1. ГЕНЕРАЦИЯ И ВЫХОД АВРОРАЛЬНОГО КИЛОМЕТРОВОГО ИЗЛУЧЕНИЯ ИЗ НЕСТАЦИОНАРНОЙ КАВЕРНЫ Т. М. Буринская ИКИ РАН, г. Москва, Россия

2. From the experimental observations it follows: AKR sources are thin cavities aligned tangent to the auroral oval. They have small latitudinal width, 10km – 100 km, compared with their longitudinal extent ~1000km - 2000 km. Plasma of AKR sources is tenuous with electron population essentially constituted by energetic particles AKR sources are separated from the denser and colder external plasma by sharp density gradients with typical scale length of a few 100 m Peculiar feature of the electron distributions observed inside the sources is an accumulation of particles with high transverse energies of the order of several KeV but low parallel velocities CMI is responsible for the generation of AKR From Ergun et al., Astrophys. Journal, 2000

3. Stationary waveguide model Key parameters Plasma density inside the source n in ~ 1 cm -3 Background plasma density n out ~ 5-10 cm -3 Energy of hot electrons ~ 4-5 KeV Parallel velocity of hot electrons ~ 0.001c – 0.005c Source width ~ 5 – 100 km

4. General solution Dispersion equation is derived from the continuity of Assuming that changes of plasma parameters have a characteristic scale larger than a source width, plasma inside and outside a source may be considered as homogeneous

5. Solutions correspond to the extraordinary X mode when a refractive index <1, and Z mode when a refractive index >1 The X mode waves can be amplified due to development of the CMI The Z mode waves are not amplified in the considered range of wavelength Each of the solutions of dispersion equation may be labeled by an integer k y - dependence of normalized frequency and growth rate for different eigenmodes (k z =0, l=60, U 0 =0)

6.  The growth rate does not practically depend on the value of electron parallel velocity U 0 for the given eigenmode in the range of U 0 /c from 0 to 0.01.  There is a preferential direction of the X mode wave generation close to the direction tangent to source frontiers.  The increase of U 0 leads to the displacement of reflection point to the region of negative k y All waves are excited with frequencies below the cutoff frequency of the background plasma for the range of parameters adapted to the AKR generation region Normalized wave frequency and instability growth rate as functions of k z for the eigenmode n=12 with different values of k y and U 0

7. Earlier proposed mechanism of wave escape from the source region Long-standing question: how radiation, generated below the cutoff frequency of the surrounding plasma, would escape from the cavity? However, X mode waves usually do not reach altitudes inside a source, where their frequencies become greater than the local cutoff frequency. The reason is that during the wave propagation upward k z increases to values at which the wave refractive index becomes greater than 1 and the wave converts to the Z mode. Wave amplification factor S as a function of altitude X mode Z mode O mode

8. Calculations of wave amplification factor S under assumption of geometric optics have shown that S rises to high values during the wave propagation inside the waveguide. However, in the source model under consideration the most part of waves cannot reach altitudes, where there frequencies become equal to the local cutoff frequencies of the surrounding cold plasma. Increase of the cut off frequency with growth of k z Thus, there is a problem of wave escape from the source.

9. 2. Waveguide with adiabatically slowly varying width Refractive index of waves escaping from the source versus the source width for the eigenmode n=12 with different values of k y For l=60 the external refractive index is greater than 1 for all waveguide modes. So the leakage of e/m energy is at Z mode. As the source width is reduced, the real part of external index rapidly decreases for waves propagating nearly tangentially to waveguide frontiers. Further width shrinkage leads to escape of all generated waves, practically, on the branch of the cold plasma dispersion. Thus the internal X mode waves can be directly connected to the external X mode waves

10. Real part of the external wave index vs the angle L=59.4 Growth rate vs the source width As the source width is narrowed, the growth rate of waves propagating almost tangentially to source frontiers, increases and becomes significantly greater than it was in the beginning, when L/2=60. At the time when all outgoing waves belong to X mode, waves propagating closest to y direction have the maximum growth rate.

11. External index versus the source width for the eigenmodes n=4; 12; 33 δω as a function of source width for n=12, k y =0; 0.945 For given parameters the eigenmodes with n 0.9 are the first that can be directly connected to the external X mode waves. For this it is enough to have 2% source compression

12. ЗАКЛЮЧЕНИЕ Проведенное исследование показало, что нестационарные низкочастотные процессы, протекающие в авроральной области, могут играть определяющую роль для выхода АКР из области генерации в окружающую плазму и возможности его распространения на большие расстояния. БЛАГОДАРЮ ЗА ВНИМАНИЕ!

13. Normalized fractional frequency vs. a growth rate for several values of the transverse electron energy By increasing the transverse electron energy, the growth rate is increased and instability domain is widen and shifted towards lower frequencies below the cutoff frequency in the background plasma

14. Polarization of the eigenmode n=12 for different Ny For N y =0, the ratio IExI/IEyI is conctant and independent of x coordinate. Electromagnetic field is dominated by E y. As the N y increases, the polarization becomes coordinate-dependent and E x >E y. Thus the Poynting flux S x =E y *H z, that corresponds to the energy escape in x direction, decreases greatly. ….