What Does the 430 MHz Radar See in an Ionospheric Modification Experiment?

Contents: The Plasma and HF Induced Instabilties and How the Radar Detects the Plasma Instabilities. The second part contains a section on incoherent scatter and on the fluctuations causing the scatter.

The Plasma and HF Induced Instabilties

The block below represents a section cut out of the ionospheric plasma. The upward propagating HF wave is reflected at a particular height. This height is shown by the red plane. The incident and reflected waves set up a standing wave shown by the alternating dark and light layers. This is a strong electric which interacts with the plasma.

The instabilities seen by the radar shortly after the HF is turned on can be divided into two types according to the degree of sophistication required in the model describing the response to the E field of the HF wave.

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1. The first kind occurs at a particular height determined by k vector and frequency matching conditions on the HF wave, the low and high frequency plasma waves, and the radar EM wave. The height shown above by the green layer might correspond to that where the primary decay instability caused by the HF pump would be seen. Higher order instabilities pumped by plasma waves resulting from the primary one would be seen at slightly different heights. These heights are not locked to the standing E field pattern; for example, a small shift in the radar frequency would cause the heights to change by a small amount. These are parametric instabilities, and they can be understood by solving fairly simple differential equations by analytic means.

2. The second kind of instability occurs at the E field standing wave maxima, primarily the first one. These are driven instabilities, and are described by the phrase Strong Langmuir Turbulence (SLT). Initially small depletions in the plasma trap Langmuir waves which become very intense as the depletion deepens. These cavitons soon burn out, and the cycle is repeated. The cavitons are very numerous and small (centimeters in size). They are predicted by simulation, not analytic solution, and the radar does not see them directly, but rather sees the characteristic spectra of the intense Langmuir waves. The spectrum consists of two parts. First, a broad part resulting from the Langmuir waves in the cavitons. It is broad because the cavitons have a range of depths at a particular altitude, and thus a range of plasma frequencies. The second part is narrow, and it occurs at the plasma resonance frequency of the ambient plasma because it results from waves launched into the ambient plasma from the cavitons.

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How the Radar Detects the Plasma Instabilities

Incoherent Scatter

The electrons in the plasma are not distributed exactly uniformly, but rather have a constantly changing random distribution, as all free particles with a non-zero temperature must. It is convenient to model the plasma as a fluid, where the individual particles are thought of as smeared out and merged together. The random distribution of the particles shows up as regions of higher and lower density in the fluid. The block below represents a small piece extracted from the plasma; the side and top show the intensity of the electron density fluctuations at the surfaces.

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The transmitter emits a pulse composed of a sinusoidal waveform that has many cycles in its length. The helix below the block shows the tip of the electric field vector of the pulse as a function of distance from the transmitter at some time t. Each electron is accelerated by the E field of the pulse, and at any one moment, the E field at the receiver is the sum of the signals transmitted from all of the electrons in a volume with a depth determined by the pulse length. If the fluctuation intensity is allowed to go to zero, all E field phases will be very nearly uniformly represented, and the E field at the receiver will go to zero. However, if the fluctuations are finite, then all phases might not be represented uniformly, and the sum is not necessarily zero. The small deviation from zero is the incoherent scatter return. The only fluctuation scale sizes that do not average to zero along the radar beam are the ones synchronized with the E field phase variation in the medium. Considering the propagation delays out and back, the single scale size that does matter is that equal to half of the radar wavelength.

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The fluctuations: thermal, photo-electron enhanced, and HF induced

Although the electron density fluctuations exist because the electrons and ions have random locations and move about with speeds determined by their temperatures, the results are not simple. At our scale length (35 cm), the electrons are tightly coupled to the heavier ions, and so most of the scatter has the narrow spectral width associated with the ion thermal motion. However, the electrons are capable of some collective motion independent of the ions at the plasma resonance frequency resulting in weak scatter, typically several MHz from the radar frequency. When the equations describing the plasma motion are solved, a complex series of wave motions is revealed. Thus the fluctuations are best thought of as propagating waves. One consequence of this is that fast photo-electrons removed from atoms by solar EUV can couple energy into the electron (also called Langmuir or high frequency) waves, thus enhancing the so-called plasma line and turning it into a useful response. More to the point here, energy can be coupled into these plasma waves from an HF wave, tremendously enhancing them. Thus the scatter produced by plasma instabilities is generally much stronger than that from the thermal irregularities.

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