Collective Thomson scattering in non-equilibrium laser produced two-stream plasmas K. Sakai1aS. Isayama2 3N. Bolouki2 4M.S. Habibi2Y.L. Liu2Y.H. Hsieh2H.H. Chu2 5J. Wang2 5 6

2025-04-29 0 0 2.87MB 14 页 10玖币

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Collective Thomson scattering in non-equilibrium laser produced two-stream

plasmas

K. Sakai,1, a) S. Isayama,2, 3 N. Bolouki,2, 4 M.S. Habibi,2Y.L. Liu,2Y.H. Hsieh,2H.H. Chu,2, 5 J. Wang,2, 5, 6

S.H. Chen,2T. Morita,7K. Tomita,8R. Yamazaki,9, 10 Y. Sakawa,10 S. Matsukiyo,3and Y. Kuramitsu1, 10, b)

1)Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871,

Japan

2)Department of Physics, National Central University, No. 300, Jhongda Rd., Jhongli, Taoyuan 320,

Taiwan

3)Department of Earth System Science and Technology, Kyushu University, 6-1 Kasuga-Koen, Kasuga,

Fukuoka 816-8580, Japan

4)Center for Plasma and Thin Film Technologies, Ming Chi University of Technology,

84 Gungjuan Rd. Taishan Dist. New Taipei City 24301, Taiwan

5)Center for High Energy and High Field Physics, National Central University, No. 300, Jhongda Rd., Jhongli,

Taoyuan 320, Taiwan

6)Institute of Atomic and Molecular Sciences, Academia Sinica, P. O. Box 23-166, Taipei,

Taiwan

7)Department of Advanced Energy Engineering Science, Kyushu University, 6-1 Kasuga-Koen, Kasuga,

Fukuoka 816-8580, Japan

8)Department of Applied Science for Electronics and Materials, Kyushu University, 6-1 Kasuga-Koen, Kasuga,

Fukuoka 816-8580, Japan

9)Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara,

Kanagawa 252-5258, Japan

10)Institute of Laser Engineering, Osaka University, 2-6 Yamadaoka, Suita, Osaka 565-0871,

Japan

(Dated: 21 October 2022)

We investigate collective Thomson scattering (CTS) in two-stream non-equilibrium plasmas analytically,

numerically and experimentally. In laboratory astrophysics, CTS is a unique tool to obtain local plasma

diagnostics. While the standard CTS theory assumes plasmas to be linear, stationary, isotropic and equi-

librium, it is often nonlinear, non-stationary, anisotropic, and non-equilibrium in high energy phenomena

relevant to laboratory astrophysics. We theoretically calculate and numerically simulate the CTS spectra in

two-stream plasmas as a typical example of non-equilibrium system in space and astrophysical plasmas. The

simulation results show the feasibility to diagnose two-stream instability directly via CTS measurements. In

order to conﬁrm the non-equilibrium CTS analysis, we have been developing experimental system with high

repetition rate table top laser for laboratory astrophysics.

I. INTRODUCTION

Laboratory astrophysics is a research ﬁeld, where space

and astrophysical phenomena are reproduced experimen-

tally in laboratories. In space plasmas, in-situ measure-

ments with spacecrafts provides us the local and mi-

croscopic information of plasmas and electric/magnetic

ﬁelds, however, it is hard to observe global structure of

phenomena. In contrast, while imaging of astrophysical

objects with telescope provides us the global and macro-

scopic information of phenomena, there is no local and

microscopic information of plasmas since they are inac-

cessible. In laboratories, we can access both global and

local information at the same time1. Besides this, while

we have to image the emissions from the astrophysical

phenomena, we can use external light sources and par-

ticle beams to diagnose the phenomena in laboratories.

These are the signiﬁcant advantages of laboratory astro-

a)kentaro.sakai@eie.eng.osaka-u.ac.jp

b)kuramitsu@eei.eng.osaka-u.ac.jp

physics, and highly challenging in space and astrophys-

ical plasmas1,2. For instance, we have investigated col-

lisionless shocks and magnetic reconnections relevant to

space and astrophysical phenomena, such as supernova

remnants, earth’s bow shocks, solar ﬂares, stellar winds,

and aurorae, with Gekko XII (GXII) laser facility3–8,

however, the number of shots is very limited due to the

low repetition rate of GXII (a few shots per day) and

there exist only several large facilities like GXII in the

world. Therefore, the opportunities of experiments on

laboratory astrophysics are limited. We are motivated to

use high repetition-tabletop lasers since there are many

more facilities to obtain much more data on laboratory

astrophysics. We also extend the laboratory astrophysics

with short pulse lasers. As the ﬁrst step, we match the in-

tensity of the tabletop lasers to that of high power lasers

and conﬁrm that the plasma with similar density and

temperature can be obtained. We will study the plasma

dynamics in the future.

