Ion-acoustic feature of collective Thomson scattering in non-equilibrium two-stream plasmas K. Sakai1aT. Nishimoto1S. Isayama2S. Matsukiyo2and Y. Kuramitsu1b

2025-05-03 0 0 4.02MB 10 页 10玖币

侵权投诉

Ion-acoustic feature of collective Thomson scattering in non-equilibrium

two-stream plasmas

K. Sakai,1, a) T. Nishimoto,1S. Isayama,2S. Matsukiyo,2and Y. Kuramitsu1, b)

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

Japan.

2)Department of Advanced Environmental Science and Engineering, Kyushu University, 6-1 Kasuga-Koen, Kasuga,

Fukuoka 816-8580, Japan.

(Dated: 20 December 2022)

We theoretically and numerically investigate the ion-acoustic features of collective Thomson scattering (CTS)

in two-stream plasmas. When the electron distribution functions of two (stationary and moving) components

overlap with each other at the phase velocities corresponding to the two resonant peaks of the ion-acoustic

feature, the theoretical spectrum shows asymmetry because the rate of electron Landau damping is diﬀerent

for the two peaks. The results of numerical simulations agree well with the theoretical spectra. We also

demonstrate the eﬀect of a two-stream-type instability in the ion-acoustic feature. The simulated spectrum

in the presence of the instability shows an asymmetry with the opposite trend to the overlapped case, which

results from the temporal change of the electron distribution function caused by the instability. Our results

show that two-stream plasmas have signiﬁcant eﬀects on CTS spectra and that the waves resulting from

instabilities can be observed in the ion-acoustic feature.

I. INTRODUCTION

Collisionless shocks are known to accelerate charged

particles to nonthermal energies. The formation of colli-

sionless shocks is mediated by electromagnetic ﬁelds due

to collective plasma eﬀects rather than Coulomb colli-

sions. Since the width of a shock transition layer is

smaller than the Coulomb mean free path, multiple plas-

mas with diﬀerent origins can coexist, especially in the

upstream regions of collisionless shocks.1Some of the up-

stream particles are reﬂected at the shock front, and the

upstream and reﬂected plasmas form a two-stream state.

The free energy of the two-stream state excites plasma

waves, and particles can be accelerated by wave-particle

interactions.1,2In some cases, the excited waves self-

organize into global structures in collisionless shocks.3,4

However, it is diﬃcult to observe the multiscale nature

of collisionless shocks in space and astrophysical plas-

mas. This is because it is challenging to obtain images

of shocks with spacecraft in space plasmas and there are

no in-situ observations of distribution functions in as-

trophysical plasmas. Recently, collisionless shocks have

been studied with laboratory experiments that have the

potential to measure both global and local information

simultaneously.5,6

In laboratory experiments, collective Thomson scat-

tering (CTS) is widely used to measure local plasma pa-

rameters and distribution functions by observing the dis-

persion properties and amplitudes of waves.7CTS is a

parametric resonance that occurs among incident electro-

magnetic, scattered electromagnetic, and plasma waves.

