enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Generation of Radio Emission from Energetic Electron Beams Robert Bingham Rutherford Appleton Laboratory, Space Science & Technology Department B. J. Kellett1, V. Graffagnino1, T.W.B. Muxlow2, A.G. Gunn2, D.C. Speirs3, I. Vorgul4, R.A. Cairns4, K. Ronald3, S.L. McConville3, A.D.R. Phelps3, A.W. Cross3, C.W. Robertson3, C.G. Whyte3, W. He3 and K. Gillespie3. 1. STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, UK. 2. Merlin/VLBI National Facility, Jodrell Bank Observatory, The University of Manchester, U.K. 3. Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK. 4. School of Mathematics and Statistics, University of St Andrews, St Andrews, Fife, KY16 9SS, UK. LOFAR and the Transient Radio Sky Amsterdam, December, 2008.
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enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. All solar system planets with strong magnetic fields (Jupiter, Saturn, Uranus, Neptune, and Earth) also produce intense radio emission – with frequencies close to the cyclotron frequency. Planetary Magnetospheres Planetary Aurora Animation courtesy of NASA Jupiter’s aurora Solar wind electron beams Radio emission region
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enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. SLAB Geometry (2) • We look for a solution in which there are only waves propagating away from the layer on each side, so that the amplitude is given by where we can choose the amplitude of the wave in x < 0 to be unity. • Imposing conditions of continuity of the amplitude and its derivative at the boundaries gives • If we put K = k/k0 and l = k0 L, then from the above we obtain the relation which determines K. ( ) 1 2 tan 2 + = K K KL i (1)
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enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. • In one direction the wave will get into a region of decreasing magnetic field and density and in a suitable geometry the wave will connect smoothly onto the vacuum wave. • In the other direction the wave will, in general, encounter a cut-off and be reflected, so we ask what happens if it re-enters the cyclotron resonance region. • For the ring distribution, the dispersion relation yields one value of k2 at each point and this value is positive, as shown here. • The wave just propagates through the region with no absorption or reflection by solving the equation the x dependence in F coming from the x dependent cyclotron frequency. Inhomogeneous System – Varying Magnetic Field Ω k ( ) 0 , 2 2 = + φ ω φ x F dx d
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enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Introduction • Cyclotron maser instabilities are important in laboratory devices like gyrotrons for generation of high power radiation and are thought to play a role in radio emission from planets and stars. • Recently we and others [1] have argued that a cycloton instability driven by a horseshoe shaped distribution in velocity space may be responsible for auroral kilometric radiation from the Earth and other planets, as well as for emission from a variety of stellar objects. • One long standing problem is that of how the radiation, generated at frequencies below the upper hybrid resonance, gets on to the higher frequency branch of the dispersion relation which connects to the regime of vacuum propagation. • We will look at some of the dispersion properties of waves in the presence of energetic particles populations and show that they have properties which suggest a solution to this problem. • We begin with a simpler problem than the horseshoe distribution, namely a monoenergetic ring distribution with zero parallel momentum and a fixed perpendicular energy.
enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Observations of auroral electrons Mountain-like surface plot of an auroral electron distribution exhibiting a distinct beam at the edge of a relatively broad plateau.
enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Evolution of an auroral electron beam distribution (Bryant and Perry, JGR, 100, 23711, 1995) A - a cold, background plasma B – inject an electron beam parallel to the magnetic field. C-G – electron beam moves down into the converging field and slowly swaps parallel velocity for perpendicular velocity H – Form complete “horseshoe” distribution
enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. FAST Observations of electron distributions in the AKR source region • Delory et al. - GRL 25 (12), 2069-2072, 1998. ! ! Delory et al. reported on high time-resolution 3-D observations of electron distributions recorded when FAST was actually within the AKR source region. In general, the electron distributions show a broad plateau over a wide range of pitch angles. They presented computer simulations of the evolution of the electron distribution which assumed plasma conditions similar to those observed by FAST and which show similar results to those observed.
enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. AKR Laboratory Analogy
enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Energy Gain and Loss E Electrons gain energy Electrons loss energy When electrons gain energy – their mass increases and cyclotron frequency decreases. When electrons loss energy – their mass decreases and cyclotron frequency increases. This will lead to bunching around the orbit. If - field slips in phase so as to gain energy from particles in bunch. || || v k − < Ω ω γ E B0 B v x B force along axis, opposite directions on opposite sides of orbit. Particles gaining and losing energy have opposite axial shifts - opposite Doppler shifts - bunching on orbit. If the relative shift in the particle and wave phase is such as to give a net loss of energy from the particles to the wave. || || v k − > Ω ω γ
enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. Strangeway et al. 2001 – FAST Data “Cartoon” The figure shows an electron distribution function acquired by FAST within the auroral density cavity (see later). This is the region where the auroral kilometric radiation (AKR) is generated. The figure also shows the envisaged flow of energy. Parallel energy gained from the electric field (stage 1) is converted to perpendicular energy by the mirror force (stage 2). This energy is then available for the generation of AKR and diffusion to lower perpendicular energy (stage 3).
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