note enlarged scale in (c) and (d). From 94.Reuse & Permissions
Figure 34
Schematic of focusing effects of an externally generated plasma wave on an initially uniform low-intensity laser pulse.Reuse & Permissions
Figure 35
Schematic of the hose-modulation instability showing the laser pulse centroid $x_{c}$ and spot size $x_{s}$ . From 267.Reuse & Permissions
Figure 36
Normalized laser intensity ${∣ a ∣}^{2}$ vs $ζ ∕ λ_{p}$ at $c τ = 0$ (dashed curve) and $c τ = 3.2 Z_{R}$ (solid curve) for the parameters $λ_{p} = r_{0} ∕ 2 = 30 μ m$ . Laser is moving to the right. From 267.Reuse & Permissions
Figure 37
Laser envelope $x_{s}$ (upper curve) and centroid $x_{c}$ (lower curve) vs $ζ ∕ λ_{p}$ at $c τ = 3.2 Z_{R}$ for an initial perturbation of 1% in $x_{c}$ . Perturbations grow at $λ_{p} = r_{0} ∕ 2 = 30 μ m$ . From 267.Reuse & Permissions
Figure 38
Transverse profiles of the axial wakefield $E_{z} ∕ E_{0}$ (solid curve) and the transverse wakefield $E_{x} ∕ E_{0}$ (dashed curve) at $c τ = 1.8 Z_{R}$ and $ζ = - 18 λ_{p}$ for a hose-dominated case. From 267.Reuse & Permissions
Figure 39
Electron energy spectrum $d N ∕ d E$ measured using a magnetic spectrometer obtained by scanning the current in the magnet and measuring the intensity on a phosphor screen. Each data point represents ten shots. The spectrum is well approximated by a Boltzmann distribution with an effective temperature of $4.6 MeV$ . From 163.Reuse & Permissions
Figure 40
(Color) Electron energy spectrum of a bunch produced by the channel-guided LWFA. The single-shot spectrum was obtained by dispersing the electron beam with a magnetic spectrometer and a charge-coupled device (CCD) imaged phosphor screen. Beam contains $2 \times 10^{9}$ electrons with energy spread of $3.6 MeV$ FWHM at $86 MeV$ . In the vertical (nondispersive) plane, the divergence was near $3 mrad$ FWHM for this bunch. From 92.Reuse & Permissions
Figure 41
(Color online) PIC simulation showing momentum phase space (top of each panel) and laser envelope (bottom of each panel) as a function of propagation distance. (a) The laser enters the plasma and (b) is modulated by the plasma response, exciting a wake and trapping electrons. Beam loading terminates trapping. (c) The trapped electrons are concentrated in energy at the dephasing length, forming a high-energy low-energy spread bunch, which (d) dissipates with further propagation. From 93.Reuse & Permissions
Figure 42
(Color) PIC simulation of electron density after laser propagation of (a) $875 μ m$ and (b) $1117 μ m$ . (a) The density perturbation just prior to self-trapping in the first bucket behind the laser. (b) A trapped electron bunch is damping the wake and suppressing further trapping, isolating the initial bunch in phase space. From 93.Reuse & Permissions
Figure 43
(Color) Single-shot electron bunch spectra of the capillary-guided LWFA (160; 211). Examples are shown of bunches at (a) ${0.50}_{- 0.015}^{+ 0.02} GeV$ (5.6% rms energy spread, $2.0 mrad$ divergence rms, $\sim 50 pC$ charge) and (b) ${1.0}_{- 0.05}^{+ 0.08} GeV$ (2.5% rms energy spread, $1.6 mrad$ divergence rms, $\sim 30 pC$ ). The $0.5 GeV$ $(1.0 GeV)$ bunch was obtained in a 225 $(310) μ m$ capillary with a density of $3.5 \times 10^{18}$ $(4.3 \times 10^{18}) {cm}^{- 3}$ and input laser power of $12 TW$ $(40 TW)$ . The black stripe denotes the energy range not measured by the spectrometer. In (b) a second bunch at $0.8 GeV$ is also visible.Reuse & Permissions
Figure 44
(Color) Momentum distributions obtained from a magnetic spectrometer for electron bunches produced by a laser focused at the downstream edge of a gas jet, showing stable bunches at $0.76 MeV ∕ c$ with $\pm 10 %$ momentum spread and $\pm 3 %$ momentum stability. Sequential single shot images are shown on the left with the centroid (*) indicated with respect to the average (square) over 45 shots. Integrated magnetic spectrum is shown on the right (vertical bar denotes the rms charge error) with the data points (blue) connected by a black line. From 91.Reuse & Permissions

Reviews of Modern Physics