As mentioned above, in laboratories global and local

information of phenomena can be obtained simultane-

ously. Collective Thomson scattering (CTS) is a unique

arXiv:2210.11382v1 [physics.plasm-ph] 20 Oct 2022

tool to measure local plasma quantities of the density,

velocity, and temperature both of electrons and ions5–9.

A conventional CTS analysis assumes plasmas to be lin-

ear, stationary, equilibrium, and stable10, however, in

many high energy space and astrophysical phenomena

as well as laser-produced plasmas relevant to laboratory

astrophysics, such as collisionless shocks and magnetic

reconnections, are highly nonlinear, non-stationary, and

non-equilibrium, and show various kinds of instabilities.

Hence, the conventional CTS analysis may not be ap-

propriate for such plasmas. For example, in the pres-

ence of a high-Mach number collisionless shock, some

part of upstream plasma can be reﬂected at the shock

front, and thus, in the upstream region of collisionless

shock two-stream plasmas are often observed11. The two-

stream plasmas can be unstable, and various wave activi-

ties resulting from the instabilities play essential roles on

particle acceleration and generation of cosmic rays. We

have analytically as well as numerically investigated the

CTS in nonlinear, non-stationary, non-equilibrium, and

unstable plasmas12. We further develop the CTS anal-

ysis for such non-equilibrium plasmas. So far, Thom-

son scattering from non-Maxwellian plasmas has been

extensively investigated for super-Gaussian13,14, Spitzer-

H¨arm15,16, and kappa distribution functions17. In this

study, we consider two-plasma states as an example of

such non-equilibrium plasmas and focus on CTS spec-

trum in the presence of the two-stream instability as well

as the high energy components. The investigations of

non-Maxwellian distribution functions13–17 in the past fo-

cus on the distribution functions symmetric about v= 0.

We consider here the two-stream plasmas that often seen

in the upstream of collisionless shocks, where the dis-

tribution function is asymmetric. The two-stream plas-

mas and the resultant instabilities are signiﬁcant since

the relevant wave dynamics play essential roles in par-

ticle acceleration. One of our long term goals is the in-

vestigation of the origins of cosmic rays; we would like

to understand the particle acceleration at collisionless

shocks in a controlled manner in laboratories. To this

end, in this paper we study the two-plasma states either

with the diﬀerent drift velocities or diﬀerent tempera-

tures. The latter can express a plasma with high en-

ergy component. In reality in space it should be mixture

of these two and can be much more complicated. We

start from the well-established CTS theory and extend it

with two Maxwellian distributions as a typical example

of upstream plasmas, which can be unstable or with high-

energy component. Observing the instabilities and high

energy component in collisionless shock via CTS will be

an essential step toward understanding the particle ac-

celeration in the universe.

When the velocity diﬀerence of two plasmas is not

large, electron distribution functions overlap each other.

The Landau damping at two peaks of CTS will be dif-

ferent from that in the presence of a single plasma,

and the CTS spectra will change the form. Moreover,

when the velocity diﬀerence of two plasmas is larger

than thermal velocity of plasmas, two-stream instabili-

ties grow18. It is considered that one of the peaks in

CTS spectrum is enhanced when the two-stream insta-

bility takes place12. In order to understand the CTS

from the non-equilibrium plasmas, we theoretically in-

vestigate the CTS spectra from two-stream plasmas in

Sec. II. In Sec. III, we numerically investigate the CTS

in the presence of two-stream instability. In Sec. IV, we

introduce our experimental approach to verify the non-

equilibrium CTS in laser produced plasmas. To verify

CTS in non-equilibrium plasma, large laser facilities are

not convenient due to the low repetition rate of laser. In

Sec. Vwe summarize our research.

