Tornadoes: Thermodynamics and Electromagnetism

Supercell Thunderstorms and Tornadoes as the
Products of Thermodynamics and Electromagnetism

Last modified: 2008-08-28 03:20:13 UTC

Tornadoes spawned by supercell thunderstorms are considered. Consistency with current research trends within the disciplines of meteorology and geophysics is neglected in the pursuit of a broader framework that can directly address the large number of anomalies in the existing theories. A tornado is proposed to be a positive ion stream responding to a focused negative charge within the storm. This negative charge is proposed to be a product of the large amount of negatively-charged precipitation that gets drawn back into the updraft within the mesocyclone. Once in the updraft, the precipitation constitutes a moving electric charge. All moving electric charges generate associated magnetic fields that consolidate the charge, and focus the lines of force. The focusing of the lines of force in a mesocyclone would result in a substantial amount of electric force being projected onto the ground. The expected response to this force would be the liberation of positive ions from the ground. These ions would constitute another moving electric charge, and this charge would generate a magnetic field of its own, consolidating the ion stream into a vortex-like structure. A wide variety of properties of supercell thunderstorms and tornadoes are considered as possible manifestations of the proposed theory.

The factors that produce tornadoes are not well understood. Existing theories based entirely on thermodynamics leave many well-known characteristics of tornadoes unexplained. It's possible that another force will have to be introduced into the theoretical framework before the entire picture will come into clear focus.

It's possible that electromagnetism is the force that needs to be considered. Electromagnetism is clearly present, and many distinctive electromagnetic properties of supercell thunderstorms and tornadoes have been documented.^1,2,3,4 Furthermore, many researchers have proposed that electromagnetism plays a causal role, in the formation and/or sustenance of tornadoes.^{5,6,7,8,9,10,11,12,13,14,15,16} (See Patton [2008]¹⁷ for a brief review.) Such research has typically focused on a small subset of the properties of supercells or tornadoes, and has frequently neglected the thermodynamic context in which these storms occur. The objective of this paper is to consider, in broad strokes, how thermodynamics and electromagnetism might plausibly work together to produce a wide range of properties associated with tornadic storms.

Since the original source of all of the energy in a thunderstorm is heat, thermodynamics should be considered first.

Thunderstorms are powered by heat stored in warm, moist air in the lower troposphere. If the upper troposphere is far cooler and drier, there is "convective potential" (i.e., the warm air wants to rise and the cool air wants to fall, so there is the potential for convective motion).

Usually this convective potential dissipates as fast as it is created, as small thermal updrafts generated by high surface temperatures rise gracefully, displacing cooler air that then falls. A mild breeze at the surface, and a few puffy cumulus clouds, a couple of kilometers above the surface, are the typical net results.

If "convective inhibition" is present, an unusually large amount of heat and humidity can build up in the lower troposphere. If there is a layer of hot, dry air above the warm, moist air at the surface, the warm air will not have the buoyancy necessary to rise. As the Sun continues to heat the surface of the Earth, air temperatures near the surface continue to increase, above those necessary for the creation of thermal updrafts had the hot air not been there. Now the convective potential can build to extreme limits.

This is actually a stable situation, assuming that the cooler air on top is far lower in pressure, and therefore is light enough to exist happily above hotter air, and so long as the middle layer keeps the other two layers from coming into contact with each other.

But if the warm, moist air at the bottom gets hot enough that it can break through the hot, dry air above it, and come into contact with the cool, dry air in the upper troposphere, the results can be explosive. The reason is not so much because of differences in temperature, but because of differences in humidity. When warm, moist air meets cool, dry air, the warm air cools, and releases its moisture content as precipitation. For the water molecules to change state from gas to liquid (or to solid), they have to get colder, so they shed their heat into the surrounding air. This is called the release of "latent heat," and so much heat is released by this process that now the updraft will be hot enough to rise all of the way to the top of the upper troposphere, 12~15 km above the surface.

The next thing that happens is that a single updraft creates an entire storm. The rising of the initial updraft creates a low pressure underneath it. This reduction in pressure encourages the air underneath to release precipitation, which releases latent heat, and this makes that air want to rise also. When it rises, it draws in more air behind it, which does the same thing. In this way, the initial updraft triggers a chain reaction that results in a continuous flow of air from the lower troposphere into the upper troposphere.

In a normal thunderstorm, this process continues for about an hour, until an equal but opposite reaction develops in the upper troposphere that will put an end to the updraft. The warm air in the updraft displaces cooler air in the upper troposphere, increasing its density, and encouraging it to fall. Far more significantly, precipitation released from the updraft evaporates in the drier air in the upper troposphere. The evaporation process cools the air, increasing its density, and this makes it fall fast. So a downdraft is created, equal in power to the updraft that initiated it. This downdraft will head straight for the low pressure under the updraft, filling it with cool air and cutting off the supply of warm, moist air to the updraft. When this happens, that updraft is finished.

Past this point, thunderstorm activity might begin in adjacent parcels of air. The downdraft displaces warm air at the surface, possibly with enough force to elevate it out of the way. If so, this might trigger a new round of precipitation, and a new updraft will form next to the old one. This new updraft will follow the same course, and in this way, a lateral chain reaction can develop across the countryside, with updrafts causing downdrafts that cause new updrafts elsewhere. This sometimes results in a cluster of thunderstorms covering hundreds of square kilometers.

But such is not the nature of a supercell thunderstorm. A supercell thunderstorm is a single-updraft storm that keeps going for several or many hours, somehow outliving its own downdraft. Explaining how a single cell can persist for so long, with thermodynamics alone, has proved challenging. There has to be some sort of force that transforms a random, low-power updraft into an organized, high-power mesocyclone, but the nature of this force is not known, and computer simulations of supercell thunderstorms, using only standard thermodynamic principles, fail to produce mesocyclones — artificial factors have to be introduced that will keep the updrafts organized, or they will fall apart in the simulations.^18,19

Furthermore, and regardless of what is organizing the updraft in a supercell thunderstorm, there's nothing in the principles of fluid dynamics or thermodynamics that can explain a tornado. There is definitely a powerful updraft within the supercell thunderstorm, and this could create enough low pressure underneath it that a free vortex would form. But a free vortex caused by low pressure has a diameter that tightens as it approaches the low pressure. Yet a tornado starts out narrow at its base and expands as it approaches the low pressure in the mesocyclone, defying the principles of low pressure free vortexes. If there was a powerful heat source on the ground, tornadoes would be explicable with thermodynamics, but it would take temperatures in the hundreds of degrees Celsius, concentrated in the narrow base of the tornado, to power wind speeds of tornadic intensity, and there's no evidence of such temperatures in the damage paths of tornadoes. In fact, there's no consistent evidence of any elevated temperatures at all within tornadoes.

