Finite Larmour Radius Research Articles

Experimental Determination of Threshold Powers for the Onset of HF-Enhanced Plasma Lines and Artificial Ionization in the Lower F-Region Ionosphere

HF heating experiment, with linear power ramp from 50 to 92 dBW, was conducted to determine the HF threshold power levels for the onset of detectable plasma waves and the onset of artificial ionization inferred from HF-enhanced plasma lines (HFPLs). The threshold free-space electric field at 200-km altitude, where HFPLs were detected, is about 53 mV/m. However, the HF electric field near the reflection height is enhanced by a swelling factor ~ 3.76 and also conversion to a linear dipole pump mode ( $\surd 2$ ); the actual threshold field is about 281 mV/m that is consistent with theory. Artificial ionization in the lower region was detectable via UHF radar. Short wavelength upper-hybrid waves, which were excited parametrically by the HF heating wave at higher threshold, implement Doppler shifted harmonic-cyclotron resonance interaction, via finite Larmour radius effect, to effectively accelerate electrons. Monitoring the spectral power of the parametric decay instability (PDI) line in the HFPLs by radar was shown to determine the artificial ionization onset time more precisely than that by observing the start of a sharp downward trend in the altitude of the HFPLs; at this time, the HF free-space electric field slightly below 200-km altitude is about 550 mV/m. Langmuir cascade lines in the HFPLs are separated by intervals about double the ion-acoustic frequency (about 4–5 kHz) generated by the PDI. These lines, observed at lower power facilities, were not observed. The upper-hybrid OTSI and PDI excited at HighPower Active Auroral Research Program (HAARP) and the mode competition nonlinear-damping mechanism are suggested as the processes, suppressing cascade enhanced HFPLs.

Electron cyclotron harmonic resonances in high-frequency heating of the ionosphere

Electron acceleration by upper hybrid waves under cyclotron harmonic resonance interaction is studied. Theory is formulated; the analytical solutions in the second and fourth harmonic cyclotron resonance cases are obtained, and in the third harmonic case, a first order differential equation governing the evolution of the electron energy is derived. The theory is applied for explaining the generation of artificial ionization layers observed in high-frequency (HF) ionospheric heating experiments. The upper hybrid waves are assumed to be excited parametrically by the O-mode HF heating wave. As the decay mode is the lower hybrid wave, the excited upper hybrid waves have wavelengths ranging from 0.25 to 0.5 m, which are short enough to effectively incorporate the finite Larmour radius effect for the harmonic cyclotron resonance interactions as well as have a frequency bandwidth of about 20 kHz, which provides an altitude region of about 10 km for continuous harmonic cyclotron resonance interaction between electrons and descending waves in the slightly inhomogeneous geomagnetic field. The numerical results on electron acceleration show that electron fluxes with energies larger than 14 eV are generated in the three harmonic cases. These energetic electrons cause impact ionizations, which are descending to form artificial ionization layers at the bottom of the ionospheric F region.

Absence of Complete Finite-Larmor-Radius Stabilization in Extended MHD

The dominant finite-Larmour-radius (FLR) stabilization effects on interchange instability can be retained by taking into account the ion gyroviscosity or the generalized Ohm's law in an extended MHD model. However, recent simulations and theoretical calculations indicate that complete FLR stabilization of the interchange mode may not be attainable by ion gyroviscosity or the two-fluid effect alone in the framework of extended MHD. For a class of plasma equilibria in certain finite-beta or nonisentropic regimes, the critical wave number for complete FLR stabilization tends toward infinity.

Coherent structures in electrostatic interchange mode turbulence

Exact nonlinear coherent vortex solutions, in the form of dipolar like configuration, are derived in a two-dimensional (2D) electrostatic interchange turbulence model. The vortex structure incorporates effects due to nonlinear diamagnetic interactions that are associated with the finite Larmour radius (FLR) of the magnetized ions. Numerical simulations indicate that the propagating dipole vortex is a long-lived, spatially well-localized coherent structure of the interchange mode that persists for several eddy turn-over times. Collisional as well as weak diamagnetic interactions have stabilizing effects on these structures.

