Numerical And Laboratory Simulations Of Auroral Cyclotron Radiation Processes

D.C. Speirs1, S.L. McConville1, K. Ronald1, A.D.R. Phelps1, A.W. Cross1,
R. Bingham1,3, C.W. Robertson1, C.G. Whyte1, I. Vorgul2, R.A. Cairns2and
B.J. Kellett3
1. SUPA Department of Physics, University of Strathclyde, Glasgow,
G4 0NG, Scotland
2. School of Mathematics and Statistics, University of St. Andrews, St. Andrews,
KY16 9SS, Scotland
3. Space Physics Division, CCLRC, Rutherford Appleton Laboratory, Didcot,
OX11 0QX, England
Abstract. Results are presented of an experimental and numerical investigation of radiation emissions from an electron
beam with a horseshoe distribution in velocity space. 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 are accelerated into the increasing magnetic field of the Earth’s dipole. In the laboratory experiment an electron
beam with an initial spread in velocity was injected into an increasing magnetic field leading to the formation of a
horseshoe shaped velocity distribution, in simulation of the auroral process. This distribution function is expected to be
unstable to emission of cyclotron radiation [1,2], and was therefore investigated as a potential mechanism for the
generation of auroral kilometric radiation. Results were obtained from electron beams with energies of 75-80keV and
cyclotron frequencies of 4.45 and 11.7GHz. The radiation emission was measured using a real time FFT spectrometer and
was observed to be close to the cyclotron frequency. Measurements of the electron beam transport characteristics confirm
that the horseshoe distribution was obtained in the experiment. Determination of the radiation antenna pattern at the
output of the experiment allowed the complex TE mode structures excited by the beam to be analysed and numerical
integration provided an estimate of the efficiency. At 11.7GHz, multimode excitation with an efficiency of ~1% was
observed whilst at the lower cyclotron frequency of 4.45GHz the highest efficiency obtained was 2% corresponding to an
output power of 19kW. This was achieved using a cyclotron detuning of 2.5% below the cut-off frequency of the TE0,1
radiation mode in the apparatus. These results are in close agreement with the predictions of the 2D PiC code KARAT.
The efficiency is also comparable with estimates for the AKR generation efficiency [3].
Keywords: Auroral Radio Emission, Cyclotron Instabilities, Laboratory Simulator
PACS: 52.25.Xz, 52.25.Xz, 94.30.cq, 52.35.-g
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 an Electron Cyclotron Maser interaction 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. We
describe numerical simulations and a laboratory experiment to investigate the evolution of an electron beam subject
to a magnetic compression of up to a factor of 30 in resonance with a microwave frequency electromagnetic field.
Figure 1 shows the design of the apparatus. A large diameter stainless steel anode tube encompasses the centrally
located co-axial cathode. A velvet ring is secured to the face of the cathode and provides electron emission as a
result of the plasma formed on the tips of the velvet material when a 75-80kV pulse from a Blumlein power supply
is applied across the gap between the cathode and the anode mesh. A low, fringing, magnetic field is generated by
solenoid 1 and ensures that the electrons have an initial spread in their pitch factors (as the angle presented by the
cathode to the magnetic field lines is a function of the radius). This is augmented by the profiling of the cathode face
to ensure that the initial radial electric field component perceived by the electrons varies as a function of their radial
coordinate. The electrons are subject to compression as they pass through coil 1 into coil 2 and reach the maximum
of the magnetic field in the centre of coil 3. The variation in the axial component of the magnetic field on the axis of
the experiment was calculated using a Maple programme.
FIGURE 1. Configuration of the experiment as described in KARAT
FIGURE 2. View of major experimental components. The main image shows the magnet coils and the smaller images from top
to bottom show the anode mesh, the cathode and the Faraday cup beam current diagnostic.
To simulate the experiment the time dependent PiC code KARAT was used. The simulation was given the
dimensions of the vacuum vessel and electrodes and the axial magnetic fields estimated by the Maple code.

To simulate the experiment the time dependent PiC code KARAT was used. The simulation was given the
dimensions of the vacuum vessel and electrodes and the axial magnetic fields estimated by the Maple code.
Solenoid 1 Solenoid 2
Solenoid 3
Solenoid 4 Solenoid 5
Solenoid 6
Gun Coil Intermediate Coil Mirror Coil
Main Coil
Shim Coils
Emission of the electrons from the cathode was simulated under the action of the applied potential (75-80kV
between cathode and anode) giving a beam current of 12A. The geometry of the simulations is illustrated in Figure
1. Using the 2D implementation of the code gave fast execution for a given accuracy of the model and because of
the R-Z symmetry of the apparatus produced very illustrative phase space plots. As the electron beam passes into the
smaller diameter region, EM waves are excited as it undergoes resonance with the near cut-off modes of the
cylindrical waveguide. In the present case the TE0,1 and TE0,3 resonances were investigated at frequencies of
4.45GHz and 11.7GHz respectively. TE modes were selected for this investigation because they exhibit similar
propagation and polarization properties to the X-mode observed by auroral satellite measurements. Figure 3
illustrates the initial horseshoe shape of the simulated electron velocity distribution, formed as a result of the
magnetic compression process as the beam enters the resonance region. The perturbed distribution function formed
due to the radio frequency interaction is also presented.

This work is supported by the EPSRC. Mr. I.S. Dinwoodie is thanked for his help in creating the apparatus.
1. Speirs D.C., Vorgul I., Ronald K., Bingham R., Cairns R.A., Phelps A.D.R., Kellett B.J., Cross A.W., Whyte C.G. and
Robertson C., 2005, Journal of Plasma Physics, 71, pp665-674.
2. Vorgul I., Cairns R.A. and Bingham R., 2005, Physics of Plasmas, 12, article: 122903.
3. Gurnett D.A., 1974, Journal of Geophysical Research, 79, pp4227-4238.

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