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Environmental ESD: Part 1 – The Atmospheric Electric Circuit

Associate Professor Neils Jonassen authored a bi-monthly static column that appeared in Compliance Engineering Magazine. The series explored charging, ionization, explosions, and other ESD related topics. The ESD Association, working with In Compliance Magazine is re-publishing this series as the articles offer timeless insight into the field of electrostatics.

Professor Jonassen was a member of the ESD Association from 1983-2006. He received the ESD Association Outstanding Contribution Award in 1989 and authored technical papers, books and technical reports. He is remembered for his contributions to the understanding of Electrostatic control, and in his memory we reprise “Mr. Static”.

~ The ESD Association

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A Dash of Maxwell’s: A Maxwell’s Equations Primer – Part Two

Maxwell’s Equations are eloquently simple yet excruciatingly complex. Their first statement by James Clerk Maxwell in 1864 heralded the beginning of the age of radio and, one could argue, the age of modern electronics.

Reprinted with permission from: Compliance Engineering Magazine, Mr. Static Column Copyright © UBM Cannon


An understanding of the atmospheric electric circuit provides an insight into the processes underlying ESD events.

When people hear about static electricity, most of them think of unpleasant shocks experienced when touching a doorknob or of electronic components being destroyed because of electrostatic discharge (ESD) events. Fifty years ago, it was more likely that static electricity would be connected with explosions in chemical or pharmaceutical factories or laboratories. However, in most cases, ESD phenomena are thought of as the result of human activity. People often overlook atmospheric electricity, which by its nature is very similar to well-known static electric processes.

If a properly grounded fieldmeter is brought outside and directed upward, the meter would likely measure an electric field directed downward with a strength of approximately 150 V·m–1. If the measurement were made on a mountaintop, the field may be 10 or more times stronger. These measurements are indicative of fair-weather conditions.

If there is a thundercloud overhead, the field is usually reversed and runs easily into the tens of kV·m–1. If a horizontal metal plate exposed to the free atmosphere is connected to ground through a sensitive ammeter, it would measure a current of about 3·10–12 A·m–2. A value of 3 pA·m–2 is not much, but when it is taken for the earth as a whole, the current amounts to about 1500 A.

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Although there are still many atmospheric electric processes that are not understood in detail, there is a general understanding of the atmospheric electric circuit (Figure 1 provides a simplified picture of the processes). Fair-weather conditions are shown on the left side of the figure, where a downward electric field drives positive charges toward ground. Most of the field lines start at positive charges in the lower atmosphere, and some extend all the way to the atmospheric electric exchange layer (at a height of about 60 km), the lower part of the ionosphere. The necessary field distribution is maintained by thunderstorms (or thunderclouds), shown on the right side of the figure. A thundercloud normally has a negative base and a positive top, which brings negative charges to ground.

1204 mrstatic fig1

Figure 1: The atmospheric electric circuit

 

Furthermore, the values of the fields below the thunderclouds may be much greater than the fair-weather values, often 5–10 kV·m–1 as compared with a fair-weather field of 100–200 V·m–1. The greater field strength may cause corona and brush discharges from the tips of leaves and branches, not to mention lightning rods, which contribute to the total current. Regular lightning discharges also represent a certain current to the ground (primarily negative), but this contribution is rather modest. The field has the same direction above, as well as below, the thunderclouds, causing a positive current to flow to the atmospheric electric exchange layer and closing the circuit (see Figure 2 for an equivalent diagram).

1204 mrstatic fig2

Figure 2: An equivalent diagram of the atmospheric electirc circuit

 

Between the exchange layer and the ground, there is a voltage difference of about 300 kV, which drives a current of about 1500 A to ground, where it is distributed over all areas with fair-weather conditions. This corresponds to a resistance R1 of 200 W, representing the parallel resistance of all fair-weather air columns. G represents the generator effect of all simultaneously active thunder systems, and R2 and R3 represent the resistances of the air columns above and below these systems, respectively.

Charge Carriers

For a current to flow in a given medium, an electric field has to be established and the medium must contain mobile charge carriers. In atmospheric air, the charge carriers are air ions (or atmospheric ions), molecular clusters that carry an electric charge.

An ion is formed when a neutral oxygen or nitrogen molecule receives enough energy to lose an electron and is left as a singly positively charged elementary ion. Within less than a microsecond, the electron will combine with (usually) an oxygen molecule, forming a negatively charged elementary ion.[1] Other types of elementary ions include hydroxonium (H3O+) and charged nitrogen oxides.

