waves and instabilities waves and instabilities in space plasmas tutorial presented at the summer...

WAVES AND INSTABILITIES WAVES AND INSTABILITIES IN SPACE PLASMASIN SPACE PLASMAS

TUTORIAL PRESENTED AT THETUTORIAL PRESENTED AT THESUMMER SCHOOL ONSUMMER SCHOOL ON

BASIC PROCESSES OF TURBULENT PLASMASBASIC PROCESSES OF TURBULENT PLASMAS

SEPTEMBER 23, 2003SEPTEMBER 23, 2003HALKIDIKIHALKIDIKI

GREECEGREECE

Dennis PapadopoulosDennis PapadopoulosUniversity of MarylandUniversity of Maryland

USAUSA

ACKNOWLEDGMENT

• USED DATA FROM THE FOLLOWING SOURCES– UCLA, R. STENZEL : LABORATORY WHISTLER

EXPERIMENTS

– UNIVERSITY OF IOWA, D. GARNETT : SATELLITE VLF MEASUREMENTS

– STANFORD UNIVERSITY, R. HELLIWELL AND U. INAN: TRIGGERED EMISSIONS AND HAARP-CLUSTER EXPERIMENTS

– ADVANCED POWER TECHNOLOGIES INC. : HAARP ELF/VLF EXPERIMENTS

Waves in Space Plasmas Waves in Space Plasmas Physics or Botany?Physics or Botany?

WAVES ARE A UBIQUITOUS FEATURE OF SPACE PLASMAS

BASICS- THEEARTH’s MAGNETICFIELD

Plasma ModelPlasma Model

Particle dynamics

with em fields

Internal Internal ResponseResponseFunctionsFunctions

J(E,B)

Field EquationsField Equations

Maxwell’sMaxwell’sEquationsEquations

withwithand Jand J

JJ

E,B E,Bself-consistent link

Linearized E-dynamics of Homogeneous PlasmasLinearized E-dynamics of Homogeneous Plasmas

),(),(),( ttrrEtrtdrdtrJt

Fluid,Fluid,

Particle,..Particle,..E-static,E-static,

quasi-static,..quasi-static,..

Electron Plasma OscillationsElectron Plasma Oscillations

Cold Electron Plasma

m(dv/dt)=-eE, J=-nevm(dv/dt)=-eE, J=-nev dJ/dt =dJ/dt = ee22EE

ee22=ne=ne22//mm

Es Field EqusEs Field Equs

t

E

JB ooo 0 Bforfort

EJ o

dd22E/dtE/dt22 + +ee22E=0 E=0 Harmonic OscillatorHarmonic Oscillator

Equivalent to LC circuits or pendulum Equivalent to LC circuits or pendulum

Non propagating modeNon propagating mode

OBSERVATIONSOBSERVATIONSFrequency-Time SpectrogramFrequency-Time Spectrogram

Voice print or Sonogram (use transducer to convert elVoice print or Sonogram (use transducer to convert el energy to sound energy) of crossing the bow shock of Jupiterenergy to sound energy) of crossing the bow shock of Jupiter

ES WAVES – DISPERSION RELATIONES WAVES – DISPERSION RELATION

Add thermal motion of electrons (pressure),

0EEE 2

e 22

2

2

eVt

Epo’s becomes wavesEpo’s becomes waves

0222

2

Vt

Standard Wave Eqs VE,c

P, cs

Pme

t eo

)(2EJ E222 )( e

oe mVenmVP

Generalized Ohm’s law neglecting ions )EEJ 222(

eeo Vt

t

E

J o

Plane Waves – Phase and Group VelocityPlane Waves – Phase and Group Velocity

Assume E~ Exp(-it+ikx)~Exp[i(x,t)]; (x,t)=constant ; d(x,t)=0Phase velocity Vp=dx/dt=/k, not a real velocity can be >c

ckVg Velocity of Energy or Info transfer-wavepacket

Wave equs kk22cc22 -> V -> Vpp=V=Vgg=c, non-dispersive propagation=c, non-dispersive propagation

