Electrostatic waves with a frequency which is small compared to the ion cyclotron frequency in a plasma confined by a magnetic quadrupole are considered. An equation is derived for the growth or damping rate due to wave-particle (Landau) resonances with the effects of temperature gradients and finite Larmor radius included. Ion Landau damping of the fundamental drift mode in the UMIST quadrupole is calculated and its effect on the net growth rate is shown.