Kinetic Effects in the Magnetosphere

Richard E Denton

Dartmouth College

What Do We Mean by Kinetic Effects?

• Related to kinetic theory, but more general• Kinetic theory is a description of a plasma using a phase

space distribution• In a phase space distribution, there is assumed to be a

smooth distribution of particles with respect to spatial position and velocity

Examples of Kinetic Effects

• Hall reconnection• Meandering orbits in reconnection• Particle drifts around the earth separating ions from

electrons• Drift shell splitting• Cusp bifurcation of trapped populations• Curvature scattering• Drift resonant acceleration of particles from fast mode

fronts

Hall Reconnection [Birn et al., JGR, 2001]

Invariants

0 constantp E

202 constantcs p B

t

/

bounce

1constant// // //p ds Lp

t

drift

1constant

t

B dA

0 and constant at mirror pointcsE Bt

Adiabatic Particle Drifts

[from Emilia Kilpuna from ?]

Meandering Orbits of Unmagnetized Electrons Can Support the Out of Plane Reconnection

Electric Field

[Hesse, Space Sci. Rev., 2011]

Separation of Particle Populations

[Thorne, GRL, 2010]

So What Do I Mean by Kinetic Effects?

• In the broadest sense, effects that cannot be described by single fluid MHD

• In a more narrow sense, effects that cannot be described by fluid equations

• In the most narrow sense, effects that occur because of a distribution of particles in velocity space

WAVES

Wave phenomenon strongly depend on kinetic effects and have a large influence on important particle distributions

Classification of Waves

• Waves are categorized by frequency or the process that generated them

• Ultra Low Frequency (ULF) have a frequency range of roughly 1 mHz to about 3 Hz (magnetospheric definition)

• The Pc (pulsation continuous) classes are– Pc 5, 1-7 mHz– Pc 4, 7-22 mHz– Pc 3, 22-100 mHz– Pc 2, 0.1-0.2 Hz– Pc 1, 0.2-5 Hz

• ELF about 3 Hz to 3 kHz (magnetospheric definition)• VLF 3 to 30 kHz

ULF Waves

• Mostly MHD waves (not Pc 1) - aspects of these waves can be described by MHD equations

• Ion scale – the ions are able to oscillate at these frequencies (electron stick with the ions to maintain quasi-neutrality)

• Pc 4-5 – often associated with fundamental or 2nd harmonic of the Alfven wave eigenmode along field lines– may be externally driven by fast mode waves related to oscillations of

the magnetopause or internally driven by the particle population

• Pc 2-4 – often associated with higher harmonics of the Alfven wave eigenmodes driven by external waves

• Pc 1-2 – often associated with electromagnetic ion cyclotron waves (EMIC) driven by the ion velocity distribution (much of the talk will focus on these)– Frequency near the proton gyrofrequency

VLF Waves

• 3 to 30 kHz • High frequency waves are associated with electrons –

only the electrons are able to oscillate at these frequencies

• Includes plasma waves (Langmuir oscillations) and whistler chorus waves

ELF Waves

• 3 Hz to 3 kHz • Range in between proton gyrofrequency and electron

gyrofrequency• Includes waves at harmonics of the proton

gyrofrequency, at the lower hybrid frequency, and in a broad range of whistler waves

• Includes whistler “hiss” waves

KINETIC DRIVING OF WAVES

Waves grow due to an instability resulting from inhomogeneity. Some waves, such as the lower hybrid drift wave and the drift Alfven ballooning mode (Pc 4-5), can be driven by spatial inhomogeneity. Here we consider velocity space instabilities.

Types of Velocity Space Instabilities

• Two stream velocity distribution, or beam velocity distribution, or bump on tail velocity distribution

• Temperature anisotropy

DISPERSION SURFACES

Fluid theory describes wave dispersion surfaces, but kinetic calculations show that these surfaces can be altered by the finite temperature of the plasma

Electromagnetic Ion Cyclotron Waves in H+, e- Plasma

[See Andre, Dispersion Surfaces,

1985]

H+, He+, e- Plasma

H+, He+, O+, e- Plasma

Group Velocity

Kinetic Effects Alter the He Dispersion Surface

ehkim@pppl.gov

[Denton et al., JGR, 2014]

Kinetic Effect on Ion Bernstein Dispersion Surface

[Denton et al., JGR, 2010]

jWhamp available from me (redenton@dartmouth.edu)

jWhamp Output

And output files with detailed field

and particle species

information

SIMULATIONS ELECTROMAGNETIC ION CYCLOTRON WAVES (EMIC)