If it's not fluid dynamics, and it's not thermodynamics, there are only two other forces that are operative at this scale, at these temperatures, and in this medium — gravity, and electromagnetism. It's not gravity, because the updraft inside the tornado is going up. That leaves electromagnetism. If there is reason to believe that electromagnetism is actually the only remaining candidate, there is no reason not to make a thorough investigation of its properties.

An earlier electromagnetic theory of tornadoes maintained that electrostatic discharges between the cloud and the ground could create enough heat to fuel the updraft within the tornado, and possibly even within the mesocyclone. There are two reasons why this is not possible. First, there is no evidence of such temperatures in the damage paths of tornadoes. Second, subsequent research has clearly demonstrated that better than 99% of the thermal energy in a tornadic storm can be attributed directly to the air temperatures and humidities at various altitudes before the storm begins. So whatever localized contribution electromagnetism might make to the temperatures within the storm, the overall contribution is too slight to be worthy of consideration, and Joule heating certainly does not "drive" the tornado, much less the mesocyclone. But this does not rule out electromagnetism as a key player. It merely establishes that if electromagnetism is a key player, then this is not the role that it plays. More recent research has shown that electromagnetic forces below the threshold for lightning are capable of generating wind speeds of tornadic intensity without the need to take elevated temperatures into account.^14,15 This means that the failure of the Joule heating theory is not relevant, and that electromagnetism is still a legitimate theoretical candidate.

This paper considers the possibility that electromagnetism is the organizing force in a supercell thunderstorm, allowing a single updraft to persist for longer than can be explained with thermodynamics alone, and that the same electromagnetic force can go on to produce a tornado. Electromagnetism is not considered to be a source of energy, but rather, an artifact of the thermodynamic forces at play that introduces a new set of properties into the phenomenon. With these properties, it becomes possible to propose answers to the questions that thermodynamics leaves open.

The known prerequisite conditions for tornadogenesis (convective potential, wind shear, etc.) are considered to be valid, but incomplete. It's possible that the conditions conducive to tornadogenesis also include an unusually strong positive charge in the upper troposphere. The source of this positive charge is proposed to be earlier thunderstorm activity. After a thunderstorm, the positive charge in the upper troposphere remains, even after the corresponding negative charge has been dissipated by negatively-charged precipitation falling to the ground, and by negative cloud-to-ground lightning.^20,21 If wind shear is present, the positively-charged upper troposphere could be repositioned over a new batch of thermal energy in the lower troposphere, and a new storm could develop. The new thunderstorm will then contribute to the existing positive charge in the upper troposphere.²² It's possible that enough positive charge could accumulate in the upper troposphere that it could offset the force of gravity and keep negatively-charged precipitation suspended within the storm. This could alter the dynamics of the system, transforming the storm into a supercell. The remainder of this paper considers exactly how tropospheric electrification might affect this transformation, and how the resulting conditions might spawn a tornado.

In any thunderstorm, there is a charge separation between larger precipitation, which is negatively charged, and smaller bits of precipitation, which are positively charged. Over time, a net negative charge accumulates in the lower portion of the cloud, as the heavier precipitation descends toward the ground, while a net positive charge accumulates at the top of the cloud, where small, positively-charged ice crystals linger, too light to fall at a measurable rate.^23,24 The negative charge at the bottom of the cloud is typically in the tens of millions of volts of electrostatic potential. This charge is diffused when the charge-bearing precipitation falls to the ground, or by lightning when too much charge builds up in too short a period of time. The positive charge at the top of the cloud can reach into the hundreds of millions of volts,²⁵ and can only be diffused less frequently by lightning, or by simple dispersal over a much longer period of time.

In a supercell thunderstorm, there is an unusual lack of precipitation falling out of the cloud as the storm develops, and there is an unusual build-up of negative charge in the middle of the cloud. The causes for these distinctive characteristics of supercell thunderstorms are not well-understood.

If there is an unusually strong positive charge in the upper troposphere (left over from previous thunderstorm activity), the electrostatic force could offset the force of gravity, and hold the negatively-charged precipitation in suspension. This electrostatic force will be the most powerful at the boundary between the upper and lower tropospheres. Higher up, negative precipitation will be surrounded by positive charge, and there will be no net directional electrostatic force. Lower down, the electrostatic force will fall off with the square of the distance separating the charges. So we would expect to see a large accumulation of negative precipitation at the upper/lower boundary, in the lower middle of the cloud. (See figure 5.)

If this precipitation is being held in suspension at the top of the lower troposphere, it's in a perfect position to get drawn back into the updraft. The updraft starts at the top of the lower troposphere, and tends to draw in new air from adjacent parcels at the top of the lower troposphere, rather than reaching vertically down to lower altitudes, because the air at the top of the lower troposphere is hotter. So the lines of motion converge laterally toward the bottom of the updraft. If precipitation that fell out of previous updrafts is hovering in this air, the precipitation will be drawn back into the updraft. From there, the precipitation will retrace its original path, carried by the updraft into the upper troposphere, falling back to the lower troposphere, and then getting drawn back into the updraft again. Hence the precipitation can go into an endless loop of motion. (See figure 6.)

The existence of an endless loop of motion explains why supercell thunderstorms can produce hail that is unusually large. In a normal thunderstorm, there are convective currents that can keep precipitation recirculating within the cloud long enough for small hail to form. But not grapefruit-sized hail. In a supercell thunderstorm, if there is actually a force that is discouraging precipitation from exiting the cloud, and if this precipitation is suspended in the same air that is being drawn into the updraft, we would expect the precipitation to make many passes through the system. If all of this is occurring at an altitude high enough that the temperature stays below freezing most of the time, then the precipitation will stay in the solid state, hail will form, and it will continue to grow in size through successive passes, eventually becoming unusually large.

Far more significantly, the negative precipitation will not just be affected by electromagnetic forces in the storm — it will exert electromagnetic forces of its own. If there is a large amount of negative precipitation that is being drawn back into the updraft, then the updraft itself will be bearing a net negative charge. The effects of this net charge should be considered.

