Dips and Waves
From RHESSI Wiki
Introduction
There have been some heated discussion (for instance [1]) as to whether the "dip" seen in the mean electron spectrum <nFV> derived from RHESSI flare observations is a real feature since it can often be removed be correcting for albedo. But for flares with relatively low thermal mission the standard "thick-target" interpretation says that the "dip" must be there. This model only accounts for Coulomb collisions between the propagating beam of accelerated electrons and the background plasma. In this nugget we present simulation results from our recent paper [2] where we show what happens to the dip when you also include wave-particle interactions between the beam and background plasma.
Wave-particle Interactions
In the standard interpretation of RHESSI's hard X-ray emission, a negative powerlaw of acceelerated electrons (F0(E) ~E-δ0) above a sharp low energy cutoff leaves the corona travelling down to the chromosphere. As they propagate they lose energy to the background plasma through Coloumb collisions, eventually losing their energy in the dense chromosphere, where they emit hard X-rays as observed by RHESSI, heating the local plasma which expands back upwards. It can be analytically shown the the resulting mean electron flux spectrum <nVF(E)> will also have a neagtive powerlaw above the cutoff (<nVF>~E-δ1) but will have a positive one (<nVF(E)>~Eδ1) below the cutoff. The combination of this positive slope (increasing with increasing energy) and the falling thermal spectrum results in a local minima or "dip" in the total <nVF>.
We have simulated the propagation of such a powerlaw of acceleration electrons, Coulomb colision acting on the beam only, as shown in the left panel of Figure 1. But we have also ran a second set of numerical simulations in which we include the wave-particle interaction of the beam and background plasma. Namely we include beam-driven Langmuir wave turbulence. We want to include the waves-particle interactions as this non-collisional process is faster than collisions and the development of Langmuir waves from electron beams in solar flares is inferred from radio observations. These are self-consitently simulated using the quasi-linear approach describing the resonant interaction between the electrons and Langmuir waves. In these simulations we follow through time the electron distribution function f(v,x,t) and spectral energy density of the waves W(v,x,t). In Figure 1 we have snapshot from during the simulations showing f(v,x,t) for the coulomb collision only simulation (left) and f(v,x,t) and W(v,x,t) for the wave-particle simulation (middle and right panel). A movie of this can also be found here.
The immediate thing that happens is that the wave-particles very quickly flatten the low energy cutoff, producing a plateau in the electron distribution at low energies or velocities. The Coulomb collision alone are far slower at removing the low energy cutoff and produce the expected positive gradient in the electron distribution below the cutoff energy.
To calculate the mean electron flux spectrum from our simulations we use the simulated f(v,x,t)/m, spatially integrating and averaging over time .
Conclusions
The work shown here is a step towards a more complete treatment of electron transport in solar flares and highlights that the inclusion of wave-particle interactions flattens sharp low energy cutoffs in the inital accelerated electron distribution.