David Nunn

A review of observational, theoretical and numerical studies of VLF triggered emissions

Abstract We review theoretical and numerical studies of VLF triggered emissions generated by manmade signals propagating in the whistler mode in the magnetosphere. Instead of listing all the past studies on the subject we select some of those works which give important ideas and the theoretical basis for future studies. The main purpose of the paper is to clarify what problems remain unresolved and to make suggestions for future studies. We first describe the phenomenon of VLF triggered emissions and give a brief review of experiments and observations. We then summarize the basic physics of VLF wave-particle interactions, which is indispensable for an understanding of the triggering mechanisms. We review important ideas and theories, as well as numerical models so far employed, summarize the present understanding of the phenomenon and consider briefly those problems which need further study. Especially, we focus our attention on numerical simulations whose capabilities in nonlinear physics are increasing with the increasing power of supercomputers.

The Numerical Simulation of VLF Chorus and Discrete Emissions Observed on the Geotail Satellite using a Vlasov Code

The work consdiers VLF chorus elements observed omn the Geotail satellite, which passes the equator at 10 earth radii. We have used a VHS Vlasov simulation code to model these emissions, employing all the ambient plasma data observed on Geotail. Excellent agreement with observation results, with steep risers and slow fallers being reproduced. The results confirm the overall validity of the non linear trapping theory of VLF emissions, and also confirm the efficacity of the Vlasov VHS code.

Observations of the relationship between frequency sweep rates of chorus wave packets and plasma density

[1] Chorus emissions are generated by a nonlinear mechanism involving wave‐particle interactions with energetic electrons. Discrete chorus wave packets are narrowband tones usually rising (sometimes falling) in frequency. We investigate frequency sweep rates of chorus wave packets measured by the Wideband data (WBD) instrument onboard the Cluster spacecraft. In particular, we study the relationship between the sweep rates and the plasma density measured by the WHISPER active sounder. We have observed increasing values of the sweep rate for decreasing plasma densities. We have compared our results with results of simulations of triggered emissions as well as with estimates based on the backward wave oscillator model for chorus emissions. We demonstrate a reasonable agreement of our experimental results with theoretical ones. Citation: Macusova, E., et al. (2010), Observations of the relationship between frequency sweep rates of chorus wave packets and plasma density,

Nucleotide sequence of the Methylobacterium extorquens AM1 moxF and moxJ genes involved in methanol oxidation.

The nucleotide sequence has been determined for two genes involved in methanol oxidation in the facultative methylotroph, Methylobacterium extorquens AM1. The two genes are moxF, encoding the 66-kDa subunit of the methanol dehydrogenase and moxJ, located immediately downstream from moxF, which encodes a 30-kDa protein with unknown function. This information completes the sequence of the 5.86-kb XhoI-SalI fragment containing the moxFJGI region in M. extorquens AM1, and the structure of this gene cluster is presented. Evidence is presented that moxJ is also present in Paracoccus denitrificans. The aa sequence of MoxJ has provided little information concerning its function, but it does appear to contain a signal sequence suggesting a periplasmic location.

Formation of VLF chorus frequency spectrum: Cluster data and comparison with the backward wave oscillator model

[1] The dependence of the frequency spectrum of individual chorus elements on the position of the observation point in and near the generation region is analyzed using recent Cluster data obtained on two different geomagnetically active days. The source of night-side chorus is localized using multicomponent measurements of the wave electric and magnetic fields. We have revealed that the spectrum of the chorus elements lacks the lower frequencies at the center of the source region. One possible explanation of this effect is provided by applying the backward wave oscillator model of chorus generation to these data. According to this model, the chorus frequency is determined by the parallel velocity corresponding to a steplike deformation in the distribution function of resonant electrons. This velocity decreases during the generation of an element as the electrons move through the source region. Thus, only a part of a chorus element is visible inside this region. For the typical case of rising-tone chorus elements, the lower frequencies are generated downstream with respect to the chorus propagation and, hence, disappear as a receiver is moved upstream towards the center of the source region. Citation: Trakhtengerts, V. Y., A. G. Demekhov, E. E. Titova, B. V. Kozelov, O. Santolik, E. Macusova, D. Gurnett, J. S. Pickett, M. J. Rycroft, and D. Nunn (2007), Formation of VLF chorus frequency spectrum: Cluster data and comparison with the backward wave oscillator model, Geophys. Res. Lett., 34, L02104, doi:10.1029/2006GL027953.

