Critical Ionization Velocity - Theory Development

Theory Development

Mathematically, the critical ionization velocity of a neutral cloud, that is, when the cloud begins to become ionized, is when the relative kinetic energy is equal to the ionization energy, that is:

where eV_ion is the ionization potential of the atoms or molecules in the gas cloud, m is the mass, v is the velocity. The phenomenon is also called the Critical velocity ionization, and also Critical velocity effect,.

Alfvén considered a neutral gas cloud entering the Solar System, and noted that a neutral atom will fall towards the Sun under the influence of gravity, and its kinetic energy will increase. If their motion is random, collisions will cause the gas temperature to rise, so that at a certain distance from the Sun, the gas will ionize. Alfvén writes that the ionization potential of the gas, V_ion, occurs when:

that is, at a distance of:

(where r_i is the ion distance from the Sun of mass M, m' is the atom weight, V_ion is in volts, k is the gravitational constant). Then when the gas becomes ionized, electromagnetic forces come into effect, of which the most important is the magnetic force which is usually greater than the gravitational force which gives rise to a magnetic repulsion from the Sun. In other words, a neutral gas falling from infinity toward the Sun is stopped at a distance r_i where it will accumulate, and perhaps condense into planets.

Alfvén found that by taking a gas cloud with an average ionisation voltage of 12V, and average atomic weight of 7, then the distance r_i is found to coincide with the orbit of Jupiter.

The critical ionization velocity of hydrogen 50.9 x 105cm/s (50.9 km/s), and helium is 34.3 x 105cm/s (34.3 km/s),.