Plasma-based Acceleration

In Plasma-Based Acceleration a laser or a particle beam excites a plasma wake, thereby generating a structure that can support accelerating fields more than three orders of magnitude above those of conventional accelerators. A (second) particle beam properly loaded into the wake, can be accelerated to very high energy in a short distance. This mechanism makes it possible to develop compact accelerators for high-energy physics, for studying new materials and for medical applications.

Short Pulse Laser Driver

In 2003 experiments at the Rutherford Appleton Laboratory (UK) using the VULCAN laser demonstrated that when an ultra-intense pico-second laser interacts with a mm-long gas jet, a hot tail in the electron energy spectrum is generated [1]. The maximum energy observed in these experiments was 350MeV, and it was the world record from a plasma-based accelerator. To investigate the mechanism responsible for the acceleration, our group incorporated particle-tracking diagnostics in the Particle-In-Cell code OSIRIS. The simulations recovered the experimentally observed spectrum and revealed that the acceleration is not due to the longitudinal wake-field, but comes directly from the electric field of the laser pulse. This is possible due to the extreme intensity of the VULCAN laser pulse, which creates a long plasma channel with strong focusing fields in which some electrons can find themselves oscillating in resonance with the field of the laser. These oscillating electrons can reach very high energy and radiate in a broadband spectrum [2]. Finally, the simulations revealed that the energetic ions, that were also measured in the aforementioned experiments, were due to the collision between ion shocks [3].

FIGURE 1 - Typical electron trajectories for the stochastic resonant acceleration by the laser fields. (See Ref. [1].)

As promising as the VULCAN results are for producing hot electrons and broadband radiation, the stochastic features of the acceleration process do not allow for the generation of the high-quality beams necessary for most of the envisioned applications.


Ultra-short Pulse Laser Driver

Laser-wake-field acceleration of electrons with energy spectra that exhibited beam-like features was first realized in experiments in 2004. All of these experiments involved ultra-short pulses. Our group used OSIRIS to model these experiments in 3D and analyze the physics [4]. At the same time we developed an analytical theory for the excitation of the plasma wake behind an intense driver, be it a particle or laser beam [5]. This allowed us to develop a detailed phenomenological theory for laser wake-field acceleration which includes both the laser evolution and electron acceleration process [6]. This theory allows one to choose the laser and plasma parameters so as to optimize the plasma-based accelerator. Its applicability was demonstrated with the generation of a 1.5GeV electron beam using a 200TW, 30fs laser pulse in a full 3D PIC simulation. The acceleration process is shown in the movie below.

MOVIE 1 - The evolution of the envelope of a 200TW 30fsec laser pulse (orange) in a plasma with electron density (blue) 1.5 × 1018cm-3 is shown on the top. The bottom part of the movie shows the electric field line-out across the center of the plasma bubble, i.e. Ex(x,y=0,z=0). (See Ref. [6].)

Since its publication, this theoretical framework has been proven helpful in designing experiments and accurate in predicting their outcome. However, scaling laws are not sufficient to generate beams with excellent beam quality. To address this issue we started from the description of the wake we had developed [5] and derived an exact analytical theory for the interaction of an electron beam with a 3D nonlinear plasma wake [7] – [8]. This theory shows how to control the quality of an electron beam produced by a plasma-based accelerator and how to transfer the energy available in the plasma wake to the accelerating electron beam with nearly 100% efficiency. Figure 2 shows how choosing the charge per unit length one can control the s hape of the plasma bubble and the accelerating field and Figure 3 the confirmation of the analytical results using PIC simulations.

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FIGURE 2 - The beam loading theory allows one to control the shape of the plasma bubble and the accelerating field by choosing the charge per unit length of the accelerating electron bunch appropriately. (See Ref. [8].)
FIGURE 3 - Confirmation of the beam loading theory using Particle-In-Cell simulations. Loading the correct charge per unit length profile into the wake leads to a constant accelerating field within the electron bunch (See Ref. [8].)

Employing the beam loading theory and the phenomenological scaling laws we compiled a list of simulations in order to demonstrate stable acceleration of high-quality beams up to 100GeV. For such simulations using a full PIC code is not practical, and therefore the quasi-static PIC code QuickPIC was used. We performed extensive benchmarks for QuickPIC comparing the results to those from the full-PIC code OSIRIS. This was done to ensure that the laser propagation is modeled accurately using the envelope approximation in QuickPIC, and that the wake-field is reproduced with high fidelity. The movie below shows the acceleration of an electron bunch (green) to 0.4GeV using a 15TW, 35fsec laser pulse in a plasma channel with electron density (blue) which has a minimum at the center of the box and is equal to 2 × 1018cm-3.

