simulations of langmuir wave generationin the inhomogeneous plasma

22/06/2010Glasgow-Meudon Collaboration, Meudon,

May, 20101

Simulations of Langmuir wave

generation in the inhomogeneous

plasma of the solar wind

Hamish A. S. Reid

Eduard P. Kontar

University of Glasgow

1


May, 20102

Solar Flare

Earth

WIND Spacecraft

detecting in-situ electrons

Impulsive Electron Beam

Parker Spiral connecting the flare and WIND of

length ~1.2AU

Turbulent

Heliosphere Plasma

Type III radio burst


May, 20103

Krucker et al, 2009

Electron Beam Broken Power Law

Lin et al 1982

Solar energetic electrons are observed as a broken power-

law distribution at the Earth with lower energies having a flatter power law index than higher energies.

Broken power-law is caused by the density

gradient of the

background plasma taking plasma waves

out of resonance with the electron beam

(Kontar & Reid 2009)


May, 20104

Initial Conditions

The initial electron beam (at time=0) is dependent on

position (as a Gaussian) and velocity (as a power-law)

−==

2

2

0 exp)()0,,(d

xvgtxvf

α

αα

v

v

v

nvg beam

omin

min

)1()(

−= ovvv ≤≤min

The initial, thermal spectral energy density is:

=

t

peeb

v

v

v

TktxvW log

4),,(

2

2

2

ω

π


May, 20105

One Dimensional QL equations

One dimensional quasilinear equations (e.g. Drummond and

Pines, 1962) describing the kinetics of energetic electrons and

Langmuir waves (Kontar, 2001) (Reid and Kontar 2010

submitted)

+

∂

∂

∂

∂=+

∂

∂+

∂

∂22

2242

v

F

dv

d

v

F

v

W

vm

eF

r

v

x

Fv

t

Fcpγ

π

++−

∂

∂=

∂

∂+

∂

∂+

∂

∂

t

sLcw

e

peTe

v

vvFW

v

FWv

nx

W

v

v

v

W

L

v

t

Wlog)(

3 222

γγγπω

Wave Generation and Absorption

Background Plasma Inhomogeneity


May, 20106

Density Fluctuations

SUNSUN

ELECTRON FLUX WAVE ENERGY DENSITY


May, 20107

Celnikier et al, 1987

Multiple Density Fluctuations

The solar wind turbulence

takes the form of a Kolmogorov 5/3 power-law

below a certain frequency

We take this power

spectra and directly enter its properties into the code

for a background density with multiple fluctuations.


May, 20108

Change the density fluctuations to a power density

spectra more realistic to the solar wind.

The constant C is normalised to the value of

<δn(x)> near the Earth

(Celnikier et al 1987)


∑=

+=N

n

nnn xCxnxn1

2/ )/2sin()()( φλπλδ β

∑=

=N

i

nxn

xnC

1

2

2

)(

)(2

βλ

δ


May, 20109

Density fluctuations close to the Sun are able to be less

prolific than density fluctuations close to the Earth.


0>ψ

2

2

2

2

2

2

1

2

1

)(

)(

)(

)1(

)(

)(

xn

xn

xn

AUn

xn

xn δδψ

=


May, 201010


SUNSUN



May, 201011


SUNSUN

SUNSUN


May, 201012

Fluence and Peak Flux

spectra at

1.2AU

Fluence

Peak Flux

Larger powers of

density fluctuations cause

the spectral index below the break

energy to be

higher



May, 201013


Largerintensities of

turbulencecause the

electron beam to relax less at

low energies

resulting in a increased

spectral indexbelow the break

energy.


May, 201014


Krucker et al 09

Observational Data Fit

Error bars

are larger for smaller

values of ψ


May, 201015

Conclusion

� The structure of the background plasma affects the

spatial build up of plasma waves induced by the

electron beam.

� Multiple small scale fluctuations are able to

reproduce the burst nature of plasma waves

observed in-situ

� Different levels of turbulence will cause more or less

relaxation of the electron beam due to the

production of plasma waves.

simulations of langmuir wave generationin the inhomogeneous plasma

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