Ampère's law states that any moving charge will create an associated magnetic field. Almost all of the early research into electromagnetism was done with wires carrying electric currents, but more recent research has studied electric currents in gases, with interesting results.²⁶ While like charges in gases typically repel each other, if the charges are moving, they are pushed together. Their associated magnetic fields combine into a more powerful unified magnetic field. The further apart the charges, the more the magnetic fields fight each other, so the magnetic force offsets the electrostatic repulsion, and consolidates the charge. This is known as the magnetic pinch effect, and this principle can be observed in the consolidation of electrons that creates lightning, as well as in the filamentary nature of the discharges from a Tesla coil, both of which are inexplicable without taking the magnetic pinch effect into account.^16,27

If there is a net negative charge in the updraft, then by Ampère's law this charge will produce an associated magnetic field, and the magnetic field will further consolidate the electric charge. This means that the precipitation in the updraft will be pushed toward the center-line of the updraft, and by virtue of collisions with surrounding air molecules, the surrounding air will be compressed as well.

This has interesting implications concerning the general description of the thermodynamic forces in mesocyclones. The magnetic field around the updraft will act like a chimney, discouraging outward expansion of the air as it rises. This means that the only direction in which the air can expand is upward, and this increases the speed of the updraft. When this air is finally released at the top of this chimney, it is released into very cool, very dry air, where the latent heat potential will be extremely high. An extra boost in the speed of the updraft at the top of the chimney will further accelerate the updraft. And the faster the updraft, the more powerful the magnetic field, since this force is a function of the amount of charge, and the speed at which the charge is moving. The more powerful the magnetic field, the more it will consolidate the updraft. So under these circumstances, the magnetic pinch effect will be self-accentuating. (See figure 7.)

The magnetic pinch effect will also encourage the updraft to grow in height. The magnetic field is the most powerful where the electric force has already been consolidated, and the updraft is moving at its fastest rate. But the magnetic field extends past this range, and will encourage the inflow to get aligned with the vertical flow before entering the updraft, and for the outflow to continue traveling vertically at the top. To the extent that inflowing and outflowing particles are traveling in the same direction, they'll contribute to the magnetic pinch effect, which further encourages consolidation in the inflow and in the outflow. So the effective inflow will start lower, and the effective outflow will extend higher. All other factors being the same this would not be significant. But in the context of a thunderstorm, extension of the length of an updraft will increase its speed, because greater temperature and humidity gradients will be traversed. So the taller the chimney, the faster the updraft. This means that a small magnetic pinch effect that might develop somewhere in the middle of the cloud will have a natural way of growing until it traverses the entire height of the upper troposphere.

In addition to being self-accentuating and self-extending, the magnetic pinch effect under these circumstances might also be self-protecting. An updraft's worst enemy is an undercutting downdraft, which seeks the low pressure under the updraft. Downdrafts are formed when precipitation that is released from the updraft subsequently evaporates in the drier air of the upper troposphere. Downdrafts also frequently bear excess precipitation that does not get the chance to evaporate. Downdrafts are actually the principle transport mechanism for precipitation to get from the top of the cloud down to the bottom (and then typically to the ground). Without downdrafts, precipitation in the upper troposphere would take hours or even days to fall all the way to the ground, not tens of minutes as in a thunderstorm.

If there is an excess of negative precipitation in the downdraft, then the downdraft will be bearing a net negative charge for the same reasons as the updraft. The difference is that the direction is reversed, and this means that the magnetic fields created by the moving electric charges in the updraft and in the downdraft will be reversed. These fields are not candidates for consolidation, and in fact will repel each other. In this way, the magnetic sheaths surrounding the updraft and the downdraft will insulate themselves from each other.

In a fully-developed supercell thunderstorm, all of the electric lines of force resolve into a toroid shape, with the updraft at the center, and with charged downdrafts pushed to the outside for the return trip. This separation of updraft and downdraft reduces the chances that the downdraft will undercut the updraft.

If the magnetic pinch effect makes an updraft self-accentuating, self-extending, and self-protecting, then this effect is an excellent candidate for the role of organizing force in a supercell thunderstorm.

The magnetic pinch effect might even help explain the formation of hail in a more fundamental sense. The current thinking is that hail forms at the top of the updraft, where precipitation released from the updraft begins to fall back through the updraft, colliding with other precipitation, creating larger aggregates.

While it's unquestionable that this does happen, it can't be the whole story. The terminal velocity of precipitation when it first forms is lower than that of dust, which follows the motion of the air first and the force of gravity last. So gravity is not a big factor during the initial formation of precipitation. Furthermore, to the extent that gravity is a factor, it will act on all of the particles in the same direction. If there were substantial differences in the sizes of the particles, they would have different terminal velocities, and therefore would achieve different speeds, resulting in particle collisions. But how are we going to get enough collisions to form aggregates of different sizes before there are aggregates of different sizes?

Further still, the same standard theory also states that wind shear must be present in order for a thunderstorm to develop to extreme limits. The reason is that without wind shear, the updraft will be perfectly vertical, and precipitation released at the top of the updraft will fall back down, through the updraft. When it does, some of the precipitation will evaporate, cooling the air and creating a downdraft right on top of the updraft, snuffing it out. Aside from the question of how microscopic ice crystals are going to "fall through" an updraft, this begs two more questions. First, how does precipitation evaporate in an updraft that is already at its dewpoint and the temperature is still dropping (otherwise it wouldn't be releasing precipitation that can fall back down)? Second, the more severe the thunderstorm, the more hail it produces — wouldn't a tilted updraft, with fewer precipitation collisions, produce less hail? It's clear that some of the tenets within the standard model are mutually exclusive, and that we're missing something fundamental in our understanding of the formation of hail.

It's possible that updrafts and downdrafts are manufacturing the aggregates of precipitation by virtue of the magnetic pinch effect. If Ampère was right about moving charges always producing magnetic fields, and if like charges are always pushed together if they are moving because of the magnetic pinch effect, and if all of the precipitation in question has the same negative charge, then such precipitation will always get consolidated whenever caught up in updrafts or downdrafts, and this will encourage the formation of larger aggregates. If this is the case, the rest of the story is much easier to follow.

It's interesting to consider the possibility that the vertical charge separation in the storm might help in the aggregate-building inside the downdrafts. The larger aggregates have the same charge-to-mass ratio, but a higher terminal velocity, so they are not as affected by the speed of the downdraft. In other words, the larger aggregates will be more affected by the charge separation, and will tend to hover, while the smaller aggregates will tend to stick with the downdraft. This increases the chances of aggregate collisions within the downdrafts.

