Fast Magnetic Energy Dissipation in Relativistic Plasma Induced by High Order Laser Modes

High Power Laser Science and Engineering, (2016), Vol. 4, e19, 5 pages. © The Author(s) 2016. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. doi:10.1017/hpl.2016.16

Fast magnetic energy dissipation in relativistic plasma induced by high order laser modes

Y. J. Gu1,Q.Yu 1,2,O.Klimo1,3,T.Zh.Esirkepov4,S.V.Bulanov4,S.Weber1, and G. Korn1 1Institute of Physics of the ASCR, ELI-Beamlines, Na Slovance 2, 18221 Prague, Czech Republic 2Institute of Modern Physics, Fudan University, Shanghai 200433, Peoples Republic of China 3FNSPE, Czech Technical University in Prague, 11519 Prague, Czech Republic 4Kansai Photon Science Institute, Japan Atomic Energy Agency, 8-1-7 Umemidai, Kizugawa-shi, Kyoto, 619-0215, Japan (Received 22 March 2016; revised 11 May 2016; accepted 25 May 2016)

Abstract Fast magnetic field annihilation in a collisionless plasma is induced by using TEM(1,0) laser pulse. The magnetic quadrupole structure formation, expansion and annihilation stages are demonstrated with 2.5-dimensional particle-in-cell simulations. The magnetic field energy is converted to the electric field and accelerate the particles inside the annihilation plane. A bunch of high energy electrons moving backwards is detected in the current sheet. The strong displacement current is the dominant contribution which induces the longitudinal inductive electric field. Keywords: high order laser mode; laser–plasma interaction; magnetic annihilation

Magnetic field annihilation (magnetic reconnection), which of hundreds picoseconds. It is easy to create a hot electron converts magnetic field energy to particle kinetic energy, bunch with high density. However, our previous work shows is a fundamental phenomenon in space and laboratory that magnetic annihilation successfully occurs in very low plasmas[1, 2]. Many processes in astrophysics and plasma density plasmas with ultra-shot laser pulses[13, 14]. One physics are related to the magnetic energy dissipation of the difficulties in the magnetic annihilation induced by such as planetary magnetosphere, γ -ray bursts, solar flares double lasers is to well synchronize the two pulses. Here we and fusion plasma instabilities. On the other hand, propose a scheme to overcome this problem by using high high power laser facilities developed quickly since the order laser mode, i.e., TEM(1,0) laser, which allows to con- invention of chirped pulse amplification (CPA) techniques[3]. trol the synchronization of the laser–wakefield–acceleration Laser intensities up to 1022 W/cm2 have been realized[4] (LWFA) in two electron bubbles. Two parallel electron and the next generation lasers are expected to reach beams are created simultaneously by a single laser pulse. 1023–1024 W/cm2 or even higher[5, 6]. With such high The corresponding magnetic field annihilation and energy intensity laser pulses, it becomes possible to investigate the conversion are demonstrated by 2.5-dimensional particle-in- magnetic field annihilation using laser–plasma interactions. cell (PIC) simulations. In the following, we present the laser field of TEM(1,0) mode and our simulation model, The pioneering experimental works by Nilson et al.[7] and Li [8] and discuss the mechanism of magnetic field generation and et al. proved the existence of high temperature electrons annihilation. Then we analyze the characteristics of particle and plasma jets generated in the plasmas irradiated by long acceleration through the inductive electric field. pulses lasers. A significant step has been done by Ping [9] The transverse electric field of a TEM laser, which propa- et al. , where magnetic reconnection occurred at relatively gates along z-direction, can be described as El,m[15]: high plasma density and the main contribution to an induced √ √ electric field came from electrostatic turbulence and electron , , 2x 2y w El m = Re El m H H 0 pressure according to Ohm’s law. The corresponding 0 l w(z) m w(z) w(z) theoretical and experimental studies have been presented 2 [10–12] r and reviewed in many papers recently . × exp − Most of the previous works on magnetic annihilation used w(z)2 solid targets and the long pulse lasers with the pulse duration kr2 × exp i[kz − ωt − (l + m + 1)ϕ(z)]+ , Correspondence to: Y. J. Gu, ELI-Beamlines, Institute of Physics 2R(z) Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Prague, Czech Republic. Email: [email protected] (1) 1

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Figure 1. (a) The distribution of the Poynting ﬂux (normalized to the peak intensity) of TEM(1,0) mode laser pulse. (b) The intensity proﬁle of TEM(1,0) mode (blue solid line) and TEM(0,0) mode (red dashed line).

