Production of antihydrogen atoms by mixing antiprotons with a cold, confined, positron plasma depends critically on parameters such as the plasma density and temperature. We discuss nondestructive measurements, based on a novel, real-time analysis of excited, low-order plasma modes, that provide comprehensive characterization of the positron plasma in the ATHENA antihydrogen apparatus. The plasma length, radius, density, and total particle number are obtained. Measurement and control of plasma temperature variations, and the application to antihydrogen production experiments are discussed. The antihydrogen was made by mixing low energy antiprotons with a cold, dense positron plasma in a nested Penning trap [4]. A knowledge of the characteristics of the positron plasma is important for several reasons. The most likely antihydrogen formation mechanisms, spontaneous recombination and three body recombination, have different dependences on both the density and the temperature of the positron plasma [5]. Knowing these parameters is crucial in helping to elucidate the antihydrogen formation mechanism. Control and simultaneous monitoring of the positron plasma temperature allow the antihydrogen formation reaction to be effectively turned off while maintaining overlap between antiprotons and positrons. This provides a good measurement of the total background signal for our unique antihydrogen detector [1]. Furthermore, the space charge potential of a * Corresponding author Email address: gemma.testera@ge.infn.it sufficiently dense (10 8 cm −3 ) and extensive (length 3 cm) positron plasma considerably alters the effective electrostatic potential in the positron trap and thus the dynamics of the antiprotons in the nested trap.Harmonically confined one component plasmas at temperatures close to absolute zero are known to form spheroids of constant charge density [6]. In our case the shape is a prolate ellipsoid characterized by the aspect ratio α = z p /r p where z p and r p are the semi-major axis and semi-minor axis respectively [ Fig. 1(a)]. A cold fluid theory [7] relating the frequencies of the low-order plasma modes to the density and the aspect ratio of spheroidal plasmas was confirmed experimentally for laser cooled ion plasmas [8,9] and successfully applied to cold electron plasmas [10]. Work on finite temperature electron plasmas demonstrated that mode detection could be used as a diagnostic of density and aspect ratio and that for a plasma of known density and aspect ratio the frequency of the quadrupole mode is dependent on the plasma temperature [11,12].Here we describe an extension to the above work which provides a non-destructive diagnostic based on measurements of the first two axial modes of a finite temperature positron plasma. The diagnostic has no discernable effect on the normal evolution of the plasma, so it can be used