Nonlinear Evolution of Whistler Turbulence

W.A. Scales, J.J. Wang, and O. Chang

Center of Space Science and Engineering Research

Virginia Tech

L. Rudakov, G. Ganguli, and M. Mithaiwala

Plasma Physics Division

Naval Research Laboratory

Outline

• Introduction and Motivation• Simulation Model• Simulation Results• Summary, Conclusions and Future Work

Motivation

• Recent 2D simulation work has considered the evolution of whistler turbulence which indicates a cascade from long to short spatial scales (e.g Saito et al, 2008).

• Such simulations may be limited and not allow development of important nonlinear wave-wave processes that may ultimately impact wave-particle interaction processes for whistler waves.

Objective• Perform 2.5D fully electromagnetic PIC

simulations to study the evolution of whistler turbulence

• Access the role of nonlinear wave-wave processes

• Compare to predictions of previous simulation works on the turbulence cascade process

• Begin to access the impact on the generation of whistler turbulence

Important physics not resolved in past simulation work

• Past simulation work considered in the simulation plane

• For at an inclination to the simulation plane, it is predicted that whistler waves decay and coalescence to produce an inverse cascade (short to long wavelengths)

• The important new physics is represented through the term

0B

0B

0)( Bnk

Importance of 3D physics

• In the case Te = Ti the high frequency whistlers can radiate lower hybrid/magneto-sonic (LH/MS) waves.

• The decay rate, assuming a narrow frequency band is given by

• In 2D (the Saito et al. case), this rate is zero because

8//

)()(

)1(1~

20

1

2||2||1

22

21

2

212

1

21

22

2222

B

W

Mm

kk

kk

bkk

k

k

k

k keNL

1/,0)( 021 BBbbkk xx

Simulation Setup

• To consider an inverse cascade from high to low frequency, and initial perturbation is used to seed whistler turbulence

• The perturbation is taken to be heavy negative particles (“muon”) with a velocity ring in phase space.

• Once the whistler waves are generated, their nonlinear evolution is studied.

lhce

Simulation Domain

• The simulation domain ( X-Y ) is 51.2 and 25.6 electron inertial lengths.

• Two Cases:

where θ is the angle between Bo and X direction.

X

Y

Z

oB

config.) (Saito0θ al. et

oB

06θ

ion)configurat 2008 . (Saito0θ 1. al et06θ 2.

Magnetic Field Energy

config.) . (Saito0θ al et 06θ

• Whistler waves linearly grow from the free energy in the perturbation in both configurations

• The nonlinear evolution is quite different

06θ config.) . (Saito0θ al et

Frequency Power Spectrum

0<Ωcet<200

0<Ωcet<650

mother whistler wave

mother/daughter whistler waves

whistler waves

whistler waves

LH/MS waves

• For the case with inclination, whistler waves decay into lower hybrid/magnetosonic

waves as predicted by weak turbulence theory.• Without inclination, this decay is not apparent.

Wavenumber Power Spectrum

config.) . (Saito0θ al et 06θ

(Ωcet=150)

whistler waves

whistler waves

(Ωcet=300)

Wave Number Power Spectrum

config.) . (Saito0θ al et06θ

06θ

whistler mother

whistler daughter

LH/MSdaughter

whistler waves

• Decay of the whistler waves is evident with inclined B0.

Wave Number Power Spectrum

config.) alet (Saito0θ

(Ωcet=450)

config.) . (Saito0θ al et 06θ

LH/MS daughter

whistler waves

• At later times, the LH/MS waves become more prominent in the spectrum.

Ion Distribution Function and Energy History

config.) (Saito0θ al. et 06θ Ωcet=450

• Ion heating is relatively small• However, at 60o the heating appears to be preferentially perpendicular to B0

Electron Distribution Function and Energy History

config.) . (Saito0θ al et 06θ Ωcet=450

• Electron tail heating is preferentially

parallel to B0 and increased at 600.• Electron heating is more

significant that ion heating

Summary• Nonlinear scattering of whistler waves by radiating low

frequency LH/MS waves is observed in numerical simulations, as predicted by weak turbulence theory.

• The simulation results indicate that 3D physics of whistler evolution is important for nonlinear wave scattering.

• Such behavior is not observed in recent simulation work which does not consider 3D effects.

• Further investigations are being undertaken to access the impact of such wave scattering processes on whister turbulence.