General Gyrokinetic Equations for Edge Plasmas

During the pedestal cycle of H-mode edge plasmas in tokamak experiments, large-amplitude pedestal build-up and destruction coexist with small-amplitude drift wave turbulence. The pedestal dynamics simultaneously includes fast time-scale electromagnetic instabilities, long time-scale turbulence-induced transport processes, and more interestingly the interaction between them. To numerically simulate the pedestal dynamics from first principles, it is desirable to develop an effective algorithm based on the gyrokinetic theory. However, existing gyrokinetic theories cannot treat fully nonlinear electromagnetic perturbations with multi-scale-length structures in spacetime, and therefore do not apply to edge plasmas. A set of generalized gyrokinetic equations valid for the edge plasmas has been derived. This formalism allows large-amplitude, time-dependent background electromagnetic fields to be developed fully nonlinearly in addition to small-amplitude, short-wavelength electromagnetic perturbations. It turns out that the most general gyrokinetic theory can be geometrically formulated. The Poincaré-Cartan-Einstein 1-form on the 7D phase space determines particles' worldlines in the phase space, and realizes the momentum integrals in kinetic theory as fiber integrals. The infinitesimal generator of the gyro-symmetry is then asymptotically constructed as the base for the gyrophase coordinate of the gyrocenter coordinate system. This is accomplished by applying the Lie coordinate perturbation method to the Poincaré-Cartan-Einstein 1-form. General gyrokinetic Vlasov-Maxwell equations are then developed as the Vlasov-Maxwell equations in the gyrocenter coordinate system, rather than a set of new equations. Because the general gyrokinetic system developed is geometrically the same as the Vlasov-Maxwell equations, all the coordinate-independent properties of the Vlasov-Maxwell equations, such as energy conservation, momentum conservation, and phase space volume conservation, are automatically carried over to the general gyrokinetic system. The pullback transformation associated with the coordinate transformation is shown to be an indispensable part of the general gyrokinetic Vlasov-Maxwell equations. As an example, the pullback transformation in the gyrokinetic Poisson equation is explicitly expressed in terms of moments of the gyrocenter distribution function, with the important gyro-orbit squeezing effect due to the large electric field shearing in the edge and the full finite Larmour radius effect for short wavelength fluctuations. The familiar “polarization drift density” in the gyrocenter Poisson equation is replaced by a more general expression. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Generation of energetic electrons at second harmonic cyclotron resonance in ionospheric HF heating experiments

The theory of electron acceleration by upper hybrid waves at second harmonic cyclotron resonance is presented. The results show that the meter‐scale upper hybrid waves can incorporate the finite Larmour radius effect to make a second harmonic cyclotron resonance interaction effective. The finite Larmour radius effect provides a positive feedback to the interaction, thus the energies of the accelerated electrons increase in time exponentially, rather than linearly as in the case of fundamental cyclotron resonance. Consequently, energetic electrons (having energies larger than 10.7 eV) can be generated even at very low upper hybrid wave intensities. The threshold field for parametric excitation of meter‐scale upper hybrid waves by O‐mode HF heating wave is shown to be very low. The theory can be a reasonable basis for explaining the enhancement of airglow at 777.4 nm observed in recent low‐heating‐power experiment at HAARP.

Scaling laws for plasma transport due toη i-driven turbulence

The scale invariance technique has been employed to discuss theη i-driven turbulent transport under a new fluid model developed by Kimet al [1]. Our analysis reveals that the finite Larmour radius effect plays a decisive role to determine the scaling behaviour of the energy transport under the new fluid model. However, the overall scaling of the transport coefficient remains unchanged as compared to that derived by Connor [2] under the traditional fluid model. The approximations considered by Connor [2] are qualified with additional requirements within the new fluid approach. In the dissipative case, which has not been discussed earlier, additional constraints on the power scaling laws of the transport properties are imposed due to the dissipative mechanisms in the basic governing equations.