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Let me try to illustrate what I mean. Consider e.g. a Solar radiation storm (Solar particle event) where high-energy protons are hurled at Earth from Solar flares. I've tried to illustrate my conception of this (I know the protons will typically not follow straight paths out from the flare due to the Parker spiral, but it's a simplification):

enter image description here

So the protons get captured by the field (given sufficiently low velocities perpendicular to the field, as far as I understand it) and are then led to the poles due to their drift velocity, as they will almost always have some velocity component that's not perpendicular to the field.

Now, to me it seems (and the same applies to the plasma in coronal loops as far as I can tell) that there's a current along the field lines themselves due to the drift of the protons, in the direction they're traveling. This should itself induce a magnetic field surrounding the imaginary magnetic field lines at the centers of the helical proton motion as if the magnetic field lines themselves are current-carrying wires, should it not? Something like this:

enter image description here

Am I correct in thinking about it roughly in this manner?

If so, does that mean that these new magnetic fields could potentially themselves partially trap particles (although I assume the stronger original field would overwhelm it) and induce new magnetic fields around them in turn? Is there a limit to this "fractal" process of magnetic field lines acting as currents inducing magnetic field lines acting as currents, and so on?

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  • $\begingroup$ While they are moving fast, they are certainly not high-energy protons. The kinetic energy is of order $10^{-6}M_p$. $\endgroup$
    – JEB
    May 11, 2023 at 16:16
  • $\begingroup$ @JEB: In terms of space weather, the term "high-energy protons" typically refers to protons with energies of 10 MeV or more, which when detected above a certain threshold is defined as a Solar radiation storm (Solar particle event). I'm not sure how relevant that is to the question anyway, it was just the first example that came to my mind; as far as I know there are both lower-energy protons and electrons moving along the field lines too. $\endgroup$
    – Outis Nemo
    May 11, 2023 at 16:23
  • $\begingroup$ well a micro $M_p$ is 938 eV. $\endgroup$
    – JEB
    May 12, 2023 at 16:27
  • $\begingroup$ @JEB: Then I understand your first comment even less, since as mentioned above the protons in question are of energies 10 MeV or more. If $10^{-6} M_p$ is 938 eV, then these protons would have energies of the order $10^{-2} M_p$, 4 orders of magnitude higher than you suggested. Perhaps I'm missing something here. In any case, they're considered high-energy protons in the context of space weather anyway. $\endgroup$
    – Outis Nemo
    May 12, 2023 at 16:47
  • $\begingroup$ do you mention the energy? I always thought solar wind was on the order of $c/1000$, which puts the Lorentz factor at $\gamma\approx 1 + \frac 1 2 10^{-6}$. $\endgroup$
    – JEB
    May 12, 2023 at 19:57

1 Answer 1

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The magnetosphere is a complicated system with different populations of ions and electrons spanning many orders of magnitude in energy. Charged particles' motion can certainly produce currents and therefore magnetic fields. The significance of the effect is determined by the number and motion of the particles.

The magnetosphere famously contains the Van Allen radiation belts, containing trapped protons with energies from $10$s to $100$s of MeV. However, it turns out that more significant currents are carried by a population of lower energy particles, with energies from $10$s to $100$s of keVs. These rotate westward around Earth to produce the so-called "ring current". The current generates a magnetic field that partly shields/counteracts the geomagnetic field generated by the Earth.

During geomagnetic storms the ring current increases. This increases the field associated with the current, producing a small but measurable change in magnetic field on Earth. Dst represents changes to horizontal magnetic field strength at the equator.

DST index for the 2003 Halloween storm.

For exceptionally strong storms, such as this one, magnetic field changes of $100$s of nT are observed. However, these changes are still far smaller than the Earth's magnetic field strength (typically $10$s of $\mu$T). Therefore, the effect of the ring current on itself via the magnetic field it generates will be somewhat limited.

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  • $\begingroup$ Thank you for the answer; I'm aware of a lot of this already, but as far as I can see it doesn't actually answer the question I'm asking. As far as I understand the ring current, as you point out, drifts around the geomagnetic equator, and thus indeed creates a magnetic field opposite that of Earth's magnetic field. My question is however about currents along the field lines, and whether or not they induce magnetic fields perpendicular to those field lines, due to the current there. $\endgroup$
    – Outis Nemo
    May 11, 2023 at 13:38
  • $\begingroup$ The intent was to acknowledge that you were correct about the basic physics premise but argue against the implications you asked about. The key points are that a) the high energy particles mentioned in the question carry less current than the moderate energy particles in the ring current and b) even the ring current under the most extreme conditions would have a small effect on the trapped particles via magnetic fields. Ring current particles are trapped particles as described in the question, though currents along field lines will average out to zero due to the rapid bounce motion. $\endgroup$
    – FTT
    May 11, 2023 at 21:58
  • $\begingroup$ I'm not quite sure I understand. To me it's understandable that the magnetic field of the ring current would not have any noticeable effect, since it's primarily canceling out the geomagnetic field. I don't see how that applies to the currents along the field lines, whose magnetic field would be perpendicular to the field lines of the geomagnetic field. Also, you say that currents along field lines will average out to zero; why is that? $\endgroup$
    – Outis Nemo
    May 11, 2023 at 22:03
  • $\begingroup$ @OutisNemo The energetic particle motion along field lines that you're asking about would affect the east-west horizontal component of Earth's magnetic field if it produced a significant net current. The fact that changes in horizontal field are orders of magnitude smaller than the mean value of the field suggests that trapped particles have a very small effect on one another via the magnetic field. Currents along field lines will tend to cancel because the equal numbers of trapped particles will be travelling northward and southward along the field lines as they bounce between mirror points. $\endgroup$
    – FTT
    May 13, 2023 at 1:36

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