Calculation of energy change and growth rate in cold and hot plasma sites by using general loss cone distribution function

The main feature of the magnetic field is the itsapplication of force to moving electric charges. Therefore, a magnetic field may trap the charged particles, such as electrons and protons, by forcing them to move forward and backward along the lines of the spiral. The charged particles are reflected in the mirror point where the field lines are close to each other and the spirals are tight. The particles in the magnetic mirror are initially dispersed spherically. At certain angle values, these particles can escape from the magnetic mirror; this is called a lost cone state. When the particles go out of the mirror in the case of the lost cone, the dispersion becomes anisotropic, which is called a loss cone distribution. The distribution tries to be isotropic again. Therefore, plasma waves emit energy. There are functions that must be calculated precisely in the equations of emitted energy waves , such as Z_(1 )and Z_2. In this study obtained analytical expressions for these functions using a different approach. The results obtained for these functions provide analytical calculation of other properties such as wave energy, perturbation distribution relationship, growth rate for cold and hot plasmas.