An analytic hybrid model of expanding cometary plasma

The dynamics of ions and electrons near a comet with moderate or low activity (łesssim 10^ 27 s -1 ) is not dominated by collisions. This regime received little attention before the Rosetta investigation of comet 67P brought collisionless and marginally collisional plasma dynamics into focus. When a molecule in a collisionless coma is ionised, most of the excess energy goes to the newborn electron. This leads to an electron pressure gradient and, hence, an ambipolar electric field maintaining quasi-neutrality by retaining electrons. This field has been identified in simulations, and Rosetta measured the resulting outwardly directed ion flow speed. We aim to explore collisionless comet plasma physics using a stationary, spherically symmetric model to provide a framework for comparison with simulations and observations. As in hybrid plasma simulations, ions are treated kinetically and electrons as a fluid. We derive the phase-space distribution function for cometary ions continuously created by ionisation and accelerated by an outwardly directed electric field of arbitrary radial dependence. For a point source, a logarithmic potential provides an exact self-consistent solution for both ions and electrons. For a finite spherical nucleus, the model is applicable beyond a few nuclear radii. An electron energy equation relates the electron temperature, from which the ambipolar field and all ion properties follow, to the electron excess energy at ionisation. The main result is the simple model itself. Our specific findings include the energy transfer from electrons to ions, yielding an electron temperature equal to 2/7 of the excess ionisation energy. For the photoionisation of water, this means an electron temperature of 3.4 eV and a water ion speed of 3.8 km/s, consistent with Rosetta observations in the diamagnetic cavity. The simple model provides scaling relations and allows us to determine all plasma properties from the comet gas production rate, ionisation frequency, and mean electron excess energy.