Epo’s -> e2 , Vp= anything, Vp=0

Plasma waves -> e2 +(3/2)k2Ve

2

Vp2=(3/2)Ve

2+ e2/k2> Ve

2 and Vg=(3/2)(Ve/Vp)Ve<Ve

Cold plasma approximation: D=Ve/21/2e if k D<<1 orVe so low that particles move less than one wavelength in e

-1

Em Waves in Isotropic PlasmasEm Waves in Isotropic Plasmas

EtJ

tJ

-EE 1-

o

2

222

2

e

ct

0EEE

222

2

2

ect

2222eck

cV

cV

ck

cV

pg

eP

2

22

222

),(1)/(2

222

kkc e

e cut-off , reflectionVp-> infinity, Vg->0 pile up

e wave evanescent, skin depth c/ e

Ionospheric ReflectionIonospheric Reflection

TYPE II AND III SOLAR RADIOBURSTSTYPE II AND III SOLAR RADIOBURSTS

Dispersion DiagramsDispersion Diagrams

e

k

VVgg

VVpp

Wave Energy-Poynting FluxWave Energy-Poynting Flux

)]([2

1)1(

2

1)(

2

1

2

1 22

2222

EEm

eEnmEW o

eooL

WVS g

)]()[(2

1 22

kc

EW oT

Negative Energy waves

Dielectric constant for drifting plasmas

kkV

k

bP

b

b

b

V

kV 2)(1),(

2

Fast and slow wave. For slow wave<W><0, negative. Meaning?

Beam+wave less average energy than beamQuiver reduces Vb

Radiation Patterns from Antenae

Introduction of AnisotropyB Finite

Modulated Beams as AntenaeModulated Beams as Antenae

Kinetic Effects - Cerenkov EmissionKinetic Effects - Cerenkov Emission

arccos(Varccos(VPP/v)/v)

Cerenkov condition -kv=0

Es but no em emission for B=0Es but no em emission for B=0

kv)vv

e

e fdk

m

t

kE

()(2

)(2

4

Spontaneous emission

Landau DampingLandau DampingStimulated Emission and Stimulated Emission and

vttx

tkxtiExpm

eE

dt

dv

)(

)]([ ])([ tkvidtExp

m

eEv

kv Doppler shifted frequencykv Doppler shifted frequency

For kv kv v=(eE/mv=(eE/mcoscost); for t); for kv kv v=eE/mkv …v=eE/mkv …

For kvkv=0 v=(eE/m)tv=(eE/m)t secular behavior, replace with 1/ (kv)+ikv)+i Landau perscription Landau perscription

Mechanical Examples of Landau DampingMechanical Examples of Landau Damping

Cyclotron damping

Cyclotron ResonanceCyclotron Resonance

)v()(,])(

[2

12

3

fdvuFu

uF

kt

E

E Tku

e

Landau Damping - GrowthLandau Damping - Growth

ku

e

u

uF

kt

E

E

])(

[2

12

3

Absorption

Stimulated Emission-Instability

Sources of Plasma WavesSources of Plasma Waves

Thermal Equilibrium expect ½ kT/ per modeBalance Cer. Emission to Landau damping to findWk=(1/2 kT) [1/1+(kD)2]Strongly damped modesweakly excited.

33)2/(

Dk n

nkTWdW

k

3Dn >>1 definition of

plasma. Low levelbroadband noise

Sources of Plasma Waves (cont)Sources of Plasma Waves (cont)

Super-thermal tailsf=fo(v)+fh(v), <<1

Wk~fh(Vp)/f’(Vp) )]1(ln[

2

2

e

h

e

h

TE

VV

VV

WW

Effective TEffective TVVhh22. Large enhancement.. Large enhancement.

Broadband , isotropic ? Depends.Broadband , isotropic ? Depends.

