Return to Answer

One way to achieve this would be to simply change the structure of Earth's magnetic field. At the moment, the field is that of a large magnetic dipole, with the field produced by the motion of fluid within the core. Maxwell's equations (see Chapter 4 of these notes) tell us that this motion should produce a magnetic field with radial component $$B(r,\theta)=B(r_{\text{core}})\left(\frac{r}{r_{\text{core}}}\right)^{-3}\cos\theta$$ Here, $B(r_{\text{core}})$ depends on the material properties of the outer core (density $\rho$, electrical conductivity $\sigma$) and the rotation rate of the Earth, $\Omega$: $$B(r_{\text{core}})\sim\sqrt{\frac{\rho\Omega}{\sigma}}$$ Unfortunately, we can't change the angular dependence of this expression, just the amplitude.

Earlier, I mentioned changing the structure of the field. We could do this by adding in some higher-order terms, creating, for instance, a quadrupole field. In the quadrupole case (with vanishing dipole term), there are actually four magnetic poles, not just two. This would presumably lead to auroras in many more places around the globe.

Here's what a quadrupole field would look like:

^{Image courtesy of Wikipedia user Andre.holzner, CC BY-SA 3.0.}

Whether you could create a physical process to generate such a field is another question. We see that $B\propto\sqrt{\Omega}$ because it's the Earth's rotation that drives the motion of the fluids that leads to the dipolar field. It seems unlikely to be that the same mechanism could generate a quadrupole field. Perhaps there are multiple cores in the planet, still in the process of merging? This would involve a complex system of moving material, which would lead to higher-order moments in the field's multipole expansion, and perhaps the effects you're looking for.

One way to achieve this would be to simply change the structure of Earth's magnetic field. At the moment, the field is that of a large magnetic dipole, with the field produced by the motion of fluid within the core. Maxwell's equations (see Chapter 4 of these notes) tell us that this motion should produce a magnetic field with radial component $$B(r,\theta)=B(r_{\text{core}})\left(\frac{r}{r_{\text{core}}}\right)^{-3}\cos\theta$$ Here, $B(r_{\text{core}})$ depends on the material properties of the outer core (density $\rho$, electrical conductivity $\sigma$) and the rotation rate of the Earth, $\Omega$: $$B(r_{\text{core}})\sim\sqrt{\frac{\rho\Omega}{\sigma}}$$ Unfortunately, we can't change the angular dependence of this expression, just the amplitude.

Earlier, I mentioned changing the structure of the field. We could do this by adding in some higher-order terms, creating, for instance, a quadrupole field. In the quadrupole case (with vanishing dipole term), there are actually four magnetic poles, not just two. This would presumably lead to auroras in many more places around the globe.

Here's what a quadrupole field would look like:

^{Image courtesy of Wikipedia user Andre.holzner, CC BY-SA 3.0.}

Whether you could create a physical process to generate such a field is another question. We see that $B\propto\sqrt{\Omega}$ because it's the Earth's rotation that drives the motion of the fluids that leads to the dipolar field. It seems unlikely to be that the same mechanism could generate a quadrupole field. Perhaps there are multiple cores in the planet, still in the process of merging? This would involve a complex system of moving material, which would lead to higher-order moments in the field's multipole expansion, and perhaps the effects you're looking for.

Speak of the devil! I just answered a related question.

The relevant part of my answer is this:

Wikipedia talks briefly about creating a quadrupole field - that is, creating four poles. Two would be "North", and two would be "South". Here is a good visualization. Unfortunately, that one isn't loading here, so I'll go with this one instead:
^{Image courtesy of Wikipedia user Geek3 under the Creative Commons Attribution-Share Alike 3.0 Unported license.}

Here is the caption:

Magnetic field lines of an idealized quadrupole field in the plane transverse to the nominal beam direction. The red arrows show the direction of the magnetic field while the blue arrows indicate the direction of the Lorentz force on a positive particle going into the image plane (away from the reader)

The caption for the other image is this (emphasis mine):

Example of a quadrupole field. This could also be constructed by moving two dipoles together. If this arrangement were placed at the center of the Earth, then a magnetic survey at the surface would find two magnetic north poles (at the geographic poles) and two south poles at the equator.

I doubt you'd see any electrical effects, but you might see an interesting aurora. An aurora is caused by the solar wind interacting with Earth's atmosphere, but the solar wind can also interact with Earth's magnetosphere to create some cool effects. A change in Earth's magnetic field means a change in the magnetosphere, which means some awesome aurora-like events.