Figure 2. (a) The initial density proﬁle of the plasma. (b) The longitudinal electric ﬁeld along y =−8λ at t = 75T0. (c) and (d) are the electron density and current distribution at 190T0.

l,m w where E0 is the electric field amplitude, 0 the beam as the case of two TEM(0,0) laser pulses. The electron width, k the wavenumber, ω the laser frequency, r = dynamics driven by TEM(1,0) lasers can also be referred in 2 2 x + y the transverse radius, and Hl is the Hermite Refs. [16, 17]. polynomial. For l = 1 and m = 0, it gives a laser of We perform PIC simulations with the relativistic electro- TEM(1,0) mode. In Figure 1(a), we present the distribution magnetic code EPOCH[18]. Hydrogen plasma with the peak of the Poynting flux of a TEM(1,0) mode laser, which is density of 0.1nc, where nc is the plasma critical density, normalized to the peak intensity. Different from a TEM(0,0) occupies the region defined as 30λ

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Figure 3. (a) and (b) show the z-component of the magnetic ﬁeld distribution at 140T0 and 340T0. (c) Contributions of different terms in Ampere–Maxwell` law at 140T0 along y = 0, transversely averaged inside the current sheet (−λ

of 5 × 1021 W/cm2 is focused on the left boundary of the be accelerated to high energy in a short distance. Due to target with the beam waist of 16λ. The normalized amplitude the distribution of the ponderomotive force of the TEM(1,0) a0 = eE0/meωc ≈ 70, the pulse duration is τ = 20 fs, E0 mode laser, two electron bubbles are generated in the plasma. and ω are the laser electric field strength and frequency, e Each of the bubbles contains an electron beam accelerated and me are the electron charge and mass, respectively, and c by the wakefield as shown in Figure 2(c). The center is the speed of light in vacuum. The effective optical axes plane (along y = 0) becomes the boundary shared by both as shown in Figure 1(b) of the laser pulse are transversely bubbles. The corresponding electric current distribution is separated by 16λ, being at y =±8λ. Open boundary shown in Figure 2(d). The LWFA electron beams form two conditions are employed for both particles and fields in all strong currents and the return currents form the bubble shells directions. The mesh size is δx = δy = λ/20. The time step surrounding the LWFA electron beam. is 0.03λ/c. The real mass ratio between proton and electron The electric currents of the bubble produce magnetic fields (m p/me = 1840) is used in the simulations. according to Ampere–Maxwell` law. The azimuthal field When the laser pulse is propagating in the plasma, a strong component Bθ with respect to the x-axis is represented in [19] wakefield is excited according to the LWFA scenario . the 2D configuration by the component Bz perpendicular We plot the longitudinal electric field along one of the to the plane. Therefore, two symmetric structures shown effective optical axes of the laser pulse (y =−8λ)at in Figure 3(a) correspond to two magnetic dipoles which 75T0 in Figure 2(b). The strength of the wakefield reaches can be regarded as a magnetic quadrupole, nearly touching about −150 GV/cm. Electron captured in such a field can the central axis at y = 0. The magnetic quadrupole is

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Figure 4. The electron longitudinal momentum px at 140T0 (a) and 340T0 (b). The ﬁgures are plotted by selecting the electrons with maximum energy in each mesh cell. The longitudinal momentum distribution comparison between current sheet electrons and side electrons at t = 140T0 and 340T0 are plotted in (c) and (d), respectively.

propagating forward with the laser pulse. When it enters without any compensation from the electric current. In the the density downramp region, the magnetic ﬁeld expands in region of 310λ

bunch can be clearly seen in the center plane which has LM2010005, IT4Innovations Centre of Excellence under higher momentum compared to the return electrons locating projects CZ.1.05/1.1.00/02.0070 and LM2011033 and by in the wings. This high energy electron bunch is similar to ECLIPSE cluster of ELI-Beamlines. The EPOCH code the hot electron jets observed in the previous experimental was developed as part of the UK EPSRC funded projects works[7, 21]. To show this effect clearly, we compare the EP/G054940/1. momentum spectrum of the electrons in center (−λ

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