Beam-plasma or Bump-on-tail instabilitye.g beam created by electrons Streaming away from shock+velocity dispersion

What is a Plasma Instability?What is a Plasma Instability?

otttortttyInstabilitExplosive

ttUnstablet

gbVt

/1~)(_,,)(lim_

,)(lim

0

222

2

ndissipationegativeeigifunstablegand

ifunstableitiExpt

gt

eo

oo

e

__._0___2/,,

0__,),(

22

2

Positive energy wave coupled to negative dissipation Positive energy wave coupled to negative dissipation unstableunstableResistive or kinetic instabilityResistive or kinetic instability

Reactive Instability – Beam PlasmaReactive Instability – Beam Plasma

Look at e2iFor iplasma reactive, like inductance.

For iplasma behaves like a resistor or conductor. Dielectric constant imaginary -ie

2Reactive plasma with drift supports negative energy waves

kkV

k

bP

b

b

b

V

kV 2)(1),(

2

ticmonochromanarrowbandnnnn

k

obeeobe

be

,;)/(/,)/(,

0(

1),(

3/13/1

2

2

2

2)bkV

Phase Space B-P Interaction

Run Movie-Event simulation concept – Karimabadi (UCSD)Run Movie-Event simulation concept – Karimabadi (UCSD)

Phase Space Bunching

Reactive instabilities aredriven by bunching of particles by the growingwave. The bunches drivethe field that amplifiesthe wave.Bunching can be due to thees force or due to theLorentz force (gyrotron andWeibel)

ump-in-tail Instabilityump-in-tail Instability

Negative damping interacts with positive energy waveNegative damping interacts with positive energy wave

oo

be

i

i

_

012

2

2

2

obe

beo

be

nn

ii

o

/)(_

0)21(1

2

2

2

2

2

2

Quasi-linear TheoryQuasi-linear Theory

Physics analogy with other instability systems- ion beam, LH, etcPhysics analogy with other instability systems- ion beam, LH, etc

How to generate em waves in an isotropic plasmaHow to generate em waves in an isotropic plasmaand why at multiples of the plasma frequencyand why at multiples of the plasma frequency

Conventional Conversion ProcessesConventional Conversion ProcessesWeak Turbulence or Else?Weak Turbulence or Else?

kk33=k=k11+k+k22

o

JBc

t

B

22

2

2

ElseElse

How to driveHow to drivecurrent vorticitycurrent vorticityat at e e and harmonicsand harmonics

Ponderomotive ForcePonderomotive Force

Requires a spatially varying high frequency E-field, e.g electronplasma wave.

x

t

x

t

weakstrong

Poo

o

oo

oooo

o

Fvdx

dmE

dx

d

m

exm

tm

eEx

txdxdEexm

TimeinAverage

tdx

dExEexxmxxx

txeExm

222

2

21

1

111

~44

cos

cos)/(

/2___

cos)()(

cos)(

Low frequency force transmitted to ions through quasi-neutrality

Zakharov EquationsZakharov Equations

2

22

2

22

2

2

2

22

~

4

~)(

2

~

2

3~

x

E

x

nc

t

n

En

n

x

EV

t

Ei

os

o

e

e

e

Envelope equation – multi-time scale analysis

])()[,(~

),( cctiExptxEtxE e

Soliton Caviton PairsSoliton Caviton Pairs

Structures Generate Current VorticityStructures Generate Current Vorticity

Plasma Non-Thermal Heating

Ion Acoustic WavesIon Acoustic Waves

s

D

Di

kc

k

k

2

222

)(1

)(

Epos 6 kHzIon sound 1-2 kHz ?

