Tue., Feb. 14 notes

We first need to finish up an example that we didn't have time for in an earlier class. It deals with what happens along an air-cloud boundary when there is an abrupt change in conductivity.

Conductivity inside a cloud is lower than in the air outside a cloud. This is because the small ions attach to much larger and much less mobile cloud particles (water droplets or ice crystals). The E field must become stronger inside the cloud so that the current density (the produce of conductivity and electric field) stays the same inside and outside the cloud. We'll see that layers of charge build up on the top and bottom surfaces of the cloud.

In the figure above, Z₂ is just above and Z₁ just below the upper edge of the cloud. We'll try to estimate how much charge is necessary along the upper edge of the cloud itself. We start with the continuity equation and assume steady state conditions. Both λ and E are functions of z only.

We don't really know E_z. The current density, J_z, on the other hand is constant with altitude and we assume we know how conductivity changes as you move across the cloud-air boundary.

So we conclude a layer of positive charge builds up on the top edge of the cloud. In a similar kind of way you could show that a layer of negative charge would build up on the bottom edge of the cloud.

The effect of these two layers of cloud is to intensify the field inside the cloud. The product of higher field times lower conductivity inside the cloud is able to keep the current density equal to the current density outside the cloud.

Screening layers that form along the edges of a thunderstorm effectively mask the main charge centers inside the cloud.

The free electrons attach to oxygen molecules in a few to a few tens of nanoseconds (1 ns = 10^-9 seconds). Click here if you'd like to read more about how this "attachment time" is determined.

Then water vapor molecules cluster around the ions to create "small ions." Water molecules have a dipole structure as shown below.

The oxygen atom carries excess negative charge and the hydrogen atoms positive charge. Because of this the water vapor molecules orient themselves differently around the oxygen and nitrogen ions. This takes a few milliseconds to occur (we won't look at how that is determined). Conceptually this would look like

More water vapor molecules are able to surround the positive ions so they are bigger and have slightly lower electrical mobility than the negative small ions (typical values are included so that you can get some feel for the difference).

Sources of atmospheric ionization
The next figure summarizes the processes that ionize air. This is new information.

Radioactive materials in the ground emit alpha and beta particles, and gamma rays. Alpha particles (i.e. a helium nucleus consisting two protons and two neutrons) are a strong source of ionization but only in the first few cm above the ground. Beta particles (electrons) ionize air in a layer a few meters thick. The effects of gamma radiation extend of 100s of meters. Cosmic rays are the dominant source of ionization everywhere over the ocean and at greater than 1 km altitude over land.

The table below gives an idea of how far these different types of radiation can travel above the ground and also typical ionization rates (ip stands for "ion pairs"). (from Chapter 11 in "The Earth's Electrical Environment," National Academy of Sciences, 1986 )

We'll start with some information about cosmic radiation (cosmic rays). This is the dominant ionization process over the oceans and over land at altitudes above 1 km.

And some historical information (that was on a class handout). It really was the study of atmospheric electricity (studies of ionization of air) that lead to the discovery of cosmic radiation.

Cosmic ray intensity decreases at the geomagnetic equator because many of the incoming cosmic rays couple to and follow the earth's magnetic field lines to the magnetic poles.

Here is some information on cosmic ray showers. Very few of the primary particles reach the ground. Rather they interact with gas molecules in the atmosphere and produce many different kinds of secondary particles. (the figure and text are from: http://www.mpi-hd.mpg.de/hfm/CosmicRay/Showers.html )

Cosmic-ray air showers

Cosmic rays
The earth is hit by elementary particles and atomic nuclei of very large energies. Most of them are protons (hydrogen nuclei) and all sorts of nuclei up to uranium (although anything heavier than nickel is very, very rare). Those are usually meant when talking about cosmic rays. Other energetic particles in the cosmos are mainly electrons and positrons, as well as gamma-rays and neutrinos.

Interactions and particle production
The cosmic rays will hardly ever hit the ground but will collide (interact) with a nucleus of the air, usually several ten kilometers high. In such collisions, many new particles are usually created and the colliding nuclei evaporate to a large extent. Most of the new particles are pi-mesons (pions). Neutral pions very quickly decay, usually into two gamma-rays. Charged pions also decay but after a longer time. Therefore, some of the pions may collide with yet another nucleus of the air before decaying, which would be into a muon and a neutrino. The fragments of the incoming nucleus also interact again, also producing new particles.

