2012 JINST 7 C04010

Feasibility study of the plasma electron density measurement by electromagnetic radiation from the laser-driven plasma wave

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2012 JINST 7 C04010

PUBLISHED BYIOP PUBLISHING FORSISSAMEDIALAB RECEIVED:December 15, 2011 ACCEPTED:February 28, 2012 PUBLISHED:April 17, 2012

15^th INTERNATIONALCONFERENCE ONLASER AIDED PLASMADIAGNOSTICS, OCTOBER 13–19, 2011

JEJU, KOREA

Feasibility study of the plasma electron density

measurement by electromagnetic radiation from the laser-driven plasma wave

D.G. Jang,^aJ.J. Kim,^aM.S. Hur^band H. Suk^a,b,1

aGraduate Program of Photonics and Applied Physics, Gwangju Institute of Science and Technology (GIST),

1 Oryong-dong, Buk-gu, Gwangju, 500-712, Republic of Korea

bSchool of Electrical and Computer Engineering,

Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Korea

E-mail:hysuk@gist.ac.kr

ABSTRACT: When an intense laser beam is focused in a plasma, a plasma wake wave is generated and the oscillatary motion of the plasma electrons produces a strong electromagnetic wave by a Cherenkov-like process. Spectrum of the genetated electromagnetic wave has dependence on the plasma density. In this paper, we propose to use the emitted electromagnetic radiation for plasma diagnostic, which may provide an accurate information for local electron densities of the plasma and will be very useful for three-dimensional plasma density profiles by changing the focal point location of the laser beam. Two-dimensional (2-D) particle-in-cell (PIC) simulation is used to study the correlation between the spectrum of the emitted radiation and plasma density, and the results demonstrate that this method is promising for the electron density measurement in the plasma.

KEYWORDS: Wake-field acceleration (laser-driven, electron-driven); Detector modelling and sim- ulations I (interaction of radiation with matter, interaction of photons with matter, interaction of hadrons with matter, etc); Plasma diagnostics - interferometry, spectroscopy and imaging; Detector modelling and simulations II (electric fields, charge transport, multiplication and induction, pulse formation, electron emission, etc)

1Corresponding author.

2012 JINST 7 C04010

Contents

1 Introduction 1

2 Two-dimensional PIC simulation results and discussions 2

3 Conclusions 4

1 Introduction

Accurate electron density measurement is critical in plasma research. So far numerous methods [1]

have been developed and used for a variety of plasma researches. Plasma diagnostic method is a very powerful tool in measuring plasma parameters since it can provide the plasma information by non-perturbing ways. Although the laser-assisted plasma diagnostic methods are well-developed, there are still some difficulties and problems in some applications. Hence, development of the new diagnostic methods is always needed. In this paper, we propose a rather new laser-aided plasma diagnostic method using laser-plasma interactions.

When a medium power laser pulse of sub-TW (terawatt) is focused in a plasma, a strong in- teraction occurs and a plasma wake wave is generated by the ponderomotive force of the laser beam [2]. In this process, a strong electromagnetic radiation will be produced by the oscillatory motion of the plasma electrons and it is known that the wavelength of the radiation depends on the plasma density [3]. In other words, the radiation frequency is the same as the plasma oscillation frequencyωp. The basic mechanism of the electromagnetic radiation generation is that the longi- tudinal plasma oscillation by the laser pulse acts like a moving electric dipole antenna so that it can emit the radiation by a Cherenkov-like process [4].

So far, extensive studies including both experimental and theoretical approaches have been performed [5,6]. However, the measurement of plasma electron density using the electromagnetic radiation from the laser-driven plasma wake wave has not been seriously considered except a brief comment in some literatures [7, 8]. For example, Sheng et al. [7] mentioned the possibility for plasma wake wave diagnostics using the THz wave from the laser-plasma acceleration process. In this paper, we seriously consider the electromagnetic radiation for plasma diagnostics (especially plasma density measurement). In this method, information about the local plasma density can be obtained by focusing the laser beam to a small size and even three-dimensional mapping of the plasma density profiles could be easily made by changing the focal point location of the laser beam in the plasma. To investigate a possibility of the plasma diagnostic method, two-dimensional (2-D) particle-in-cell (PIC) simulations are used and some detailed results are presented below.

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Figure 1. Schematic of the electromagnetic radiation from the laser-driven plasma wave, where the radiation is produced mainly from the focal point.

2 Two-dimensional PIC simulation results and discussions

If a medium power laser pulse of sub-TW is focused onto a small spot size in an underdense plasma, the focused laser beam will diffract rapidly (as shown in figure1) over a distance of the Rayleigh range, which is given by LR=πr₀²/λ0 for a Gaussian beam. Here, r₀ is the beam waist radius andλ₀ is the laser wavelength. Generally the Rayleigh range is very small compared with most plasma sizes. For example, it is calculated asLR∼=0.4 mm with a radius of 10µm forλ₀=0.8µm (Ti: sapphire laser wavelength). Hence, the emitted electromagnetic radiation contains the local plasma density information around the focal point of the laser pulse and the emitted electromagnetic radiation can propagate forward or backward if the underdense plasma density is not perfectly uniform (the radiation will be self-absorbed in a uniform density plasma). In this method, the focused spot location in the plasma can be changed easily by moving the reflecting off-axis mirror or a focusing lens, so that mapping of the plasma density profiles can be easily obtained, which is very important in plasma research.