In a normal thunderstorm, that might be the whole story. In a supercell thunderstorm, the far more powerful charge separation will slow down the descent of precipitates to the point that they become candidates for recirculation back through the updraft. Inside the updraft, the magnetic pinch effect will once again encourage consolidation of aggregates. Then, at the top of the updraft, heavier aggregates could fall through the updraft and become larger still. So even with a tilted updraft, there could still be a substantial amount of aggregate-building.

In fact, the true significance of the tilt in the updraft in encouraging thunderstorm development might be very different. First, the tilt will make the downdraft fall further from the bottom of the updraft, reducing the chances of undercutting the updraft. A downdraft that hits the ground close to an updraft, but without undercutting it, will actually accentuate the updraft, because it displaces warm air that then joins the updraft with force. So a tilt in the updraft can help it survive the first wave of descending cold air. Second, the tilt might not be so much a cause, but rather just one of the side-effects of wind shear, where wind shear is doing the job in another way. Without wind shear, the thunderstorm has a limited supply of warm, moist air in its immediate vicinity with which to work. Once that's gone, that cell is done. But with wind shear, a storm in the upper troposphere can stay organized while it is fed with an endless supply of new thermal energy from below. Cold air from the downdraft is swept away, replaced by warm, moist air that can keep the updraft going. And one of the side-effects of wind shear is a tilted updraft.

Putting all of this together, a far simpler description of the general nature of supercell thunderstorms becomes possible.

The consolidated negative charge in the mesocyclone, and its associated magnetic field, will have an effect at the ground level as well. The magnetic sheath around the updraft will organize and focus the electric force, like a laser beam.^28,29 Once outside the scope of the magnetic field, the electric lines of force will do whatever they must in order to close, wrapping around the outside of the magnetic field to reenter from the other end. This results in a splaying of the lines of force, and a vast reduction in the concentration of force. But if the mesocyclone is 10 km tall, and only 1 km above the surface, at the bottom the lines of force will hit the ground before an appreciable amount of splaying has occurred. This means that a substantial percentage of the force concentration will still be present at the ground level.

If powerful enough, this electric force exerted on the ground could overcome the force of gravity, and accelerate positively-charged particles in the ground toward the negative charge in the mesocyclone. This is proposed to be the essence of a tornado. Put loosely, the supercell thunderstorm produces an electric tractor beam and points it at the ground, and the ground responds by giving up any loose particles it may have. (See figure 8.)

It may seem odd that there would be an abundance of positive ions in the ground, ready to respond to a powerful negative charge above, but the electromagnetic forces in any thunderstorm can achieve hundreds of millions of volts of potential. If all of that potential is focused on a small enough area on the ground, the negative charge will be capable of pushing electrons deeper into the ground, thereby creating positive ions that will then be attracted to the negative charge. Charge migrations in the ground have been demonstrated even with the 30 million volts of electrostatic potential typically seen between the ground and the bottom of a normal thunderstorm.²³

How many positive ions would have to be liberated in order for the tornado to take shape? If we think of tornadoes as suction vortexes, then we would expect for there to be an enormous amount of particulate matter involved in the flow. So much, in fact, that we would expect the tornado to evacuate many centimeters of soil from the surface of the Earth wherever it went. In cases where a tornado has remained stationary for several minutes, we would expect for there to be a distinct depression in the ground where all of the loose soil was vacuumed away. This, of course, is not what happens. There is a low pressure within the tornado, but not that low, and something is wrong with the basic precept that tornadoes are low-pressure free vortexes. Electromagnetic theory shows how tornadic properties can emerge out of a far smaller volume of matter. Wind speeds at the low end of the tornadic range can be generated with a current of 0.4 microamps per square meter.¹⁵ The total amount of current in a tornado has been estimated in the range of 100~225 amperes.^3,30 In short, there would be enough loose particles on an unswept city street to supply the ions necessary to drive a tornado.

It's also possible that the air itself is a source of positive ions. Any molecule exposed to a powerful negative charge will lose electrons, become positively-charged, and then be attracted to the negative charge. If this is happening in the air itself, then the air will be accelerated upward. This, combined with upward acceleration due to collisions with particles coming out of the ground, could be the source of the low pressure within the vortex.

Once the tornado gets established, it's possible that triboelectric charging (i.e., "static electricity") contributes to the positive charge in the ground. Air drawn in by the low pressure inside the tornado will impart a positive charge into the ground.⁹ This will be true especially along the outer edge of the tornado, where wind speeds at the ground level are the fastest. Particulate matter in the ground, stirred up by the tornado and positively charged by the inflowing air, will be capable of responding dramatically to a powerful negative charge.

So why does this enormous negative charge produce a tornado and not cloud-to-ground lightning?

The proposed conditions under which supercells form will discourage negative cloud-to-ground lightning strikes. The reason is that the negative charge in the mesocyclone is not free to release electrons downward, because it is under the influence of a strong positive charge above it. If the positive charge in the upper troposphere is powerful enough to overcome gravity and keep precipitation in suspension, then it's more than powerful enough to prevent free electrons, which have no mass, from moving toward the ground. So stepped leaders will never form, and lightning in that direction will not occur. This means that the negative charge in the mesocyclone will either do nothing at all, or it will draw positive ions out of the ground. But it cannot create lightning under these conditions. Only late in the storm's life-cycle will it start to produce negative cloud-to-ground lightning.³¹ It's possible that enough negative precipitation eventually builds up within the cloud that late in the cycle, it shields lower precipitation from the positive charge at the top of the cloud, freeing it up to fall to the ground and/or create negative cloud-to-ground lightning.

The cloud-to-ground lightning that typically will occur in a supercell thunderstorm will be positive strikes.^31,32 These are unusual for thunderstorms, because the positive charge in the thunderstorm tends to accumulate in the upper reaches of the cloud, 8+ km above the surface, where the updraft lingers after releasing precipitation, and it takes a lot more electrostatic potential for lightning to span that altitude than it does to span the 1 km from the bottom of the cloud to the ground. What is distinctive about supercell thunderstorms is that some of the positive cloud-to-ground strikes come from the bottom of the cloud. The presence of that much positive charge, that low in the storm, is further evidence of an unusually strong positive charge in the upper troposphere. If this charge is powerful enough to keep negative precipitation suspended, and to prevent negative cloud-to-ground lightning, then it will be powerful enough to force positive precipitation downward, by simple electrostatic repulsion. This will create the low-level positive charge necessary for positive strikes between the bottom of the cloud and the ground.

