n is the electron density (in this case produced by intense heating in the lightning channel) e is the charge of an electron (-1.6 x C) m is the mass of an electron (9 x kg) ε 0 is the permittivity of free space (8.85 pF m -1 ) A key feature here is how the plasma frequency compares to the frequency of the incident radar wave N on order of – m -3

Williams et al. (1989), J. Atmos. Sci. Plasma frequency as a function of temperature. Also illustrated are frequencies of various radar bands. The key physical process here is the relationship between the plasma frequency and the frequency of the incident (radar) radiation impinging on it. The plasma frequency is basically determined how hot the plasma is, ie, its temperature. The temperature of the plasma determines the level of ionization, which is given by the concentration of electrons (or ionized species). For T > 5000K, plasma frequency is larger than the frequency at the various radar wavelengths. Plasma frequency refers to how rapidly the electron density changes with time. Viscous and EM forces are at work in the plasma.

Radar detection of lightning has a long history λ

Overdense Plasma For an overdense plasma, the characteristic frequency of the plasma is greater than the frequency of the EM wave that impinges on it. That is, f P > f EM The plasma can be considered to have a period of oscillation or natural frequency. Recall that the period of an EM wave (or oscillation) is inversely proportional to frequency. So for an overdense plasma, T p < T EM That is, the oscillation period of the plasma is short compared to the EM wave period. This means that the plasma can respond to the EM wave by having electrons on its outer sheath oscillate at the frequency of the incident wave. So the plasma acts as a conductor since the incident wave only interacts with the outer portion of the sheath. Just like a metal conductor.

Underdense plasma For an underdense plasma, f P < f EM or T P > T EM The period of oscillation of the plasma is longer than that of the incident EM wave so in this case the response of the plasma is “sluggish”. That is, it behaves as a dielectric. In this case the incident wave penetrates into the plasma and the backscatter of the incident EM is greatly reduced. Cold plasmas are generally underdense.

Incident waveReflected wave Overdense Underdense Conductor Dielectric As the lightning channel cools, the electron density will fall rapidly so the ability of the channel to backscatter radar waves will diminish. Observations and theory show the reflectivity falls at 0.2 db/ms (Holmes et al., 1980). So the observation of lightning channels is a very transient thing! Debye distance is short for overdense plasmas. Debye distance is related to ratio of viscous forces to EM forces in the plasma. So for short Debye distance, EM forces large compared to viscous forces and plasma can “respond” to impinging EM wave.

Dielectric response regime Overdense plasma regime 5000K 3500K A-scope display of lightning “spikes” Ligda, 1956

Ligda, radarmet.atmos.colostate.edu/AT741/papers/Ligda_Film/

Broad spectrum from lightning—greater spatial complexity of the target compared to weather echo. We expect λ -4 dependence for Rayleigh targets (r < 0.07λ). Reflectivities from lightning plasma.

Illustrates masking effects of precipitation. Lightning channels “emerge” from the Rayleigh backscatter at long wavelengths.

Z DR mostly negative Vertical channels Ray plots during flash High L dr as well

Courtesy Chilbolton radar facility, UK Negative phi dp in anvil associated with strong vertical E fields

Radar Detection of Lightning: Conclusions 1. Lightning plasma is generally overdense at all meteorological wavelengths. Hence, lightning channel responds like a metallic conductor for times on the order of hundreds of ms (when high T is maintained). 2. The lightning echo behaves as a volume target to radar. Attributed to a 3-D dendritic structure composed of overdense channel segments, which are long and thin compared to the radar wavelength. 3. Apparent radar wavelength dependence of lightning echoes is highly variable and strongly influenced by precipitation masking - on average, λ light ~1/λ 2 4. Tendency of strongest lightning echoes to occur in regions of more intense precipitation. 5. Infrequent detection of lightning at radar wavelengths attributed to precipitation masking, especially at shorter wavelengths (S-band and below).