The Atacama Large Millimetre/submillimetre Array (ALMA) presents a great opportunity for solar physics due to its capacity for observations at unprecedentedly high spatial, temporal and spectral resolutions in an unexplored spectral window. One field where ALMA may be of particular use is studying solar prominences/filaments, where current observations suggest the presence of ever finer structures. A major advantage of ALMA observations is that, at the wavelengths where it operates, the brightness temperature of the emission is very closely related to the electron temperature. This could allow the temperature structure of solar prominences, and the prominence-corona transition region, to be measured better than ever before.

In preparation for ALMA observations, it is important to first understand what we would expect to see, given the formation conditions for the continuum emission we will observe. In this study we present new calculations of brightness temperatures at ALMA wavelengths, given a set of internal parameters based on density and temperature data from the 2D cylindrical radiative transfer models of hydrogen and helium of Gouttebroze and Labrosse (2009). We investigate under which conditions the millimetre continuum is optically thin or optically thick. The non-LTE nature of the electron and ion population densities inside prominences means that in all cases the interpretation of the observed radiation has to be accompanied by model calculations such as the ones presented here. We show preliminary results on potential plasma diagnostics from ALMA observations.