So perhaps a planet with four magnetic poles could see auroras all over the globe.

One way to achieve this would be to simply change the structure of Earth's magnetic field. At the moment, the field is that of a large magnetic dipole, with the field produced by the motion of fluid within the core. Maxwell's equations (see Chapter 4 of these notes) tell us that this motion should produce a magnetic field with radial component $$B(r,\theta)=B(r_{\text{core}})\left(\frac{r}{r_{\text{core}}}\right)^{-3}\cos\theta$$ Here, $B(r_{\text{core}})$ depends on the material properties of the outer core (density $\rho$, electrical conductivity $\sigma$) and the rotation rate of the Earth, $\Omega$: $$B(r_{\text{core}})\sim\sqrt{\frac{\rho\Omega}{\sigma}}$$ Unfortunately, we can't change the angular dependence of this expression, just the amplitude.

Earlier, I mentioned changing the structure of the field. We could do this by adding in some higher-order terms, creating, for instance, a quadrupole field. In the quadrupole case (with vanishing dipole term), there are actually four magnetic poles, not just two. This would presumably lead to auroras in many more places around the globe.

Here's what a quadrupole field would look like:

^{Image courtesy of Wikipedia user Andre.holzner, CC BY-SA 3.0.}

Whether you could create a physical process to generate such a field is another question. We see that $B\propto\sqrt{\Omega}$ because it's the Earth's rotation that drives the motion of the fluids that leads to the dipolar field. It seems unlikely to be that the same mechanism could generate a quadrupole field. Perhaps there are multiple cores in the planet, still in the process of merging? This would involve a complex system of moving material, which would lead to higher-order moments in the field's multipole expansion, and perhaps the effects you're looking for.

Speak of the devil! I just answered a related question.

The relevant part of my answer is this:

Wikipedia talks briefly about creating a quadrupole field - that is, creating four poles. Two would be "North", and two would be "South". Here is a good visualization. Unfortunately, that one isn't loading here, so I'll go with this one instead:
^{Image courtesy of Wikipedia user Geek3 under the Creative Commons Attribution-Share Alike 3.0 Unported license.}

Here is the caption:

Magnetic field lines of an idealized quadrupole field in the plane transverse to the nominal beam direction. The red arrows show the direction of the magnetic field while the blue arrows indicate the direction of the Lorentz force on a positive particle going into the image plane (away from the reader)

The caption for the other image is this (emphasis mine):

Example of a quadrupole field. This could also be constructed by moving two dipoles together. If this arrangement were placed at the center of the Earth, then a magnetic survey at the surface would find two magnetic north poles (at the geographic poles) and two south poles at the equator.

I doubt you'd see any electrical effects, but you might see an interesting aurora. An aurora is caused by the solar wind interacting with Earth's atmosphere, but the solar wind can also interact with Earth's magnetosphere to create some cool effects. A change in Earth's magnetic field means a change in the magnetosphere, which means some awesome aurora-like events.

So perhaps a planet with four magnetic poles could see auroras all over the globe.

Speak of the devil! I just answered a related question.

The relevant part of my answer is this:

Wikipedia talks briefly about creating a quadrupole field - that is, creating four poles. Two would be "North", and two would be "South". Here is a good visualization. Unfortunately, that one isn't loading here, so I'll go with this one instead:
^{Image courtesy of Wikipedia user Geek3 under the Creative Commons Attribution-Share Alike 3.0 Unported license.}

Here is the caption:

Magnetic field lines of an idealized quadrupole field in the plane transverse to the nominal beam direction. The red arrows show the direction of the magnetic field while the blue arrows indicate the direction of the Lorentz force on a positive particle going into the image plane (away from the reader)

The caption for the other image is this (emphasis mine):

Example of a quadrupole field. This could also be constructed by moving two dipoles together. If this arrangement were placed at the center of the Earth, then a magnetic survey at the surface would find two magnetic north poles (at the geographic poles) and two south poles at the equator.

I doubt you'd see any electrical effects, but you might see an interesting aurora. An aurora is caused by the solar wind interacting with Earth's atmosphere, but the solar wind can also interact with Earth's magnetosphere to create some cool effects. A change in Earth's magnetic field means a change in the magnetosphere, which means some awesome aurora-like events.

So perhaps a planet with four magnetic poles could see auroras all over the globe.