Small Ions. By polarization, both polarities of elementary ions will bind 10–20 molecules of water around themselves (a few more for positive than for negative ions) within a fraction of a second, thereby forming small molecular clusters. These molecular clusters are called air ions, and they are almost 100% responsible for charge neutralization by air ions.[2]

Large Ions. However, any atmosphere will contain aerosol particles or condensation nuclei in numbers from a few thousand to several hundred thousand per cubic centimeter. These are particles or molecular clusters with radii ranging from 10–10 to 10–7 m. If a small ion collides with a condensation nucleus, the two may attach to form a large ion.

Ion Sources

An air molecule may receive the necessary ionization energy from a colliding atomic particle or from a quantum of electromagnetic radiation energy. In the lower atmosphere, ions are predominantly produced by radiation from radioactive materials in the soil, in building materials, and, first of all, in the air (radon and its daughter products). Although all three types (alpha, beta, and gamma) of radiation may ionize the air, alpha radiation is by far the most important.

An alpha particle (with energies in the order of 4–8 MeV [6–13 x 10–13 J]) emitted from a decaying radioactive atom (see Figure 3) will, along its trajectory through the surrounding air, knock off electrons from oxygen and nitrogen molecules—at the expense of about 34 eV per successful collision. Cosmic radiation contributes maybe 10% to the ionization at ground level. However, at higher altitudes, the partitioning shifts dramatically both because the radiation from the soil and airborne materials decreases and because the intensity of the cosmic radiation increases.

1204 mrstatic fig3

Figure 3: A decaying radioactive atom emitting an alpha particle.

 

Mobility

Normally, ions are characterized by their mobilities. If an ion is exposed to an electric field E, it will move with a constant velocity v given by:

1204 mrstatic eq1    (1)

For positive ions, v is in the direction of the field, and for negative ions, v is in the opposite direction.

The factor of proportionality, k, represents the mobility of the ion. The unit of k is (m/second)/(V/m) = m2·V–1·s–1. Small positive ions have mobilities of approximately 1.4 x 10–4 m2·V–1·s–1, and small negative ions have about 1.8 x 10–4 m2·V–1·s–1. The difference in mobility reflects the difference in the numbers of attached water molecules in the ions. Large ions cover a range of mobilities from about 3 x 10–7 to 8 x 10–8 m2·V–1·s–1, depending partially on the nature and size distribution of the aerosol particles in the air.

Removal Processes

An ion has a limited lifetime. It may deposit on a surface either by diffusion or by the aid of an electric field. An ion may combine with oppositely charged ions or particles and hence cease to exist as an ion, or with aerosol particles and then either be neutralized or become a large ion. This latter process usually determines the lifetime of an ion. In polluted city air, the average lifetime may be in the order of 10–20 seconds, whereas in polar air, poor in aerosols, the lifetime may be as long as 300–400 seconds.


Conductivity

For a current to flow in a medium, that medium must contain mobile charge carriers. Consider an atmosphere containing one type of ions with the concentration n and the mobility k,
with each ion carrying a single elementary charge e. If an electric field E is established in the medium, a current with the density j will flow in the medium in the direction of the field (for positive ions) given by j = enkE or

1204 mrstatic eq2    (2)

Equation 2 is Ohm’s law in differential form. The factor

1204 mrstatic eq3    (3)

is called the conductivity of the air, and the unit is W–1·m–1.

It appears from Equation 3 that, of two groups of ions with the same concentration, the group with the greatest mobility contributes the most to the conductivity. It is often convenient to separate the contributions to the conductivity of positive and negative ions by introducing the polar conductivities, that is, the conductivities caused by the positive and negative ions, separately. In the case of an atmosphere with the concentration n+ and mobility k+ for positive ions and n and k for negative ions, the polar conductivities are
g+ = en+k+ and g = enk. Both polar conductivities are positive quantities, causing positive currents to flow in the direction of the field, with positive and negative charge carriers moving in opposite directions.

Usually, the ions do not all have the same mobility but are, in general terms, distributed according to some function of frequency f(k) in such a way that the concentration dn of ions with mobilities from k to k + dk is given by dn = f(k)dk. The conductivity may then be written as

1204 mrstatic eq4    (4)

Normally, only small ions contribute significantly to the conductivity of the air because their mobility is much greater than that of large ions and charged particles.

At ground level, under fair-weather conditions, the average value of the conductivity is about 2 x 10–14 W–1·m–1. The conductivity shows annual and diurnal variations, depending on variations in the ionization and aerosol conditions. The conductivity increases with increasing altitude both because of the decrease in aerosol concentration and because of the increase in the cosmic radiation intensity. At an altitude of 5 km, the conductivity may be about 10 times greater than at ground level.

