# Can magnetic fields convert gas into plasma

Can a strong magnetic field convert gas into plasma? If so can how powerful would it need to be, can I see a chart on the matter?

Stationary homogeneous magnetic field and gas at rest

In principle, the orbit of an electron in an atom has a magnetic moment and as such has a different energy if aligned correctly with the magnetic field. So this should be possible with a strong enough magnetic field, the question is how strong.

We can even study this effect of the shift of the energy levels of an atom in a magnetic field, these are called the Zeeman effect in weak fields and the Paschen-Back effects in the strong field. In the strong field the energy levels of the atom shift simply by an energy of order $B \mu_b$, where $\mu_b \approx 6 \times 10^{-5} eV/T$.

Now we see that if we want to deform the orbit so that the binding energies of an electron in the atom $\sim 10 eV$ are shifted to zeros and the electrons are freed, we need a magnetic field of order $10^6 T$. This is an immense magnetic field. To my knowledge, such a field can be produced only on extreme astrophysical objects such as white dwarfs, neutron stars, or near accreting black holes. Certainly not your terrestrial laboratory, where we are typically able to produce fields up to tens of tesla (tokamaks, particle accelerators).

Time-variable field

Let's see whether we can make a "shortcut" to the release of an electron from the atom by varying the field very quickly or by injecting the gas into the field at high velocity.

The time-scales of the orbits of the electron in the atom are $\sim 10^{-15} s$. This means that unless you have a magnetic field of frequencies $\sim 10^{15} Hz$ (which you dont for more than one reason), the effect of a time-variable magnetic field on a standing atom must be understood as a stationary one because it will always change much slower than any dynamical scale of the electron orbit and the orbit will always be able to change between the states given by different values of the magnetic field in a quasi-stationary fashion.

Now for the atom being injected into the magnetic field. We must assume that there is a finite transition between the field of zero and full strength. With some generosity, this can be assumed to be of orders $10^{-3} m$ but will probably be longer. If we then want the magnetic field to change, in the reference frame of the atom, on a time-scale $\sim 10^{-15} s$, we must do a relativistic analysis because a naive Newtonian one gives us a required speed $\sim 10^{12} m s^{-1}$, four orders above the speed of light.

In the relativistic case, we have a contraction of lenghts proportional to $\gamma^{-1} =\sqrt{1-v^2/c^2}$ in the atom rest frame, so we get that the velocity fulfils $$\frac{v}{\sqrt{1-v^2/c^2}} \sim 10^{12} ms^{-1}$$ which leads to a velocity extremely close to the speed of light and a gamma factor $\gamma \sim 10^8$. That is many orders more than the $\gamma \sim 10^3$ we squeeze out of the LHC for single protons!

Induced potential

But there is one more effect to consider and that is that in the frame of the moving atom, the stationary magnetic field transforms into a static electric one which is $E =\gamma vB$ for the velocity perpendicular to the magnetic field. I automatically include the relativistic factor because we will need it. This is because since the electron binding energy is $\sim 10 eV$ the potential energy from one end of the atom to another has to be $\sim 10V$!

Let us now assume that the magnetic field is $B\sim 10 T = 10 V m^{-2} s$. The potential energy over the short distance is simply $E r_a$, where $r_a \sim 10^{-10} m$ is the distance between the electron and the nucleus in the atom. this means that the velocity has to fulfil $\gamma v B r_a \sim 10 V$ or $$\frac{v}{1-v^2/c^2} = 10^8 m s^{-1}$$ which again corresponds to a velocity close to speed of light and a gamma factor of order one (but up to units larger than one). We know how to accelerate charged particles to these speeds, but certainly not neutral objects, so this is also unrealistic.

So the answer is yes, in principle it is possible either by injecting the gas into a magnetic field at high speeds or exposing it to extremely strong magnetic fields, but we certainly do not have the tools to do that in a terrestrial laboratory.

Ordinarily no. However, with an extraordinary magnetic field or a highly relativistic gas passing into a magnetic field you could. A hydrogen atom has $13.7$ev ionization energy. The force holding the electron to the proton has magnetidue $$F~=~k\frac{e^2}{r^2}, k~=~9\times 10^9Nm^2/coul^2$$ which for $r~=~a$ $\simeq~.5\times 10^{10}m$. This force is about $9\times 10^{-8}N$. If a hydrogen atom enters into a magnetic field region so the electron experiences a force equal or larger than this it might then escape. The magnitude of the Lorentz force $\vec F~=~q\vec v\times\vec B$ for velocity perpendicular to the $10^6G$ magnetic field would require $v~\sim~10^4m/s$ to pull the electron out of the atom. A gas entering a magnetic field with this strength and at this velocity would ionize.

• Beware that you are missing a $10^{-4}$ factor because you use the unit Gauss instead of the SI unit Tesla. (Or in other words, your magnetic field is $10^6 T$ which is enough to strip even a static atom anyways.)
– Void
Commented Apr 7, 2017 at 23:56