The gamma-rays from the neutral pions may also create new particles, an electron and a positron, by the pair-creation process. Electrons and positrons in turn may produce more gamma-rays by the bremsstrahlung mechanism.

Shower development
The number of particles starts to increase rapidly as this shower or cascade of particles moves downwards in the atmosphere. On their way and in each interaction the particles loose energy, however, and eventually will not be able to create new particles. After some point, the shower maximum, more particles are stopped than created and the number of shower particles declines. Only a small fraction of the particles usually comes down to the ground. How many actually come down depends on the energy and type of the incident cosmic ray and the ground altitude (sea or mountain level). Actual numbers are subject to large fluctuations.

In fact, from most cosmic rays nothing comes down at all. Because the earth is hit by so many cosmic rays, an area of the size of a hand is still hit by about one particle per second. These secondary cosmic rays constitute about one third of the natural radioactivity.

When a primary cosmic ray produces many secondary particles, we call this an air shower. When many thousand (sometimes millions or even billions) of particles arrive at ground level, perhaps on a mountain, this is called an extensive air shower (EAS). Most of these particles will arrive within some hundred meters from the axis of motion of the original particle, now the shower axis. But some particles can be found even kilometers away. Along the axis, most particles can be found in a kind of disk only a few meters thick and moving almost at the speed of light. This disk is slightly bent, with particles far from the axis coming later. The spread or thickness of the disk also increases with distance from the axis.

Shower detection
Extensive air showers with many particles arriving on the ground can be detected with different kinds of particle detectors. In the air the particles may also emit light by two different processes: Cherenkov light almost along the shower axis and fluorescence light in all directions.

Other introductory material found on the net (HTML format):

Cosmic Rays by Richard Mewaldt
Cosmic Rays by James Schombert
Further reading found on the net (Postscript or PDF format):
Particle Data Group: review of cosmic rays
Introduction to high energy cosmic ray physics
Cosmic Ray Spectrum and Composition: Ground Observations

This page was written by Konrad Bernlöhr.

Radioactive decay and radon
In addition to being a source of atmospheric ionization, radon is a significant health hazard and is the 2nd leading cause of lung cancer after cigarettes. Here are links to articles concerning radon from the World Health Organization, Wikipedia, and the Environmental Protection Agency.

The following table shows a portion of the decay series that ultimately yield isotopes of radon (the half life is shown in parenthesis). The elements in the final row are stable.

Because of its relatively short half life compared to the age of the earth, all the Neptunium in the ground has decayed away. Two isotopes of radon (Rn-222 and Rn-220, indicated with *) have half lives long enough to be able to diffuse out of the soil and into the air.

The article from the World Health Organization gives a typical outdoor radon concentration of 5 to 15 Becquerels/m³ (Bq/m³). 1 Becquerel is one disintegration per second. This is something you could measure with a detector of some kind, maybe a Geiger counter. This is not really a concentration, rather a decay rate (dN/dt in the equation below). We can do a calculation to see what this implies in terms of radon concentration and ion pair production rate.

The rate at which a radioactive material decays is described by the following equation

(note: so far in this course we have used λ to represent linear charge density, atmospheric conductivity, and now decay constant).

We can solve the equation above to give

Now that we know the decay constant we'll substitute back into the decay rate equation to determine the radon concentration needed to produce an average outdoors decay rate of 10 Bq/m³.

(the number density for air, 2.67 x 10¹⁹ air molecules/cm³ is sometimes known as Loschmidt's number).

We can divide these two numbers to determine the number of ion pairs produced by each distintegration. Then we multiply by the Rn concentration and the decay constant (which give the decay rate) to determine the ionization rate.

These decay products can attach to dust particles which are then inhaled and stay trapped in the lungs. Since the decay products are themselves radioactive, long term exposure can ultimately lead to lung cancer. Radon is apparently the 2nd leading cause of lung cancer in the US after cigarette smoking.

Radon concentration indoors can build to levels that are much higher than normally found outdoors. An extreme case is mentioned below.

emission type	distance of travel	ionization rate [ ip/(cm³ sec) ]
alpha particles	only a few cm above the ground	not well known
beta particles	a few meters above the ground	0.1 to 10
gamma rays	100s of meters above the ground	1 to 6
radon	depends on atmospheric conditions	1 to 20 at 1-2 m above ground
cosmic rays	1 to 2 ip/(cm³ sec) near the ground

			all of the Neptunium in the soil has decayed away..
			Rn-222, Rn-219, and & Rn-220 are sometimes referred to as "radon", "actinon", and "thoron" respectively. All three are also known as "emanatium."