T = 2·Ek,mean /(3·kB)
This equation shows a linear dependence between the two physical quantities and the proportionality constant is equal to 2/(3·kB) where kB is the Boltzmann’s constant (kB = 1,381·10⁻²³J/K = 8,631·10⁻⁵eV/K).
Replacing the value of the Boltzmann’s constant in the equation you get
T = 2·Ek,mean /(3·8,631·10⁻⁵eV/K) = 7˙724K/eV · Ek,mean
The equation shows that when the mean kinetic energy assumes the value of 1eV, the temperature is 7˙724K (about 7˙450°C or 13˙400°F).
The increase the speed of an electrically charged gaseous particle is possible through the electric field between two electrodes immersed in the gas. When the gas pressure is sufficiently low to ensure a mean free path (which is the average distance between two collisions with other gas particles) greater than the distance between the two electrodes, the energy acquired by the particle is equal to the voltage applied to the electrodes multiplied by the electric charge of the particle.
With unitary electric charge and a voltage of 1V between the electrodes, the kinetic energy of a particle that is accelerated for the distance that separates the two electrodes increases by 1eV.
From the relation above, the kinetic energy of 1eV corresponds to a particle’s temperature of 7˙724K.
If the potential between electrodes is increased from 1V to 10V, the temperature increase by ten times becoming 77˙240K. Raising potential to 100V, the temperature grows to 772˙400K and at 1000V the temperature is well over 7 million Kelvin degrees.
It is important to note that not all the gas is at these incredibly high and apparently absurd temperatures, but only those particles that have been accelerated by the electric field between the two electrodes.
At this point the question is if an hydrogen atom that has purchased an electron (ion H⁻) or an hydrogen atom that has lost its electron (H+ ion) in the gas phase may acquire with this method enough energy to overcome the Coulomb repulsion barrier when an impact with other atoms occurs so offering a reaction mechanism for nuclear fusion.
If the reaction mechanism described in this article will be experimentally confirmed, will it be listed as hot fusion or cold fusion?