Quasi-NeutralityQuasi-Neutrality

Supermassive black hole emission – 57 octaves below middle CSupermassive black hole emission – 57 octaves below middle C

Anisotropic PlasmasAnisotropic Plasmas

Ray VelocityPhase velocity in the directionof the group velocity

phase velocity anglephase velocity angle group velocity anglegroup velocity angledifferent than zerodifferent than zero

Refractive Index and Associated Surfaces

Phase velocity surfaceVp/c vs

Ray velSurfacevs

Polar diagramsPolar diagrams

Group velocity surface Vg/c vs

Refractive index surface vs

WaWave normal k makes an angle to the normal to the refractive indextan=-

Whistler RangeWhistler Range

WhistlersWhistlers

Saucer

V-shaped saucer signature – short duration key difference to hissV-shaped saucer signature – short duration key difference to hiss

Chorus

RH pol whistler – chirping birds or windRH pol whistler – chirping birds or wind

HissHiss

BroadbandBroadbandbeambeamdrivendrivenspin modulatedspin modulated

AKRAKR

WhistlersWhistlers

WhistlersWhistlers

22

2

2

)/(

)/(1

)/(

e

e

e

kc

kc

kc

Parallel whistlers (VParallel whistlers (Vp p parallel to Vg)parallel to Vg)

Oblique whistlers with parallel group velocityOblique whistlers with parallel group velocityResonance cone – quasi-es waves (VResonance cone – quasi-es waves (Vpp perp to V perp to Vgg))

Identify modes from VIdentify modes from Vpp and V and Vgg

Beam ExcitationBeam Excitation

Test wave along beamTest wave along beamOblique modes up to limiting phase velocity angleOblique modes up to limiting phase velocity angleOblique growth at resonance angleOblique growth at resonance angleDecay backwardsDecay backwards

Large AmplitudeLarge Amplitude

BASICS- THEEARTH’s MAGNETICFIELD

• Magnetic Configuration• L - Shells• Inner RB (1.5<L<2.2)• Slot (2.2<L<3)• Outer (L>3)• Invariant Latitude

RADIATION BELTS

• Inner Radiation Belt (1.5<L<2.2)

• Outer Radiation Belt (L>3)

• Slot (2.2<L<3)

• L = R/RE

• MEO and half-GEO (GPS location) especially challenging

• To minimize radiation dose, many commercial satellite orbits use the slot

>106

>105

104

L = 2 L = 3

L = 7

• Reduction in the Electron Flux desirable

FACTORS CONTROLLING ELECTRON FLUX• Energetic electron flux in the radiation belt: - Balance of sources, transport to lower L-shells, and losses

• Collisions and interaction with LF waves can scatter particles into the loss cone [Kennel and Petschek, 1966]

• Waves in the Radiation belt:

(1) Natural sources:- Plasmaspheric hiss (500-800 Hz)

- Lightning: Whistlers (4-6 kHz)

(2) Anthropogenic sources:- VLF transmitters: mostly Navy (17.1 kHz & 22.3 kHz )

B0

mv• Losses depend on particle pitch angle:

- Particles in the loss cone are precipitated

THEORETICAL DIRECTIONSTHEORETICAL DIRECTIONS

cos1

2

2

22

eck

2

22

e

ck

• RB – TWO CLASSES OF ELECTRON POPULATION• COLD – ( eV ; 102 – 5x103 #/cc); Supports Whistlers

• HOT – (tens of KeV to MeV) – Anisotropic Distribution – loss cone• Cyclotron Resonance with whistlers when

,...2,1,0 nnvk zz

zzvk particle and wave counter-streaming

• For resonance with electrons, wave frequency is Doppler shifted by motion along B.

• For propagation along B, whistler For propagation along B, whistler waves and electrons must waves and electrons must propagate in opposite directionspropagate in opposite directions

• Electric field rotates in same Electric field rotates in same sense as electronssense as electrons

• E field remains in phase with E field remains in phase with particleparticle

• Efficient exchange of energyEfficient exchange of energy

KENNEL-PETSCHEK

ppRp

h

eR

R

fppdpnniqck

])[)(/()()( 22

2

22

zz p

fppfpgrowth

anisotropy

growth~(nh/n)

• Resistive instability• RPA• Broadband spectrum• Qlinear theory OK no traping or phase bunching• Space integrated growth balanced by reflection• Marginal stability KP

WAVE-PARTICLE INTERACTION

/ezz nvk

• Particle lifetime given by

)/2ln()/)(/1( 2 eBB woe

• Increasing the wave amplitude by a factor of 3 reduces the lifetime by a factor of 10.

