Electron Trapping Times and Trap Densities in Solar Flare Loops Measured withCOMPTONandYOHKOH

We measure energy-dependent time delays of ≈ 20-200 keV hard X-ray (HXR) emission from 78 flares observed simultaneously with the Compton Gamma Ray Observatory and Y ohkoh . Fast time structures ( ≲ 1 s) are filtered out, because their time delays have been identified in terms of electron time-of-flight (TOF) differences from directly precipitating electrons (Aschwanden et al.). For the smooth HXR flux , we find systematic time delays in the range of τ S = t 50 keV - t 200 keV ≈ -(1 ... 10) s, with a sign opposite to TOF delays, i.e., the high-energy HXRs lag the low-energy HXRs. We interpret these time delays of the smooth HXR flux in terms of electron trapping, and we fitted a model of the collisional deflection time t Defl ( E ) ∝ E 3/2 n −1 e to the observed HXR delays in order to infer electron densities n in the trap. Independently, we determine the electron density n in flare loops from soft X-ray (SXR) peak emission measures EM=∫ n 2 e dh , using loop width ( w ) measurements to estimate the column depth dh ≈ w . Comparing the two independent density measurements in HXR and SXR, we find a mean ratio of q e = n / n ≈ 1, with a relatively small scatter by a factor of ≈ 2. Generally, it is likely that the SXR-bright flare loops have a higher density than the trapping regions (when q e < 1), but they also are subject to filling factors less than unity (when q e > 1). Our measurements provide comprehensive evidence that electron trapping in solar flares is governed in the weak - diffusion limit , i.e., that the trapping time corresponds to the collisional deflection time, while pitch-angle scattering by resonant waves seems not to be dominant in the 20-200 keV energy range. The measurements do not support a second - step acceleration scenario for energies ≤200 keV.