A dispersion relation has been derived to study the stability of ion cyclotron (IC) propagation at the second harmonic of the minority component deuterium in a mirror confined plasma that has hydrogen as the majority species. We have worked in the frame of the majority ions; our dispersion relation can thus be used to study IC propagation in a single ion plasma also. Analysis of the dispersion relation yields two modes — one below and the other above the ion gyro-frequency Θ_H of hydrogen. The expression for the growth rate is used to explicitly show that an instability can arise in the plasma when the loss-cone indexj⩾3; this instability being a result of the coalescing of the two modes supported by the plasma. Unfortunately, the minority component deuterium does not decrease this instability and thus the proposed scheme of IC heating at the second harmonic of the minority component seems unsuited to mirror devices.

A dispersion relation for the perpendicular propagation of the electromagnetic ion cyclotron wave around the second harmonic of the deuterium ion gyrofrequency in a mildly relativistic, anisotropic Maxwellian plasma with hydrogen as the majority species and deuterium as the minority component has been derived. The work has been carried out in the frame of reference of the majority hydrogen ions; to these ions the waves at 2Θ_D would be at its own gyrofrequency.

Using a small quantityɛ to order all relevant parameters of the plasma, it was possible to derive the dispersion relations in a simple form. To the lowest order the relativistic factors do not enter the dispersion relation. The plasma can now support two modes—one above and the other below the hydrogen gyrofrequency in agreement with the assumptions. This was also verified numerically using a standard root solver thereby justifying the correctness of the ordering scheme.

In the next higher order, the dispersion relation is a quartic equation and is sensitively dependent on the relativistic factors. The plasma can now support four modes, both above and below the hydrogen gyrofrequency and consistent with the ordering scheme used. However the modes can now coalesce resulting in complex conjugate roots to the dispersion relation thereby indicating an instability.

The advantage of such a scheme is that two dispersion relations — one of which is independent of the relativistic factors and the other which is sensitively dependent on them can be separated out.

The problem of coronal heating remains one of the greatest unresolved problems in space science. Magnetic reconnection plays a significant role in heating the solar corona. When two oppositely directed magnetic fields come closer to form a current sheet, the current density of the plasma increases due to which magnetic reconnection and conversion of magnetic energy into thermal energy takes place. The present paper deals with a model for reconnection occurring in the solar corona under steady state in collisionless regime. The model predicts that reconnection time in the solar corona varies inversely with the cube of magnetic field and varies directly with the Lindquist number. Our analysis shows that reconnections are occurring within a time interval of600 s in the solar corona, producing nanoflares in the energy range $10^{21}–10^{23}$ erg/s which matches with Yohkoh X-ray observations.