7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

A New Ion beam Instability and Radio Emission Driven by Shocks
Iver H. Cairns1,1
School of Physics, University of Sydney
e-mail (speaker): iver.cairns@sydney.edu.au

Abundant observational evidence and theoreticalanalyses demonstrate that shocks can accelerate beams
of electrons and ions into their upstream regions and thatthese particles drive multiple types of plasma waves,including Langmuir and ion acoustic waves. In addition,
the electrons and Langmuir waves often lead to theproduction of radio emission near the electron plasma
frequency fp and near 2fp.
This presentation is in two parts..The first is a newtheoretical description of an instability for the growth ofion acoustic by a cold, relatively, slow ion beam.
Although investigated here in connection withphenomena observed by NASA’s Parker Solar Probenear the Sun, this instability should also be relevant inforeshock regions upstream of shocks. The second is the3D shape of the source regions for fp and 2fp radiation
upstream of Earth’s bow shock, produce from Langmuir
waves driven by shock-accelerated electron beams in theforeshock. These predictions are also relevant to type II
solar radio bursts and the 2-3 kHz radiation observed by
the Voyager spacecraft in the outer solar system.
1.

Ion beam-driven Ion Acoustic Instability

Recent observations by R. Ergun and collaborators(unpublished) show the generation of trains of ion
acoustic wave packets with rising tones and a relatively
broadband character typical. A numerical dispersion
solver with a slow proton beam showed growth but theorigin was unclear. Here I show analytically using
kinetic theory that a cold proton beam instability exists
and can explain several aspects of the numericalcalculations and observations. Starting from theelectrostatic dispersion equation

density to be determined by data-theory comparisons,
thereby constraining the origin of the proton beam.
2.

Radio emission from Earth’s Foreshock

The standard theory for this radio emission involves
shock-drift (aka mirror-reflection) of electrons at theshock, development of electron beam distributions bytime-of-flight effects, driving of Langmuir waves by thebeam instability, and generation of fp and 2fp radio
emission by nonlinear processes involving the Langmuir
waves [1]. Each of these processes can be modelledanalytically. Recently P. Oppel and I revised the theory[2] and extended it to include fp radiation produced bylinear mode conversion (LMC) of Langmuir waves at
density irregularities [3] and to predict the shape of theradio source. Figure 1 shows the predicted shape of thenonlinear fp radio source for nominal solar windparameters as viewed from the 1st Lagrange point. The
radio source is strongly elongated perpendicular to theinterplanetary B field. The total flux is ~7x10-19 Wm-2
Hz-1, not inconsistent with data, a factor ~3 larger and~60 smaller than the LMC fp and nonlinear 2fp fluxes.
These and other results will be discussed in the context
of other radio emissions produced near shocks.
References[1] Z. Kuncic et al, Geophys. Res. Lett., 29(8), 10.1029
2001GL024524, 2-1 (2002).
[2] P. Oppel, Masters thesis “Radio Emissions
from Bolides”, KTH Roy. Inst. Tech., (2021)[3] F. Schleyer et al., J. Geophys. Res., 119, 3392 (2014).

1 + 𝐾𝐾𝐿𝐿𝑒𝑒 + 𝐾𝐾𝐿𝐿𝑖𝑖 + 𝐾𝐾𝐿𝐿𝑏𝑏 = 0 ,where KLj is the contribution for species j = e (thermalelectrons), i (thermal ions) and b (ion beam), theinstability is described by an equation reminiscent of acold electron beam instability, α (α + α0)2 = ½. Here α isthe scaled difference from the (complex) wave frequency
ω and the ion acoustic wave frequency, while and α0 is
the scaled frequency offset (ω – k.vb), respectively,
where k and vb are the wavevector and the ion beam
velocity, respectively. In detail, the instability is areactive (or fluid-type) instability associated with a beammode and the instability is favoured when the proton
beam speed is close to the ion acoustic speed and thebeam is relatively dense and cold. In principle, thistheory allows the ion beam speed and relative number

Figure 1. Nonlinear fp radio source viewed from the L1
point, with Earth located at (0,0,0) and B in the X-Yplane. Units are Wm-2Hz-1Rm-2, where Rm is an Earthradius.