Energy balance in coronal funnels

The energy balance in magnetic flux tubes is examined semianalytically for the case in which thermal conduction balances radiation or in which enthalpy transport occurs. Different values are considered for areal constriction, shape, length, and maximum temperature. The overall energy budget of the solar corona is not significantly affected by magnetic constriction. A bowl-shaped funnel with a constriction factor of 4 describes the empirical differential-emission measure for log-T values between approximately 5.3 and 6.0. Loop-scaling relationships are derived for the full range of models to illustrate the dependence of the constant of proportionality on the properties of the magnetic constriction. Constriction can reduce the total energy requirement of the funnel by a factor of 5 and not affect the differential emission in flow-dominated models.