Mitigating the relativistic laser beam filamentation via an elliptical beam profile

T. W. Huang, C. T. Zhou, A. P. L. Robinson, B. Qiao, H. Zhang, S. Z. Wu, H. B. Zhuo, P. A. Norreys, and X. T. He

Phys. Rev. E 92, 053106 – Published 16 November 2015

Abstract

It is shown that the filamentation instability of relativistically intense laser pulses in plasmas can be mitigated in the case where the laser beam has an elliptically distributed beam profile. A high-power elliptical Gaussian laser beam would break up into a regular filamentation pattern—in contrast to the randomly distributed filaments of a circularly distributed laser beam—and much more laser power would be concentrated in the central region. A highly elliptically distributed laser beam experiences anisotropic self-focusing and diffraction processes in the plasma channel ensuring that the unstable diffractive rings of the circular case cannot be produced. The azimuthal modulational instability is thereby suppressed. These findings are verified by three-dimensional particle-in-cell simulations.

Received 15 May 2015
Revised 9 October 2015

DOI:https://doi.org/10.1103/PhysRevE.92.053106

Authors & Affiliations

T. W. Huang^1,2, C. T. Zhou^1,3,4,*, A. P. L. Robinson^2,†, B. Qiao^1,‡, H. Zhang³, S. Z. Wu³, H. B. Zhuo⁴, P. A. Norreys^2,5, and X. T. He^1,3

¹HEDPS, Center for Applied Physics and Technology and School of Physics, Peking University, Beijing 100871, People's Republic of China
²Central Laser Facility, STFC Rutherford-Appleton Laboratory, Didcot, OX11 0QX, United Kingdom
³Institute of Applied Physics and Computational Mathematics, Beijing 100094, People's Republic of China
⁴Science College, National University of Defense Technology, Changsha 410073, People's Republic of China
⁵Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom

^*zcangtao@iapcm.ac.cn
^†alex.robinson@stfc.ac.uk
^‡bqiao@pku.edu.cn

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Vol. 92, Iss. 5 — November 2015

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Images

Figure 1
(a) The growth rate of the AMI as a function of the wave number at different initial temperatures, where $m = \frac{M}{k_{L} \bar{r}}, a_{0} = 2$ , and $n_{e} = 0.2 n_{c}$ . (b) The maximum growth rate of AMI for different laser amplitudes and plasma densities. (c) The phase space of the maximum growth rate of AMI. Here, $P_{in} / P_{cr} = 0.84 π a_{0}^{2} \frac{r_{0}^{2} n_{e}}{λ_{L}^{2} n_{c}}$ and $r_{0} ω_{p} / c = 2 π \frac{r_{0}}{λ_{L}} \sqrt{\frac{n_{e}}{n_{c} γ_{0}}}$ , where $λ_{L}$ is the laser wavelength and $γ_{0} = \sqrt{1 + a_{0}^{2}}$ is the Lorentz factor. The beam radius $r_{0}$ is set as $8 λ_{L}$ and the laser wavelength is $1 μ m$ .
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Figure 2
The 3D particle-in-cell simulation results. (a–c) The isosurface of laser intensity at $T = 400$ fs for different elliptical beams, where the isovalue is $1.2 \times 10^{18} W / {cm}^{2}$ and the color depicts the maximum intensity. (d–o) The corresponding cross-sections of the laser intensity at different propagation distances. (a), (d), (g), (j), and (m) correspond to $h = 1.0$ ; (b), (e), (h), (k), and (n) correspond to $h = 1.2$ ; and (c), (f), (i), (l), and (o) correspond to $h = 1.5$ . The simulation parameters correspond to the point C in Fig. 4.
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Figure 3
The numerical simulation results based on the physical model Eq. (1). (a) The isosurface of laser intensity for the initial conditions with $a_{0} = 0.8, n_{e} = 0.2 n_{c}, r_{0} = 8 μ m$ , and $h = 1$ , where the isovalue is $1.2 \times 10^{18} W / {cm}^{2}$ , and the color depicts the maximum intensity. These parameters correspond to the point C in Fig. 4. (b) The corresponding cross-sections of the laser intensity at different propagation distances. The unit of laser intensity is $W / {cm}^{2}$ . The displayed space scale is $30 \times 30 μ m$ , and the simulation box is $40 \times 40 μ m$ .
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Figure 4
The numerical simulation results based on the physical model Eq. (1). (a) The evolutions of the normalized laser power concentrated in the central region for different initial parameters, where the solid blue line corresponds to the point A in (d), the red dashed line corresponds to the point C in (d) and also corresponds to the simulation result in Fig. 3, and the black dash-dotted line corresponds to the point C in (d) but with an initial ellipticity of $h = 1.5$ . (b) The averaged value of $η$ as a function of the normalized radius of the laser beam for different initial input powers and beam ellipticity. (c) The phase space of the averaged value of $η$ , where the white line approximately depicts the stability boundary of filamentation instability and the initial beam ellipticity is $h = 1.0$ . (d) Stability map of different elliptical laser beams propagating in underdense plasmas.
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Figure 5
The 3D particle-in-cell simulation results at $T = 400 f s$ . (a), (c), and (d) The evolutions of the normalized laser power concentrated in the central region $[η (x)]$ for different elliptical cases and the simulation parameters are, respectively, corresponding to the A, B, and C points in Fig. 4. Panel (d) also corresponds to the result in Fig. 2. (b) Isosurface of the laser intensity corresponding to (a), where the isovalue is $2 \times 10^{18} W / {cm}^{2}$ and the initial beam ellipticity is $h = 1.0$ . The dashed lines in (a) indicate the positions of the first and second self-focusing points. The dashed lines in (c) and (d) show the region of the occurrence of filamentation instability.
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Figure 6
The 3D particle-in-cell simulation results at $T = 400 fs$ . (a) and (b) The evolutions of the normalized laser power concentrated in the central region $[η (x)]$ for different initial parameters, where (a) corresponds to the C point in Fig. 4 but for a linearly polarized laser beam and (b) corresponds to the C and D points in Fig. 4 for a circularly polarized laser beam. The D point corresponds to the initial conditions with $a_{0} = 1.6, r_{0} = 4 μ m$ , and $n_{e} = 0.2 n_{c}$ . This gives a normalized radius as $r_{0} ω_{p} / c \approx 8.2$ and a normalized input power of $P_{in} / P_{cr} = 22$ , which keeps the same value of $P_{in} / P_{cr}$ as the C point. The dashed line in (a) shows the region of the occurrence of filamentation instability.
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