Role of kinetic Alfvén waves in the non-extensive anisotropic earth’s magnetospheric plasma

Kinetic Alfvén waves (KAWs) contribute significantly to particle acceleration in the magnetosphere of Earth. In this paper, we discussed how the charged particles’ (electrons and ions) speeds vary with distance during the wave-particle interaction. We employed the temperature-anisotropic non-extensive distribution function to model the magnetospheric plasma. Our findings show that the charged particles take more energy from the wave in the non-extensive state; consequently, the particles are accelerated to higher velocities. Our results also show that when the perpendicular ion temperature <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊥</mml:mo> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> of the system increases, the accelerated charges have a lower velocity. In addition to the velocity of charged particles, we found that the magnitude of the KAW’s group velocity was larger in the Maxwellian <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">q</mml:mi> <mml:mo>→</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> case, and the waves were more energetic and heat the magnetospheric plasma for larger distances. Finally, we calculated the characteristic length scale over which the waves get damped. Our findings show that the damping scale length is of the order of several Earth radii (R E ), consistent with observations. The effects of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:mi mathvariant="normal">q</mml:mi> </mml:mrow> </mml:math> and the temperature anisotropy on the damping scale length are such that for small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"> <mml:mrow> <mml:mi mathvariant="normal">q</mml:mi> </mml:mrow> </mml:math> (i.e., the non-extensive state), and larger <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊥</mml:mo> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , the damping scale length becomes large enough, which implies that the waves can interact with the charged particles far away from the locations where they are excited. The findings of this study help us understand the formation of the beams of charged particles, which can precipitate into different regions of the magnetosphere, and are critically important in the formation of auroras.