Effects of inhomogeneity on electrostatic ion cyclotron instability excited by a particle beam

Electrostatic ion cyclotron (EIC) waves excited by a particle beam are studied in a magnetized inhomogeneous collisionless plasma using linear Vlasov theory. The dispersion relation of the beam-plasma system is established based on some relevant assumptions and the numerical results are presented. The behavior of EIC waves with account of parameters such as plasma inhomogeneity, propagation angle and beam velocity is studied. In particular, mode frequencies, growth rate maxima and perpendicular wavevectors are investigated in terms of these parameters. It is shown that, for lower inhomogeneities, the growth maxima are highly affected by the value of relative beam velocity. However, for higher inhomogeneities, the system is more stable for all beam velocities. It is also shown that the beam velocity has a major effect on the growth maxima only before reaching a maximum value on the curves and after the maximum, there is a declining trend in the effect of beam velocity on the growth maxima. Furthermore, for larger propagation angles, there is a more sensitive dependency on the beam velocity. At large values of relative beam velocities, the dependency of growth maxima on beam velocity becomes very weak for all propagation angles. It is found that the perpendicular wavevector decreases with both inhomogeneity and beam velocity. The decrease is smoother at larger values of propagation angle or higher inhomogeneities. In other words, for faster beams and higher inhomogeneities, the system is unstable at larger perpendicular wavelengths. It is also found that the values of maximum instability in terms of propagation angles strictly depend on inhomogeneity. For a relatively high inhomogeneity, the maxima occur over a wide range of propagation angles at almost the same value of perpendicular wavevector. A direct relationship between the magnitudes of mode frequency and growth rate is observed, implying that a higher frequency is a prerequisite for a positive (and relatively steep) slope on the growth rate curve.