How does a lightning bolt choose its path from a cloud to the ground?
Lightning is complex. A lightning bolt has turns, forks, little branches and takes place in about 2/10 of a second. The air at the lightning bolt is heated to about 30,000 degrees, three times the temperature at the surface of the sun. The current carried in a lightning flash can be as high as 10,000 to 20,000 amps.
What is lightning?
What is lightning? The start of lightning occurs with an intense electric field. This field accelerates the few free ions in the atmosphere to very high velocities. These ions smash into molecules and atoms of oxygen and nitrogen and break them apart, creating even more ions and electrons. The new ions and electrons are then accelerated by the electric field, hit and break up new atoms and molecules.
For lightning to occur, the electric field must be sufficiently large, that the air can be broken down by the process described above. In dry air it takes an electric field of about 3 million volts per meter for lightning. In moist air the breakdown field is much smaller.
How can we describe the lightning strike?
We try to concentrate on the main features only. Since lightning is a breakdown of the air by electric fields we need to know the electric field at each point in space. But the breakdown field of the air depends on a lot of thing we don't know -- the local temperature, the amount of moisture, and the density.
We model the whole thing by breaking space up into a grid. Each little square of the grid is assigned a random number (between 0 and 1) -- this is supposed to represent the local variations of the properties of the air. When the random number, r, in some region is large, then the square is brighter and it is easier for this region to break down.
Dark squares correspond to regions where it is harder for breakdown to occur. But we need to find the electric field at each position too! Once we have done this (using Maxwell's Equations) we guess that the next region to break down will be one with the largest electric field and with the largest random number and one that is connected to the current strike. How is this done? We look at the product breakdown number = (Electric field)a(random #)
Then the cell with the largest "breakdown number" is connected to the lightning strike.
Why do we have the electric field raised to some power? It is because we don't know which is more important, the field or the fluctuations in the properties of the air. We can vary to power alpha to change the relative importance of electric field or of the random number.