Erosion protection of Tokamak and magnetic force on single charge

Abstract: The walls of Tokamaks are heavily eroded by plasma which suggests that a mysterious force pushes the plasma to the wall. We have theoretically discovered this force and named it extra-force. This force appears only on single charges but not on current carrying wire, which is why the Lorentz force law does not contain it. This discovery not only brings new knowledge to electromagnetism, but also gives a solution against the erosion, which could improve the technology for controlled nuclear fusion. We have proposed an experiment to test this new force.


A promising way to achieve controlled nuclear fusion is Tokamak which holds fusion fuel at around 100 million kelvins in a toroidal chamber. At this temperature the fusion fuel is in plasma state which is a mixture of positive ions and electrons. The plasma is confined with a powerful magnetic field which makes charged particles circling the confinement field lines. The coils of Tokamaks are so designed that the confinement field lines are parallel to the wall of the chamber and the Lorentz force is expected to retain the plasma not to hit the wall. However, the walls of running Tokamaks are heavily eroded by plasma as if charged particles do not completely obey the Lorentz force law. So, we suspect that on top of the Lorentz force a mysterious force is acted on the charged particles, which makes the particles escape the binding of the confinement field.

Previously, we have shown a flaw in the Lorentz force law, that it ignores the parallel-to-current force, see « From Coulomb’s force to magnetic force and experiments that show magnetic force parallel to current»[1]. This flaw suggests that the mysterious force could also be  a force that the Lorentz force law ignores. In the following, we will derive the expression for the mysterious force by starting from the Coulomb’s law that expresses the electrostatic force that a charge qb exerts on another charge qa:

When qa and qb move, relativistic effects come into play and modify the Coulomb’s force given in (1). There are two such effects : the dynamic effect and changing distance effect. Changing distance effect means that when the distance between qa and qb changes, the force on qa changes. Dynamic effect means that the intensity of the force is directly modified by the relative velocity.

See « Erosion protection of Tokamak and magnetic force on single charge » for more detail.

Kuan Peng


Letter to readers

Dear readers,

I have derived the extra-force because I thought that the magnetic force on a single charge could be different from the Lorentz force. Why did I have that intuition? We know that currents are composed of positive charges and moving electrons. So, the Lorentz force is surely the difference between the force on the positive charges and that on the moving electrons. Because the moving electrons have a velocity while the positive charges do not, it is surely the velocity that modifies the electrostatic force. The only way physical quantities could be modified in moving frame is through relativity. So, I have tried to modify electrostatic force with relativity and fortunately, was successful in deriving the 4 magnetic forces.

I have proposed to inject additional electrons into functioning Tokamak to protect its wall. This technique would not only make Tokamak work longer, but also allow higher temperature of the plasma because the latter would no longer touch the wall. This technique would increase the density of the plasma because the extra-force is a compressing force so that more plasma can be loaded. In consequence, the confinement time, temperature and density would all be improved at once, making the Lawson criterion and controlled nuclear fusion closer to reach.

The Maxwell’s theory is very successful for explaining the majority of electromagnetic phenomena, which makes us believe that it can correctly predict all electromagnetic phenomena. However, there are things it does not predict but really exist, for example, the extra-force. When these things happen, for example, the erosion of the wall of Tokamaks, we do not understand why they occur, let alone to fix their consequence if disastrous. So, it is important to correct the Maxwell’s theory when a flaw is found.

The missing of the extra-force is a flaw in the Maxwell’s theory and its discovery a breakthrough for electromagnetism. So, this article topples the Maxwell’s theory again and will be no doubt rejected by all respectable journals. In consequence, I will not submit it for publication but only post online. I’m sure that you, my online readers, would have the wise to recognize its value and would promote it either by sharing it with your colleagues or by performing the proposed experiments. If you succeed in doing the experiments, you will get honorable credit for your contribution.

Kuan Peng, 13 March 2024

See « Erosion protection of Tokamak and magnetic force on single charge » for more detail.