Adding an Earth-sized magnetic field to Mars


Mars has only the ancient remnants of a magnetic field. What little chunks of field it does have (imprinted into magnetic rocks) are regional in scale and do nothing at all for radiation shielding (I once calculated this). Additionally, over a long enough timescale (tens of millions of years), the solar wind will erode the atmosphere of a terraformed Mars. So, let’s just get on with replacing the lost magnetic field.

To do this, we aren’t going to do something silly like restart the core. We’re going to rely on a tried and true existing technology: cryogenic superconductors. Just put a superconducting ring around the equator of Mars. Turns out, this wouldn’t even cost that much to build. I will be using Magnesium Diboride (MgB2) because it’s cheap, has pretty good performance (critical temperature of 39K, critical current of like 105 A/cm2 at 5K), and both Boron and Magnesium are known to exist fairly commonly on Mars. (Magnesium is super common, and Boron has been found in clays at >150ppm concentrations–according to this paper–and probably exists in far higher concentrations somewhere since Mars once had a quite active water cycle. I’ll assume that by the time the residents of Mars want to do this sort of thing, the costs of extracting these minerals will be similar to that of Earth (maybe a poor assumption, but why would you do this unless there are like millions of people on Mars, at a minimum?). We’ll also assume that because of the ridiculous scale being operated at, and because MgB2 is a pretty easy superconductor to make (just need to heat the mixture of Magnesium and Boron powders), the cost of actually building the ring will be some single-digit multiple of the raw costs of the material.

Okay. So just how big is the Earth’s magnetic field? We’ll use its total energy (when approximated as current on a sphere) to estimate what we’ll need as far as current in the ring. According to this, the Earth’s magnetic field stores about 1026 erg, or 1019J (roughly half the energy the world uses in a year). The energy stored in an inductor is just:
E\,=\,\frac{1}{2}\,L\,I^{2}
(according to Wikipedia)
Where L is inductance and I is the current in the ring.

To calculate the inductance L of a ring of radius R with wire radius a and number of turns N, we use the approximation:
L \approx N^2 R \mu_0 \mu_r \left ( \textup{ln}\left ( \frac{8 R}{a} \right ) - 2\right )

(from here)

Since N=1 and we’ll conservatively (very conservatively) say the relative permeability  \mu_r = 1, and since the current I is related to the critical current density Jc such that: I=J_c \pi a^2, we can write the equation as:

E\,=\,\frac{1}{2}\,R \mu_0 \left ( \textup{ln}\left ( \frac{8 R}{a} \right ) - 2\right )\cdot\left (J_c \pi a^2\right )^{2}
If we let a=.42m, R=rMars, and Jc = 105 A/cm2:
https://www.google.com/webhp?#q=.5*r_Mars*(mu_0)*(ln(8*r_Mars/(.42m))-2)*(10^5A/cm^2*pi*(.42m)^2)^2 = 1.047*10^19 Joules, when we only needed 10^19 J to equal the same energy as Earth’s magnetic field.

Given the density of MgB2 is 2.57g/cc (source), the mass of the superconductor is:
https://www.google.com/search?q=2*pi*r_Mars*pi*(42cm)^2*2.57g/cc or about 3*1010kg, 30 million tons, almost have of which is boron. The Earth mines about 4 million tons of Boron a year, so the Earth produces enough boron to build that thing in about 4 years (we’ll mine this on Mars, of course). Pretty reasonable, considering we’re doing some pretty hardcore terraforming, here.

Given a price of about 10USD/kg for Boron (just spitballing here, since Ferroboron is half boron by molarity and 15-20% boron by mass and is 1-2USD/kg… of course, boron ore is much cheaper) and like 2USD/kg for magnesium metal (just look up the spot prices for Mg and Ferroboron), so about USD6/kg of bulk MgB2.

This whole thing would cost about 180B USD in raw materials but would store about 3 trillion kWh for a ridiculously low price per kWh of storage (like 6 cents/kWh! For storage that can be reused!). Of course, there is also insulation and cooling, plus some method to inject power into the ring.

 

NOTE: Some Japanese researchers recently (last 2-3 years I think?) published a paper about the thing I am proposing here. I can’t find the paper now, but I assume they did I better job than I did. Also, I don’t really buy into Jim Greene’s L1 magnetosphere, since the solar wind does actually shoot straight out from the sun but actually follows the spirals of the Interplanetary Magnetic Field, so I’m pretty sure solar wind would hit Mars because the shadow of a big magnetosphere at L1 would miss Mars.

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Chris Stelter

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5 Responses to Adding an Earth-sized magnetic field to Mars

  1. gbaikie says:

    –Additionally, over a long enough timescale (tens of millions of years), the solar wind will erode the atmosphere of a terraformed Mars. So, let’s just get on with replacing the lost magnetic field.–
    Why should people be concerned about the future of Mars in terms of say, 1000 years in the future?
    I sort get why people might concerned about Earth more than 1000 years into future.
    But I sort of think they are not considering we could be spacefaring civilization.
    For example nuclear waste. Earth nuclear waste is non problem on Earth if humans are spacefaring.
    I guess one can imagine all humans going to die off, and they we leave a nuclear waste problem. Or perhaps humans are evolving into more and incompetent people, and so might forget where put the nuclear waste within 100 years or something.

