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.

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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.
https://www.academia.edu/116178626/Erosion_protection_of_Tokamak_and_magnetic_force_on_single_charge

https://pengkuanem.blogspot.com/2024/03/erosion-protection-of-tokamak-and.html

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.
https://www.academia.edu/116178626/Erosion_protection_of_Tokamak_and_magnetic_force_on_single_charge

https://pengkuanem.blogspot.com/2024/03/erosion-protection-of-tokamak-and.html