It must be noted that the actual charge structure of supercell thunderstorms is far, far more complex, and way outside the scope of this paper. Nevertheless, it's undeniable that 1) there is a notable lack of precipitation exiting supercell thunderstorms in the early stages of development, 2) a large volume of precipitation is getting recirculated within supercell thunderstorms, and 3) a causal relationship has been observed between earlier thunderstorm activity and large positive charge accumulations in supercell thunderstorms that developed subsequently.²² This paper considers the possibility that these facts are related, and goes on to consider the significance.

The material presented thus far constitutes the theoretical core of this paper. Next, a broader range of tornado-related phenomena are examined, to see if the overall picture becomes clearer if the effects of electromagnetism are taken into account.

Tornadoes are commonly thought to be suction vortexes, vacuuming the surface of the Earth with intense low pressure. The source of the low pressure is presumed to be the updraft within the mesocyclone.

By the principles of thermodynamics, a suction vortex will always be narrowest at the source of the low pressure, and expand as the distance from the source increases. The low pressure creates the centripetal force necessary to convert linear motion into angular motion, and the greater the centripetal force, the smaller the radius. Since energy always decreases as distance from the source increases, the lowest pressure will be at the source of the low pressure. Therefore, the radius will be the smallest nearest the source. (See figures 15 and 16 for examples.) If a tornado was a suction vortex, considering that it is narrowest at the ground level and splays outward with altitude, the direction of flow would be from the cloud to the ground, and the source of the low pressure would be on, or in, the ground. This, of course, means that tornadoes are not suction vortexes.

With thermodynamics, the only way to get a free vortex that expands in the direction of the flow is with high pressure. The high pressure itself will not rotate, because high pressure has no internal centripetal force — it will expand outward, in a linear direction, the first chance it gets. But an extremely powerful jet of high pressure can create a Venturi effect in the surrounding air, thereby drawing in air to the source of the high pressure, and accelerating it in the direction of the flow. As the high pressure dissipates moving away from the source, so too does the low pressure created by the Venturi effect, and hence the vortex radius will increase. But this is an extremely inefficient way of transferring energy, and the volume and speed of a high pressure jet that could create a tornado would be a bit ridiculous to consider.

If a tornado is a positive ion stream, electromagnetic principles can explain the expansion of the vortex in the direction of the flow. The ion stream constitutes a moving electric charge, and this charge will create a magnetic field around it. The magnetic pinch effect will then organize and consolidate the motion.¹⁴ The strength of the magnetic field will be a function of the amount of charge in the ion stream, and the speed at which the charge is moving.

Unlike suction vortexes that draw in air along the entire length of the vortex, tornadoes only draw in air at the surface level.³³ So once a tornado touches down, the particles accelerated upward at or near the surface level are the only particles involved, and the amount of positive charge inside the tornado will not change with altitude. This means that the only factor that varies with altitude is the speed of the particles.

There are three factors that could increase the speed of the particles as they ascend. First, electrodynamic force is inversely proportional to the distance (not the square of the distance as is the case with electrostatic force). So the closer the positive ions get to the mesocyclone, the more powerful the electric force that is accelerating them. More significantly, to the extent that the negative charge in the mesocyclone is splaying outward at the bottom, there will be more force concentration at the bottom of the mesocyclone than there will be at the surface. So as the positive ions get close to the mesocyclone, the amount of electric force acting on them will increase greatly, and the acceleration will increase exponentially. Finally, and least significantly, positive ions have mass, so when exposed to a force they will accelerate, instead of instantaneously achieving the speed of which they are capable in the given medium, given the amount of force. Hence the particle speed would increase going up the tornado, even if the force that was causing the acceleration did not increase.

The faster the particle speed, the more powerful the magnetic field that is created around the ion stream. As the magnetic field increases, its effective diameter increases — air further away from the ion stream is accelerated to the speed sufficient to generate condensation. Hence the vortex will start out small at its base, and as the particle speed increases going up the tornado, the diameter of the vortex will increase.

Tornado videos reveal that in a stable, well-organized tornado, the upward motion in the main body of the outside of the vortex is inexplicably slow. Considering how much air is being drawn into the tornado, we would expect for there to be a sharp upward spiral in the vortex. Yet the motion in the main body of the vortex is closer to horizontal rotation. Distinctive forms in the condensation can be seen to rotate around the center-line of the vortex repeatedly, moving upward slowly, if at all.

By the principles of fluid dynamics, we would expect the perimeter of the vortex to be the part that is moving upward, while the inside of the vortex should be a relative void. Since the outside of the vortex is not moving upward at a rate appropriate for the amount of inflow, then the upward motion has to be contained mainly within the core of the vortex. No construct of fluid dynamics can explain this.

If there is an ion stream within the vortex of a tornado, surrounded by a magnetic sheath, then electromagnetic principles can explain the motion. The magnetic lines of force generated by a moving electric charge are angular, and on a plane that is perpendicular to the direction of the current. Because water molecules are diamagnetic, they will be accelerated in a circular path around the ion stream, and on the horizontal plane.¹⁴ So if the updraft is an ion stream within the core of the vortex, then the visible outside of the vortex is a horizontally-rotating sheath of air that is actually just an artifact of the updraft, and not a part of it. This matches the observations.

Tornado photography sometimes reveals that there is an inner structure to the vortex. (See figures 18~20, Gene Moore's photography from June 24, 2003, and Gene Rhoden's photography from June 23, 2002, for examples.) There is often a visible difference between the condensation funnel and a semi-transparent sheath that is forming nearer to the ground. There is also sometimes a dust funnel that forms at the ground level, surrounded by a semi-transparent sheath.

It has been proposed that this is the result of particles of different masses getting centrifuged out of the vortex at different rates.³³ But this does not explain why those particles would accumulate at specific distances from the center of the vortex, forming distinct layers of materials. In the thermodynamic model, there is no centripetal force that will selectively impede the centrifugal force, and stratify particles within the vortex.

Electromagnetic principles can very definitely supply such a selective centripetal force, on the basis of the magnetic responsiveness of the materials. The inner core of the vortex is the ion stream, which may be visible if the outer sheath is not well-formed. The outer sheath is the effect of the magnetic field surrounding the ion stream, that is accelerating the air to the point that water molecules are condensing. Despite high angular velocities, the water molecules are not centrifuged out of the vortex because they are diamagnetic, and get trapped by the magnetic field around the ion stream.

