1. Generation of Energetic Protons and the -ray Radiation During Solar Flares
Gottfried Mann and Rositsa Miteva
Astrophysikalisches Institut Potsdam,
An der Sternwarte 16, D Potsdam, Germany
-ray imaging by RHESSI
temporal correlation
- hard X-ray emission at 200 – 300 keV (e)
- -line emission – 2228 keV (p)
separation of the source regions  20” (= 15 Mm)
(Hurford 2003, 2006)
 Electrons and protons are simultaneously
accelerated at separated places in the
corona during a flare.
Oct. 28, 2003

2. Hirayoma 1974, Kopp & Pneumann 1976)
Flare Scenario
standard model
(Carmichael 1964, Starrock 1966,
Hirayoma 1974, Kopp & Pneumann 1976)
outflow jet establishes a shock
(TS, termination shock)
- TS source of energetic particles
(Tsuneta & Naito 1998)
- application for electron acceleration
(Mann et al. 2007, 2009)
 supported by RHESSI observations
(Warmuth et al. 2007, 2009)
The TS approach is adopted
for proton acceleration.

3. Shock Drift Accelerationp
transformation {in,ll , in,  {ref,ll , ref,
(1)
(2)
with sn = 0 sec B,n/c and 0 = vsh/c
(Mann et al. 2006)
(Holman & Pesses 1983, Ball & Melrose 2001,
Mann & Klassen 2005)

4. Cross-Shock Potential
cross-shock potential due to the different inertia of electrons and protons
It is frame dependent. In the normal incident frame (NIF):
as the thermal proton speed
- determination of the number density Nref of reflected protons
condition of reflections:
fM - Maxwell distribution function
0 - error function

5. Distribution Function of Accelerated Protons
A beam-like distribution function
results from the shock drift acceleration
Here, Nacc = Nref has been assumed.
magnetic field aligned proton flux:

6. Flux of Accelerated Protons at the TS
The magnetic field topology at the TS
is medelled by a segment of a circle.
Then, protons with different energies
are accelerated at different places of
the TS.
total flux of accelerated protons
averaged over the TS.
with 0 = 0/cos min and max = arccos (1/0)
differnetial flux of accelerated protons:

7. Numerical Results plasma parameters in the upstream region
N = 1.12 x 109 cm-3
B = 11 G
vA = 720 km/s
vsh = 2000 km/s
T = 10, 40 Mk
Vth,p = 290, 580 km/s
N1/N0 = 2
 Nacc/N0 = for 10 Mk
Nacc/N0 = for 40 Mk
Protons can be accelerated up to energies
in the GeV range at the TS.

8. Discussion Bn  Bn  Wp (MeV) 2.5 79.46° 0.756 3 80.39° 0.690 10
84.74°
0.379 30
86.95°
0.220
100
88.30°
0.123
300
88.97°
0.074
1000
89.35°
0.047
We (keV)
Bn  12
87.16°
0.205 25
88.00°
0.144 50
88.54°
0.105
100
88.90°
0.079
300
89.22°
0.056

9. Summary
● The TS able to accelerate protons up to energies in the GeV range.
● These protons lead to the emission of the -ray lines.
● The TS is able to accelerate electrons up to energies in the MeV range.
● These electrons lead to the hard X-ray emission.
● Protons and electrons are simultaneously accelerated at different places
on the TS.
● That can explan the separation of the hard X-ray and -ray line sources
as observed by RHESSI.
Or in other words:
● Since the model is in agreement with the observations it confirms
the model.