Energetic electrons
acceleration: combined radio
and X-ray diagnostics
Hamish Reid1,2 Nicole Vilmer2
Eduard Kontar1
1University of Glasgow
13/07/2017
2Observatoire de Paris
1
13/07/2017
Where are electron accelerated ?
2
April 15th 2002
Solar Flare.
Background is
SOHO/EIT 195
Small Red
contours are
RHESSI 15-30 kev
Coloured
Contours are NRH
432 MHz Blue to
164 MHz Yellow
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Where are electron accelerated ?
3
Basic Concept
• Assume a common acceleration region for
upward and downward propagating energetic
electron beams (e.g. Ashwanden et al 1995)
• Use the X-ray data from HXR emission to
constrain parameters of downward and
upward electron beams
• Estimate parameters regarding the common
acceleration region.
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4
Basic Concept
Consider an electron cloud with size d, spectral index 
located at initial acceleration site r=0 described by:
 r
f 0 (v, r , t  0)  g 0 (v) exp 
 d




g 0 ( v ) ~ v 
Langmuir waves are generated when their growth rate is
larger than the background Maxwellian plasma collisional
absorption.
c 
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pe
2 f
v
 c
n
v
c 
 e
2 2
pe
3
e Te
4m v
ln 
5
Basic Concept
Langmuir waves are expected to grow at distance r =
htypeIII – hacceleration. We can constrain r from the
growth rate for Langmuir waves



n
1
c
r  d  
vg0 (v) 



pe


The collisional absorption is small so we can derive the
simple relationship
htypeIII  d  hacceleration
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April 15th 2002 Solar Flare.
TOP: Phoenix-2 spectral
radio data from 700 – 100
MHz
MIDDLE: NRH radio flux
from 432 – 164 MHz
BOTTOM: RHESSI HXR
flux at 25, 13, 6 keV
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Take the spectral
index of HXR
every 2 seconds
Take the starting
frequency of radio
emission with
criteria of 2x the
quiet background
level
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Starting Frequency vs Photon Spectral Index
Scatter plot of
the starting
frequency vs
the photon
spectral index
Points have
an anti
correlation
with a
coefficient of
-0.65
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Starting Distance vs Spectral Index
htypeIII  d  hacceleration
Assume an
exponential electron
density model for the
solar corona (Paesold
et al 2001).
Assume the thick
target model to get
the electron spectral
index from the photon
spectral index.
d = 10.5 ± 1.6 Mm
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hacceleration = 52.3 ± 21.2 Mm
10
15th
April
2002
Solar Flare.
Acceleration
Region
Background is
SOHO/EIT 195
Small Red
contours are
RHESSI 15-30 kev
Coloured
Contours are NRH
432 MHz Blue to
164 MHz Yellow
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11
Simulation Initial Conditions
The initial electron beam (at time=0) is dependent on
position (as a Gaussian) and velocity (as a power-law)
 | r |
f (v, r , t  0)  g 0 (v) exp 

 d 

(  1)  vmin 
g o (v)  nbeam


vmin  v 
vmin  v  vo
The initial, thermal spectral energy density is:
2
v
kbTe  pe
W (v, r , t )  2 2 log  
4 v
 vt 
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One Dimensional QL equations
One dimensional quasilinear equations (e.g. Drummond and
Pines, 1962) describing the kinetics of energetic electrons and
Langmuir waves (Kontar, 2001) (Reid and Kontar 2010 in press
ApJ)
2 2
F
v

4

e   W F 
d  f 
2

(r  r0 ) f 

 c
 2
2
2
t (r  r0 ) r
dv  v 
m v  v v 
v
W v 2 W 3vTe2 W pe 2 F



vW
 ( cw   L )W   s vF log  
t L v
v r
ne
v
 vt 
Wave Generation
and Absorption
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Spontaneous
Emission
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Sample Simulation
Electron Flux
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Plasma Waves
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Sample Simulation
Assume Langmuir
waves are induced
at a certain level
above the thermal
background W/WTh
A linear fit
recovers the value
for hacceleration and
d
htypeIII  d  hacceleration
d = 14.9 ± 0.75 Mm
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104 W/WTh gives the best fit
hacceleration = 49.4 ± 8.61 Mm
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Conclusion
• Combined analysis of HXR
and radio observations
provided reasonable
insight into the
acceleration region height
and size.
• Numerical simulations
validated the results and
shows the main starting
height dependence comes
from the spectral index
and acceleration region
size.
d = 10.5 ± 1.6 Mm
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hacceleration = 52.3 ± 21.2 Mm
16