Radio emissions produced by cosmic- ray extensive air showers traversing thunderclouds Joseph R. Dwyer Department of Physics and Space Sciences Florida Institute of Technology

Lightning 101

Lightning Initiation Problem Years of balloon, aircraft and rocket observations have shown thunderstorms never seem to make big enough electric fields to actually make a spark This has led to the cosmic-ray model of lightning initiation….

NASA/CXC/Rutgers/J. Warren & J.Hughes et al. T Tycho supernova remnant as seen in x-rays by Chandra Step 1: Blow up one medium to large size star

Step 2: Have the explosion accelerate cosmic-rays, which then fly around the galaxy for about 10 million years until… NASA FERMI all sky gamma-ray image

Step 3: One of them slams into the Earth’s atmosphere and carves a conductive path through a thunderstorm.

Step 4: Voilà!

Nice idea, but, unfortunately, air showers alone will not increase the conductivity enough to initiate lightning. If air showers are involved in lightning initiation then there must be some other mechanism to increase the ionization…. Runaway Electrons

25 MeV electron moving through air at 1 atm

25 MeV electron moving through air at 1 atm in a 3 kV/cm electric field (mechanism developed by Wilson 1925 and Gurevich et al. 1992)

Energy loss and gain experienced by an electron in air From Dwyer (2004)

Inside a thundercloud: Strong electric fields accelerate electrons to nearly the speed of light. These electrons emit gamma-rays. Electric field Gamma-rays High-energy runaway electrons

There’s more: Relativistic Breakdown due to x-ray and positron feedback. The central avalanche is due to the injection of a single, 1 MeV seed electron. All the other avalanches are produced by x-ray and positron feedback. The top panel is for times, t < 0.5  s. The middle panel is for t < 2  s, and the bottom panel is for t < 10  s. From Dwyer (2003 and 2007)

Example of runaway electron production: x-rays from rocket-triggered lightning dart leaders From Dwyer et al. (2004)

Cartoonists had it right all along From Scientific American, May 2005

Runaway electrons inside thunderclouds Photo by Mindi Holcomb

Another example of runaway electron production: CGRO/BATSE Terrestrial Gamma-ray Flash (TGF) Fishman et al and

Where do they come from?

Where do they come from? – 2005: Here

Where do they come from? – 2005: Here After 2005: Here

Terrestrial Gamma-Ray Flash (TGF) spectrum and results of Monte Carlo simulation for different source altitudes From Dwyer and Smith (2005)

RF emissions from Cosmic-ray extensive air showers (EAS) plus runaway electrons When cosmic-rays strike the atmosphere they produce large showers containing millions of high- energy particles, mostly electrons, positrons and gamma-rays. These air showers can provide the seed particles for runaway electron avalanche multiplication. It has been suggested that this process may lead to lightning initiation. If correct, then EASs and runaway electron multiplication should produce measurable RF emissions.

Simplified analytical model In order to gain insight into the RF emissions, a simple analytical model has been developed. In this model, the air shower may have an inclined trajectory but has no longitudinal or lateral extent. The runaway electron avalanches are seeded by the air shower along the entire trajectory through the high field region. However, additional spreading of the electrons due to longitudinal or lateral diffusion is ignored. The distance to the observer is assumed to be much larger than the avalanche length so that only the radiation field need be calculated.

Charge and current densities Convolving the runaway electron density produced by each seed particle with the seed particle distribution from the air shower gives the charge density of runaway electrons Including the drifting low-energy (few eV) electrons produced by ionization gives the total current density where l is the electron-ion pairs per unit length; v e is the drift speed of the low-energy electrons and  a is the low-energy electron attachment time.

Electromagnetic (RF) pulse: The electromagnetic emission produced by the current is given by The solution is The limits of integration are given by the conditions that the runaway electron avalanches are confined to the avalanche (high field) region and that the electrons move in the direction opposite the electric field. These limits are functions of the air shower velocity vector and the direction to the RF observer. For example, for an upward thunderstorm electric field this gives the radiation electric field on the ground:

Numerical model of radio frequency electromagnetic emission Because the current densities produced by runaway electron avalanches seeded by extensive air showers may be calculated by the Monte Carlo simulations, the RF emission may be calculated [Uman, 2001]. The numerical model includes: Realistic air shower with correct longitudinal and lateral distributions and development in electric field. Accurate runaway electron avalanche propagation, including correct avalanche growth, and longitudinal and lateral distributions. Low-energy electron production, drift and attachment.

Calculation of the vertical electric field measured on the ground (5 km away), produced by runaway electron avalanches seeded by a eV air shower

The magnitude of the RF pulse versus position on the ground. (The air shower is eV and strikes the ground at +5 km in this figure.)

The RF pulse shape measured remotely, e.g. on the ground, is very sensitive to the thundercloud electric field (air shower is a eV). The black curve is for a thundercloud electric field of 1250 kV/m; the red curve is for 625 kV/m; the blue curve is 375 kV/m, and the green curve is 250 kV/m.

A new 8-station cosmic-ray air shower array and RF electric field antenna has been constructed at the UF/Florida Tech International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, FL

Summary The RF pulses generated by cosmic-ray extensive air showers and runaway electron avalanches are short with durations ranging from microseconds. Most pulses are small with peak electric fields of a few tens of mV/m, depending upon the energy of the cosmic-ray air shower. Although the RF pulses are usually small, they occur in coincidence with the air showers striking the ground, so air shower measurements may be used to help identify the correct RF pulses. Modeling of the RF emission of runaway electron avalanches seeded by extensive air showers shows that these small RF pulses may be used to remotely measure the magnitude and orientation of thundercloud electrostatic fields, potentially addressing questions about lightning initiation. Many mysteries remain about lightning, including how it gets started and how it moves. It is interesting that cosmic-ray air showers may play a role, either by initiating lightning or as a tool for studying it.