Transcript Pitch-Angle Scattering of Relativistic Electrons at Earth

Pitch-Angle Scattering of Relativistic
Electrons at Earth’s Inner Radiation
Belt with EMIC Waves
Xi Shao and K. Papadopoulos
Department of Astronomy
University of Maryland
College Park, MD 20742
Motivation
Dispersion Relation for Parallel Propagation
Gyro-resonant Pitch Angle
Scattering with Low
Frequency (ω < Ωi) Wave
• Have discussed
Scattering of Relativistic
Protons with Alfven wave
• Have discussed efficient
ways to generate ULF
waves.
• Scattering of
Relativistic Electrons
with Electromagnetic IonCyclotron (EMIC) Wave
Minimum Energy (Emin) vs. k for GyroResonant Interaction with Electron
Gyro-Resonant Condition
of Relativistic Electron
  k|| v||  
| e |

k|| v|| 
k > k0
for Emin < 1MeV
| e |

k0
For conditions at equator, L = 2
• To resonant-scatter 1 MeV electrons, wave-vector needs to
satisfy k > k0.
Along L=2 magnetic field line
Density of Electron, H+, He+, O+
along L = 2 dipole magnetic field
line (from GCPM)
Earth
Equator Earth
O+ gyro-frequency
along L = 2 field line
Equator
Dispersion Relation of EMIC Waves
Dispersion Relation for L Mode with Multi-Ion
(H+, He+,O+) Species
2
2
3


pe
pj
 2  k 2c 2 

0
(  | e |) j 1 (   j )
Parallel Wave Number
Gyro-resonant Scatterings of Electron by EMIC Wave
Dispersion Relations for LMode EMIC Wave
Emin of Gyro-resonant
Electron with He+ Band
(along L=2 magnetic field line)
1 MeV
For conditions at equator, L =2;
fH+= 60 Hz.
Magnetic field: dipole
Plasma Density: GCPM
Ray-Tracing of Multi-Frequency (within He+ band)
EMIC Wave (along L=2 field line)
Ray Tracing Applicable
Group Velocity Vg along Ray Path
 dk
(
k ds
)  1
Piling-up Factor (1/(Vg*A))
Interaction Region of Gyro-resonant Scattering of
Electrons by Broad-Band Wave within He+ Band
14.94 Hz
16.5 Hz
1 MeV
f ()  exp((  0 )2 /  2 )
f0 = 15.72 Hz
Δf = 0.05 f0
Interaction Region with 1
MeV Electron
• Latitude Range:
7.85 degree.
•Distance Range along
Field Line:
~1800 km.
• Pitch Angle Range: 0 –
88 degree.
Pitch Angle Diffusion Analysis
Local Diffusion Rate:
• Quasi-linear diffusion
analysis
D
– Small scattering with each
wave
– Gaussian-shape spectrum
– Diffusion is proportional to
wave power
 j B 2 1
2k 2

exp((   m ) 2 /  2 )
2
2
 B0  dk
d
Summers and Thorne, 2003
Bounce Averaged Diffusion Rate:
M 2
1
cos( )
7
D 
D
d

cos
( )

2


2S ( 0 ) M 1
cos ( 0 )
Bounce Averaged Pitch Angle Diffusion Equation:
f 0
1


t
S ( 0 ) sin( 0 ) cos( 0 )  0

f 0  f 0
S
(

)
sin(

)
cos(

)
D
0
0
0


 
atm


0 

f 0 (t , 0 )  F (t ) g ( 0 )
(
1
 atm

1 F

g
) g ( 0 ) S ( 0 ) sin( 0 ) cos( 0 ) 
S ( 0 ) sin( 0 ) cos( 0 ) D
F t
 0
 0
(Life Time)
1 F 1
 p  (
)
F t
Lyons and Williams, 1984
Pitch-Angle Diffusion Rate for Electrons
(along L = 2)
Local Diffusion Rate
Bounce-Averaged Diffusion Rate
1MeV Electron
f ()  exp((  0 )2 /  2 )
f0 = 14.94 Hz
Δf = 0.05 f0
f0 = 15.72 Hz
Δf = 0.05 f0
Co-Latitude =85.48 deg.
δB = 300 pT
400 W input, ΔL=0.1
Life Time and Equilibrium Equatorial Particle
Flux Distribution
Equilibrium Distribution Function
g(α0) vs. Pitch Angle α0
f ()  exp((  0 )2 /  2 )
1MeV Electron
f0 = 15.72 Hz
Δf = 0.05 f0
He+ Branch EMIC
Wave
400 W power input over
shells ΔL=0.1, L=2
Life time= 5.2 days
Conclusions
• Scattering of relativistic particles into losscone through low-frequency waves (ω < Ωi)
provide viable ways to do inner (Proton
and Electron) radiation belts remediation.
• For electron belt remediation, need to
have better understanding of the resonantabsorption, reflection, tunneling, modeconversion of EMIC waves at resonant
region. Need to include full-wave effects.
Electron (> 300 keV) Belt Dynamics (1979-1999)
(from NOAA 5-14 POES Satellites)
21 years
• Inner (peak near L=1.6 ) and Outer (peak near L= 4-5)
Electron Belts; Slot Region (L=3).
• Variability of outer belt; Relative stable inner belt.
• Hazardous to satellites, astronauts, and spacecraft.