    On topic adding atmosphere- as said, I don’t think need to add atmosphere. But not going repeat myself. But a slightly different idea, occurred to me, why make vast domes of ice. There seems couple problems, it seems ice dome might get too warm, and evaporation of ice of the dome.
    I don’t particularly like idea.
    Why would make dome out of ice rather than say glass or clear plastic. Only thing I think of is, might be cheaper. And cheaper mainly because energy cost could be high.
    Hard to go any further unless know price of electrical power and water.
    And leads me to question how can transport ice by the ton at cheap cost.
    And kind thinking of things like pyramid building- slabs of ice one drag a fairly long distance. Can use ice to make roads. Does help to have roads of frozen CO2. Can you use frozen CO2 ice to make roads. Anyways, ice is slippery due to pressure. Live Science says that is wrong {old theory}. https://tinyurl.com/y8yhfx6h
    Though if water or CO2 are not slippery on Mars, that makes them road material for vehicle with wheels. So if had really cheap liquid CO2 that give me ability to make CO2 snow which could used for roads.
    Also can spray an outside of ice dome with the cheap CO2 snow. So, maybe have solved the one of problems by going around in circles:)
    Dome get too warm. If making refrigerant on Mars which cheap- solves that problem too.
    Next do dome get warm. Make plastic greenhouse put 1 psi air in it. Put at equator, how warm does it get?
    So you want to add atmosphere to add pressure and I assume you think make air warmer. Or Greenhouse Effect of Earth. And also an actual greenhouse. And/or you park your cars in parking lot, with windows rolled up and get really hot in the sunlight- which due an actual greenhouse rather than the Greenhouse of effect of Earth’s atmosphere. Of course parked cars with windows rolled, will cool down when not in the sunlight. Or Earth’s greenhouse effect is mostly about making nights warmer- roughly.
    But actual greenhouse are used stop freezing temperature at night also. And to do better job at keeping actual greenhouse warmer at night can done by adding thermal mass. And 1 psi pressure has less thermal mass than 14.7 psi on Earth.
    But with dome of ice one adding a lot thermal mass {depending on how thick going to make it]. How about say 1 foot thick. First that allow enough sunlight to go thru it, and for plants growth, I believe even less direct and more diffused sunlight works for plant and general lighting. 1 foot doesn’t do a lot in terms radiation shielding. Don’t know effect of GCR on plants- must be some people who thought it.
    How about 1 foot ice in terms structure strength of greenhouse. Has anyone made dome of ice on Earth?
    Ice dome made using novel construction method
    https://www.sciencedaily.com/releases/2011/02/110201101732.htm
    “Following a thorough preparatory and research phase, a new ice dome construction method is now being put to the test in Obergurgl — a world first. This structure, showing more than 10 meters free span, is now home to a bar — for as long as the temperatures are low enough.” And:
    “First, a 20 cm-thick plate of ice is cut into 16 segments. These two-dimensional segments have then to be transformed into a three-dimensional structure.”
    So 8″ rather than 12 inches. But I think want 12″.
    That seems like it would work on Mars.
    I have few problems making a thicker atmosphere on Mars.
    It could make surface of Mars dimmer.
    You need a lot gas.
    Winds could stronger
    Make higher atmosphere for rockets leave Mars.
    Cannon or other mass driver should work fairly ok with Mars thin atmosphere.
    Though thicker atmosphere makes easier to land on Mars.
    Balloons and airplanes work better.
    But I don’t helps much will suborbital travel [other than landing].
    And don’t think it makes Mars warmer or how much warmer are going
    make planet with average temperature of about – 60 C.
    If only somehow made it -40 C, you could not be effective making it colder-
    but making colder makes to easier to cool things,
    Or vacuum there is problem with systems which provide cooling-
    or normal car overheats in in vacuum or thin atmosphere of Mars because
    it’s using the air to cold- Earth dense air cools better.
    But then again, I think one can make pretty cheap liquid CO2 and water works
    well for cooling purposes.

  2. MBMelcon says:

    Chris Stelter, adding turns reduces the total mass of wire. The ln term appears in the energy equation but not in the mass equation. For example,

    If N = 1 and a = 0.420 m, then E = 1.05E19 J and mass = 3.0E10 kg.
    If N = 4 and a = 0.420 m, then E = 1.68E20 J and mass = 3.0E10 kg.
    If N = 4 and a = 0.206 m, then E = 1.01E19 J and mass = 7.3E9 kg.

    In the second case the mass is the same but the energy is higher than necessary.
    In the third case the energy is the same but the mass is reduced.