The Vertical Field

It has been known for more than two centuries that the normal prevailing condition in the atmosphere is best described in today’s language as an electric field directed downward, bringing a positive charge to the ground. At ground level, the field strength is about 100–150 V·m–1. The field strength decreases rapidly with increasing altitude, and at 5 km, the field strength is about one-tenth of the value at ground level.

The potential of the atmosphere can be found by integrating the field strength with respect to height. At a height of approximately 60 km, the field strength is virtually zero, and, consequently, the potential does not change with further increases in height. This is the location of the atmospheric electric exchange layer shown in Figure 1. The mean value of the potential of the exchange layer is about 300 kV.

The current density (see Equation 2) is more or less constant in a given vertical column of air and can be written as

1204 mrstatic eq5    (5)

where V is the potential of the atmospheric electric exchange layer and Rc is the columnar resistance (i.e., the resistance of an air column that extends from the ground to the exchange layer and has a unit area cross section).

Equation 5 expresses two important relations. For a given value of V, the conductivity g and the field strength E are inversely proportional, which is in good accordance with experiments. For locations where the conductivity exhibits small changes with time (e.g., over the oceans), the field strength is, at a given place, proportional to the potential of the exchange layer, and recordings of the field strength may therefore reveal patterns in the value of this potential.

The top graph of Figure 4 shows an example of an atmospheric field strength recording, normalized to the mean value, as a function of Greenwich mean time (GMT). It appears that the field strength, and therefore the exchange layer potential, has a minimum at 3 GMT and a maximum at 19 GMT.

1204 mrstatic fig4

Figure 4: Example recordings of field strength as a function of Greenwich mean time.

 

Because the atmospheric field and potential are maintained by active thunderstorms, it is therefore to be expected that variations in the field and potential reflect corresponding variations in concurrent thunderstorm activity. Such a relationship is shown in the bottom graph of Figure 4. The graph plots areas where, at a given time, thunderstorms are active in major parts of the world. A place is regarded as having been in a thunder area at a specified time if thunder was audible in the interval from 60 minutes before to 60 minutes after that time. Although this is a rather uncertain estimate, the curve for the world as a whole does show a correspondence with the field strength curve plotted in the top graph, allowing a causal relationship to be deduced.

Atmospheric Currents

The effect of the ground-level field strength of 150 V·m–1 and conductivity of 2 x 10–14 W–1·m–1 is, according to Equation 2, a current to the ground with the density j @ 3 x 10–12 A·m–2. This is the fair-weather vertical current density, but this field-induced charge transport is not the only way by which charge is brought to the ground.

It has long been known that most precipitation elements, such as rain drops, snowflakes, and hailstones, are often charged. If large raindrops are falling in a strong turbulent updraft, they may split into smaller droplets. The majority of the smallest droplets are negatively charged because of the Lenard effect, that is, the breakup of the electrical double layer at a water-air interface.

A similar process may charge snow particles, but it should be mentioned that charging processes are much more complicated with solid materials. The charging involves contact and friction, and the result therefore depends on the physical state of the contacting materials (temperature, purity, origin, etc.). For example, it has been shown that when two ice pellets are rubbed against each other, the ice pellet with the higher conductivity will become negative, regardless of whether the higher conductivity is caused by higher temperature or lower purity.
The charge brought to the ground by precipitation is normally positive, averaging about 30 C/km2 per year, or about 10–12 A·m–2. The charge from precipi-tation together with the fair-weather vertical current yields a positive current to the ground of about 4 x 10–12 A·m–2, or a total current of about 2000 A to the earth as a whole.

The second part of this article on atmospheric electricity will show that the collective effects of thunderstorms are enough to balance the current brought to the ground. In addition, the physics of lightning discharges will be discussed. favicon


References

  1. Niels Jonassen, “Ions” in Mr. Static, Compliance Engineering 16, no. 3 (1999): 24–28.
  2. Niels Jonassen, “Neutralization of Static Charges by Air Ions: Part I, Theory” in Mr. Static, Compliance Engineering 19, no. 2 (2002): 28–31.

 

author_jonassen-niels

Niels Jonassen, MSc, DSc

worked for 40 years at the Technical University of Denmark, where he conducted classes in electromagnetism, static and atmospheric electricity, airborne radioactivity, and indoor climate. After retiring, he divided his time among the laboratory, his home, and Thailand, writing on static electricity topics and pursuing cooking classes. Mr. Jonassen passed away in 2006.

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