Polarization, hosing and long time evolution of relativistic laser pulses
N. M. Naumova
General Physics Institute RAS, Moscow, Russia
J. Koga
Advanced Photon Research Center, JAERI, Kyoto-fu, Japan
K. Nakajima
Advanced Photon Research Center, JAERI, Kyoto-fu, Japan
and High Energy Accelerator Research Organization, Tsukuba, Japan
T. Tajima
Department of Physics, University of Texas at Austin, Austin, Texas 78712-1081
T. Zh. Esirkepov
Moscow Institute of Physics and Technology, Dolgoprudny, Russia
S. V. Bulanov
General Physics Institute RAS, Moscow, Russia
F. Pegoraro
Department of Physics, Pisa University and IFNM, Pisa, Italy
͑Received 11 January 2001; accepted 26 June 2001͒
The effect of the pulse polarization and of the accelerated fast electrons on the propagation
anomalies ͑‘‘hosing’’ and ‘‘snaking’’͒ of a high-intensity laser pulse in an underdense plasma is
investigated with two dimensional particle in cell simulations. The pulse deflection and the type of
plasma modes ͑solitons, vortices͒ into which the laser pulse energy is eventually deposited, are
shown to depend on the pulse polarization. © 2001 American Institute of Physics.
͓DOI: 10.1063/1.1395566͔
I. INTRODUCTION
Recently in Refs. 1, 2 it has been shown that the relativ-
istic self focusing in three dimensions ͑3D͒ of a linearly po-
larized laser pulse propagating in an underdense plasma with
power above the threshold power P
cr
Ӎ2m
e
2
c
5
2
/e
2
pe
2
Ӎ17(
/
pe
)
2
GW is anisotropic and evolves differently in
the plane in which the pulse electric field oscillates ͑denoted
as the p-plane͒ and in the plane where the magnetic field
oscillates (s-plane͒. Here
is the pulse carrier frequency
and
pe
(
Ͼ
pe
) is the ͑nonrelativistic͒ Langmuir fre-
quency of the plasma. Furthermore it has been shown that
this different behavior is directly related to the behavior of p-
and of s-polarized pulses in 2D.
In the present paper we are interested in the effect of
polarization on what we call the propagation ‘‘anomalies’’ of
the pulse, i.e., of the lateral oscillations and deflections of the
pulse that can affect the efficiency and the rate at which its
energy is transported through the plasma. In Ref. 3 it was
predicted that a laser pulse propagating through a plasma
channel can undergo lateral oscillations because of the exci-
tation of a ‘‘hosing’’ instability. A similar mechanism was
discussed in Refs. 4, 5 for a self-guided pulse in a homoge-
neous plasma. The physical picture behind this mechanism
was recently given in Ref. 6. In the strongly relativistic re-
gime the occurrence of a long-wave-length hosing instability
was predicted in Refs. 7, 8 by using two dimensional ͑2D͒
particle in cell ͑PIC͒ simulations and a variational approach
to the so-called envelope equation describing the pulse
propagation. All these hosing instabilities are driven by a
feedback mechanism between the lateral displacements of
the centers of mass of the laser pulse and of the electrostatic
wake wave generated by the pulse. The long-wave-length
instability is due to the relativistic mass correction and has a
threshold corresponding to a pulse power P in excess of 3P
cr
͑see Ref. 8͒. In Ref. 7 this long-wave-length instability was
shown to affect the front part of the pulse in its ‘‘final’’
nonlinear state. The laser beam bending in the direction per-
pendicular to its axis has been observed with 2D and 3D PIC
simulations ͑see Refs. 7, 9, 10͒.
Here, with 2D PIC simulations, we show that the laser
beam excursions in the direction perpendicular to the direc-
tion of its propagation are of two types. The first are quasi-
periodic, antisymmetric oscillations of the laser wake which
have a relatively low amplitude. They depend on the pulse
polarization and do not bend the laser pulse substantially.
The second are aperiodic lateral oscillations that depend only
weakly on the pulse polarization and can cause a ‘‘snaking’’
instability. This corresponds to a net deflection of the laser
pulse propagation that was observed in Ref. 9 ͑see Fig. 1 of
this reference͒. This phenomenon is particularly effective in
the case of semi-infinite laser beams and leads to the forma-
tion of lateral filaments that move aside from the original
direction of propagation of the pulse. These lateral filaments
eventually close, thus allowing the beam to revert tempo-
rarily to straight propagation before a new deflection takes
place. This snaking instability has a strong limiting effect on
PHYSICS OF PLASMAS VOLUME 8, NUMBER 9 SEPTEMBER 2001
41491070-664X/2001/8(9)/4149/7/$18.00 © 2001 American Institute of Physics