There are two kinds of spectra in unmagnetized plas-

mas — resonances with Langmuir waves create electron

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

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

features, and those with ion-acoustic waves create ion-

acoustic features. Both of these have two peaks, asso-

ciated with waves propagating toward and against the

observation direction. In an electron feature, the wave-

length diﬀerence between peaks, the widths of the peaks,

and the Doppler shift correspond to the electron den-

sity, temperature, and velocity, respectively, when the

distribution function is Maxwellian. In an ion-acoustic

feature, the wavelength diﬀerence between peaks, the

widths of the peaks, the Doppler shift, and the asym-

metry in the peaks correspond to the sound velocity, ion

temperature, ion velocity, and velocity diﬀerence between

the electrons and ions, respectively. It is known that the

dynamic structure factor represents the CTS spectrum

in quasi-equilibrium plasmas.7The CTS spectra of non-

equilibrium plasmas are still a subject of investigation8–14

and the analysis of CTS spectra normally assumes the

distribution function to be Maxwellian. However, non-

equilibrium plasmas with distributions that are far from

Maxwellian are ubiquitous in high-energy phenomena,

such as collisionless shocks. In collisionless shock ex-

periments, CTS can be used to observe the structure of

shocks and sometimes two components of the ion fea-

ture, which correspond to the two-stream state.15–20 Al-

though non-equilibrium plasmas are essential in shock

formation and particle acceleration, most analyses as-

sume a Maxwellian distribution function. Therefore, in

this work, we investigate CTS for non-equilibrium plas-

mas and the resulting waves associated with collisionless

shocks.

We have previously investigated the electron features

of CTS in two-plasma states.12 When the relative drift

of two plasmas is larger than the electron thermal veloc-

ity, the CTS spectrum is not explained by the dynamic

structure factor and shows a large asymmetry reﬂecting

the directional wave generated by the two-stream-type

instability. In this paper, we focus on the ion-acoustic

arXiv:2210.11086v3 [physics.plasm-ph] 19 Dec 2022

features of CTS in two plasmas. We theoretically cal-

culate the CTS spectra in the two-plasma state in Sec.

II. When two electron distribution functions overlap with

each other, spectral asymmetry arises due to the diﬀer-

ent rates of electron Landau damping for the two peaks.

We perform numerical simulations to calculate the CTS

spectra in Sec. III. In the presence of the electron two-

stream-type instability, we observe a new spectrum corre-

sponding to the excited wave and the spectral asymmetry

of the ion-acoustic feature due to the change in the elec-

tron distribution function. We provide a discussion and

summary of our research in Sec. IV.

II. DYNAMIC STRUCTURE FACTOR IN A

TWO-PLASMA STATE

We theoretically calculate the CTS spectrum in a two-

plasma state. We consider the electron and ion distribu-

tion functions to be the sum of two Maxwell distributions:

fe,i(v) = X

e,i

ne,i

e,i(v),(1)

where fj

e,i(v) and nj

e,i are the distribution function and

number density of the j-th plasma species, respectively.

The total number density is given by ne,i =Pjnj

e,i. The

individual distribution functions are written as fj

e,i(v) =

exp[−(v−vdj )2/v2

te,i]/(π1/2vte,i), where vdj is the j-th

drift velocity. We assume there are no net currents, so

J=Pj[(qenj

e+qinj

i)vdj ] = 0, where qe,i is the charge

of an electron or ion. The thermal velocity is given by

vte,i = (2kBTe,i/me,i)1/2, where kB,Te,i, and me,i are

the Boltzmann constant, temperature, and mass, respec-

tively. In this paper, we assume the temperatures of the

two components (electrons and ions) are the same for

simplicity. We set the ion-to-electron mass ratio to 100.

The reduced mass is employed to compare the dynamic

structure factor with the simulated spectrum in Sec. III.

The dynamic structure factor with a realistic mass ratio is

presented in Appendix A. The dynamic structure factor

that describes the spectral shape of Thomson scattering

near the equilibrium plasmas is expressed as7

S(k, ω) = 2π

k1−χe

ε

2feω

k+Z

χe

ε

2fiω

k.

(2)

The ﬁrst and second terms on the right-hand side in

Eq. (2) are associated with the non-collective scattering

or Langmuir (electron plasma) waves and ion-acoustic

waves, respectively. The susceptibility χe,i is given by

χe,i =4πq2

e,ine,i

me,ik2Z∞

−∞

∂fe,i (v)