• v Bw force changes momentum direction, i.e., the pitch angle

B0

trapped

• Scattering energy independent (almost elastic)

with e

PARTICLE LIFETIMES

REQUIREMENTS TO INCREASE THE LOSS RATE BY A FACTOR OF 10

•FOR L BETWEEN 1.3 AND 2.6 AND 1-1.5 MeV ELECTRONS CYCLOTRON RESONANCE REQUIRES WAVES WITH FREQUENCY.5 TO 2 kHz.• TOTAL ENERGY STORED FOR THIS VOLUME BETWEEN 100-200 KJ ( LESS IF ONLY A FRACTION, SAY .1 L IS CLEARED.• WAVE CONFINEMENT TIME OF 2-3 SECS RESULTS IN INJECTED POWER REQUIREMENT OF 50-70 kW.

• CLEARLY TOO MUCH• ANY WAY OUT – TRIGGERED EMISSIONS AND AMPLIFICATION

• How many satellites are needed to reduce lifetime to ten days ?

• Too many (100s).

• Is there a way out ?

• Yes - Amplification

• The energy of the relativistic electrons can amplify the waves10 dB amplification reduces the# of satts to tens while 20 dBto few.Is there evidence for amplification ?

BRUTE FORCE SOLUTION – INJECT VLF FROM SATELITES

VLF Wave-Injection Experiments

Interaction Region

VLF Wave-injection from

Siple Station, AntarcticaHelliwell et al.

ASE FEATURESASE FEATURES

• SIGNALTHRESHOLD BEHAVIOR• POWER-PULSE LENGTH• NARROW BANDWIDTH

• TRIGGERED EMISSIONS• EXPONENTIAL GROWTH – 25-250 dB/sec• SATURATION – 20-35 dB• FREQUENCY LOCK (~100-200Hz)• BURSTY BEHAVIOR-Oscillator ?• FREE ENERGY

• FREQUENCY BEHAVIOR• LOCK FOLLOWED BY RISE OR FALL• PREDOMINANCE OF RISERS FOR LONG PULSES AND FALLERS FOR SHORT

PHYSICS OF THE AMPLIFICATION

• DETAILS STILL CONTROVERSIAL BUT GENERAL PICTURE ACCEPTED (SEE REVIEW BY MATSUMOTO 1979)• FREE ENERGY SOURCE-> LOSS CONE DISTRIBUTION

V||

V

• WHEN LOSS CONE FILLS WE HAVE MAXIMUM LOSSRATE

THE HELLIWELL HYPOTHESIS

• Introduce complex gain function G=Bs/B, group delay Tg, and transit time Te to get feedback loop. For G>1 get oscillator withexponential growth. For G<1 get amplifier with gain dependenton the propagation loss.

• KEY ISSUE COMPUTE THE GAIN.

sinww BvBv

=0

=

Helliwell and Crystal 1973

• Non linearity related to phase bunching of the electrons traversing the field of the injected wave

B Bw ( ˆ x cos ko z ˆ y sin ko z)[exp( /2o )]

that acts as a wiggler – like an FELwiggler- to phase bunch the electrons

The bunched electrons act as anon-linear resonant current to inducethe triggered emissions as a Cerenkovor sideband instability (Sudan)

• The interaction strength is controlled by the trapping frequency given by

t (ew )1/ 2

• The injected wave was guided by a density cavity

COHERENT INTERACTION

)]()()[2/1( 00 pppppf zz

]

2)([(])([))(/1()( 2

222200

02222

ckkV

nnck Zh

e

00 / zkV

For e->0 gives the dispersion relation of the gyrotron and toBakcward Wave Oscillator (BWO)

Fourth order equ in k. A pair of beam modes in addition to usual Weibel term. Reactive instabilities.

