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VLF chorus emissions observed by CLUSTER satellites inside the generation region: comparison with the backward wave oscillator model. - PowerPoint PPT Presentation
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E. E. Titova, B. V. Kozelov Polar Geophysical Institute, Apatity, Russia V.Y.Trakhtengerts, A. G. Demekhov Institute of Applied Physics, Nizhny Novgorod, Russia O. Santolik, E. Macusova Charles University, Prague, Czech Republic and IAP/CAS, Prague, Czech Republic D. A. Gurnett, J. S. Pickett University of Iowa, Iowa City, IA, USA VLF chorus emissions observed by CLUSTER satellites inside the generation region: comparison with the backward wave oscillator model
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Page 1: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

E. E. Titova, B. V. Kozelov Polar Geophysical Institute, Apatity, Russia

V.Y.Trakhtengerts, A. G. DemekhovInstitute of Applied Physics, Nizhny Novgorod, Russia

O. Santolik, E. Macusova Charles University, Prague, Czech Republic and IAP/CAS, Prague, Czech Republic

D. A. Gurnett, J. S. Pickett University of Iowa, Iowa City, IA, USA

VLF chorus emissions observedby CLUSTER satellites inside the generation region:

comparison with the backward wave oscillator model

Page 2: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Magnetospheric backward wave oscillator (BWO) modelof VLF chorus generation: predictions and comparison with data

Content Magnetospheric BWO: property of the source region of magnetospheric chorus

• Field aligned scale of the source region• Variations of chorus source location • Influence of length of the BWO on chorus characteristics

Magnetospheric BWO: parameters of chorus elements

• Growth rate for BWO regime• Frequency drift• Saturation amplitude

Conclusions

V. Y. Trakhtengerts, 1995, 1999

Page 3: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

According to Trakhtengerts (1995), the interaction length l of whistler waves and energetic electrons can be written for the dipole magnetic field as follows:

lBWO = (R02L2/k)1/3

where R0 is the Earth's radius, L is the geomagnetic shell,

and k is the whistler wave number.

The backwardwave oscillator (BWO) regime of the whistler cyclotron instability takes place in a narrow near equatorial region:

lBWO ~ 103 km

LeDocq et al., 1998; Parrot et al., 2003; Santolik et al. 2003, 2005

Field aligned scale of chorus source region

Page 4: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Size and central position of the source region from multipoint measurement of the Poynting flux by the Cluster satellites Santolik et al. 2003, 2005

Poynting flux measurements show • the size of the source region is a few thousands of km along the filed line • strong variations of the central position of the chorus source region

Page 5: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Dynamical magnetic field model Deviation of the observed magnetic field from value modeled by Tsyganenko-96 model:

96Tsyobserved BBB

For two currents and two positions of CLUSTER satellites:

2

22,12

22,1222

12,11

12,11102,1

)(

)]([

)(

)]([

2 rpi

rpi

rpi

rpiB

II

p1,2 are known positions of two CLUSTER satellites, I1 and I2 are two line currents, i1 and i2 are unit vectors of their directions, r1 and r2 are points at the line currents

The main characteristics of the magnetospheric BWO: effective length along the magnetic filed line (LBWO) position at the magnetic filed line (position of Bmin)

Kozelov, Demekhov, Titova, Trakhtengerts et al., 2008

Page 6: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

The experimentally derived BWO length LBWO is then obtained as finding the distance between such points z1 and z2 that

Estimation of effective BWO length

))(1()( zbz HLH

||||)( vkzH

2

1

2

1

)(),(||||

21

z

z

HLz

z

dzzbvv

dzzz

12 zzLBWO

Introduce the relative magnetic-field perturbation b(z):

The cyclotron resonance frequency mismatch is

The cyclotron resonance phase mismatch is obtained using the known magnetic-field profile as

)()(and, 21 zbzb

Page 7: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Results of modeling of the magnetospheric BWO configurations on 31 March 2001 for a magnetic field line at the CLUSTER-1 position.

• thin line (not seen) is the observed strength of the magnetic field, dashed line - calculated by Tsy-96, solid line - fitted by a model with 2 additional currents.

• the modeled magnetic field along the magnetic field line.

• symbols mark the calculated positions of the magnetic field minimum, solid and dashed lines show, respectively, the smoothed evolution of this position and the CLUSTER orbit.

