Dynamic, explosive phenomena occur throughout the Universe, particularly in plasma threaded by magnetic fields. Examples are found in the magnetospheres of the Earth and other planets (aurora); flares and other dynamic phenomena on the Sun and other late-type stars; magnetar flares; flares in compact object magnetized accretion disks. We do not yet completely understand the precise mechanisms by which energy is stored in the magnetic field and released suddenly. Usually some particles at least gain energies well above thermal so that questions of particle acceleration go hand in hand with the problems of energy release. Solar flares give a prototypical example. These events involve the release of 10²w to 10³³ erg in the space of at most a few minutes, manifested as radiation across the electromagnetic spectrum and mass motions. Compared to more remote astrophysical phenomena they can be observed in enormous detail, across a very wide range of wavelengths. The processes that can be studied in great detail in the case of flares constitute "ground truth" for understanding more dramatic energetic processes at much greater distance.In some flares, gamma-ray lines as well as energetic neutrons detected in space indicate that ions have been accelerated to MeV energies and above. In the largest gamma-ray flares the fluxes in these lines imply an energy content in ions comparable to that manifested in X-ray emitting electrons. Moreover these energetic particles can embody several tenths of the total energy released from the magnetic field in the flare. They are believed to transport energy from the coronal energy release site to the deeper atmosphere and they can account, for instance, for all the radiation of the flare at optical and UV wavelengths. Thus the problem of explaining the flare energy release is intimately tied up with the problems of accelerating particles; particle acceleration is central to magnetic reconnection in tenuous plasmas, not just an amusing sideshow.The most energetic ions will produce secondary electrons and positrons at MeV - GeV energies, by a couple of mechanisms. These particles in turn will radiate synchrotron radiation at mm and shorter wavelengths - the very wavelength range whose exploration has been pioneered by Brazilian scientists, now opening up as never before via LLAMA, ALMA and other new instruments. Detailed study of the radiation of these secondary particles, its spatial, temporal and spectral characteristics, may open up an entirely new window on the highest energy particles in flares. While gamma-ray observations tell us that ~GeV ions are present at the Sun, any spatial information at all is still very difficult to obtain. Fine spatial resolution, even sub-arc-second, is quite feasible at mm and sub-mm wavelengths, however. Thus we may realistically hope to constrain the location of the acceleration region and possibly the nature of the accelerator via such observations.In this project we propose to carry out detailed modelling of secondary production by energetic ions, studying both their synchrotron and gamma radiation. This modelling will provide a framework for interpreting the detailed observations expected from leading-edge instruments such as ALMA, as well as existing gamma-ray measurements from Fermi and earlier experiments. It will improve over all previous efforts by employing realistic magnetic field models, including primary transport, secondary production and secondary (and indeed tertiary, etc.) particle transport in these realistic magnetic fields.
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