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Two stream Langmuir mode instability in pulsar magnetosphere
Pulsars are a class of fast rotating (~ milliseconds to seconds) and strongly magnetized (10^8 to 10^12 gauss) neutron stars that emit beamed electromagnetic radiation received as periodic pulses of light at the rotational frequency of the pulsar. The origin of radio emission from pulsars is fundamentally different from emission processes in other wavebands. In radio astronomy, we define the brightness temperature for a radio source as the equivalent blackbody temperature that would give the same intensity at a given radio wavelength. The brightness temperature of pulsar radio emission is around 10^25 - 10^27 K. This points not only to a non-thermal process but a highly coherent emission process as well. Coherent radiation involves in-phase emission of a collection of charges acting as a single entity referred to as a ``charge'' bunch. The physics of the emergence and maintenance of these "charge bunches'' has remained an open problem since the discovery of pulsars 50 years back. The formation of charge bunches requires the collective motion of charged particles. It requires amplification of an unstable electrostatic plasma mode in a pulsar beam-plasma system. Pulsar beam-plasma consists of tens of millions of kelvin hot and dense electron-positron pair plasma and tenuous and charged beams of positron and ion, confined to a one-dimensional and ultra-relativistic outflow. The extreme physical conditions make it a unique astrophysical laboratory for studying plasma effects unavailable in terrestrial plasmas. In this talk, I will show how observational and theoretical advances in the last two decades have provided us inputs to estimate realistic growth rates for various scenarios of two-stream instability for different cases of particle flows in the pulsar magnetosphere. Our approach has three unique features. These are using a) hot plasma treatment of the distribution functions, b) a non-resonant hydrodynamic branch of the relativistic Langmuir dispersion relation, and c) the effect due to the highly non-dipolar surface magnetic configuration of the neutron star is taken into account. We have been able to identify a spatial window of opportunity of around 100-1000 km above the neutron star surface where large amplitude waves in the dense pair plasma can participate in the coherent radio emission process.