∂v

k−vdv

=−4πq2

e,i

me,ik2X

j"nj

e,i

te,i

Z0ω

k−vdj

vte,i #,

(3)

where Z0(ζ) is the derivative of the plasma dispersion

function. The wavenumber and frequency of the ob-

served density ﬂuctuation are given by k=kS−kIand

ω=ωS−ωI, where kS,kI,ωS, and ωIare the scattered

wavenumber, incident wavenumber, scattered frequency,

and incident frequency, respectively. The dielectric func-

tion satisﬁes ε= 1+χe+χi. The peaks of the CTS spec-

trum are mainly determined by ε∼0, which represents

the resonant condition of parametric resonance. The dis-

persion relations of the Doppler-shifted ion-acoustic and

electromagnetic waves are given by (ω−k·vd)2=c2

Sk2

and ω2=ω2

p+c2k2, where vd,cS, and ωpare the ﬂow

velocity, sound velocity, and plasma frequency, respec-

tively. Considering the dispersion relations and the res-

onant condition, we ﬁnd the peak wavenumbers of the

CTS spectra kS±:

S±'c2+ (vd±cS)2

c2−(vd±cS)2kIsin θ

2+2(vd±cS)

c2−(vd±cS)2ωI2

+k2

Icos2θ

(4)

where θis the angle between the incident and scattered

wavenumbers. The peaks are determined not only by ε∼

0 but also by the electron susceptibility in the numerator

in Eq. (2). Substituting the dielectric function into the

absolute value term in Eq. (2), we get



χe

ε

2=

1 + x

(1 + Re[x])2+ (Im[x])2,(5)

where x= (1 + χi)/χe. The peak is determined to be

at the wavenumber with the smallest denominator in Eq.

(5) where Re[x]∼ −1 and Im[x]∼0 are satisﬁed.

We plot Eqs. (1), (2), and (5) in Fig. 1with the param-

eters Te/(mec2)=2×10−3,Te1=Te2= 10Ti1= 10Ti2,

e,i/n2

e,i = 1, Z= 1, vd1= 0, ckI/ωpe = 5, and θ= 90°.

We compare the spectra obtained from f=f1+f2

(S1+2) and the sum of the spectra obtained indepen-

dently from f1(S1) and f2(S2) by changing the drift

velocity vd2/vte = 0, 1, and 3. Figures 1(a)–1(c) show

the scattered spectrum in terms of the wavenumber shift,

∆k=kS−kI, normalized to ωpe/c, where ωpe is the

electron plasma frequency. The black, green dashed, red

dotted, and blue dotted curves in Figs. 1(a)–1(c) show

the CTS spectra of S1+2,S1+S2,S1, and S2, respec-

tively. The red and blue curves in Figs. 1(d)–1(f) are

the real and imaginary parts of (1 + χi)/χein terms of

the wavenumber shift, respectively. The resonant condi-

tion of Re[(1 + χi)/χe]∼ −1 is shown by the horizontal

red dashed line, and that of Im[(1 + χi)/χe]∼0 is shown

as the horizontal blue dashed line. We plot Eq. (4) as

the vertical dotted lines in Figs. 1(a)–1(f) as a criterion

of the peaks determined by Eq. (5). The insets in Figs.

1(b), 1(c), 1(e), and 1(f) are enlarged versions of the left

spectrum for ease of view. Figures 1(g)–1(i) represent the

electron (blue) and ion (red) distribution functions. The

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

Ion-acousticfeatureofcollectiveThomsonscatteringinnon-equilibriumtwo-streamplasmasK.Sakai,1,a)T.Nishimoto,1S.Isayama,2S.Matsukiyo,2andY.Kuramitsu1,b)1)GraduateSchoolofEngineering,OsakaUniversity,2-1Yamadaoka,Suita,Osaka565-0871,Japan.2)DepartmentofAdvancedEnvironmentalScienceandEngineering,KyushuUni...

展开>> 收起<<

Ion-acoustic feature of collective Thomson scattering in non-equilibrium two-stream plasmas K. Sakai1aT. Nishimoto1S. Isayama2S. Matsukiyo2and Y. Kuramitsu1b.pdf

共10页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Ion-acoustic feature of collective Thomson scattering in non-equilibrium two-stream plasmas K. Sakai1aT. Nishimoto1S. Isayama2S. Matsukiyo2and Y. Kuramitsu1b

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: