Laser-plasma accelerators driven by incoherently combined lasers

Laser-plasma accelerators (LPAs), capable of accelerating electrons to high energies over exceptionally short distances, have received significant interest in recent years. The ability of these devices to sustain extremely large acceleration gradients enables the development of very compact structures.¹ In an LPA, a short and intense laser pulse propagating in an underdense plasma drives an electron plasma wave (or wakefield). This wave is the result of the laser field energy density gradient providing a force (i.e., the ponderomotive force) that creates a space charge separation between the plasma electrons and the neutralizing ions, from which the wakefield arises. For example, in a plasma with a density of ∼10¹⁷cm⁻³, a ∼20fs laser pulse with an intensity of ∼10¹⁸W/cm² produces a wake characterized by an accelerating gradient of ∼30GV/m. This gradient is three orders of magnitude larger than that which is achievable in conventional accelerators. In experiments, LPAs have produced electron beams of ≳1GeV over plasmas of a few centimeters, with percent-level energy spread.^{2, 3}

Applications for LPAs that produce electron beams with energies between 1 and 10GeV include free-electron lasers in the x-ray regime^{4, 5} and accelerator modules for linear colliders.^6,7 In one conceptual design for a 1TeV center-of-mass electron-positron LPA-based linear collider,⁷ both the electron and positron arms of the collider require ∼50 LPA stages with 10GeV energy gain per stage, operating at a density (n₀) of ∼10¹⁷cm⁻³. Each LPA stage is independently powered by a ≲100fs laser pulse, with an energy of a few tens of joules. These requirements can be met with present laser technology. However, the laser repetition rate—as dictated by the required collider luminosity—is ∼10kHz (corresponding to an average power of 100s of kW), which is orders of magnitude beyond what is currently possible.

To date, LPAs are typically driven by solid-state lasers (e.g., titanium-doped sapphire), which are characterized by a low repetition rate (typically 1–10Hz, corresponding to an average power of ∼100W) and low wall-plug efficiency (defined as the ratio of the optical output and the electrical input power, typically ≪1%). For example, the Berkeley Lab Laser Accelerator laser delivers 40J pulses on target at 1Hz.⁸ Since virtually all LPA applications will benefit greatly from higher repetition rates, the continued development of high-average-power, high-efficiency laser technology is essential.

Several laser technologies are currently being developed with this aim in mind.^{9, 10} In one approach,¹⁰ a large number of diode-pumped fiber systems (delivering pulses with ∼mJ energy at a kHz repetition rate) are combined in such a way that the relative phases of the output beams constructively interfere and produce a single, high-power output beam with high efficiency. This coherent combination of a large number of fiber lasers to drive an LPA (e.g., ∼10⁴ fibers for a total pulse energy of 10s of J) is extremely challenging, requiring short pulse beams (<1ps) that are matched in phase, time, and space.

Analytically, and using computer simulations, we have shown that an LPA does not require a fully coherent laser pulse.¹¹ This is due to the fact that, in an LPA, the wakefield is excited by the laser ponderomotive force, but the plasma response to this force is not instantaneous. The plasma typically responds on a time scale T_p=2π/ω_p, where ω_p=(4πn₀e²/m)^{1/ 2} is the electron plasma frequency for a plasma with density n₀ (e and m are electron charge and mass, respectively). Large-amplitude wakefield excitation requires sufficient electromagnetic energy within a given volume, typically on the order of (cT_p)³, where c is the speed of light in vacuum.¹ Since the wakefield response behind the driver depends on the time-integrated behavior of the electromagnetic energy density of the driver over the time scale T_p, its amplitude is therefore largely insensitive to fluctuations in the driver field on time scales ≪T_p. This allows for the use of incoherently combined laser pulses as the driver. Under certain conditions, we found that the wake generated by an incoherent combination of pulses is regular behind the driver and its amplitude is equal to that obtained by using a single (coherent) pulse with the same energy.

To illustrate the physics of wake generation by incoherently combining multiple laser pulses, we considered a collection of short and narrow laser beamlets placed side-by-side, both longitudinally and transversely, tiling a prescribed volume. The laser phases are random. Each pulse has high peak intensity but low energy, owing to the limited spatial extent of the beamlets. As the generalization to the 3D case is straightforward, we implemented 2D Cartesian geometry for simplicity. The beamlets (each one with a duration of ∼10fs and a spot size of ∼15μm) are initially arranged in a uniform spatial grid: see Figure 1. The total number of beamlets is 208 and the tiled domain is about 50μm long and 140μm wide.

Figure 1. Snapshot of the energy density for the incoherent combination of multiple laser pulses at the beginning of the simulation.

The incoherent combination can be guided over long distances by using a plasma channel with steep walls.¹ Figure 2 shows a snapshot of the energy density for the incoherent combination after propagating 6mm in a plasma with n₀≃10¹⁷cm⁻³. The laser field exhibits a clear incoherent pattern. The wakefield generated by the incoherently combined beamlets is shown in Figure 3, with a map of the longitudinal wakefield (E_z) after a propagation distance of 1.8mm. In Figure 4, the on-axis lineout of the longitudinal wakefield for the incoherent combination is compared to that of a single coherent pulse with the same energy. Behind the driver region, the wake from incoherent combination is regular and its amplitude is the same as that of the single coherent pulse.

Figure 2. Snapshot of the energy density after the multiple laser pulses have propagated 6mm in the plasma. The laser field exhibits a clear incoherent pattern.

Figure 3. Map of the longitudinal wakefield (E_z) generated by the incoherent combination of laser pulses after a propagation distance of 1.8mm.

Figure 4. On-axis lineout of the longitudinal wakefield for incoherent combination (red line) and for a single coherent pulse with the same energy (black plot).

In summary, we have shown that it is possible to efficiently excite a wakefield for LPA applications with an incoherent combination of multiple, low-energy laser pulses. Based on this theoretical work, we expect the fundamental requirements for achieving incoherent combination to be more relaxed compared to coherent combination. Incoherent combination may therefore provide an alternative and technically simpler path to the realization of high-average-power, high-efficiency laser drivers for LPAs and associated applications. We are currently planning experiments to validate the concept of incoherent laser combination.

This work was supported by the Director, Office of Science, and Office of High Energy Physics of the U.S. Department of Energy, under Contract No. DE-AC02-05CH11231. We used the computational facilities at the National Energy Research Scientific Computing Center (NERSC).