    MBMelcon

  3. Andrew says:

    Do you think something similar would work on a smaller body? Ceres, or maybe even a smaller asteroid?

  4. gbaikie says:

    It seems what Mars needs is space power satellites.
    I think Mars could have SPS before Earth does.
    Generally I assume SPS for Earth would be at Geostationary orbit, but they don’t have to be in GEO. And the infrastructure involved with SPS probably wouldn’t limited to GEO.
    Other than in sun synchronous orbit, it seem you wouldn’t collect solar energy in LEO due to the Earth blocking the sunlight.
    One say there could be advantage of having the beamed energy from Space being in the same spot in the sky. Sort of the idea of 1 SPS and 1 collector at Earth surface.
    But I tend of think of SPS being network of solar collector and network relying the power to Earth surface. Or advantage of SPS is having a constant source energy and 1 point at GEO is not constant source of energy because even at that distance the Earth blocks the sunlight. The other aspect in getting power to earth surface when and where it’s needed. Or instead of solar panel on Earth surface making an imbalance, SPS can function to balance the global electrical grid, and provide power where there isn’t any electrical power available {other than from Space}.
    So, rough SPS evenly spaced along Geostationary orbit, and power transfer and to relay satellites at closer orbits to Earth. But it could be in sun synchronous orbit.
    Now if sun synchronous orbit, it seem the Van Allen belts are a bit of problem, or a possible problem- or simply I am unaware much experience related to operations in within an Van Allen belts.
    Of course Mars doesn’t have a Van Allen belt, therefore it seems to eliminates much this uncertainty. Therefore with Mars instead of loosely thinking SPS will be in Areostationary orbit, one could start with general idea of SPS being Mars sun synchronous orbits.
    Now with SPS with Earth and Mars are not going to limited to beaming power to the surface.
    I would say to have SPS one needs cheap electrical power in Space and SPS makes electrical power in Space cheap. Or need market for electrical power in Space, in order to provide electrical power to the surface market. And with Earth the surface is huge electrical market for SPS, but if got SPS, then SPS also creates huge market for electrical power in space.
    Now if you have any towns on Mars, that would pretty big market for electrical power, unlike most towns on Earth, a town on mars has large growth needs. A mars town is like China- needing huge amounts electrical power faster than they make electrical power plants. Though one say China is now not in that situation- still needs more powerplants, obviously, but less frantic about it. And with Mars it could be more extreme than China was. Or one town on Mars could need say near infinite amount rate of increase energy supply for a few decades. It can’t get enough, particularly if Musk sending boatloads of people. Or having a near infinite amount rate of increase energy supply, could drive boatloads of people faster than Musk can get them there.
    Plus, Mars is good place to deliver space rocks to. And if have space rocks {and Mars starts small moons which are big space rocks. Or one going to try to choose the space rocks to deliver, but got two unchosen which are already there.

    And plus if got electrical power and got space rock at Mars Space, if you want to create magnetic field it could in Mars orbit. Could be at say, Mars L-1 and it’s van allen belts could be not close to the Mars planet.

  5. gbaikie says:

    Oh while here. I am listening to Scott Adam who constantly confesses he doesn’t know science {and he imagines global warming is big problem]. So, I guess Scott doesn’t know we living an coldest Ice Age in Earth long history. But currently, Scott is excited by news that Mars has oxygen. But he imagine it’s likely fake news, but wow, it would important if Mars has oxygen. But of course Mars has oxygen:
    “Major : Carbon Dioxide (CO2) – 95.1% ; Nitrogen (N2) – 2.59%
    Argon (Ar) – 1.94%; Oxygen (O2) – 0.16%; Carbon Monoxide (CO) – 0.06% ”
    And in terms a 25 trillion ton atmosphere, a lot of oxygen.
    Not that matter much as Mars and the Moon have lots of oxygen- you need energy to split it from oxidized rocky surface- which is 40% oxygen.
    But in terms of “free oxygen” Mars atmosphere has it, Sun is spewing Oxygen, and lunar regolith has some “free oxygen”. Though Moon probably has a lot more “free H2”.
    What seems important is the general public does not know much “space”.
    So, NASA has been proving how utterly stupid there are. Or it seems all NASA can do is talk geek porn.
    So, for decades I have had a thought, why don’t we have lunar bases, already.
    And currently and for quite awhile I have been thinking we don’t need lunar bases, immediately. And always thought NASA as class A losers when comes to PR.
    And come up with various reason we aren’t a spacefaring civilization, yet.
    But, NOW I narrowed it down to a single reason, all has to do with NASA’s utter stupidity in regards to their primary function of informing public and/or PR – or given function for their existence.
    Anyhow Scott talking about how great it is to have restaurants having seating outside and out on the streets. And he live in California and probably most well know thing about California {to rest of world] is the “outside living kind of nature of living in California”.
    But made me think, one eat in small greenhouse outside and you do this even when raining. And key aspect would involve ventilation. And not having a wind problem with such structures. So could eat if raining or in tornado conditions

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