II. THEORETICAL SPECTRUM FROM TWO-STREAM

PLASMAS

Figures 1(a) and (b) shows the schematic images of

CTS spectra and the dispersion relation in the presence

of a single plasma. An incident light wave with the fre-

quency ωIand the wavenumber kIcan be parametri-

cally scattered by the Langmuir waves and by the ion

acoustic waves. As shown in Fig. 1(a), while the light

scattered by the ion acoustic waves corresponding to the

CTS ion feature has the higher peak intensity (I) and the

narrower spectral width, the light scatted by the Lang-

muir waves corresponding to the CTS electron feature

has the lower and broader spectra, where the horizontal

axis ∆k≡kS−kIshows the wavenumber diﬀerence be-

tween the scattered and incident waves and the subscripts

Land Rrepresent left and right. In the collective regime,

there are two peaks in each feature coming from the scat-

tering by the waves propagating in the same and oppo-

site directions. For instance, the left peak of the electron

feature in Fig. 1(a) comes from the resonant interaction

between the incident light, the scattered light (kSL, ωSL),

and the Langmuir wave (kL, ωL) forming a parallelo-

gram in Fig. 1(b), where the incident and the Langmuir

mode co-propagate. Similarly, the right peak of the elec-

tron feature comes from the other parallelogram com-

posed by the incident (kI, ωI), scatter (kSR, ωSR), and

Langmuir (kR, ωR) waves in Fig. 1(b), where the inci-

dent and the Langmuir mode counter-propagate. Fig-

ures 1(c) and (d) show the same as Figs. 1(a) and

(b) except with two-stream instability. The velocity of

beam component of plasma is expressed by the oblique

line with the velocity vbin Fig. 1(d). When the line

intersects with the Langmuir branch, the two-stream in-

stability can grow. Since the electron feature of CTS

is the resonance interaction between the incident elec-

tromagnetic, electron plasma (Langmuir), and scattered

electromagnetic waves, the amplitude of scatter wave or

the peak intensity of CTS is proportional to the density

ﬂuctuation of Langmuir waves. The Langmuir waves en-

hanced by the two-stream instability will enhance the

scattered wave amplitude. When the phase velocity of

plasma wave observed in CTS is in unstable region in

FIG. 1. (a) Schematic image of CTS spectra with a single plasma. (b) Dispersion relations of light, Langmuir, and ion acoustic

waves in a single plasma. (c) Schematic image of CTS spectra in two-stream plasmas. (d) Dispersion relations in two-stream

plasmas. Two-stream instability grows in the orange region. When the region corresponds to one of the peaks of CTS, the

peak is enhanced as shown in (c).

Fig. 1(d) that is expressed as ω/k ∼vb, the plasma

wave grows and the corresponding peak of CTS can be

enhanced as shown in Fig. 1(c). Since the electron dis-

tribution function becomes non-Maxwellian with a beam

component of plasma, the shape of electron distribution

function also changes the CTS spectra. The two-stream

instability is not included in the theory, but we simply

include two plasmas in the theory. In this section, we dis-

cuss CTS spectrum with electron distribution functions

diﬀerent from Maxwellian. We consider two cases where

two plasmas coexist either with ﬁnite relative velocity or

with ﬁnite temperature diﬀerence.

We calculate the scattering form factor assuming two-

stream plasmas. The spectrum shape of Thomson scat-

tering is related to the scattering form factor, which is

expressed as

S(k, ω) = 2π

k1−χe



2feω

k+Z

χe



2fiω

k,

(1)

where k,ω,χe,,Z,fe(v), and fi(v) are the scattering

wavenumber, scattering frequency, electron susceptibil-

ity, permittivity, ion valence, electron distribution func-

tion, and ion distribution function, respectively10. This

formula assumes quasi-equilibrium plasma. In this pa-

per, we consider only the electron feature of CTS, and

ignore the second term of the right hand side. We as-

sume electron distribution functions as superposition of

two Maxwellian distributions, which is written as

fe1+2(v) = X

nej

fej (v),(2)

where nej ,fej (v), and neare the electron density and

electron distribution function of the j-th plasma species,

and total electron density, respectively. The electron dis-

tribution function of the j-th plasma is given by fej (v) =

q1/(πv2

tej ) exp(−(v−vdj )2/v2

tej ), where vtej and vdj are

j-th electron thermal velocity and j-th drift velocity, re-

spectively. The j-th electron thermal velocity is written

as vtej =p2kTej /me, where Tej is j-th electron tem-

perature. With the electron distribution function, the

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摘要：

CollectiveThomsonscatteringinnon-equilibriumlaserproducedtwo-streamplasmasK.Sakai,1,a)S.Isayama,2,3N.Bolouki,2,4M.S.Habibi,2Y.L.Liu,2Y.H.Hsieh,2H.H.Chu,2,5J.Wang,2,5,6S.H.Chen,2T.Morita,7K.Tomita,8R.Yamazaki,9,10Y.Sakawa,10S.Matsukiyo,3andY.Kuramitsu1,10,b)1)GraduateSchoolofEngineering,OsakaUniversi...

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Collective Thomson scattering in non-equilibrium laser produced two-stream plasmas K. Sakai1aS. Isayama2 3N. Bolouki2 4M.S. Habibi2Y.L. Liu2Y.H. Hsieh2H.H. Chu2 5J. Wang2 5 6.pdf

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Collective Thomson scattering in non-equilibrium laser produced two-stream plasmas K. Sakai1aS. Isayama2 3N. Bolouki2 4M.S. Habibi2Y.L. Liu2Y.H. Hsieh2H.H. Chu2 5J. Wang2 5 6

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