1. Electron Propagation in RHESSI flares Markus J. Aschwanden (LMSAL) 5 th General RHESSI Workshop, Locarno, Switzerland, 7-11 June 2005 Group 1 : Electron Acceleration and Propagation

2. Analysis of energy-dependent hard X-ray time delays: 1)Electron time-of-flight distance from dt/dE<0 2)Electron density in coronal trap from dt/dE>0 3)Neupert effect from dt/dE (E<15 keV) 4)Proton speed from (dt_e-dt_p)/dE

3. Electron velocity Dispersion: Pitch angle: Magnetic twist: Electron energy: Photon energy: (Bremsstrahlung cross-section)

4. Electron time-of-flight measurements enable the localization of the acceleration region. Aschwanden (2002)

5. Previous TOF measurements from CGRO and Yohkoh: L_TOF/h_loop = 1.4  0.3 Aschwanden et al. (1996)

6. Previous TOF measurements from CGRO and Yohkoh: L_TOF/h_loop = 1.4  0.3 Aschwanden et al. (1996)

7. Can we reproduce electron time-of-flight measurements with comparable accuracy from RHESSI as from CGRO ? Problems: 1)Reduced sensitivity due to smaller detector area (9*40/2=180 cm^2 for RHESSI vs. 2000*4*cos(45)=5600 cm^2 for BATSE/CGRO)  5600/180=30 x less sensitivity  sqrt(30)=5.5 larger uncertainties in timing

8. Can we reproduce electron time-of-flight measurements with comparable accuracy from RHESSI as from CGRO ? Problems: 2) Demodulation of high-resolution time profiles introduces additional data noise and artifact residuals.

9. 2-s highpass-filtered demodulated time profiles Residuals from demodulation algorithm with periods of ~1.8 s

10. 4-s highpass-filtered demodulated time profiles Residuals from demodulation algorithm with periods of ~2.7 s

11. 8-s highpass-filtered demodulated time profiles Residuals from demodulation algorithm with periods of ~2.7 s

12. Residuals from demodulation algorithm prevent analysis of highpass- filtered data  TOF measurements not feasible with RHESSI data

13. Analysis of energy-dependent hard X-ray time delays: 1)Electron time-of-flight distance from dt/dE<0 2)Electron density in coronal trap from dt/dE>0 3)Neupert effect from dt/dE (E<15 keV) 4)Proton speed from (dt_e-dt_p)/dE

14. Generally, the HXR pulses or fine structure show TOF delays, while the lowpass-filtered flux shows delays of opposite sign (trapping)

15. Weak-diffusion trapping model: Trapping time is given by Collisional deflection time: Coulomb logarithm: Photon energy: (Bremsstrahlung cross-section)

16. Highpass-filtered HXR time pulses  Injection profile Lowpass-filtered HXR time profile  Trap-precipitating flux Observed time profile in HXR: = convolution of direct-precipitation and trapped-precipitation

17. (Schmahl & Hurford 2002) single source

18. Spectral variation of 2 subsequent loops Noise due to demodulation residuals

19. Krucker & Lin (2002) Lowpass-filtered time profile contains multiple loops with different timing

20. (Schmahl & Hurford 2002; Wang et al. 2002)

21. (Saint-Hilaire & Benz 2002; Schmahl & Hurford 2002) Spectral variation at >20 keV Neupert effect <20 keV

22. Alexander & Metcalf (2002) Fletcher & Hudson (2002) Krucker & Lin (2002)

27. Results: # Date Start GOES Density Energy [UT] class log(n_e) E[keV] 1) 2002-Feb-20 09:58 M4.3 11.2+1.5 15-35 2) 2002-Feb-20 11:07 C7.5 … pulse overlap 3) 2002-Feb-20 21:10 M2.4 11.0+0.2 25-40 4) 2002-Feb-26 10:26 C9.6 … pulse overlap 5) 2002-Mar-14 01:41 M5.7 … incomplete data 6) 2002-Mar-17 19:26 M4.0 11.7+0.1 25-60 10.5+0.1 15-60 7) 2002-Mar-18 19:15 C8.9 10.6+0.3 15-25 10.2+0.1 15-30 20) 2002-Jun-02 11:44 M1.0 11.5+0.1 20-60 11.4+0.1 20-60 23) 2002-Jul-23 00:00 X4.8 11.6+0.2 35-60

28. Comparision with electron densities obtained from CCGRO and Yohkoh

29. RHESSI

30. Conclusions : 1) Electron time-of-flight measurements cannot be carried out with current RHESSI demodulation algorithm (modulation residuals). 2) Energy-dependent HXR delays of lowpass-filtered (>4 s) RHESSI time profiles in the energy range of ~15-60 keV show delays that are consistent with a trap-plus-precipitation model with a timing of t(E)~E^3/2. 3) The resulting trap densities are found in the range of log(n_e [cm^-3])=10.2-11.7 and are consistent with CGRO data (obtained with the same technique) and with Yohkoh/SXT data (obtained from EM and loop geometry). 4) In 3 out of 9 flares trap densities could not be evaluated, most likely because subsequent HXR pulses with different spectra cannot be separated on >4s time scales. 5) The obtained trap densities can be used to model coronal HXR emission in Masuda-Sui-Holman-type sources.