• evolution of the estimated length of the magnetospheric BWO.

Kozelov, Demekhov, Titova, Trakhtengerts et al., 2008

Page 8: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Comparison of the minimum B location obtained from local magnetic field modeling with the center of the chorus source obtained from the

VLF STAFF data

• Solid line and symbols – position of the BWO center (minimum-B point) estimated from the dynamical model of the local magnetic field; red dashed line – position of the VLF source from [Santolik et al., 2005]; long dashed lines – satellite trajectories.

• Parallel component of the Poynting vector normalized by its standard deviation for CLUSTER-1 [Santolik et al., 2005].

The obtained variation of the position of minimum B along the field line qualitatively agrees well with the variation of the chorus source location previously obtained from the STAFF data [Santolik et al., 2005].

Kozelov, Demekhov, Titova, Trakhtengerts et al., 2008

Page 9: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Results of simulations of nonlinear equations for the magnetospheric BWO [Demekhov and Trakhtengerts, 2005] with two magnetic field profiles corresponding to different time intervals of April 18, 2002.

the geomagnetic field dependences

total Poynting flux in arbitrary units as a function of time and z-coordinate. The center of the source region corresponds to Stot = 0.

The plots demonstrate that the center of the chorus source region in the simulations remains near the local minimum of the geomagnetic field.

Page 10: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

The estimated threshold flux (cm-2s-1sr-1) for the BWO generation in “on-off” intermittency regime.

The threshold electron flux Sthr for the BWO

generation (Trakhtengerts et al., 2004)

2

2res

2BWOstep

2res

2e

thr v

v

Lhe

vcmS

HLpe

3/2HLHL

||

HLrez

ω/ωω

ω/ω1cω=

k

ωω=v

A B C

36.4 17 5.6Average chorus power, mV m-1 min-1

197 141 44Average number of elements in minute

vres is the parallel velocity of the resonant electrons, for this event Ne= 5 cm-3 we assume for estimates that hstep ≈ 0.1 and v┴ ≈ vres,

Page 11: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Estimation of growth rate of the BWO regime of VLF chorus generation using frequency sweep rate of chorus elements

According of BWO model of chorus generation (Trakhtengerts, 1999) the frequency sweep rate df/dt at the exit from BWO generation region can be written as

df/dt = ( γ2BWO + S1 ) 1.5 ω /(ωH + 2ω)

where γ 2BWO the growth rate of the absolute (BWO) instability,

S1 = 0.3 V|| (d ωH/dz)

characterizes the magnetic field inhomogeneity effect.

We introduce the "reduced" frequency sweep rate G, which is equal the growth rate of the BWO regime for γ 2

BWO >> S1.

G 2 df/dt (ω H + 2 ω)/ 1.5 ω = γ2BWO

Page 12: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

G2 = 2 BWO = df/dt (H + 2)/ 1.5

The reduced sweep rate G2 as a function of L shell.

The solid line shows the running average over 100 points of G2.

The mean of the "reduced" frequency sweep rate G(L) varies within a small interval 100–300 s–1, that is in a good agreement with estimates of γ2

BWO from the BWO theory obtained from chorus elements on MAGION 5 satellite as a function of L shell.

The chorus growth rate, estimated from the frequency sweep rate, is in accord with that inferred from the BWO generation mechanism

The frequency sweep rate of VLF chorus emissions as inferred from Magion 5 satellite

Titova et al., 2003

Page 13: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

The growth rate of the absolute (BWO) instability γ2BWO

γ BWO / Ω tr ≈ 32/ (3π)

where the trapping frequency Ώ tr is determined by the expression

Ω tr = (k u ωH b)1/2

Here b = B~ /B L , B~ is the whistler wave magnetic field amplitude, BL is the geomagnetic field, and u is the electron velocity component across the geomagnetic field.

G2 = df/dt (ωH + 2ω)/ 1.5ω = γ 2 BWO ~ b

the BWO model predicts an increase in frequency sweep rate df/dt and G2 with chorus amplitude

B~ = (10 m c / e k u)*γ2BWO

The growth rate of the absolute (BWO) instability, the frequency sweep rates and the chorus amplitudes

Page 14: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

The frequency sweep rate of VLF chorus emissions on CLUSTER satellite

The frequency sweep rate increases with chorus amplitude, in accordance with the BWO model.