Fluid theory and kinetic dispersion codes can give valuable information about waves, but ultimately observed waves result from nonlinear growth, which is usually best modeled by simulations

General Wave Properties

• Electromagnetic (dB as well as dE)• < cp

• Driven by properties of the ion (normally proton) velocity distribution function, temperature anisotropy T > T// or possibly a loss cone distribution function

• Waves driven near magnetic equator where h// is large

• Resonance particles see Doppler shifted wave frequency that matches the proton gyrofrequency

• For parallel propagation (kB 0), the waves are left hand polarized, but they become linearly polarized at large kB

• Heavy ions make a difference since they alter the wave dispersion surfaces

Causes of EMIC Waves

Waves driven by compressions (ephemeral waves) or by replenishment of anisotropic ring current H+ (driven waves)

Drift shell

splitting

Stagna-tion

Pdyn

Hybrid Code Description

• Self-consistent hybrid code simulation of electromagnetic ion cyclotron waves

• Full dynamics particle ions and/or electrons, inertialess fluid electrons to bring about charge neutrality

• Dipole coordinates• Can have reflecting conductor boundary conditions, but

here we are damping waves at the boundaries• Initialize particle distribution from anisotropic MHD

equilibrium• Waves driven by hot protons with T/T// 2 near the

magnetic equator• Hot protons, cold H+, cold He+, and cold O+• Some runs include a plasmapause for cold species

Hybrid Code Description – New Features

• Now making full scale runs at geostationary orbit with realistic parameters

• Can make particles relativistic– Evolve u = v = p/m0 rather than v

– 2 = 1 + u2/c2

– du/dt = FLorentz/m0

– dx/dt = u/ • Can remove precipitating particles

– Mark time of precipitating particles (and stop evolving) if sin2 = u

2/u2 < Bb/( L0

3*sqrt( 4 – 3/L ) ) when particles cross the ionospheric boundary (otherwise reflect them)

• Simple 1D Matlab hybrid code available (not this one) – email redenton@dartmouth.edu

Normalized Equations

Geometry

Ah sqrt(h//) From Anisotropic MHD Code

Finding equilibrium

Evolution of EMIC Wave Fields

Evolution of kB

Spectra

Observed in plume

(data courtesy Brian Fraser)

Simulation in plasmasphere (different time and location)

2D Ellipticity-Power Color Map

Wave Power on Curvilinear Grid at Different Times(14% He+, 0.5% O+)

Wave Power Development and Poynting Vector

Effect of O+ Concentration on Wave Development

O+ Heating

Effect of Gradients – Coherence Length

[Hu and Denton, 2009]

q

Effect of Plasmapause

Heavy Ion Composition

[Craven et al., JGR, 1997] [Denton et al., JGR, 2011]

L Profiles of Plasma Parameters From Vania’s Jordanova’s Simulation of 9 June 2001 EMIC Event

Cold Compo-

sition Constant

Cold Compo-sition

Variable

Simulations with low O+ and large O+ in trough

Frequencies

WHAMP

Simulation

Effect of Waves on Ring Current H+

Run with Realistic Parameters and Full Scale Size

Pitch Angle Distribution Functions

2sin 2 ,vn d dvv f v Now integrate over v, and define normalized

pitch angle distribution function

/2

0

1 | | sin | | | |d f

1.52 2

1

cos sin /T T

fR R

for bi-Maxwellian with RT = T/T//

Pitch Angle Distribution Functions for Run

t=0, q<0.2

t=2000, q<0.2

t=2000, precipitated

Precipitation of Ring Current H+

Precipitation (loss) to Ionosphere of Radiation Belt Electrons

Wave Power

Fields

Wave Proper-

ties

Probability of Precipi-tation in

1 s

Probability Versus Pitch Angle and Energy

Diffusion Coefficients

Conclusions

• Kinetic effects usually refer to effects arising from a distribution of particle velocities. In the broadest sense, a multifluid description could be considered to be kinetic.

• Kinetic effects give rise to different evolution for different particle populations, either differences due to a difference in species (westward versus eastward drift), or differences due to different velocities (drift shell splitting)

• Kinetic effects influence processes such as magnetic reconnection

• Kinetic effects alter wave properties• Kinetic effects cause waves to grow and these waves affect

different parts of the velocity distribution differently