Clouds form on extrasolar planets and brown dwarfs where lightning could occur. Lightning is a tracer of atmospheric convection, cloud formation and ionization processes as known from the Solar System, and may be significant for the formation of prebiotic molecules. We study lightning climatology for the different atmospheric environments of Earth, Venus, Jupiter and Saturn. We present lightning distribution maps for Earth, Jupiter and Saturn, and flash densities for these planets and Venus, based on optical and/or radio measurements from the WWLLN and STARNET radio networks, the LIS/OTD satellite instruments, the Galileo, Cassini, New Horizons and Venus Express spacecraft. We also present flash densities calculated for several phases of two volcano eruptions, Eyjafjallajökull's (2010) and Mt Redoubt's (2009). We estimate lightning rates for sample, transiting and directly imaged extrasolar planets and brown dwarfs. Based on the large variety of exoplanets, six categories are suggested for which we use the lightning occurrence information from the Solar System. We examine lightning energy distributions for Earth, Jupiter and Saturn. We discuss how strong stellar activity may support lightning activity. We provide a lower limit of the total number of flashes that might occur on transiting planets during their full transit as input for future studies. We find that volcanically very active planets might show the largest lightning flash densities. When applying flash densities of the large Saturnian storm from 2010/11, we find that the exoplanet HD 189733b would produce high lightning occurrence even during its short transit.

Results are presented from a numerical investigation of radiation emission from an electron beam with a horseshoe-shaped velocity distribution. This process is relevant to the phenomenon of auroral kilometric radiation (AKR) which occurs in the polar regions of the Earth's magnetosphere. In these regions of the auroral zone, particles accelerated into the increasing magnetic field of the Earth's dipole develop a horseshoe-shaped velocity distribution through conservation of magnetic moment. It has been shown theoretically that this distribution is unstable to a cyclotron maser instability. A 2D particle-in-cell (PIC) code model was constructed to simulate a scaled laboratory experiment in which an electron beam subject to significant magnetic compression may be studied and brought into resonance with TE modes of an interaction waveguide. Results were obtained for electron beam energies of 75-85 keV, magnetic compression factors of up to 30 and electron cyclotron frequencies of 4.42 and 11.7 GHz. At 11.7 GHz, beam-wave coupling was observed with the TE 03 mode and an RF output power of 20 kW was obtained corresponding to an RF conversion efficiency of 1.3%. At 4.42 GHz, excitation of the TE 01 mode was observed with an RF output power of 35 kW for a cyclotron-wave detuning of 2%. This corresponds to an RF conversion efficiency of 2.6%. In both cases PiC particle velocity distributions show the clear formation of a horseshoe-shaped velocity distribution and subsequent action of a cyclotron maser instability. The RF conversion efficiencies obtained are also comparable with estimates for the AKR generation efficiency.

This version is available at https://strathprints.strath.ac.uk/63095/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. AbstractAuroral kilometric radiation occurs in regions of depleted plasma density in the polar magnetosphere. These emissions are close to the electron cyclotron frequency and appear to be connected to the formation of high pitch angle electron populations due to the conservation of the magnetic moment. This results in a horseshoe type distribution function being formed in velocity space where electrons are magnetically compressed as they descend towards the Earth's atmosphere. Satellites have observed that radio emissions occur in conjunction with the formation of this distribution and show the radiation to have propagation and polarization characteristics of the extraordinary (X-mode) plasma mode with emission efficiency observed at ∼1-2%. To investigate this phenomenon a laboratory experiment, scaled to microwave frequencies and lab dimensions by increasing the cyclotron frequency, was constructed whereby an electron beam propagated through a region of increasing magnetic field created by five independently variable solenoids. Results are presented for two experimental regimes of resonant coupling, 11.7 and 4.42 GHz, achieved by varying the peak magnetic field. Measurements of the experimental radiation frequency, power and efficiency were undertaken as a function of the magnetic compression. Results showed the radiation to be polarized in the near cut-off transverse electric radiation modes, with efficiency of emission ∼1-2%, peak power outputs of ∼19-30 kW and frequency close to the cyclotron frequency. This represented close correlation between the laboratory radiation efficiency, spectra, polarization and propagation with that of numerical predictions and the magnetospheric observations.

If an initially mainly rectilinear electron beam is subject to significant magnetic compression, the conservation of the magnetic moment results in the ultimate formation of a horseshoe distribution in phase space. A similar situation occurs where particles are accelerated into the auroral region of the Earth's magnetic dipole. Such a distribution has been shown to be unstable to a cyclotron resonance maser type of instability and it has been postulated that this may be the mechanism required to explain the production in these regions of auroral kilometric radiation (AKR) and also possibly radiation from other astrophysical objects such as stars with a suitable magnetic field configuration. In this paper we describe a laboratory experiment to investigate the evolution of an electron beam subject to a magnetic compression of up to a factor of 30

This paper describes a model for cyclotron maser emission applicable to planetary auroral radio emission, the stars UV Ceti and CU Virginus, blazar jets and astrophysical shocks. These emissions may be attributed to energetic electrons moving into convergent magnetic fields that are typically found in association with dipole like planetary magnetospheres or shocks. It is found that magnetic compression leads to the formation of a velocity distribution having a horseshoe shape as a result of conservation of the electron magnetic moment. Under certain plasma conditions where the local electron plasma frequency ω pe is much less than the cyclotron frequency ω ce the distribution is found to be unstable to maser type radiation emission. We have established a laboratory-based facility that has verified many of the details of our original theoretical description and agrees well with numerical simulations. The experiment has demonstrated that the horseshoe distribution produces cyclotron emission at a frequency just below the local electron cyclotron frequency, with polarization close to X-mode and propagating nearly perpendicularly to the electron beam motion. We discuss recent developments in the theory and simulation of the instability including addressing radiation escape problems, and relate these to the laboratory, space, and astrophysical observations. The experiments showed strong narrow band EM emissions at frequencies just below the cold-plasma cyclotron frequency as predicted by the theory. Measurements of the conversion efficiency, mode and spectral content were in close agreement with the predictions of numerical simulations undertaken using a particle-in-cell code and also with satellite observations confirming the horseshoe maser as an important emission mechanism in geophysical / astrophysical plasmas. In each case we address how the radiation can escape the plasma without suffering strong absorption at the second harmonic layer.