If this is the case, then another anomaly becomes a little easier to explain. The tornado vortex itself (not the debris cloud) is almost always white, as it is formed by water that condenses because of the low pressure. Occasionally, a tornado will become the color of the dust and dirt upon which it is rotating. The anomaly is that this is the occasional case. If a tornado was a free vortex simply vacuuming the surface of the Earth, the vortex would be mostly dust and some condensation, not the other way around. But if a tornado is an ion stream surrounded by a magnetic sheath, the dust is on the inside, and we will typically only see the condensation caused by the magnetic sheath, which is white. For example, consider the tornado in figure 10. It's obvious that there is plenty of loose particulate matter on the ground, because we can see it in the debris cloud. It's understandable how some of the particles would get ejected out of the vortex by high angular velocities at the surface. But why isn't there any particulate matter in the vortex itself?

In cases where a tornado vortex does become the color of the dirt in the ground, the most common colors are black and red. Common minerals found in the soil in the Great Plains include ferrous and ferric oxide, which are black and red (respectively). It's possible that the magnetic responsiveness of the iron oxides make them candidates for getting trapped in the magnetic field around the ion stream, instead of being drawn inside the ion stream or being ejected into the debris cloud. Then, if the relative humidity in the air at the surface level is low enough, we will see more dirt and less condensation in the outer sheath.

The historical literature is full of accounts of objects such as people, cars, and sometimes entire houses being picked up and carried for some distance by tornadoes.^34,35,36

The standard explanation for this phenomenon is that high wind speeds are creating local high and low pressures sufficient to generate the lift necessary to levitate the objects.

There's no doubt that high wind speeds are present, and that special circumstances might create unbelievable high and low pressures. A tornado may have sustained 100 m/s winds at its base, but when going in and around buildings, local speeds could be 200 or 300 m/s. Such wind speeds will be capable of lifting up very heavy objects, even if those objects do not have shapes that are conducive to aerodynamic uplift.

But the behaviors of objects picked up by tornadoes are not always explicable in terms of the effects of high wind speeds. For example, there are numerous accounts of people being picked up and carried over 50 meters, and then set back down gently enough that they were relatively unharmed.³⁷ High wind speeds could certainly have picked up the people, but then the people would have been rapidly accelerated to a substantial percentage of the speed of those winds. It's hard to imagine how a person could hit the ground at such speeds and be relatively unharmed. For another example, during the tornado that hit La Plata, MD, on April 28, 2002, a bus with 30 people aboard was lifted off the ground, kept suspended in air for several seconds, and then set back down on the wheels. After recovering his composure, the driver put the engine back in gear and drove off. High wind speeds could have picked up the bus, but then the bus would have been accelerated horizontally, and it would have hit the ground hard and rolled several times, destroying the bus and probably killing many of the passengers.

For yet another example, and perhaps the most anomalous of all, there have been a few cases where entire houses have been picked up and carried, and then set back down, damaged but still relatively intact. The anomalous aspect of this is not that an object as big as a house could be picked up. Houses are mainly empty space, with lots of surface area upon which the winds can exert force. But houses simply are not built in such a way that they can be picked up, except from underneath, without falling apart. Without being able to get underneath the house to pick it up, the only other way to generate the necessary uplift without destroying the house is with a force that can act on the entire mass at once. There are only two such forces in nature operative at this scale — gravity and electromagnetism. It's not gravity, because the houses were picked up. That leaves electromagnetism.

As the tornado approaches, objects are exposed to high wind speeds. Triboelectric charging will develop a strong positive charge in them. After becoming positively charged, the focused negative charge generated by the mesocyclone will exert a powerful uplifting force on them. Since the electromagnetic force is 39 orders of magnitude more powerful than the force of gravity,³⁸ and since the electric force in a thunderstorm can reach hundreds of millions of volts of potential, there's little doubt that this force, if well-focused, could overcome gravity. And this uplift, being created by the sum of billions of charged particles, hundreds or thousands of meters away, will neither appear nor disappear suddenly. It will slowly increase and then slowly decrease, unlike tornadic winds that fluctuate dramatically. Now it becomes possible for objects to be gently lifted up, and then gently set back down, and for relatively fragile objects to be carried without being destroyed.

There have been a variety of reports of unusual luminosity within tornadic storms. Tornadoes have been said to glow in the dark, like neon lights.^5,39,40 From the inside, eye witnesses have reported seeing "fingers" or "rings" of continuous lightning at the top of the tornado.^41,42,43 From the outside, there have been reports of continuous ring lightning at the top of the tornado.^5,7,36

These phenomena are not observed in every tornado, and because of this, thermodynamicists have dismissed the possibility of a causal role for electromagnetism in tornadogenesis.⁴⁴ But the present theory does not state that tornadic lightning is a driving force, wherein lightning creates heat, thereby making the rest of the tornadic phenomena explicable with thermodynamics. Rather, the present theory dismisses thermodynamics as a reasonable explanation for the properties of tornadoes, regardless of the source of the heat. Thermodynamics is only significant in the present theory to the extent that it is the driving force in the mesocyclone, while it is the electromagnetic properties of the mesocyclone that drive the tornado.

If positive ions coming from the ground are interacting with a strong negative charge at the bottom of the mesocyclone, it's possible that the potential will be sufficient to create glow discharges, or even open lightning. In this way, tornadic lightning is an artifact of the electrical potential that is present, where the electrical potential creates the tornado, whether it exceeds the resistance of the air or not.

Tornadic storms also produce sustained RF interference, and this is on a more consistent basis.⁴⁵ The fact that these emissions are sustained is unusual for thunderstorms, and can only be explained by the presence of continuous electrical activity. With simple electrostatics, as in a normal thunderstorm, continuous activity is not likely to happen, but in an electrodynamic system, this is possible. If a steady positive ion stream is interacting with a large mass of negatively-charged precipitation in the mesocyclone, the result would be continuous electrical activity, and sustained RF emissions.

One tornadic storm that had an unusually high degree of electrical activity (the storm that spawned the F5 tornadoes in Blackwell/Udall, May 25, 1955), produced a number of occurrences of St. Elmo's Fire in front of the advancing tornado.⁴⁶ This electrical phenomenon is caused by ionization occurring in the air due to exposure to a powerful electric field. This phenomenon is rare, though it is not unique to tornadic storms. It is mentioned here simply as another observation that is consistent with the present theory, which contends that the focused charge in the mesocyclone will be capable of stripping electrons from molecules in the air and in the ground, thereby creating positive ions that will be accelerated upward in the tornado.

