Plasma Frequency Probe Theory

In a plasma frequency probe, sinusoidal signals are used to excite the plasma in which a sensor head is immersed.  The frequency of the sinusoidal signal is varied to eventually match the resonant frequency of the plasma.  The resonant frequency of the plasma is related to the plasma density by the following equation: [2]

,

where                         ω_p = plasma resonant frequency,
                                    n_e = electron density,
                                    q = electron charge,
                                    m_e = electron mass,
                                    ε₀ = permittivity of free space.

Solving for electron density yields:

.

            In order to locate the resonant frequency of the plasma, we rely on the fact that the plasma impedance has an imaginary component.  When passing through the resonant frequency, this reactance switches from being capacitive to inductive.  Moreover, this resonance causes the returning current signal from the sensor head to be in phase with the excitation voltage signal. [3]

            It is important to note that at the altitudes of the proposed investigation, the Earth’s magnetic field causes a shift in the frequency response of the plasma.  The frequency sensed by the PFP method is known as the upper hybrid frequency, w_uh, determined by:

,

where ω_ce is the electron cyclotron frequency.  This frequency is directly related the magnetic field strength, B, that is present by: [4]

In order to properly design the HPP, some analysis needed to be carried out to gain an order of magnitude understanding of these parameters.  Two reasonable assumptions were made: that the NASA Wallops Flight Facility would be flown over in the spacecraft’s orbit and that the spacecraft altitude would be between 100 an 1000 km.  Using data from the International Reference Ionosphere (IRI) Model and International Geomagnetic Reference Field (IGRF) Model the plot shown in Figure 2 below was created. [6], [7]

Figure 2: Upper-hybrid frequency analysis from IRI and IGRF data models

            If it is assumed that LionSat will be launched from the space shuttle, the altitude range of 300-400 km is significant.  In this altitude range, the upper-hybrid frequency that the PFP action of the HPP would have to track is between 14 and 25 MHz depending on the time of year, solar activity, day/night, and other factors.

            Overall, the Plasma Frequency Probe provides the best in situ measurements of plasma density because it is not affected by the potential of the spacecraft carrying the probe, and is not sensitive to sensor head surface contamination.