Mathematical equivalence of non-local transport models and broadened deposition profiles

Old and recent experiments show that there is a direct response to the heating power of transport observed in modulated electron cyclotron heating (ECH) experiments both in tokamaks and stellarators, which is commonly known as non-local transport. This is most apparent for modulated experiments in stellarators such as LHD and W7-AS. We show that this power dependence and its corresponding experimental observations such as the so-called hysteresis in flux [Inagaki, NF, 113006, 2013] can be reproduced by broadened ECH deposition profiles. In other words, many mathematical models proposed to describe non-local transport are equivalent to an deposition (effective) profile in its linearized forms [vanBerkel, NF, 106042, 2018]. This also connects with new insights on microwave scattering due to density fluctuations in the edge plasma which shows that in reality the deposition profiles are much broader than expected [Chellai, PRL, 105001, 2018] but it is unclear if this effect is sufficient to explain non-local transport. These relationships can be further studied by separating the transport in a slow (diffusive) and a fast (heating/non-local) time-scale using perturbative experiments.