It's also significant to note that while supercell thunderstorms have been known to produce cloud-to-cloud lightning at an incredibly high rate (sometimes as fast as 25 strikes per second),⁵ the strike rate subsides just before the formation of the tornado, and continues to stay low until the tornado dissipates.⁴⁷ This subsidence coincides directly with the emergence of sustained electromagnetic radiation from the heart of the storm. If the tornado is a positive ion stream, and if the electromagnetic radiation is being caused by interaction between these ions and the negatively-charged updraft, then this interaction will diffuse some of the electrostatic potential between the negative charge in the middle of the cloud and the positive charge at the top of the cloud, thereby reducing cloud-to-cloud lightning strikes.

Supercell thunderstorms that are releasing precipitation tend to do so in a comma-shaped pattern. This distinctive radar signature is one of the most reliable indicators of tornadic potential. (Note that in figure 21, the image shows an area about 56 km wide, and the actual supercell was less than 10 km wide, so the bulk of the precipitation shown is not part of the hook echo.)

This paper states that negative precipitation will be held in suspension by the positive charge in the upper troposphere. This will be true all the way around the supercell thunderstorm, with one exception. Doppler radar studies have shown that there can be as much as a 15° tilt in the mesocyclonic updraft, due to wind shear.⁴⁸ Since the updraft is negatively charged, the tilted updraft will shield the lower troposphere from the positive charge in the upper troposphere. As a result, as air in the lower troposphere spirals inward, once per revolution it passes under the electrostatic shadow of the tilted updraft. If rain is going to fall out of the bottom of the cloud, it will begin its descent here. Factor in the varying speeds of rotation in the storm, and the rain will exit the bottom of the cloud and hit the ground in an involute curve pattern. (See figure 22.)

The largest hail produced by supercell thunderstorms can be over 10 cm in diameter. The structure of these hailstones strongly suggests that at least 2 complete passes had to be made through the system: one to form the smaller aggregates, and the other to create the larger aggregate from the smaller ones. It's unknown whether the final aggregate was created in the updraft, or in the downdraft. But it's safe to say that hailstones of substantial size had to be in the updraft at some point in the process. (See figure 23.)

The anomaly is that it is hard to imagine how, in the standard thermodynamic model, hail even of the smaller size could have risen within the updraft without being centrifuged out of it. With rotational speeds in the mesocyclone approaching 150 m/s, hail would be spun out of the updraft and distributed on the ground in a 360° pattern. This, of course, is not what happens — hail only falls more or less along the inside edge of the hook echo, with the larger hail falling nearer to the mesocyclone. (See figure 24.)

We can, of course, employ the proposal in the previous section, to say that hail could be ejected in all directions, and then held in suspension by its electrostatic charge until it passed under the electrostatic shadow of the updraft. But if that part is true, then the other part of the construct is true also, that there is a magnetic sheath around the updraft. This magnetic sheath will force the hail to the inside of the updraft, and therefore discourage centrifugal ejection.

Within the present theory, since hail can be manufactured in the updraft, at the top of the updraft, in the downdraft, and at the bottom of the downdraft, we almost have more chances than we need for hail to form, and it's even possible that grapefruit-sized hail could be formed in only one pass through the system. If the initial clumping of precipitation starts with excess precipitation within the updraft being pinched into aggregates, then at the top of the updraft, differing terminal velocities of precipitation, combined with the force of gravity, will contribute to the size. Further aggregation can occur during the downdraft, and then differing speeds at the bottom of the downdraft, due to charge separations in the cloud, can finish the job. Smaller hail will be more likely to stick with the downdraft and hit the ground further out in the FFD region, while larger hail will be more likely to stay suspended, and will only be released from suspension when fully under the electrostatic shadow of the updraft. So the present theory does not necessarily have to answer the hail~centrifuge question, but if in fact hail is making more than one pass through the system, the present theory does not have a problem with this.

A supercell thunderstorm tends to travel in a direction that is roughly 30° to the right of the average wind direction 3~6 km above the surface. The speed of the storm is roughly 75% the speed of these winds.⁴⁹

By thermodynamic standards, this is inexplicable. The updraft begins at roughly 1 km above the surface. From there, the updraft will certainly be influenced by the prevailing winds at each altitude, whose directions and speeds may vary dramatically. But there is no obvious reason why winds at 2~5 km above the base would have any bearing on the overall direction and speed of the storm. It should be the winds at the bottom of the storm that determine the movement of the storm. In other words, smoke coming out of the smokestack of a ship will be influenced significantly by the winds that it encounters as it rises. But the higher-level winds will exert no force on the smoke at lower levels, and therefore will not influence the overall direction or speed of new smoke. This will be determined simply the direction and speed of the source of the smoke (the ship).

Sophisticated theories concerning interactions among various thermodynamic forces in the storms have been proposed, with qualified success in explaining the observations.⁵⁰ But such theories are arguably after-the-fact descriptions of a phenomenon that we still do not actually understand.

Another anomaly in the thermodynamic model is that the updraft tends to be perfectly straight, with a 15° tilt because of wind shear. This is anomalous because wind speeds typically increase with altitude, and therefore we would expect the updraft to curve as it ascends. When the updraft enters the jet stream, at roughly 10~12 km above the surface, we would expect the curvature to be dramatic. But this is not what happens.

Electromagnetism can explain why the updraft is straight, and in so doing, enables a much simpler explanation for the way upper-level winds affect the speed and direction of supercell thunderstorms.

One of the properties of the magnetic pinch effect is that it tends to align all of the lines of force. The electric lines of force are straightened, and the magnetic lines of force are brought into concentricity. If the updraft within a mesocyclone develops this effect, the updraft will tend to be straight, even if winds at different altitudes are traveling in different directions and at different speeds. (See figure 25.)

This goes on to provide an explanation for the 30° offset in the direction of the storm relative to the 3~6 km winds. If we take a second look at the typical wind directions and speeds, 30° to the right of the 3~6 km winds is typically the direction of the jet stream. By thermodynamic standards, there's no way that the jet stream could be influencing the direction of the storm, but by electromagnetic standards, this is easily possible. If the updraft has a powerful force that is keeping it straight, and if the jet stream is exerting a lateral force on the updraft at the top, then this will exert a force on the bottom of the updraft, dragging it along wherever the top is being pushed.

