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.

(Left & Center) A depiction of how a planetary magnetic field and a single-loop solenoid’s magnetic field are similar. (Right) An example of a closed torus (single-loop solenoid), the ideal solution for a system of minimum electrical resistance to generate a magnetic field. We will require a small hole at the center for our magnetic field to pass through.

All we need now is a strategically chosen value for power input to solve for everything else. If you really wanted to, you could slap some standard solar panels on your spacecraft and use a (relatively) small power input to generate your planet-sized magnetic field. This is a bad idea. It turns out that the lower your power input, the larger your copper solenoid has to be to compensate. Even using more than 4000 m² of 20% efficient solar panels, the solenoid would have more mass than all of the copper available in the Earth’s crust. To make a solenoid which is small and light enough to reasonably manufacture and launch to Mars’ orbit, we are going to need a big power generator.

Modern fission reactors can produce more than a Gigawatt of power, about 1/3 of it useful towards generating electricity. Using this as a template, we can theorize a powerful, futuristic fission reactor to supply our defensive Martian magnetosphere. After several iterations regarding sizing of both the solenoid and the fission reactor, I found that an 830 Megawatt reactor is the ideal solution, assuming a 50% thermal efficiency. This means that 415 Megawatts of useful power are going into the solenoid to generate our magnetic field. Now we can successfully solve for all the other parameters from before:

Some results from a MATLAB code I wrote because who wants to do all this by hand??

Some things to note are the exceptionally low voltage for the system of about 2 volts, and the dimensions/mass of the copper solenoid which come out to a torus with a total diameter of ~3.5 meters and a mass of ~57 tonnes. This is a big copper doughnut. It would fill the average living room area wall-to-wall and weigh more than 6x the legal mass of a loaded semi truck on the freeway. A magnetic field of ~81 Teslas is generated at the surface of the solenoid; nearly twice the strength of the strongest artificial continuous magnetic field ever produced to date. Another thing to note is the fact that a fission reactor of this size will require over 40 tonnes of uranium every two years to remain in operation. This may be the biggest problem for any future Martian-magnetosphere endeavor, seeing as a launch to Mars from Earth takes about 18 months and the abundance of uranium on Mars itself is unknown.

There are still a few things we haven’t addressed about the spacecraft itself. 415 Megawatts of power are being pumped into the copper solenoid for the magnetic field, but 415 Megawatts of additional power are simultaneously being converted to waste heat. To rid of this heat, we are going to require a powerful thermal control system. The sunshield will protect the spacecraft from absorbing any additional heat from the Sun, but we will still need some high emitting radiator panels to draw heat away from the reactor. Silicon-carbide has a relatively high emissivity of 0.7, and can attain temperatures of ~2000 K without suffering deformation or loss of radiative efficiency. Using silicon-carbide radiators emitting waste heat from both sides, my design requires 325 m² of panels. This equates to 4 panels with square dimensions of about 9 meters per side.

Formula for the effective radiator surface area from Stephan-Boltzmann Law.

After factoring all of this in, I was able to make some estimates on the mass of such a ship. I used a Kapton-coated aluminum sunshield with a thickness of 2 cm and a diameter large enough to block the entire spacecraft from sunlight, radiators and all. The hull I assumed to have a 5 cm thickness, constructed from aluminum alloys. The casing for the fission reactor is 5 cm of solid lead. I also tacked on some extra mass for both RCS maneuvering fuel, as well as computers and electronics. At the end of the day, here were my spacecraft sizing results:

Spacecraft sizing results. Note that RCS propellant and extraneous mass were treated as percentages of the overall craft mass and the dry mass of the hull respectively.

Not too far-fetched at all. The total mass of the craft is about 317 tonnes. This would require 3 separate launches to Mars L1 from SpaceX’s proposed BFR, which Musk boasts will be operational by the mid 2020's. It is interesting to note that the fission reactor and the copper solenoid account for more than 50% of the spacecraft’s mass. For some more perspective on spacecraft sizing, I have included an image of a possible layout for the hull & systems created by my good friend jack:

A sketch of the spacecraft for sizing reference. Parts labeled accordingly.

Some Issues

The biggest issue here is the shipment of 40 tonnes of uranium to Mars L1 every two years. This could probably be mitigated by the development of fusion power in the relatively near future. Another issue is the enormous levels of magnetism in close proximity to the copper solenoid, and radiation from the fission reactor. Strategic shielding of electronic and computer components of the spacecraft will be required to prevent issues regarding these phenomena. The manufacturing of a giant, copper doughnut is also probably high on the list of challenges facing an artificial Martian magnetosphere.

Another potential issue that I have no idea how to solve (or if it will even be an issue at all), is the fact that we are redirecting a ~500,000 kilometer swath of charged particles from the sun moving 300 km/s directly into the center of a copper doughnut from both sides. On Earth, these redirected particles hit the atmosphere of the poles and create a beautiful display of lights known as the Corona Borealis. In our case, I have no idea what would happen. Whatever the consequences, we will have to cope accordingly!

Conclusion

A cheesy MATLAB rendering of the extension of the artificial Martian magnetosheath. The blue plus sign is the origin of the field at Mars L1, and the red circle is Mars.

And thus, with nothing more than ~300 tonnes of material and some human ingenuity, Mars could once again boast a firm line of defense against solar winds. Such a field would allow for an atmosphere to be grown around the planet without the threat of being stripped away, and an ozone layer to defend against high energy UV light. Electronic devices and biological entities on Mars could finally be safe from the endless barrage of protons and electrons careening from the sun.

**If you have any further questions on my calculations or assumptions, please consult me in the comments or by private message. I did a lot more work than I actually wrote about here!**