)(

2))(/()()/]()/[( 222

2

0000

200

222 ckkVkVnnkVck zz

hze

Can we Experiment by Injecting Waves Without Large Ground Antennas?Frequency Downshift

HF

IONOSPHERE

• HF-PLASMA CURRENT DRIVE - USE ABSORPTION OF MODULATED HF POWER IN THE IONOSPHERE TO DRIVE AC CURRENTS AT ULF/ELF FREQUENCIES

~

• BEST RESULTS HAVE BEEN IN MODULATING PREEXISTING IONOSPHERIC CURRENTS - ELECTROJETS - AURORAL AND EQUATORIAL

HMD E

H

Electrojets driven by Solar Wind

• Solar Wind varies with solar activity (Space Weather)

• Increased Solar activity results in increased intensity and spreading of electrojets (Geomagnetic Storms)

Auroral Currents

Aurora Borealis

Negative terminal

Positive terminal

Auroral Oval

Earth

Primary Currents

Primary Currents

Evening side

Morning side

Magnetosphere and the earth from above Primary and secondary electrical discharge currents across the polar cap

Evening side

Morning side

Day side

Night side

Primary current

Secondary current

Primary current

Secondary current

Auroral Oval

Rotate or move

horizontallyN

S

Conventional Generator

Solar Wind

Solar wind and earth's magnetic field create a natural generator

Function of Ionospheric Heaters

• Ionospheric Heaters are RF Transmitters with a mostly vertical beam that deposit energy into the ionospheric electrons at altitudes of 70-95 km and 200-300 km

• HAARP - Phased Array f = 3-10 MHz ERP .86-98 dBW Highly Flexible Operation

• Present Heaters f = 3-6 MHz ERP 70-85 dBW Operation Not Flexible

Ground

f1 < f2 < f3

f3f2

f1

Principle of ELF Generation

Dawn Dusk

Heater

Pulsed Heating

t =

t = 0

t = 2

J

E E

Ek

B

Use an ionosphpheric heater to inject VLFUse an ionosphpheric heater to inject VLF

HIPAS

HAARP – THE WIND TUNNEL

HAARP-CLUSTER EXPERIMENTSSTANFORD UNIVERSITY

POWER SPECTRA INSIDE MINE

ADVANCED POWER TECHNOLOGIES, INC. 100

101

102

103

104

10-6

10-5

10-4

10-3

10-2

10-1

100

Frequency (Hz)

Pow

er S

pect

ral D

ensi

ty (

pT2 /H

z)

100 Hz

200 Hz 500 Hz

1 kHz

2 kHz

5 kHz

SCALING WITH FREQUENCYM

agn

etic

Mom

ent

Frequency

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 1 2 3 4 5 6 7 8 91000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 700

100

200

300

400

500

600

700

800

900

1000

0 10 20 30 40 50 60 701000

1500

2000

2500

3000

3500

4000

4500

5000

10-100 Hz , 80 secFrequency sweeps

PHYSICS PROPERTIES

),(),(

),(),;,(),(

tzAtzB

tzJtztzGtdzdtzAt

�

zcc

zt

zc

zttzB

zz

c

zztzJ

zz

zdtzA

phph

ph

)()(~),(

),(~),(

',

2

,

,

z

z’

PRE-CAMPAIGN RESULTSRESOLVED WAVEFORMS

DOMINANCE OF IMPULSE RESPONSE

GREEN’S FUNCTION OFTHE IONOSPHERE

ECHOES - .5 msec

CODE VALIDATION

SIGNAL WITH ECHO

RESOLVED WAVEFORMS

0.05 0.1 0.15 0.2 0.25 0.3

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

Time(mS)

field

(pT

)

March 4, Modulated Signal (f=10000 Hz) Trailer, ns 5:32:00

0.2 0.3 0.4 0.5 0.6 0.7

-3

-2.5

-2

-1.5

-1

-0.5

0

Time(mS)

field

(pT

)


