tokens: indeed become an important ionization source in T Tauri disks. However, our model should be seen as a first attempt at a comprehensive modelling of SP ionization in protoplanetary disks. In the following we discuss further important aspects like variability, non-stellar origin of SPs, the importance of magnetic fields and future prospects for SP modelling in protoplanetary disks. 4.3.1. Flares and variability In our models we assumed continuous (i.e. time-averaged) particle fluxes and X-ray luminosities. Although this is a reasonable assumption (see Sect. 2.2 ) it is likely that the disk is also hit by singular powerful X-ray and/or SP flares. From the X-ray COUP survey of the ONC cloud, Feigelson et al. (2002) and Wolk et al. (2005) derived a median X-ray flare luminosity of , comparable to the X-ray luminosity in our high X-ray models, and peak flare luminosities up to . The duration of such flares can last from hours up to three days with a typical frequency of roughly one powerful flare per week. Ilgner Nelson (2006) argue that for such flare properties the disk ion chemistry responds to time-averaged ionization rates. However, in case the duration between two flares is longer than the recombination time scale in the disk, such singular and strong flares would produce asymmetric features in molecular ion emission (i.e. a singular flare only affects a certain fraction of the disk). The spatially resolved SMA observations of TW Hya show indeed such an asymmetric structure ( Cleeves et al. 2015 ). However, as discussed by Cleeves et al. (2015) these features could also have a different origin like spiral arms or an hidden planet locally heating the disk. If such asymmetric structures are caused by stellar flares they would provide complementary constraints on the X-ray/SP activity of the star. Multi-epoch data of spatially resolved molecular ion emission is required to prove the flare scenario (i.e. the features should disappear quickly). The current (sub)mm interferometers like ALMA, NOEMA and SMA provide the required spatial resolution and might even allow for monitoring of disks in molecular ion lines on a daily/weekly basis in the future. Modelling of such observations does not necessarily require 3D chemical models. Assuming that the disk physical structure is not affected by flares, radial cuts through the disk can be modelled with 2D (time-dependent) thermo-chemical models as presented here. 4.3.2. Magnetic fields In our model we neglect the impact of magnetic fields on the SP transport. Stellar and disk magnetic fields are in particular relevant for the question if particles actually hit the disk (see Feigelson et al. 2002 , for a discussion). Magnetic fields can either drag the particles away from the disk (e.g. like in a wind) but could also funnel the particles and concentrate the ionizing flux in particular regions of the disk. In the first scenario SPs can still have an impact on the upper layers of the disk but certainly not on
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