Critical density gradients for small‐scale plasma irregularity generation in the E and F regions

Abstract

Electron density gradients that can make plasma unstable in the ionospheric E and F regions are analyzed. We focus on critical gradient values required for plasma instability to become operational to produce decameter‐scale plasma irregularities observed by the Super Dual Auroral Radar Network (SuperDARN) without any nonlinear wave cascade. Analytic expressions are developed for the critical gradients using a recently developed general formalism for arbitrary geometry and with the ion inertia and stabilizing thermal diffusion effects included. It is demonstrated that the problem can be analyzed using a single equation applicable in both the E and F regions that only differs in the sign of the main term related to convection strength. Analytic expressions are obtained, and results are presented for (1) critical gradient strength for arbitrary gradient and propagation directions, (2) range of propagation directions with unstable primary waves, (3) most favorable configuration and minimum critical gradient, and (4) most favorable propagation direction for arbitrary gradient direction. It is shown that the most favorable configuration is achieved for propagation along the differential drift and gradient perpendicular to it and that an unexpected exception is the F region under strong convection when propagation and gradient are both rotated by a certain angle. It is estimated that in the F region, from which most of the SuperDARN backscatter comes, primary decameter waves can be generated for gradient scales as large as 100 km for favorable orientations and strong plasma convection >500 m/s and that much smaller scales of 200–1000 m are required for unfavorable orientations.

Statistical Analysis of the Electron Density Gradients in the Polar Cap F Region Using the Resolute Bay Incoherent Scatter Radar North

“…In the previous theoretical study by Makarevich (), the critical electron density gradients required for primary wave generation in the linear regime of electrostatic plasma instabilities were analyzed. It was proposed that a turbulent cascade, where the waves are generated in the nonlinear regime by the breakage of large‐scale waves into smaller irregularities, may not be needed for the generation of decameter‐scale irregularities in cases when strong enough density gradients are present (Makarevich, ). An analytic expression for the minimum critical gradient strength was derived (Makarevich, , see equation A6) that describes a minimum required strength of the gradients for the generation of GDI waves as a function of convection velocity V E .…”

“…It is important to specify the difference of how GDI operates in cold plasma, where the thermal diffusion term is neglected, and in a plasma that is being stabilized by the thermal diffusion. In the cold plasma, the gradient of any strength G gives the positive growth rate for the GDI waves, whereas in the plasma with finite temperature, the gradient strength needs to be higher than a certain critical value to overcome the stabilizing thermal diffusion (Makarevich, ).…”

Toward an Integrated View of Ionospheric Plasma Instabilities: 4. Behavior in the Transitional Valley Region

“…The origin of the factor of 2 in V E >2 C s warrants an additional discussion in the context of general expressions for the convection thresholds . In the present study, we used the same model estimates of collision and gyrofrequencies as in the previous studies (Makarevich, , , ) and, in this selection, the ratio r i happens to be just below unity at 120 km. In this case, the lower convection limit from is , while the top limit is very large.…”

Toward an Integrated View of Ionospheric Plasma Instabilities: 3. Explicit Growth Rate and Oscillation Frequency for Arbitrary Altitude

“…This geometry is completely general since the choice of the coordinate system with the x axis along the background electric field E preserves generality. The angle definitions are also the same as in Makarevich (), with an additional angle β defined as …”

“…This geometry is completely general since the choice of the coordinate system with the x axis along the background electric field E preserves generality. The angle definitions are also the same as in Makarevich (2017), with an additional angle defined as The exact vector directions in Figure 1 refer to an E region altitude of 110 km where r i ≈ 5. For the F region, r i ≪ 1 and ≈ 0.…”