For our studies, we used the 2-D PIC code developed by Hur at UNIST. The code incor- porates the standard Yee-mesh scheme [9] for the electromagnetic field solver and Villasenor- Buneman method [10] for electric current from the simulation particles. The code employs the moving window technique, where the simulation window moves at the speed light along thexaxis.

The two-dimensional simulation window has a dimension of 200µm×200µm in the longitudi- nal and transverse directions. In these simulations, a Gaussian laser pulse with a wavelength of λ₀=0.8µm is focused in the plasma, where the focused laser spot radius is 5µm, the laser pulse duration isτ=π/ωp, and the plasma densities are in the range of 2×10¹⁷∼5×10¹⁸cm⁻³whose cut-off frequency is 2.52×10¹³∼1.26×10¹⁴rad/sec. The plasma density decreases slightly along the x axis (5% decrease over a distance of 6LR) for forward direction propagation of the gener- ated electromagnetic radiation, as shown in figure2. In these simulations, the normalized vector potential of the focused laser beam has a₀=0.1, which implies the focused laser beam is not so intense. Hence, the relativistic effect like the self-focusing effect can be completely ignored.

Here, the normalized vector potential is defined bya₀=eE/mcω, where E is the laser electric field,ω is the laser frequency,cis the light speed, andeandmare the electron charge and mass, respectively.

2012 JINST 7 C04010

Figure 2. Schematic of the plasma density profile and the laser pulse for simulations, where the laser pulse propagates in the plasma with a slightly decreasing density profile. In the case of an increasing density profile, the generated electromagnetic radiation will propagate in the backward direction.

Figure3shows snap shots of the two-dimensional magnetic field plot for the generated elec- tromagnetic radiation at two different times. In these figures, the focal point of the laser pulse is located at x=230µm and the laser pulse propagates to the right direction in the plasma with a nearly uniform density ofn_e=1×10¹⁸cm⁻³. As shown in the figures, a very strong electro- magnetic radiation is generated and it propagates in the plasma. The generated magnetic field strength is about cBz=9 MV/m and this is about 0.1% of the wakefield strength of the plasma wave, where the longitudinal electric field by a wake wave is given byE∼=mcω_p/eaccording to the 1-dimensional linear cold-fluid approximation [2]. The emitted electromagnetic radiation from the laser-driven plasma wake wave is a fairly high power although a moderate intensity laser beam ofa₀=0.1 was used in the simulation, where the normalized vector potential ofa₀=0.1 corre- sponds to an intensity ofI=2.2×10¹⁶W/cm²for a wavelength ofλ₀=0.8µm and this intensity can be easily obtained with a one box laser system nowadays. Hence, it is expected to be measured easily outside the plasma.

The electromagnetic radiation is generated by the oscillatory motion of the plasma electrons, where the oscillation frequency is given byωp= (nee²/mε₀)^1/2. Hereε₀is the electric permittivity of free space. Hence, analysis of the radiation spectrum will give us the plasma density information near the focal point in the plasma and this result is shown in figure4. Figure4shows the spectrum for three different plasma densities, where the dotted lines denote the plasma frequency for the given density. The result clearly shows that there is a very strong correlation between the peak spectrum frequency and the plasma density. It is interesting to point out that the 2-D PIC simulation results are in very good agreement with the 1-D linear cold-fluid theory and this is because the 1-D motion is dominant in the process. Another interesting point to note is that the spectrum is not symmetric. This is understandable because the low frequency part will be self-absorbed by the plasma as the electromagnetic radiation propagates along the slightly decreasing density profile.

Figure 5 shows the relation between the peak spectrum frequency and the plasma density, which gives a calibration between them. This result indicates the present method for plasma diag- nostics works and can give the density information by measurement of the electromagnetic radia- tion spectrum.

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Figure 3. Snap shots of the two-dimensional magnetic field plot for the generated electromagnetic radiation at (a)t/T =375 and (b)t/T=500 (T is the laser oscillation period), where the plasma has a nearly uniform density of 1×10¹⁸cm⁻³and the laser pulse is focused atx=230µm. As shown in these figures, a strong electromagnetic radiation is generated and it propagates forward with an angle.

3 Conclusions

Focusing a medium power laser pulse in plasma can produce a strong electromagnetic radiation from the laser-driven plasma wake wave and our 2-D PIC simulation studies confirmed that plasma densities can be measured easily by the spectrum of the radiation. The accuracy is expected to be very good as the produced radiation is very intense. Furthermore, it can provide the plasma density information with a very high spatial resolution on the order of the Rayleigh range. Nowadays

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Figure 4. The radiation spectra forn_e=2×10¹⁷, 1×10¹⁸, and 5×10¹⁸cm⁻³, respectively, where the dotted lines denote the plasma frequencyω_pfor the given density.

Figure 5. Comparison of the 2-D PIC simulation result and the 1-D linear cold-fluid theory, where the red line is from the 1-D theory and the square dots are from the 2-D simulations.

compact table-top high-power (∼TW) lasers in one box size are available in the market, where the CPA (chirped-pulse amplification) technique [11] is used and the laser pulse duration can be changed easily depending on plasma densities. Therefore, the method proposed in this paper could be a good alternative way for plasma diagnostics.

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Acknowledgments

This work was financially supported by the National Research Foundation (NRF) of Korea (No. 2011-0018748 and 2011-0000337).

References

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