0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time(mS)

field

(pT

)


0.5 1 1.5

-2.5

-2

-1.5

-1

-0.5

0

Time(mS)

field

(pT

)


0.6 0.8 1 1.2 1.4 1.6 1.8

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

Time(mS)

field

(pT

)


0.5 1 1.5 2 2.5

-3

-2.5

-2

-1.5

-1

-0.5

Time(mS)

field

(pT

)


RESOLVED WAVEFORMS

1 1.5 2 2.5 3 3.5

-2.6

-2.4

-2.2

-2

-1.8

-1.6

-1.4

-1.2

-1

Time(mS)

field

(pT

)


0.5 1 1.5 2 2.5 3 3.5 4 4.5

-2.5

-2

-1.5

-1

-0.5

Time(mS)

field

(pT

)


1 2 3 4 5 6 7-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Time(mS)

field

(pT

)

Modulated Signal (f=500 Hz) Trailer, ns 5

2 4 6 8 10 12 14

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Time(mS)

field

(pT

)


18 20 22 24 26 28 30 32 34 36

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time(mS)

field

(pT

)


0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time(mS)

field

(pT

)


COHERENT SWEEPING CONCEPT

• GIVEN THE LIMITATIONS OF THE SHORT RESPONSETIME ( ~ 100 MICROSECS) OF THE IONOSPHERE CAN WE INCREASE THE LOW FREQUENCY EFFICIENCY BY SYNTHESIZING SHORT TIME PULSES ?

• COHERENT SWEEPING

ELF

HF

MODIFIED SPOT

COHERENT SWEEPING - DELTA

0 500 1000 1500-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

time (S)

field

(pT

)

Pulse Scan, Mar-13-01, mine-ns-0700ut

NONLINEAR MAGNETIC DIPOLE

Potential source for triggered oscillator

• Laboratory experiments have shown that whistlers “duct”; i.e., focus in low-density channels [Stenzel, 1976].

• A high intensity whistler can create its own duct: - ponderomotive force expels plasma from propagation path (similar to laser self-focussing)

• Excitation at very high near field can be achieved with a magnet rotating at the wave frequency

• Initial simulation of this excitation processdensity

DUCTING AND FILAMENTATION

STENZEL

RADIATION FROM A ROTATING MAGNET

In Vacuum – like a neutron star- Magnetic moment MP~(d2Mperp/dt2)2~4 M sinFor low frequencies very inefficient

In a plasma the large near field (>1-10 T) induces large electroncurrents – differential motion between ions and electrons.If currents match radiation pattern of normal mode I can getexcellent coupling as well as create density cavities that trap the wave

Bx(z,t)=(M/4πz3) cost , Bz(z,t)=(2 M/4πz3) sint

By(z,t)= (M/4πz3) cos(t+π/2) , Bz(z,t)= (2 M/4πz3) sin(t+π/2)

Dipole in x-z plane rotating about y-axis

Dipole in y-z plane rotating about x-axis

B0

Axial distance

Radiation Pattern

B0

driver

PRELIMINARY 2D SIMULATIONS

pnqt

nm

BvEvv

0v

nt

n

Plasma

0

Ect

B

BcJt

E

4

Fields

),(0 trBBB

Initialization

B = 10 T at 25 kHz, c/pe= 0.1 km

• Simulation studies EM coupling (self-focussing not included in this simulation)

GANGULY AND LAMPE

STATIC MAGNETIC WIGGLERSAn unpowered excitation source

/ezz nvk

• Since ethe resonance condition simplifies to

• No power input necessary!

• An array of stationary magnets serves as a “wave”

• As effective in exciting amplification as a true whistler (similar to use of a static wiggler in a FEL)

B0

v

• Resonance condition for wave amplification

/ezz nvk

waves and instabilities waves and instabilities in space plasmas tutorial presented at the summer...

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