Linear analysis of bump on tail instability with non-Maxwellian distribution function

The growth rate of bump on tail instability propagating in unmagnetized plasma has been derived. The dispersion relation has been characterized for (r, q) distribution function with spectral indices r and q which ultimately contributes towards tails and shoulder of distribution function. The growth rate of the bump on tail instability has been estimated numerically for different ratios of temperature and number density using solar wind data and also by varying values of indices r and q . The higher value of q play the role towards decreasing the growth rate where the instability has the higher value when the number density of the superthermal electrons in the bump is higher and the temperature is low. The maximum growth rate increases with the increase in number density of electrons and decreases with the increasing temperature in the bump.