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MOVIE 2 - The evolution of the envelope of a 15TW laser pulse (yellow) and an externally injected electron beem (green) in a plasma channel (blue) from a Particle-In-Cell simulation with QuickPIC. (The movie plays twice from different viewing angles.)
FIGURE 4 - Generation of high-quality electron beams with energy up to 100GeV from Particle-In-Cell simulations with QuickPIC. (See Ref. [9].)

This simulation parameters were then scaled up to 25GeV and to 100GeV and the corresponding energy spectrum is shown in Figure 4. These results were included in M. Tzoufras' dissertation titled “Generation of Multi-Giga-Electron-Volt monoenergetic electron beams via laser wakefield acceleration” (2008) [9]. In collaboration with J. Vieira from IST Portugal, he also examined the evolution of the laser pulse to provide an analytic description of the effect of frequency shifts on the early laser dynamics [10].

Our group is currently studying the effect that imperfections of the initial beam profile can have on the final beam quality and is working to produce truly monoenergetic beams and to demonstrate the potential of using such accelerators as radiation sources.


[1] S. P. D. Mangles, B. R. Walton, M. Tzoufras, Z. Najmudin, R. J. Clarke, A. E. Dangor, R. G. Evans, S. Fritzler, A. Gopal, C. Hernandez-Gomez, W. B. Mori, W. Rozmus, M. Tatarakis, A. G. R. Thomas, F. S. Tsung, M. S. Wei and K. Krushelnick, Phys. Rev. Lett. 94, 245001 (2005) “Electron Acceleration in Cavitated Channels Formed by a Petawatt Laser in low-Density Plasma.”

[2] S. Kneip, S. R. Nagel, C. Bellei, N. Bourgeois, A. E. Dangor, A. Gopal , R. Heathcote, S. P. D. Mangles, J. R. Marquès, A. Maksimchuk, P. M. Nilson, K. Ta Phuoc, S. Reed, M. Tzoufras, F. S. Tsung, L. Willingale, W. B. Mori, A. Rousse, K. Krushelnick, and Z. Najmudin, Phys. Rev. Lett. 100, 105006 (2008) “Observation of Synchrotron Radiation from Electrons Directly Accelerated in a Petawatt-Laser-Generated Plasma Cavity.”

[3] M. S. Wei, S. P. D. Mangles, Z. Najmudin, B. Walton, A. Gopal, M. Tatarakis, A. E. Dangor, E. L. Clark, R. G. Evans, S. Fritzler, R. J. Clarke, C. Hernandez-Gomez, D. Neely, W. B. Mori, M. Tzoufras and K. Krushelnick, Phys. Rev. Lett. 93, 155003 (2004) “Ion Acceleration by Collisionless Shocks in High-Intensity-Laser-Underdense-Plasma Interaction.”

[4] F. S. Tsung, W. Lu, M. Tzoufras, W. B. Mori, C. Joshi, J. M. Vieira, L. O. Silva and R. A. Fonseca, Phys. Plasmas 13, 056708 (2006) “Simulations of monoenergetic electron generation via laser wakefield acceleration for 5-25 TW lasers.”

[5] W. Lu, C. Huang, M. Zhou, M. Tzoufras, F. S. Tsung, W. B. Mori and T. Katsouleas, Phys. Plasmas 13, 056709 (2006) “A nonlinear theory for multi-dimensional relativistic plasma wave wakefields.”

[6] W. Lu, M. Tzoufras, C. Joshi, F. S. Tsung, W. B. Mori, J. Vieira, R. A. Fonseca and L. O. Silva, Phys. Rev. ST Accel. Beams 10, 061301 (2007) “Generating multi-GeV electron bunches using single stage laser wakefield acceleration in a 3D nonlinear regime.”

[7] M. Tzoufras, W. Lu, F. S. Tsung, C. Huang, W. B. Mori, T. Katsouleas, J. Vieira, R. A. Fonseca and L. O. Silva, Phys. Rev. Lett. 101, 145002 (2008), also included in the Virtual Journal of Biological Physics Research, Vol. 17, Issue 6, (2008) “Beam Loading in the Nonlinear Regime of Plasma-Based Acceleration.”

[8] M. Tzoufras, W. Lu, F. S. Tsung, C. Huang, W. B. Mori, T. Katsouleas, J. Vieira, R. A. Fonseca and L. O. Silva, Phys. Plasmas 16, 056705 (2009) “Beam loading by electrons in nonlinear plasma wakes.”

[9] M. Tzoufras, Ph.D. thesis, UCLA, June 2008, Advisor: W. B. Mori “Generation of Multi-Giga-Electron-Volt monoenergetic electron beams via laser wakefield acceleration.”

[10] J. Vieira, F. Fiúza, L. O. Silva, M. Tzoufras, W. B Mori, New J. Phys. 12, 045025 (2010) “Onset of self-steepening of intense laser pulses in plasmas.”