The reduced sweep rate G2 as a function of chorus amplitude for event CLUSTER 1, 18.04.2002

The reduced sweep rate G2 as a function of chorus amplitude for event CLUSTER 1, 31.03.2001

Page 15: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Summary of chorus parameters in the BWO model for Cluster data 18.04.2002

Basic parameters : L = 4. 4, cold plasma density Nc ~ 2 cm -2 , ω/ωH ≈ 0.45 , Wres = me/2 (ωH – ω)2/k2 = 62 keV, the wavelength 26 km.The flux density of energeticelectrons is assumed to be S ~ 4*108 cm2 s-1

The growth rate

γ BWO

Characteristic period of succession T > T0

Frequency drift df/dt

Wave amplitude B~

γ BWO = π2/4T0 T0 = lBWO (1/vg +1/vstep)

0.5 γ 2BWO (10mc / eku)*γ 2

BWO

102 s-1 > 0,025 s 0,7*104 Hz s-1 100 pT

34-420 s-1 0,02-0,05 s 1,5 104 Hz s-1 100-300 pT

Page 16: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

• We study the sweep rate of the emission frequency as a function of the cold plasma density in the equatorial plane and than we compare it with the prediction of BWO model.

• We investigate wave packets from detailed time-frequency spectrograms measured by the WBD instrument on board the Cluster spacecraft.

• The local electron densities during 15 processed time intervals were obtained from the WHISPER instrument.

Page 17: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

December 22, 2001

An example of chorus elements measured on board the Cluster satellites on December 22, 2001 by the wideband (WBD) plasma wave instrument. Spacecraft position is given on the bottom: UT-universal time; λm-magnetic dipole latitude; RE - Earth radius; MLT-magnetic local time.

[t1 , f1] [t2 , f2] f1 ‹ f2

(sweep rate)

Page 18: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

08.02.2005 (11:51-12:13 UT) The electron density was

about 11 cm−3 and the Kp index was 2-.

08.02.2001(ne-=9 cm-3) df/dt:10.61 kHz/s (N=236) and -9.64 kHz/s (N=156) 22.12.2001(ne-=10 cm-3) df/dt: no risers and -11.02 kHz/s (N=1036)06.12.2003(ne-=10 cm-3) df/dt: 9.36 kHz/s (N=5568) and no fallers

06.12.2003 (14:30 - 15:00 UT)

22.01.2002 (17:40-17:50 UT)

The Kp index was 30 and the electron density was about 10 cm−3

Page 19: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

08.02.2005 (11:51-12:13 UT) The electron density was

about 192 cm−3 and Kp index was 8−

12.4.2001 (ne-= 27 cm-3) df/dt: 5.97 kHz/s (N=351) and no fallers 25.03.2002 (ne-= 39 cm-3) df/dt: 3.91 kHz/s and no fallers 21.10.2001 (ne-= 192cm-3) df/dt: 1.69 kHz/s (N=972) and -3.11 kHz/s

25.03.2002 (13:56 - 14:20 UT)

21.10. 2001 (23:15 - 23:35 UT)

The Kp index was 20 and the electron density was about 39 cm−3

Page 20: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

The sweep-rate estimate on base of BWO model of Trakhtengerts et al., 2004 yields the following scaling:

df/dt =C * n -2/3

where n is the plasma density and C is a free parameter.

Page 21: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Conclusions

Within the framework of the BWO generation model, it is possible to explain the properties of the chorus emissions at frequencies below fH/2, observed by Cluster satellites, such as

– field aligned scale of the source region and the direction of the energy flux

– this motion of chorus source by deviation of the magnetic field minimum (the local “magnetic equator”)

– influence of effective length of the magnetospheric BWO on chorus characteristics

– chorus growth rate, estimated from the frequency sweep rate, is in accord with that inferred from the BWO generation mechanism.

– correlation between the frequency sweep rates and the chorus amplitudes.

– amplitude of chorus

– The theoretical scaling based on the BWO theory predict increasing sweep rate of chorus elements for decreasing cold plasma density as df/dt =C * n -2/3. The results observations on CLUSTER consistent with these predictions

Page 22: Content  Magnetospheric BWO: property of the source region of magnetospheric chorus

Some principal questions remain unclear

Relation between chorus and hiss emissions

Formation of a step-like distortion at the electron distribution function

Nonducted propagation

Damping of chorus emission on fH/2


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