Giving Mars a Magnetosphere

An addendum to “Terraforming Mars”

The Problem

Any future colonization efforts directed at the Mars all share one problem in common; their reliance on a non-existent magnetic field. Mars’ magnetosphere went dark about 4 billion years ago when it’s core solidified due to its inability to retain heat because of its small mass. We now know that Mars was quite Earth-like in its history. Deep oceans once filled the now arid Martian valleys and a thick atmosphere once retained gasses which may have allowed for the development of simple life. This was all shielded by Mars’ prehistoric magnetic field.

Mars used to have oceans! Then it lost it’s magnetosphere :(

When Mars’ magnetic line of defense fell, much of its atmosphere was ripped away into space, its oceans froze deep into the red regolith, and any chance for life to thrive there was suffocated. The reduction of greenhouse gasses caused Mars’ temperature to plummet, freezing any remaining atmosphere to the poles. Today, Mars is all but dead. Without a magnetic field, a lethal array of charged particles from the Sun bombards Mars’ surface every day threatening the potential of hosting electronic systems as well as biological life. The lack of a magnetic field also makes it impossible for Mars to retain an atmosphere or an ozone layer, which are detrimental in filtering out UV and high energy light. This would seem to make the basic principles behind terraforming the planet completely obsolete.

The Solution

I’ve read a lot of articles about the potential of supplying Mars with an artificial magnetic field. By placing a satellite equipped with technology to produce a powerful magnetic field at Mars L1 (a far orbit around Mars where gravity from the Sun balances gravity from Mars, so that the satellite always remains between Mars and the Sun), we could encompass Mars in the resulting magnetic sheath. However, even though the idea is well understood and written about, I couldn’t find a solid mathematical proof of the concept to study for actual feasibility. So I made one!

**This is where things get technical. There is no shame in skimming through to find the basic results!**

Concept for an artificial Martian Magnetosphere at Mars L1. Here, the white dot is our satellite equipped with the technology to produce a powerful magnetic field. Credit: NASA/Jim Green.

Earth’s magnetic field, originating at it’s core, has a strength of ~6*10^-5 Teslas at the distance of the Earth’s surface. This is the force which deflects compass needles. It is also the strength required to defend our atmosphere against deadly solar wind. However, a space-based magnetic field at Mars does not have to be quite this powerful. First of all, our goal is only to encompass Mars in the magnetosheath of the field; it does not need to extend as far as the Earth’s does. Earth’s magnetosheath extends to ~6 million kilometers. Mars L1 is only about 1 million km from Mars. Of course, we are going to want to allow some leeway for potential solar flare events, but extending the field ~1.5 million km is probably sufficient.

Another thing to take into account is the fact that the intensity of solar wind at Mars’ distance is less than half that at 1 AU. This means that we only need a magnetic field half as powerful as what we would have needed to defend a planet at Earth’s distance from the sun. Taking both of these factors into account, a space-based magnetic field around Mars only needs to have a strength of roughly 11% that of Earth’s. This will create a magnetosheath long enough to extend 500,000 kilometers beyond Mars.

Formula for magnetic field strength (B) in Teslas.

Using the magnetic field magnitude equation, we can now solve for the amperage of the “wire” required to produce such a field. This yields a current of ~200 Mega-amperes. Any electrician knows right now that we are going to need a BIG ASS wire.

The next part of the calculations was probably the hardest thing to wrap my head around. To solve for the size of the wire, we need to know its resistance. To get the resistance, we need to know the voltage running through the wire. To find the voltage, we need to know the total power being pumped into the wire to produce the current. It turns out that we need to strategically select the power input of the magnetic field in order to solve for any of this, because everything affects everything else in the derivation.

Some electronics equations. Note that if you know the power input (P) and the current (I), you can solve for everything else here given a certain material.

Being that we want the power input (P) to be as low as possible (less stringent power requirements for a spacecraft), we also want voltage (V) and thus resistance (R) to be low. Keeping the resistance low requires that we use a wire that has the smallest possible length (L), but also a large cross sectional area (A). The only other unknown that we have is the resistivity (rho) of the wire. Resistivity is a property of a material which defines its ability to resist electrical current. We want to keep this value low as well. Copper is the logical choice of material to use, being that it is both abundant and boasts a very low resistivity of ~1*10^-8. We can make this value about an order of magnitude lower by keeping it at cryogenic temperatures, which isn’t hard to do in space with a sunshield.

The only conundrum remaining is creating a wire which has a short length, a large cross sectional area, and can generate a magnetic field. To create a magnetic field, we usually run a current through a long, thin wire wrapped around a cylinder; a solenoid. However, the goal here is to make a solenoid which has a short length and a large radius. The ideal solution is then a single-loop solenoid, a “doughnut” if you will, wrapped so tightly that the hole at the center is nonexistent. This, however, does not allow any space for magnetic field lines to pass through, and would induce a counterproductive reverse current on itself. If we instead use a solenoid with a small opening at the center, we will have optimized the resistance of the wire.