Generation of Energetic Protons and the -ray Radiation During Solar Flares Gottfried Mann and Rositsa Miteva Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany e-mail: GMann@aip.de -ray imaging by RHESSI temporal correlation - hard X-ray emission at 200 – 300 keV (e) - -line emission 2218 – 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

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.

Shock Drift Acceleration p 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)

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

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:

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:

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 = 0.12 for 10 Mk Nacc/N0 = 0.16 for 40 Mk Protons can be accelerated up to energies in the GeV range at the TS.

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

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.