Analogously, if a rigid, buoyant object such as a pencil is suspended by one end in a denser fluid such as water, the pencil's buoyancy will tend to keep it pointed straight up. If the water is moving at the top of the pencil, the pencil will lean in the direction of the movement. Because of its buoyancy and because of its rigidity, the pencil will transfer the force to the bottom, and the entire pencil will move in the direction of the water, even if the water is only acting on the top of the pencil.

Similarly, the updraft in a mesocyclone is buoyant, so it would otherwise tend to be perfectly vertical. If it is fully-developed, with the top of the updraft reaching into the jet stream, the updraft will be tilted. Because of the updraft's buoyancy and because of its rigidity, and because the jet stream is so much more powerful than any of the lower-level winds, the bottom of the storm will tend to follow the top, rather than the top following the bottom as we would expect. This will be true to the extent that the mesocyclone is well-developed in the jet stream. Weaker thunderstorms, even in the same general vicinity, will tend to follow the lower-level winds. So called "left-moving" supercells (that travel in a direction that is to the left of what is expected) might then be "left-movers" simply because they are not typically as fully-developed as "right-moving" supercells, not because of their anti-cyclonic rotation, or any other factor. In other words, normal thunderstorms, and weak supercells, will tend to be "left-movers." Fully-developed supercells will tend to be "right-movers." In the transition from a normal thunderstorm to a supercell, the storm will tend to make a right-hand turn compared to its original course. As the storm weakens, it will turn back to the left. The critical factors are proposed to be the strength of the magnetic pinch effect, the extension of the updraft into the jet stream, and the speed and direction of the jet stream. (See figure 26.)

For example, during the tornado in Moore, OK, on May 3, 1999, the upper-level winds were from the southwest, while the lower-level winds were from the south. The storm tracked in a northeast direction during its most intense stages, following the upper-level winds. As it dissipated, it turned to the north, no longer controlled by the jet stream and then moving in the direction of the lower-level winds. This was true during its final dissipation stage, as well as during a brief dissipation period as it crossed the Canadian River. (See figures 27~29.)

A violent tornado tends to last longer than a weak one. This is inexplicable in that we can make a pretty good accounting of the amount of potential energy available to these storms, but we cannot account for why a violent tornado expends so many more orders of magnitude of energy on the ground per second, and on top of that, lasts an order of magnitude longer than a weak tornado, even in cases where both storms had roughly the same amount of potential energy. This begs a reconception of how these storms work. If, in fact, the longer the storm lasts, the more powerful the electromagnetic forces become, then the observations make more sense. The longer the storm lasts, the more powerful it will be, because of how long it lasts. Hence supercells will not be unimodal, where extremely powerful storms will go through their energy faster, and weaker storms will expend energy at a slower rate, and therefore last longer. Instead, supercells will be bimodal, where either a powerful tornado is produced that stays organized for a long time, or a weak tornado is produced that quickly dissipates. The difference between these two outcomes, given the same amount of thermal energy, is given by the effectiveness of electromagnetism in each case, acting as a force multiplier within the mesocyclone.

A wall cloud is a "ragged curtain" hanging down below a supercell thunderstorm, and it's under the wall cloud that the tornado forms. The formation of a wall cloud is considered to be one of the telltale signs that a tornado is about to form. (See figures 30~32. For extensive collections of wall cloud photography, see Sam Barricklow's page, and Roger Edward's page.) Here's the standard explanation for how wall clouds form, from NSSL:

This does not explain why wall clouds form under supercells that are not releasing precipitation. Furthermore, supercells that are releasing precipitation will do so only on one side. If the wall could was condensation coming in from one side, it would spiral inwards like the inflow bands. Sometimes there is a wall cloud tail leading from the precipitation area to the updraft (called the "beaver's tail" — see figure 32 for an example), but more typically this is not present. Further still, even when this is present, the ragged ends of the wall cloud are not limited to the end of the beaver's tail, where the convergence under the updraft would twist the condensation into a spiral at the center — the ragged ends are present all the way around the wall cloud, and the motion is convergently upward, not convergently inward.

Most researchers believe that the wall cloud is a simple extension of the updraft. If the updraft gets powerful enough, it will stop drawing in air laterally, from the top of the lower troposphere, and start drawing in air from directly below it, regardless of temperature. (Then, if air coming in from one direction happens to be higher in humidity, the water vapor will condense sooner than that in the surrounding air, thus creating a beaver's tail.) But this doesn't explain why the wall cloud isn't shaped like a cone pointing downward, where the lowest pressure at the center would draw in the most air, and force condensation earlier than higher pressures further away from the center-line.

Perhaps it's just coincidence, but the general shape of the wall cloud conforms closely with the electric lines of force at the bottom of the supercell. It's possible that these clouds are actually nitrogen polymer fogs that form in the presence of an electric field. It's also possible that the condensation is water vapor, but that the accelerating force is not so much low pressure, but electromagnetism. The splaying of the lines of force results in a fairly even distribution of force, and accounts for the flared tips all the way around the bottom. It also accounts for the cloud-base striations that are sometimes visible directly above the wall cloud, where the lines of electric force have converged to the point that the magnetic field begins accelerating water molecules around the updraft.

The broad scope of this work has precluded thorough treatment of any of the topics, and substantial portions of this work may be considered not specific enough to be worthy of being called wrong. Nevertheless, there is a time and place for broad-stroke theory, and interestingly, with a relatively simple framework, a wide variety of difficult-to-explain properties of supercell thunderstorms and tornadoes seem to become far easier to explain.

The work that remains to be done, of course, is to see if the present theory can stand up to an increase in specificity. Considering the scope of this work, and assuming that this theory is correct, achieving a degree of specificity to match that of current works within the disciplines of meteorology and geophysics will take many volumes of material. But if electromagnetism is a driving force in tornadic storms, producing this material will be easier than never being able to adequately explain the phenomena.

Thanks to Kevin Linzey for listening patiently to many early versions of this theory, and for smirking quietly rather than laughing out loud.

Thanks to Michael Gmirkin, Wallace Luchuk, and Thomas Beck for many comments, corrections, and suggestions.

10. Sozou, C., 1984: Electrical Discharges and Intense Vortices. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, Vol. 392, Issue 1803, 415-426.

20. Vonnegut, B., 1979: Tropospheric electrification. NASA Goddard Space Flight Center Middle Atmosphere Electrodynamics, N79-25608 16-46, 157-168.

26. Phillips, J. A., 1983: Magnetic Fusion. Los Alamos Science, Winter/Spring.