Cyclotron acceleration of radiation belt electrons by whistlers

The work consdiers the non linear scattering of energetic electrons in the earths radiation belts due to cyclotron interaction with VLF whistlers. In particular we consdier the acceleration of electrons which may result from trapping in the inhomogeneous medium. It is shown that considerable electron heating may result, and that the very anisotorpic electron distribution functions observed by Bell etal may be explained

Electron acceleration in the magnetosphere by whistler-mode waves of varying frequency

Acceleration of relativistic electrons in an inhomogeneous geomagnetic field during their resonant interaction with longitudinally propagating whistler-mode waves of varying frequency has been considered. Specific features of acceleration of electrons trapped by the wave field have been studied. Previous estimates of the efficiency of such acceleration have been generalized with regard to relativistic effects, and the simple formula for energy gain in a wide range of initial energies has been obtained. It has been indicated that the energy gain during a single interaction between electron and a whistler-mode wave packet, with typical parameters of an element of chorus emissions in the Earth’s magnetosphere, can reach several keV. The conditions of this acceleration mechanism realization are discussed. Specifically, it has been found that, in the case of chorus emissions in the Earth’s magnetosphere, this mechanism can be effective for electrons with perpendicular energies several times as high as such an energy of electrons generating chorus.

A computational and theoretical investigation of nonlinear wave‐particle interactions in oblique whistlers

Most previous work on nonlinear wave-particle interactions between energetic electrons and VLF waves in the Earths magnetosphere has assumed parallel propagation, the underlying mechanism being nonlinear trapping of cyclotron resonant electrons in a parabolic magnetic field inhomogeneity. Here nonlinear wave-particle interaction in oblique whistlers in the Earths magnetosphere is investigated. The study is nonself-consistent and assumes an arbitrarily chosen wave field. We employ a “continuous wave” wave field with constant frequency and amplitude, and a model for an individual VLF chorus element. We derive the equations of motion and trapping conditions in oblique whistlers. The resonant particle distribution function, resonant current, and nonlinear growth rate are computed as functions of position and time. For all resonances of order n, resonant electrons obey the trapping equation, and provided the wave amplitude is big enough for the prevailing obliquity, nonlinearity manifests itself by a “hole” or “hill” in distribution function, depending on the zero-order distribution function and on position. A key finding is that the n = 1 resonance is relatively unaffected by moderate obliquity up to 25°, but growth rates roll off rapidly at high obliquity. The n = 1 resonance saturates due to the adiabatic effect and here reaches a maximum growth at ~20 pT, 2000 km from the equator. Damping due to the n = 0 resonance is not subject to adiabatic effects and maximizes at some 8000 km from the equator at an obliquity ~55°.

Numerical simulation of whistler‐triggered VLF emissions observed in Antarctica

The British Antarctic Survey VLF database from Halley (L = 4.3) and Faraday (L = 2.3) stations, Antarctica, has been searched for clear examples of whistler-triggered emissions (WTEs). Dominant events were the triggering of risers or quasi-constant frequency emissions from the upper arm of a whistler. A fairly frequent occurrence was the triggering of steep fallers from the whistler upper arm. At Faraday most WTE events were the triggering of long steep risers from the lower whistler arm. A VHS/VLF Vlasov hybrid simulation code was run and successfully simulated the main categories of WTE: risers and fallers off the upper arm and risers from the lower arm. Agreement with observations was generally very good, although in the case of triggered fallers and risers from the lower arm, very high frequency sweep rates were not obtained. The Vlasov code is highly efficient and well suited to this problem.

Determining the size of lightning‐induced electron precipitation patches

VLF trimpi signatures are analysed at 4 sites in the Antarctic Peninsula, looking at VLF transmissions from 4 US VLF transmitters, namely NAA,NSS,NPM and NLK. The Trimpi effect is numerically modelled on all of these paths, concentrating particularly on actual events observed on many paths simulataneously. Very good agreement with observation is secured. By careful analysis of the results it is concluded that the physical size of precipitation patches is greater than previously thought, typically some 800km wide and 2000km long.